sr!com.femlab.server.ModelFileHeaderD%LtagstLcom/femlab/util/FlStringList;Ltypesq~LvrsntLcom/femlab/util/FlVersion;xpwsrcom.femlab.util.FlVersion%/B = IbuildImajorLdatetLjava/lang/String;Lextq~Lnameq~Lrcsq~L reactionExtq~L reactionNameq~L scriptExtq~L scriptNameq~xpwtCOMSOL Script 1.3tt#COMSOL Reaction Engineering Lab 1.5q~t COMSOL 3.5q~wt $Name: $t$Date: 2008/09/19 16:09:48 $xur[Ljava.lang.String;V{Gxpt modelinfotxfemtguitfem0tg75tg90tfem8tfem8.0q~q~tfem10tfem10.0q~q~t mfileinfouq~ q~t femstructt guistructq~tdrawq~tgeomtmeshtsolutiontxmeshq~q~q~ q~!q~xsrcom.femlab.api.client.ModelInfo^%Ldescrq~LdocURLq~[imaget[Bxpwptpxuq~ tclear xfem clear vrsn vrsn.name = 'COMSOL 3.5'; vrsn.ext = ''; vrsn.major = 0; vrsn.build = 494; vrsn.rcs = '$Name: $'; vrsn.date = '$Date: 2008/09/19 16:09:48 $'; xfem.version = vrsn; xfem.id = 1; xfem.geomdata = 'geom'; xfem.eqvars = 'on'; xfem.cplbndeq = 'on'; xfem.cplbndsh = 'off'; xfem.drawvalid = 'on'; xfem.geomvalid = 'on'; xfem.solvalid = 'on'; xfem.linshape = 'on'; xfem.linshapetol = 0.1; xfem.meshtime = 'TIME'; clear appl appl.mode.class = 'PerpendicularCurrents'; appl.mode.type = 'cartesian'; appl.dim = {'Az','redAz'}; appl.sdim = {'x','y','z'}; appl.name = 'emqa'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_emqa'; clear prop prop.elemdefault='Lag2'; prop.analysis='static'; prop.biasapplmode='none'; prop.solvefor='ATot'; prop.backgroundFieldSpec='A_external'; prop.frame='ale'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.I0 = {'0'}; pnt.style = {{{'0'},{'0','0','0'}}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.name = {'',''}; bnd.H0 = {{'0';'0'},{'0';'0'}}; bnd.Js0z = {'0','0'}; bnd.A0z = {'0','0'}; bnd.murbnd = {{'1','0';'0','1'},{'1','0';'0','1'}}; bnd.murext = {'1','1'}; bnd.epsilonrbnd = {'1','1'}; bnd.sigmabnd = {'0','0'}; bnd.eta = {'1','1'}; bnd.Esz = {'0','0'}; bnd.d = {'0','0'}; bnd.index = {'0','0'}; bnd.chsrcdst = {'0','0'}; bnd.pertype = {'sym','sym'}; bnd.nsect = {'2','2'}; bnd.type = {'cont','A0'}; bnd.weakconstr = {'1','1'}; bnd.wcshape = {[1],[1]}; bnd.wcgporder = {{1},{1}}; bnd.wcinit = {{'0';'0'},{'0';'0'}}; bnd.style = {{{'0'},{'0','0','255'},{'solid'}},{{'0'},{'0','0','0'},{'solid'}}}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.H0 = {{'0';'0'}}; pair.Js0z = {'0'}; pair.A0z = {'0'}; pair.murbnd = {{'1','0';'0','1'}}; pair.murext = {'1'}; pair.epsilonrbnd = {'1'}; pair.sigmabnd = {'0'}; pair.eta = {'1'}; pair.Esz = {'0'}; pair.d = {'0'}; pair.index = {'0'}; pair.chsrcdst = {'0'}; pair.pertype = {'sym'}; pair.nsect = {'2'}; pair.type = {'cont'}; pair.usage = {1}; pair.pair = {{'Pair 1'}}; bnd.pair = pair; appl.bnd = bnd; clear equ equ.shape = {[2],[2],[2],[2],[2],[2]}; equ.gporder = {{2},{2},{2},{2},{2},{2}}; equ.cporder = {{1},{1},{1},{1},{1},{1}}; equ.init = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.name = {'','','','','',''}; equ.mur = {{'1','0';'0','1'},{'mat2_MUR(normB_emqa[1/T])','0';'0','mat2_MUR(normB_emqa[1/T])'}, ... {'mat1_mur','0';'0','mat1_mur'},{'mat1_mur','0';'0','mat1_mur'},{'mat1_mur', ... '0';'0','mat1_mur'},{'mat4_mur','0';'0','mat4_mur'}}; equ.elconstrel = {'epsr','epsr','epsr','epsr','epsr','epsr'}; equ.Pz = {'0','0','0','0','0','0'}; equ.Drz = {'0','0','0','0','0','0'}; equ.magconstrel = {'mur','Br','Br','Br','Br','Br'}; equ.M = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.Br = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.fH = {{'1/mu0_emqa*Bx_emqa';'1/mu0_emqa*By_emqa'},{'1/mu0_emqa*Bx_emqa'; ... '1/mu0_emqa*By_emqa'},{'1/mu0_emqa*Bx_emqa';'1/mu0_emqa*By_emqa'},{'1/mu0_emqa*Bx_emqa'; ... '1/mu0_emqa*By_emqa'},{'1/mu0_emqa*Bx_emqa';'1/mu0_emqa*By_emqa'},{'1/mu0_emqa*Bx_emqa'; ... '1/mu0_emqa*By_emqa'}}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.epsilonr = {'1','mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.Jez = {'0','0','0','0','0','0'}; equ.v = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.deltaV = {'0','0','-240','240','240','0'}; equ.L = {'1','1','0.11','0.11','0.11','1'}; equ.maxwell = {{},{},{},{},{},{}}; equ.nTsrcpnt = {{{'0';'0'}},{{'0';'0'}},{{'0';'0'}},{{'0';'0'}},{{'0';'0'}},{{'0'; ... '0'}}}; equ.Sd = {{'Sdx_guess_emqa';'Sdy_guess_emqa'},{'Sdx_guess_emqa';'Sdy_guess_emqa'}, ... {'Sdx_guess_emqa';'Sdy_guess_emqa'},{'Sdx_guess_emqa';'Sdy_guess_emqa'}, ... {'Sdx_guess_emqa';'Sdy_guess_emqa'},{'Sdx_guess_emqa';'Sdy_guess_emqa'}}; equ.dr = {'dr_guess_emqa','dr_guess_emqa','dr_guess_emqa','dr_guess_emqa', ... 'dr_guess_emqa','dr_guess_emqa'}; equ.S0 = {{'S0x_guess_emqa';'S0y_guess_emqa'},{'S0x_guess_emqa';'S0y_guess_emqa'}, ... {'S0x_guess_emqa';'S0y_guess_emqa'},{'S0x_guess_emqa';'S0y_guess_emqa'}, ... {'S0x_guess_emqa';'S0y_guess_emqa'},{'S0x_guess_emqa';'S0y_guess_emqa'}}; equ.R0 = {'R0_guess_emqa','R0_guess_emqa','R0_guess_emqa','R0_guess_emqa', ... 'R0_guess_emqa','R0_guess_emqa'}; equ.user = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.Stype = {'none','none','none','none','none','none'}; equ.coordOn = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.rOn = {'0','0','0','0','0','0'}; equ.srcpnt = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.srcaxis = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.style = {{{'0'},{'193','193','193'}},{{'0'},{'0','0','255'}},{{'0'},{'0', ... '255','0'}},{{'0'},{'0','255','255'}},{{'0'},{'0','0','255'}},{{'0'},{'193', ... '193','193'}}}; equ.ind = [1,2,3,4,5,3,3,5,5,3,3,5,5,3,3,5,5,3,3,5,5,3,3,5,5,3,1,2,6]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7'}; xfem.appl{1} = appl; clear appl appl.mode.class = 'MovingMesh'; appl.mode.type = 'cartesian'; appl.dim = {}; appl.sdim = {'X','Y','Z'}; appl.name = 'ale'; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.sshape = 1; appl.border = 'off'; appl.assignsuffix = '_ale'; clear prop prop.elemdefault='Lag2'; prop.smoothing='laplace'; prop.analysis='transient'; prop.allowremesh='off'; prop.definesframe='ale'; prop.origrefframe='ale'; prop.frame='ref'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; prop.constrtype='non-ideal'; appl.prop = prop; clear bnd bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.constrcoord = {'global','global','global','global','global','global'}; bnd.type = {'def','def','def','def','def','def'}; bnd.deform = {{'0';'0'},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{'0';'0'}}; bnd.veldeform = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; bnd.defflag = {{'1';'1'},{'1';'1'},{'1';'1'},{'1';'1'},{'1';'1'},{'0';'0'}}; bnd.veldefflag = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; bnd.weakconstr = {'1','1','1','1','1','1'}; bnd.wcshape = {[1;2],[1;2],[1;2],[1;2],[1;2],[1;2]}; bnd.wcgporder = {{1;1},{1;1},{1;1},{1;1},{1;1},{1;1}}; bnd.wcinit = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; bnd.style = {{{'0'},{'0','0','0'},{'solid'}},{{'0'},{'0','0','0'},{'solid'}}, ... {{'0'},{'0','0','0'},{'solid'}},{{'0'},{'0','0','0'},{'solid'}},{{'0'}, ... {'0','0','0'},{'solid'}},{{'0'},{'0','0','0'},{'solid'}}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.constrcoord = {'global'}; pair.type = {'def'}; pair.deform = {{'0';'0'}}; pair.veldeform = {{'0';'0'}}; pair.defflag = {{'0';'0'}}; pair.veldefflag = {{'0';'0'}}; pair.usage = {1}; pair.pair = {{'Pair 1'}}; bnd.pair = pair; appl.bnd = bnd; clear equ equ.shape = {[3;4],[3;4],[3;4],[3;4],[3;4],[3;4]}; equ.gporder = {{2;2},{2;2},{2;2},{2;2},{2;2},{2;2}}; equ.cporder = {{1;1},{1;1},{1;1},{1;1},{1;1},{1;1}}; equ.init = {{'xinit_ale';'yinit_ale'},{'xinit_ale';'yinit_ale'},{'xinit_ale'; ... 'yinit_ale'},{'xinit_ale';'yinit_ale'},{'xinit_ale';'yinit_ale'},{'xinit_ale'; ... 'yinit_ale'}}; equ.usage = {1,1,1,1,1,1}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.type = {'none','pres','none','pres','pres','pres'}; equ.physexpr = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.presexpr = {{'0';'0'},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'0';'0'},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.dinit = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.style = {{{'0'},{'193','193','193'}},{{'0'},{'193','193','193'}},{{'0'}, ... {'193','193','193'}},{{'0'},{'193','193','193'}},{{'0'},{'193','193','193'}}, ... {{'0'},{'193','193','193'}}}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; xfem.appl{2} = appl; xfem.geom = flbinary('fem8','geom','12-8complete-+.mph'); xfem.mesh = flbinary('fem8.0','mesh','12-8complete-+.mph'); xfem.sdim = {{'X','Y'},{'x','y'}}; xfem.frame = {'ref','ale'}; xfem.shape = {'shlag(''order'',2,''basename'',''Az'',''frame'',''ale'')','shlag(2,''lm1'')'}; xfem.gporder = {4,30}; xfem.cporder = 2; clear sshape sshape.dvolname = 'dvol'; sshape.frame = 'ref'; sshape.sorder = 2; sshape.type = 'fixed'; xfem.sshape{1} = sshape; clear sshape sshape.dvolname = 'dvol_ale'; sshape.frame = 'ale'; sshape.sorder = 2; sshape.type = 'fixed'; xfem.sshape{2} = sshape; clear sshape sshape.dvolname = 'dvol_ale'; sshape.frame = 'ale'; sshape.sorder = 2; sshape.type = 'moving_expr'; sshape.sdimexprs = {'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y','sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y'}; xfem.sshape{3} = sshape; xfem.simplify = 'on'; xfem.border = 1; xfem.form = 'weak'; clear units; units.basesystem = 'SI'; xfem.units = units; clear equ equ.shape = {[1],[1],[1],[1],[1],[1],[1],[1]}; equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1}}; equ.init = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; equ.dinit = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; equ.weak = {{'dVol_emqa*(Jz_emqa*test(depAz_emqa)-Hx_emqa*test(curlAx_emqa)-Hy_emqa*test(curlAy_emqa))'; ... '0';'0'},{'dVol_emqa*(Jz_emqa*test(depAz_emqa)-Hx_emqa*test(curlAx_emqa)-Hy_emqa*test(curlAy_emqa))'; ... '0';'0'},{'dVol_emqa*(Jz_emqa*test(depAz_emqa)-Hx_emqa*test(curlAx_emqa)-Hy_emqa*test(curlAy_emqa))'; ... '0';'0'},{'dVol_emqa*(Jz_emqa*test(depAz_emqa)-Hx_emqa*test(curlAx_emqa)-Hy_emqa*test(curlAy_emqa))'; ... '0';'0'},{'dVol_emqa*(Jz_emqa*test(depAz_emqa)-Hx_emqa*test(curlAx_emqa)-Hy_emqa*test(curlAy_emqa))'; ... '0';'0'},{'dVol_emqa*(Jz_emqa*test(depAz_emqa)-Hx_emqa*test(curlAx_emqa)-Hy_emqa*test(curlAy_emqa))'; ... '0';'0'},{'dVol_emqa*(Jz_emqa*test(depAz_emqa)-Hx_emqa*test(curlAx_emqa)-Hy_emqa*test(curlAy_emqa))'; ... '0';'0'},{'dVol_emqa*(Jz_emqa*test(depAz_emqa)-Hx_emqa*test(curlAx_emqa)-Hy_emqa*test(curlAy_emqa))'; ... '0';'0'}}; equ.dweak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; equ.constrf = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; equ.sshape = {[1;2],[1;2],[1;2],[1;2],[1;2],[1;3],[1;3],[1;3]}; equ.sshapedim = {{2;1;1},{2;1;1},{2;1;1},{2;1;1},{2;1;1},{3;1;1},{3;1;1},{3;1; ... 1}}; equ.ind = [1,2,3,4,5,3,3,5,5,3,3,5,5,3,3,5,5,3,3,5,5,3,3,5,5,3,6,7,8]; equ.dim = {'Az','x','y'}; equ.var = {'dr_guess_emqa',{'0','0','0','0','0','0','0','0'}, ... 'R0_guess_emqa',{'0','0','0','0','0','0','0','0'}, ... 'Sx_emqa',{'x','x','x','x','x','x','x','x'}, ... 'S0x_guess_emqa',{'0','0','0','0','0','0','0','0'}, ... 'Sdx_guess_emqa',{'0','0','0','0','0','0','0','0'}, ... 'Sy_emqa',{'y','y','y','y','y','y','y','y'}, ... 'S0y_guess_emqa',{'0','0','0','0','0','0','0','0'}, ... 'Sdy_guess_emqa',{'0','0','0','0','0','0','0','0'}, ... 'curlAx_emqa',{'Azy','Azy','Azy','Azy','Azy','Azy','Azy','Azy'}, ... 'curlAy_emqa',{'-Azx','-Azx','-Azx','-Azx','-Azx','-Azx','-Azx','-Azx'}, ... 'dVol_emqa',{'detJ_emqa','detJ_emqa','detJ_emqa','detJ_emqa','detJ_emqa', ... 'detJ_emqa','detJ_emqa','detJ_emqa'}, ... 'Bx_emqa',{'curlAx_emqa','curlAx_emqa','curlAx_emqa','curlAx_emqa', ... 'curlAx_emqa','curlAx_emqa','curlAx_emqa','curlAx_emqa'}, ... 'By_emqa',{'curlAy_emqa','curlAy_emqa','curlAy_emqa','curlAy_emqa', ... 'curlAy_emqa','curlAy_emqa','curlAy_emqa','curlAy_emqa'}, ... 'Hx_emqa',{'Bx_emqa/(mur_emqa*mu0_emqa)','(Bx_emqa-Brx_emqa)/(mur_emqa*mu0_emqa)', ... '(Bx_emqa-Brx_emqa)/(mur_emqa*mu0_emqa)','(Bx_emqa-Brx_emqa)/(mur_emqa*mu0_emqa)', ... '(Bx_emqa-Brx_emqa)/(mur_emqa*mu0_emqa)','Bx_emqa/(mur_emqa*mu0_emqa)', ... '(Bx_emqa-Brx_emqa)/(mur_emqa*mu0_emqa)','(Bx_emqa-Brx_emqa)/(mur_emqa*mu0_emqa)'}, ... 'Hy_emqa',{'By_emqa/(mur_emqa*mu0_emqa)','(By_emqa-Bry_emqa)/(mur_emqa*mu0_emqa)', ... '(By_emqa-Bry_emqa)/(mur_emqa*mu0_emqa)','(By_emqa-Bry_emqa)/(mur_emqa*mu0_emqa)', ... '(By_emqa-Bry_emqa)/(mur_emqa*mu0_emqa)','By_emqa/(mur_emqa*mu0_emqa)', ... '(By_emqa-Bry_emqa)/(mur_emqa*mu0_emqa)','(By_emqa-Bry_emqa)/(mur_emqa*mu0_emqa)'}, ... 'mu_emqa',{'mu0_emqa*mur_emqa','mu0_emqa*mur_emqa','mu0_emqa*mur_emqa', ... 'mu0_emqa*mur_emqa','mu0_emqa*mur_emqa','mu0_emqa*mur_emqa','mu0_emqa*mur_emqa', ... 'mu0_emqa*mur_emqa'}, ... 'muxx_emqa',{'mu0_emqa*murxx_emqa','mu0_emqa*murxx_emqa','mu0_emqa*murxx_emqa', ... 'mu0_emqa*murxx_emqa','mu0_emqa*murxx_emqa','mu0_emqa*murxx_emqa','mu0_emqa*murxx_emqa', ... 'mu0_emqa*murxx_emqa'}, ... 'muxy_emqa',{'mu0_emqa*murxy_emqa','mu0_emqa*murxy_emqa','mu0_emqa*murxy_emqa', ... 'mu0_emqa*murxy_emqa','mu0_emqa*murxy_emqa','mu0_emqa*murxy_emqa','mu0_emqa*murxy_emqa', ... 'mu0_emqa*murxy_emqa'}, ... 'muyx_emqa',{'mu0_emqa*muryx_emqa','mu0_emqa*muryx_emqa','mu0_emqa*muryx_emqa', ... 'mu0_emqa*muryx_emqa','mu0_emqa*muryx_emqa','mu0_emqa*muryx_emqa','mu0_emqa*muryx_emqa', ... 'mu0_emqa*muryx_emqa'}, ... 'muyy_emqa',{'mu0_emqa*muryy_emqa','mu0_emqa*muryy_emqa','mu0_emqa*muryy_emqa', ... 'mu0_emqa*muryy_emqa','mu0_emqa*muryy_emqa','mu0_emqa*muryy_emqa','mu0_emqa*muryy_emqa', ... 'mu0_emqa*muryy_emqa'}, ... 'Jpz_emqa',{'sigma_emqa*deltaV_emqa/L_emqa','sigma_emqa*deltaV_emqa/L_emqa', ... 'sigma_emqa*deltaV_emqa/L_emqa','sigma_emqa*deltaV_emqa/L_emqa','sigma_emqa*deltaV_emqa/L_emqa', ... 'sigma_emqa*deltaV_emqa/L_emqa','sigma_emqa*deltaV_emqa/L_emqa','sigma_emqa*deltaV_emqa/L_emqa'}, ... 'Jz_emqa',{'Jpz_emqa+Jvz_emqa+Jez_emqa','Jpz_emqa+Jvz_emqa+Jez_emqa', ... 'Jpz_emqa+Jvz_emqa+Jez_emqa','Jpz_emqa+Jvz_emqa+Jez_emqa','Jpz_emqa+Jvz_emqa+Jez_emqa', ... 'Jpz_emqa+Jvz_emqa+Jez_emqa','Jpz_emqa+Jvz_emqa+Jez_emqa','Jpz_emqa+Jvz_emqa+Jez_emqa'}, ... 'Q_emqa',{'Jz_emqa*(vx_emqa*By_emqa-vy_emqa*Bx_emqa+deltaV_emqa/L_emqa+Jez_emqa/sigma_emqa)', ... 'Jz_emqa*(vx_emqa*By_emqa-vy_emqa*Bx_emqa+deltaV_emqa/L_emqa+Jez_emqa/sigma_emqa)', ... 'Jz_emqa*(vx_emqa*By_emqa-vy_emqa*Bx_emqa+deltaV_emqa/L_emqa+Jez_emqa/sigma_emqa)', ... 'Jz_emqa*(vx_emqa*By_emqa-vy_emqa*Bx_emqa+deltaV_emqa/L_emqa+Jez_emqa/sigma_emqa)', ... 'Jz_emqa*(vx_emqa*By_emqa-vy_emqa*Bx_emqa+deltaV_emqa/L_emqa+Jez_emqa/sigma_emqa)', ... 'Jz_emqa*(vx_emqa*By_emqa-vy_emqa*Bx_emqa+deltaV_emqa/L_emqa+Jez_emqa/sigma_emqa)', ... 'Jz_emqa*(vx_emqa*By_emqa-vy_emqa*Bx_emqa+deltaV_emqa/L_emqa+Jez_emqa/sigma_emqa)', ... 'Jz_emqa*(vx_emqa*By_emqa-vy_emqa*Bx_emqa+deltaV_emqa/L_emqa+Jez_emqa/sigma_emqa)'}, ... 'W_emqa',{'Wm_emqa','Wm_emqa','Wm_emqa','Wm_emqa','Wm_emqa','Wm_emqa', ... 'Wm_emqa','Wm_emqa'}, ... 'dW_emqa',{'dVol_emqa*W_emqa','dVol_emqa*W_emqa','dVol_emqa*W_emqa', ... 'dVol_emqa*W_emqa','dVol_emqa*W_emqa','dVol_emqa*W_emqa','dVol_emqa*W_emqa', ... 'dVol_emqa*W_emqa'}, ... 'Wm_emqa',{'0.5*(Hx_emqa*Bx_emqa+Hy_emqa*By_emqa)','0.5*(Hx_emqa*Bx_emqa+Hy_emqa*By_emqa+(Brx_emqa*Bx_emqa/murxx_emqa+Bry_emqa*By_emqa/muryy_emqa)/mu0_emqa)', ... '0.5*(Hx_emqa*Bx_emqa+Hy_emqa*By_emqa+(Brx_emqa*Bx_emqa/murxx_emqa+Bry_emqa*By_emqa/muryy_emqa)/mu0_emqa)', ... '0.5*(Hx_emqa*Bx_emqa+Hy_emqa*By_emqa+(Brx_emqa*Bx_emqa/murxx_emqa+Bry_emqa*By_emqa/muryy_emqa)/mu0_emqa)', ... '0.5*(Hx_emqa*Bx_emqa+Hy_emqa*By_emqa+(Brx_emqa*Bx_emqa/murxx_emqa+Bry_emqa*By_emqa/muryy_emqa)/mu0_emqa)', ... '0.5*(Hx_emqa*Bx_emqa+Hy_emqa*By_emqa)','0.5*(Hx_emqa*Bx_emqa+Hy_emqa*By_emqa+(Brx_emqa*Bx_emqa/murxx_emqa+Bry_emqa*By_emqa/muryy_emqa)/mu0_emqa)', ... '0.5*(Hx_emqa*Bx_emqa+Hy_emqa*By_emqa+(Brx_emqa*Bx_emqa/murxx_emqa+Bry_emqa*By_emqa/muryy_emqa)/mu0_emqa)'}, ... 'FLtzx_emqa',{'-Jz_emqa*By_emqa','-Jz_emqa*By_emqa','-Jz_emqa*By_emqa', ... '-Jz_emqa*By_emqa','-Jz_emqa*By_emqa','-Jz_emqa*By_emqa','-Jz_emqa*By_emqa', ... '-Jz_emqa*By_emqa'}, ... 'FLtzy_emqa',{'Jz_emqa*Bx_emqa','Jz_emqa*Bx_emqa','Jz_emqa*Bx_emqa', ... 'Jz_emqa*Bx_emqa','Jz_emqa*Bx_emqa','Jz_emqa*Bx_emqa','Jz_emqa*Bx_emqa', ... 'Jz_emqa*Bx_emqa'}, ... 'normFLtz_emqa',{'sqrt(abs(FLtzx_emqa)^2+abs(FLtzy_emqa)^2)','sqrt(abs(FLtzx_emqa)^2+abs(FLtzy_emqa)^2)', ... 'sqrt(abs(FLtzx_emqa)^2+abs(FLtzy_emqa)^2)','sqrt(abs(FLtzx_emqa)^2+abs(FLtzy_emqa)^2)', ... 'sqrt(abs(FLtzx_emqa)^2+abs(FLtzy_emqa)^2)','sqrt(abs(FLtzx_emqa)^2+abs(FLtzy_emqa)^2)', ... 'sqrt(abs(FLtzx_emqa)^2+abs(FLtzy_emqa)^2)','sqrt(abs(FLtzx_emqa)^2+abs(FLtzy_emqa)^2)'}, ... 'normM_emqa',{'sqrt(abs(Mx_emqa)^2+abs(My_emqa)^2)','sqrt(abs(Mx_emqa)^2+abs(My_emqa)^2)', ... 'sqrt(abs(Mx_emqa)^2+abs(My_emqa)^2)','sqrt(abs(Mx_emqa)^2+abs(My_emqa)^2)', ... 'sqrt(abs(Mx_emqa)^2+abs(My_emqa)^2)','sqrt(abs(Mx_emqa)^2+abs(My_emqa)^2)', ... 'sqrt(abs(Mx_emqa)^2+abs(My_emqa)^2)','sqrt(abs(Mx_emqa)^2+abs(My_emqa)^2)'}, ... 'normBr_emqa',{'sqrt(abs(Brx_emqa)^2+abs(Bry_emqa)^2)','sqrt(abs(Brx_emqa)^2+abs(Bry_emqa)^2)', ... 'sqrt(abs(Brx_emqa)^2+abs(Bry_emqa)^2)','sqrt(abs(Brx_emqa)^2+abs(Bry_emqa)^2)', ... 'sqrt(abs(Brx_emqa)^2+abs(Bry_emqa)^2)','sqrt(abs(Brx_emqa)^2+abs(Bry_emqa)^2)', ... 'sqrt(abs(Brx_emqa)^2+abs(Bry_emqa)^2)','sqrt(abs(Brx_emqa)^2+abs(Bry_emqa)^2)'}, ... 'normH_emqa',{'sqrt(abs(Hx_emqa)^2+abs(Hy_emqa)^2)','sqrt(abs(Hx_emqa)^2+abs(Hy_emqa)^2)', ... 'sqrt(abs(Hx_emqa)^2+abs(Hy_emqa)^2)','sqrt(abs(Hx_emqa)^2+abs(Hy_emqa)^2)', ... 'sqrt(abs(Hx_emqa)^2+abs(Hy_emqa)^2)','sqrt(abs(Hx_emqa)^2+abs(Hy_emqa)^2)', ... 'sqrt(abs(Hx_emqa)^2+abs(Hy_emqa)^2)','sqrt(abs(Hx_emqa)^2+abs(Hy_emqa)^2)'}, ... 'normB_emqa',{'sqrt(abs(Bx_emqa)^2+abs(By_emqa)^2)','sqrt(abs(Bx_emqa)^2+abs(By_emqa)^2)', ... 'sqrt(abs(Bx_emqa)^2+abs(By_emqa)^2)','sqrt(abs(Bx_emqa)^2+abs(By_emqa)^2)', ... 'sqrt(abs(Bx_emqa)^2+abs(By_emqa)^2)','sqrt(abs(Bx_emqa)^2+abs(By_emqa)^2)', ... 'sqrt(abs(Bx_emqa)^2+abs(By_emqa)^2)','sqrt(abs(Bx_emqa)^2+abs(By_emqa)^2)'}, ... 'normJ_emqa',{'abs(Jz_emqa)','abs(Jz_emqa)','abs(Jz_emqa)','abs(Jz_emqa)', ... 'abs(Jz_emqa)','abs(Jz_emqa)','abs(Jz_emqa)','abs(Jz_emqa)'}, ... 'Jvz_emqa',{'sigma_emqa*Evz_emqa','sigma_emqa*Evz_emqa','sigma_emqa*Evz_emqa', ... 'sigma_emqa*Evz_emqa','sigma_emqa*Evz_emqa','sigma_emqa*Evz_emqa','sigma_emqa*Evz_emqa', ... 'sigma_emqa*Evz_emqa'}, ... 'Evz_emqa',{'vx_emqa*By_emqa-vy_emqa*Bx_emqa','vx_emqa*By_emqa-vy_emqa*Bx_emqa', ... 'vx_emqa*By_emqa-vy_emqa*Bx_emqa','vx_emqa*By_emqa-vy_emqa*Bx_emqa','vx_emqa*By_emqa-vy_emqa*Bx_emqa', ... 'vx_emqa*By_emqa-vy_emqa*Bx_emqa','vx_emqa*By_emqa-vy_emqa*Bx_emqa','vx_emqa*By_emqa-vy_emqa*Bx_emqa'}, ... 'normEv_emqa',{'abs(Evz_emqa)','abs(Evz_emqa)','abs(Evz_emqa)','abs(Evz_emqa)', ... 'abs(Evz_emqa)','abs(Evz_emqa)','abs(Evz_emqa)','abs(Evz_emqa)'}, ... 'normv_emqa',{'sqrt(abs(vx_emqa)^2+abs(vy_emqa)^2)','sqrt(abs(vx_emqa)^2+abs(vy_emqa)^2)', ... 'sqrt(abs(vx_emqa)^2+abs(vy_emqa)^2)','sqrt(abs(vx_emqa)^2+abs(vy_emqa)^2)', ... 'sqrt(abs(vx_emqa)^2+abs(vy_emqa)^2)','sqrt(abs(vx_emqa)^2+abs(vy_emqa)^2)', ... 'sqrt(abs(vx_emqa)^2+abs(vy_emqa)^2)','sqrt(abs(vx_emqa)^2+abs(vy_emqa)^2)'}, ... 'xinit_ale',{'X','X','X','X','X','X','X','X'}, ... 'yinit_ale',{'Y','Y','Y','Y','Y','Y','Y','Y'}, ... 'dx_ale',{'x-X','x-X','x-X','x-X','x-X','x-X','x-X','x-X'}, ... 'dy_ale',{'y-Y','y-Y','y-Y','y-Y','y-Y','y-Y','y-Y','y-Y'},'Pz_emqa',{'0','0','0','0','0','0','0','0'}, ... 'Drz_emqa',{'0','0','0','0','0','0','0','0'}, ... 'normfH_emqa',{'normB_emqa/mu0_emqa','mat2_HB(normB_emqa[1/T])[A/m]', ... 'normB_emqa/mu0_emqa','mat2_HB(normB_emqa[1/T])[A/m]','normB_emqa/mu0_emqa', ... 'normB_emqa/mu0_emqa','mat2_HB(normB_emqa[1/T])[A/m]','normB_emqa/mu0_emqa'}, ... 'epsilonr_emqa',{'1','mat2_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat1_epsilonr','1','mat2_epsilonr','mat4_epsilonr'}, ... 'sigma_emqa',{'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma', ... 'mat1_sigma','mat3_sigma','mat2_sigma','mat4_sigma'}, ... 'Jez_emqa',{'0','0','0','0','0','0','0','0'}, ... 'deltaV_emqa',{'0','0','-240','240','240','0','0','0'}, ... 'L_emqa',{'1','1','0.11','0.11','0.11','1','1','1'}, ... 'dr_emqa',{'dr_guess_emqa','dr_guess_emqa','dr_guess_emqa','dr_guess_emqa', ... 'dr_guess_emqa','dr_guess_emqa','dr_guess_emqa','dr_guess_emqa'}, ... 'R0_emqa',{'R0_guess_emqa','R0_guess_emqa','R0_guess_emqa','R0_guess_emqa', ... 'R0_guess_emqa','R0_guess_emqa','R0_guess_emqa','R0_guess_emqa'}, ... 'ispml_emqa',{'0','0','0','0','0','0','0','0'}, ... 'srcpntx_emqa',{'0','0','0','0','0','0','0','0'}, ... 'srcpnty_emqa',{'0','0','0','0','0','0','0','0'}, ... 'userx_emqa',{'0','0','0','0','0','0','0','0'}, ... 'usery_emqa',{'0','0','0','0','0','0','0','0'}, ... 'Sdx_emqa',{'Sdx_guess_emqa','Sdx_guess_emqa','Sdx_guess_emqa','Sdx_guess_emqa', ... 'Sdx_guess_emqa','Sdx_guess_emqa','Sdx_guess_emqa','Sdx_guess_emqa'}, ... 'Sdy_emqa',{'Sdy_guess_emqa','Sdy_guess_emqa','Sdy_guess_emqa','Sdy_guess_emqa', ... 'Sdy_guess_emqa','Sdy_guess_emqa','Sdy_guess_emqa','Sdy_guess_emqa'}, ... 'S0x_emqa',{'S0x_guess_emqa','S0x_guess_emqa','S0x_guess_emqa','S0x_guess_emqa', ... 'S0x_guess_emqa','S0x_guess_emqa','S0x_guess_emqa','S0x_guess_emqa'}, ... 'S0y_emqa',{'S0y_guess_emqa','S0y_guess_emqa','S0y_guess_emqa','S0y_guess_emqa', ... 'S0y_guess_emqa','S0y_guess_emqa','S0y_guess_emqa','S0y_guess_emqa'}, ... 'SRcoord_emqa',{'','','','','','','',''}, ... 'rCylx_emqa',{'','','','','','','',''}, ... 'rCyly_emqa',{'','','','','','','',''}, ... 'detJ_emqa',{'1','1','1','1','1','1','1','1'}, ... 'Jxx_emqa',{'1','1','1','1','1','1','1','1'}, ... 'invJxx_emqa',{'1','1','1','1','1','1','1','1'}, ... 'Jxy_emqa',{'0','0','0','0','0','0','0','0'}, ... 'invJxy_emqa',{'0','0','0','0','0','0','0','0'}, ... 'Jyx_emqa',{'0','0','0','0','0','0','0','0'}, ... 'invJyx_emqa',{'0','0','0','0','0','0','0','0'}, ... 'Jyy_emqa',{'1','1','1','1','1','1','1','1'}, ... 'invJyy_emqa',{'1','1','1','1','1','1','1','1'}, ... 'depAz_emqa',{'Az','Az','Az','Az','Az','Az','Az','Az'}, ... 'mur_emqa',{'murxx_emqa','murxx_emqa','murxx_emqa','murxx_emqa','murxx_emqa', ... 'murxx_emqa','murxx_emqa','murxx_emqa'}, ... 'Mx_emqa',{'Bx_emqa/mu0_emqa-Hx_emqa','Bx_emqa/mu0_emqa-Hx_emqa', ... 'Bx_emqa/mu0_emqa-Hx_emqa','Bx_emqa/mu0_emqa-Hx_emqa','Bx_emqa/mu0_emqa-Hx_emqa', ... 'Bx_emqa/mu0_emqa-Hx_emqa','Bx_emqa/mu0_emqa-Hx_emqa','Bx_emqa/mu0_emqa-Hx_emqa'}, ... 'Brx_emqa',{'0','0','0','0','0','0','0','0'}, ... 'My_emqa',{'By_emqa/mu0_emqa-Hy_emqa','By_emqa/mu0_emqa-Hy_emqa', ... 'By_emqa/mu0_emqa-Hy_emqa','By_emqa/mu0_emqa-Hy_emqa','By_emqa/mu0_emqa-Hy_emqa', ... 'By_emqa/mu0_emqa-Hy_emqa','By_emqa/mu0_emqa-Hy_emqa','By_emqa/mu0_emqa-Hy_emqa'}, ... 'Bry_emqa',{'0','0','0','0','0','0','0','0'}, ... 'murxx_emqa',{'1','mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur', ... 'mat1_mur','1','mat2_MUR(normB_emqa[1/T])','mat4_mur'}, ... 'murxy_emqa',{'0','0','0','0','0','0','0','0'}, ... 'muryx_emqa',{'0','0','0','0','0','0','0','0'}, ... 'muryy_emqa',{'1','mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur', ... 'mat1_mur','1','mat2_MUR(normB_emqa[1/T])','mat4_mur'}, ... 'murinvxx_emqa',{'1/mur_emqa','1/mur_emqa','1/mur_emqa','1/mur_emqa', ... '1/mur_emqa','1/mur_emqa','1/mur_emqa','1/mur_emqa'}, ... 'murinvxy_emqa',{'0','0','0','0','0','0','0','0'}, ... 'murinvyx_emqa',{'0','0','0','0','0','0','0','0'}, ... 'murinvyy_emqa',{'1/mur_emqa','1/mur_emqa','1/mur_emqa','1/mur_emqa', ... '1/mur_emqa','1/mur_emqa','1/mur_emqa','1/mur_emqa'}, ... 'vx_emqa',{'0','0','0','0','0','0','0','0'}, ... 'vy_emqa',{'0','0','0','0','0','0','0','0'}}; equ.expr = {}; equ.bnd.weak = {{'0';'0';'0'}}; equ.bnd.gporder = {{1;1;1}}; equ.bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; equ.bnd.var = {}; equ.bnd.expr = {}; equ.lock = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; equ.mlock = {[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]}; xfem.equ = equ; clear bnd bnd.weak = {{'0';'0';'0';'0';'0';'0'},{'0';'-test(-Az)*lm1+test(lm1)*Az'; ... '0';'0';'0';'0'},{'0';'-if(dst2src_ip2,0,test(-Az))*lm1-test(lm1)*if(dst2src_ip2,0,-Az)-if(dst2src_ip2,lm1TX,0)*test(lm1TX)-if(dst2src_ip2,lm1TY,0)*test(lm1TY)'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'-if(src2dst_ip2,test(Az-src2dst_ip2(Az)),test(-Az))*lm1-test(lm1)*if(src2dst_ip2,Az-src2dst_ip2(Az),-Az)'; ... '0';'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}}; bnd.constr = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}}; bnd.constrf = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}}; bnd.shape = {[1],[1;2],[1;2],[1],[1;2]}; bnd.sshape = {[1;2],[1;2],[1;2],[1;3],[1;3]}; bnd.sshapedim = {{2;2;1;1;1;1},{2;2;1;1;1;1},{2;2;1;1;1;1},{3;3;1;1;1;1},{3;3; ... 1;1;1;1}}; bnd.gporder = {{1;2;1;1;2;2},{1;2;1;1;2;2},{1;2;1;1;2;2},{1;2;1;1;2;2},{1;2; ... 1;1;2;2}}; bnd.cporder = {{1;1;1;1;1;1},{1;1;1;1;1;1},{1;1;1;1;1;1},{1;1;1;1;1;1},{1;1; ... 1;1;1;1}}; bnd.init = {{'';'0';'';'';'0';'0'},{'';'0';'';'';'0';'0'},{'';'0';'';'';'0'; ... '0'},{'';'0';'';'';'0';'0'},{'';'0';'';'';'0';'0'}}; bnd.dinit = {{'';'';'';'';'';''},{'';'';'';'';'';''},{'';'';'';'';'';''},{''; ... '';'';'';'';''},{'';'';'';'';'';''}}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,3,3,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5, ... 4,4,4,4,4,4,4,4,4,4,4,4,5,5,4,4,4,4,4,4,4,4]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; bnd.var = {'dVolbnd_emqa',{'1','1','1','1','1'}, ... 'murbnd_emqa',{'murbndxx_emqa','murbndxx_emqa','murbndxx_emqa','murbndxx_emqa', ... 'murbndxx_emqa'}, ... 'Jsz_emqa',{'unx*(Hy_emqa_down-Hy_emqa_up)-uny*(Hx_emqa_down-Hx_emqa_up)', ... 'unx*(Hy_emqa_down-Hy_emqa_up)-uny*(Hx_emqa_down-Hx_emqa_up)','unx*(Hy_emqa_down-Hy_emqa_up)-uny*(Hx_emqa_down-Hx_emqa_up)', ... 'unx*(Hy_emqa_down-Hy_emqa_up)-uny*(Hx_emqa_down-Hx_emqa_up)','unx*(Hy_emqa_down-Hy_emqa_up)-uny*(Hx_emqa_down-Hx_emqa_up)'}, ... 'unTx_emqa',{'-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dnx+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*Bx_emqa_up', ... '-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dnx+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*Bx_emqa_up', ... '-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dnx+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*Bx_emqa_up', ... '-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dnx+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*Bx_emqa_up', ... '-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dnx+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*Bx_emqa_up'}, ... 'dnTx_emqa',{'-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*unx+(unx*Hx_emqa_down+uny*Hy_emqa_down)*Bx_emqa_down', ... '-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*unx+(unx*Hx_emqa_down+uny*Hy_emqa_down)*Bx_emqa_down', ... '-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*unx+(unx*Hx_emqa_down+uny*Hy_emqa_down)*Bx_emqa_down', ... '-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*unx+(unx*Hx_emqa_down+uny*Hy_emqa_down)*Bx_emqa_down', ... '-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*unx+(unx*Hx_emqa_down+uny*Hy_emqa_down)*Bx_emqa_down'}, ... 'unTy_emqa',{'-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dny+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*By_emqa_up', ... '-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dny+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*By_emqa_up', ... '-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dny+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*By_emqa_up', ... '-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dny+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*By_emqa_up', ... '-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dny+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*By_emqa_up'}, ... 'dnTy_emqa',{'-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*uny+(unx*Hx_emqa_down+uny*Hy_emqa_down)*By_emqa_down', ... '-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*uny+(unx*Hx_emqa_down+uny*Hy_emqa_down)*By_emqa_down', ... '-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*uny+(unx*Hx_emqa_down+uny*Hy_emqa_down)*By_emqa_down', ... '-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*uny+(unx*Hx_emqa_down+uny*Hy_emqa_down)*By_emqa_down', ... '-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*uny+(unx*Hx_emqa_down+uny*Hy_emqa_down)*By_emqa_down'}, ... 'FsLtzx_emqa',{'-Jsz_emqa*By_emqa','-Jsz_emqa*By_emqa','-Jsz_emqa*By_emqa', ... '-Jsz_emqa*By_emqa','-Jsz_emqa*By_emqa'}, ... 'FsLtzy_emqa',{'Jsz_emqa*Bx_emqa','Jsz_emqa*Bx_emqa','Jsz_emqa*Bx_emqa', ... 'Jsz_emqa*Bx_emqa','Jsz_emqa*Bx_emqa'}, ... 'normFsLtz_emqa',{'sqrt(abs(FsLtzx_emqa)^2+abs(FsLtzy_emqa)^2)','sqrt(abs(FsLtzx_emqa)^2+abs(FsLtzy_emqa)^2)', ... 'sqrt(abs(FsLtzx_emqa)^2+abs(FsLtzy_emqa)^2)','sqrt(abs(FsLtzx_emqa)^2+abs(FsLtzy_emqa)^2)', ... 'sqrt(abs(FsLtzx_emqa)^2+abs(FsLtzy_emqa)^2)'}, ... 'xinit_ale',{'X','X','X','X','X'}, ... 'yinit_ale',{'Y','Y','Y','Y','Y'},'Js0z_emqa',{'0','0','0','0','0'}, ... 'A0z_emqa',{'0','0','0','0','0'}, ... 'murext_emqa',{'1','1','1','1','1'}, ... 'epsilonrbnd_emqa',{'1','1','1','1','1'}, ... 'sigmabnd_emqa',{'0','0','0','0','0'}, ... 'eta_emqa',{'1','1','1','1','1'}, ... 'Esz_emqa',{'0','0','0','0','0'}, ... 'd_emqa',{'0','0','0','0','0'}, ... 'index_emqa',{'0','0','0','0','0'}, ... 'nsect_emqa',{'2','2','2','2','2'}, ... 'nx_emqa',{'nx','nx','nx','nx','nx'}, ... 'ny_emqa',{'ny','ny','ny','ny','ny'}, ... 'murbndxx_emqa',{'1','1','1','1','1'}, ... 'murbndxy_emqa',{'0','0','0','0','0'}, ... 'murbndyx_emqa',{'0','0','0','0','0'}, ... 'murbndyy_emqa',{'1','1','1','1','1'}, ... 'H0x_emqa',{'0','0','0','0','0'}, ... 'H0y_emqa',{'0','0','0','0','0'}, ... 'nX_ale',{'','','','',''}, ... 'nY_ale',{'','','','',''}}; bnd.expr = {}; clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.src.map.frame = 'ale'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; pair{1}.dst.map.frame = 'ale'; bnd.pair = pair; bnd.lock = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; bnd.mlock = {[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]}; xfem.bnd = bnd; clear pnt pnt.weak = {{'0';'0';'0'},{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'},{'0';'0';'0'}}; pnt.constrf = {{'0';'0';'0'},{'0';'0';'0'}}; pnt.shape = {[1],[1]}; pnt.sshape = {[1;2],[1;3]}; pnt.sshapedim = {{2;1;1},{3;1;1}}; pnt.init = {{'';'';''},{'';'';''}}; pnt.dinit = {{'';'';''},{'';'';''}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, ... 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]; pnt.dim = {'Az','x','y'}; pnt.var = {'xinit_ale',{'X','X'}, ... 'yinit_ale',{'Y','Y'},'I0_emqa',{'0','0'}}; pnt.expr = {}; clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.src.map.frame = 'ale'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pair{1}.dst.map.frame = 'ale'; pnt.pair = pair; pnt.lock = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; pnt.mlock = {[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]}; xfem.pnt = pnt; xfem.var = {'epsilon0_emqa','8.854187817000001e-012','mu0_emqa','4e-007*pi','Azt','AzTIME-xTIME*Azx-yTIME*Azy','Aztt','AzTIMETIME','Azxt','AzxTIME-xTIME*Azxx-yTIME*Azxy','Azyt','AzyTIME-xTIME*Azyx-yTIME*Azyy','xt','xTIME','xtt','xTIMETIME','xXt','xXTIME','xYt','xYTIME','yt','yTIME','ytt','yTIMETIME','yXt','yXTIME','yYt','yYTIME'}; xfem.expr = {}; clear elemmph clear elem elem.elem = 'elcplextr'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{'dVol_emqa'}}; equ.map = {{'1'}}; equ.ind = {{'1','2','3','4','5','6','7','8','9','10','11','12','13', ... '14','15','16','17','18','19','20','21','22','23','24','25','26','27', ... '28','29'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); clear pnt pnt.map = {{'1'}}; pnt.ind = {{'1','2','3','4','5','6','7','8','9','10','11','12','13', ... '14','15','16','17','18','19','20','21','22','23','24','25','26','27', ... '28','29','30','31','32','33','34','35','36','37','38','39','40','41', ... '42','43','44','45','46','47','48','49','50','51','52','53','54','55', ... '56','57','58','59','60','61','62','63','64','65','66','67','68','69', ... '70','71','72','73','74','75','76','77','78','79','80','81','82','83', ... '84','85','86','87','88','89','90','91','92','93','94','95','96','97', ... '98','99','100','101','102','103','104','105','106','107','108','109', ... '110','111','112','113','114','115','116','117','118','119','120','121', ... '122','123','124','125','126','127','128','129','130','131','132','133', ... '134','135','136','137','138','139','140','141','142','143','144','145', ... '146','147','148','149','150','151','152','153','154','155','156','157', ... '158','159','160','161','162','163','164','165','166','167','168','169', ... '170','171','172','173','174','175','176','177','178','179','180','181', ... '182','183','184','185','186','187','188','189','190','191','192'}}; geomdim{1} = {pnt,{},{}}; elem.geomdim = geomdim; elem.var = {'dVol_emqa'}; map = cell(1,1); clear submap submap.type = 'local'; submap.expr = {'X','Y'}; map{1} = submap; elem.map = map; elemmph{1} = elem; clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); src{1} = {{},{},{}}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {}; elem.global = {}; elemmph{2} = elem; clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); src{1} = {{},{},{}}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {}; elem.global = {}; elemmph{3} = elem; clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); src{1} = {{},{},{}}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {}; elem.global = {}; elemmph{4} = elem; clear elem elem.elem = 'elcplextr'; elem.g = {'1'}; src = cell(1,1); src{1} = {{},{},{}}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {{},{},{}}; elem.geomdim = geomdim; elem.var = {}; map = cell(1,0); elem.map = map; elemmph{5} = elem; clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{'-qual_ale'}}; equ.ipoints = {{'4'}}; equ.ind = {{'1','2','3','4','5','6','7','8','9','10','11','12','13', ... '14','15','16','17','18','19','20','21','22','23','24','25','26','27', ... '28','29'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'minqual_tmp1_ale'}; elem.global = {'1'}; elem.maxvars = {'1'}; elemmph{6} = elem; clear elem elem.elem = 'elconst'; elem.var = {'minqual1_ale','-minqual_tmp1_ale'}; elemmph{7} = elem; xfem.elemmph = elemmph; clear elemcpl clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elem.maxvars = {}; elemcpl{1} = elem; xfem.elemcpl = elemcpl; clear draw draw.p.objs = {}; draw.p.name = {}; draw.c.objs = {}; draw.c.name = {}; draw.s.objs = {flbinary('g75','draw','12-8complete-+.mph'),flbinary('g90','draw','12-8complete-+.mph')}; draw.s.name = {'CO1','CO3'}; xfem.draw = draw; xfem.const = {'t','0[s]','rpm','60[1/min]','A','pi*(0.028[cm])^2','L','1','NN','300'}; xfem.globalexpr = {}; clear fcns xfem.functions = {}; xfem.sol = flbinary('xfem','solution','12-8complete-+.mph'); xfem.xmcases = [0]; xfem.mcases = [0]; flbinary clear; xfem.rulingmode = 'emqa'; xfem.solform = 'weak'; clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; xfem.lib = lib; clear ode clear units; units.basesystem = 'SI'; ode.units = units; xfem.ode=ode; uq~ t2gui.solvemodel.toutcomp='on'; gui.solvemodel.currsolver='stationary'; gui.solvemodel.solveroption=''; gui.solvemodel.postsolver='stationary'; gui.solvemodel.nonlin='auto'; gui.solvemodel.ntol='1.0E-6'; gui.solvemodel.maxiter='25'; gui.solvemodel.segterm='tol'; gui.solvemodel.maxsegiter='100'; gui.solvemodel.segiter='1'; gui.solvemodel.manualdamp='off'; gui.solvemodel.damping='on'; gui.solvemodel.hnlin='off'; gui.solvemodel.initstep='1.0'; gui.solvemodel.minstep='1.0E-4'; gui.solvemodel.rstep='10.0'; gui.solvemodel.useaugsolver='off'; gui.solvemodel.autoaugcomp='on'; gui.solvemodel.augcomp=''; gui.solvemodel.augtol='0.0010'; gui.solvemodel.augmaxiter='25'; gui.solvemodel.augsolver='lumped'; gui.solvemodel.nlsolver='manual'; gui.solvemodel.timenonlin='auto'; gui.solvemodel.useratelimit='on'; gui.solvemodel.timentolfact='0.2'; gui.solvemodel.timemaxiter='7'; gui.solvemodel.timesegterm='tol'; gui.solvemodel.timemaxsegiter='10'; gui.solvemodel.timesegiter='1'; gui.solvemodel.timemanualdamp='off'; gui.solvemodel.timedtech='const'; gui.solvemodel.timedamp='1.0'; gui.solvemodel.timejtech='once'; gui.solvemodel.timeinitstep='1.0'; gui.solvemodel.timeminstep='1.0E-2'; gui.solvemodel.timerstep='10.0'; gui.solvemodel.atol='Az 1e-3 lm1 5e3'; gui.solvemodel.rtol='0.01'; gui.solvemodel.tlist='0:0.01:0.25'; gui.solvemodel.tout='tlist'; gui.solvemodel.tsteps='free'; gui.solvemodel.odesolver='bdf_ida'; gui.solvemodel.timestep='0.01'; gui.solvemodel.incrdelay='off'; gui.solvemodel.incrdelaysteps='15'; gui.solvemodel.manualreassem='off'; gui.solvemodel.emassconst='on'; gui.solvemodel.massconst='on'; gui.solvemodel.loadconst='on'; gui.solvemodel.constrconst='on'; gui.solvemodel.jacobianconst='on'; gui.solvemodel.constrjacobianconst='on'; gui.solvemodel.manualstep='off'; gui.solvemodel.maxstepauto='on'; gui.solvemodel.initialstepauto='on'; gui.solvemodel.initialstep='0.0010'; gui.solvemodel.maxorder='5'; gui.solvemodel.minorder='1'; gui.solvemodel.maxstep='0.1'; gui.solvemodel.rhoinf='0.75'; gui.solvemodel.predictor='linear'; gui.solvemodel.timeusestopcond='off'; gui.solvemodel.timestopcond=''; gui.solvemodel.paramusestopcond='off'; gui.solvemodel.masssingular='maybe'; gui.solvemodel.consistent='bweuler'; gui.solvemodel.estrat='0'; gui.solvemodel.complex='off'; gui.solvemodel.neigs='6'; gui.solvemodel.shift='0'; gui.solvemodel.maxeigit='300'; gui.solvemodel.etol='0.0'; gui.solvemodel.krylovdim='0'; gui.solvemodel.eigname='lambda'; gui.solvemodel.eigref='0'; gui.solvemodel.pname=''; gui.solvemodel.plist=''; gui.solvemodel.pdistrib='off'; gui.solvemodel.porder='1'; gui.solvemodel.manualparam='off'; gui.solvemodel.pinitstep='0.0'; gui.solvemodel.pminstep='0.0'; gui.solvemodel.pmaxstep='0.0'; gui.solvemodel.autooldcomp='on'; gui.solvemodel.oldcomp=''; gui.solvemodel.outform='auto'; gui.solvemodel.symmetric='auto'; gui.solvemodel.symmhermit='auto'; gui.solvemodel.method='eliminate'; gui.solvemodel.nullfun='auto'; gui.solvemodel.blocksize='1000'; gui.solvemodel.blocksizeauto='on'; gui.solvemodel.uscale='auto'; gui.solvemodel.manscale=''; gui.solvemodel.rowscale='on'; gui.solvemodel.conjugate='off'; gui.solvemodel.complexfun='off'; gui.solvemodel.matherr='on'; gui.solvemodel.solfile='off'; gui.solvemodel.adaptgeom='currgeom'; gui.solvemodel.eefun='l2'; gui.solvemodel.eefunc=''; gui.solvemodel.maxt='10000000'; gui.solvemodel.rmethod='longest'; gui.solvemodel.resmethod='weak'; gui.solvemodel.resorderauto='on'; gui.solvemodel.resorder='0'; gui.solvemodel.l2scale='1'; gui.solvemodel.l2staborder='2'; gui.solvemodel.eigselect='1'; gui.solvemodel.tpfun='fltpft'; gui.solvemodel.ngen='2'; gui.solvemodel.tpmult='1.7'; gui.solvemodel.tpworst='0.5'; gui.solvemodel.tpfract='0.5'; gui.solvemodel.autosolver='on'; gui.solvemodel.varcomp=''; gui.solvemodel.oldvarcomp=''; gui.solvemodel.manualhessupd='off'; gui.solvemodel.manuallimitexpr='off'; gui.solvemodel.designsolver='sensitivity'; gui.solvemodel.sensmethod='adjoint'; gui.solvemodel.sensfunc=''; gui.solvemodel.sensfuncauto='on'; gui.solvemodel.qpsolver='cholesky'; gui.solvemodel.gradient='analytic'; gui.solvemodel.limitexpr=''; gui.solvemodel.nsolvemax='500'; gui.solvemodel.hessupd='10'; gui.solvemodel.opttol='1.0e-6'; gui.solvemodel.feastol='1.0e-6'; gui.solvemodel.majfeastol='1.0e-6'; gui.solvemodel.funcprec='1.0e-6'; gui.solvemodel.callblevel=''; gui.solvemodel.callblevelshow=''; gui.solvemodel.callbfreq=''; gui.solvemodel.callbackrough='0'; gui.solvemodel.callbclose='off'; gui.solvemodel.solcomp='lm1,Az'; gui.solvemodel.outcomp='lm1,Az'; gui.solvemodel.reacf='on'; gui.solvemodel.inittype='init_expr_currsol_radio'; gui.solvemodel.initsolnum='Automatic'; gui.solvemodel.inittime='0'; gui.solvemodel.utype='u_init_radio'; gui.solvemodel.usolnum='Automatic'; gui.solvemodel.utime='0'; gui.solvemodel.scriptcommands=''; gui.solvemodel.usescript='off'; gui.solvemodel.autoscript='off'; gui.solvemodel.sameaxis='off'; gui.solvemodel.linsolvernode.currlinsolver='umfpack'; gui.solvemodel.linsolvernode.type='linsolver'; gui.solvemodel.linsolvernode.droptol='0.0'; gui.solvemodel.linsolvernode.thresh='0.1'; gui.solvemodel.linsolvernode.umfalloc='0.7'; gui.solvemodel.linsolvernode.preorder='nd'; gui.solvemodel.linsolvernode.preroworder='on'; gui.solvemodel.linsolvernode.pivotstrategy='off'; gui.solvemodel.linsolvernode.pardreorder='nd'; gui.solvemodel.linsolvernode.pardrreorder='on'; gui.solvemodel.linsolvernode.pivotperturb='1.0E-8'; gui.solvemodel.linsolvernode.errorchk='on'; gui.solvemodel.linsolvernode.errorchkd='off'; gui.solvemodel.linsolvernode.termination='tol'; gui.solvemodel.linsolvernode.iter='2'; gui.solvemodel.linsolvernode.itol='1.0E-6'; gui.solvemodel.linsolvernode.rhob='400.0'; gui.solvemodel.linsolvernode.maxlinit='10000'; gui.solvemodel.linsolvernode.prefuntype='left'; gui.solvemodel.linsolvernode.prefuntype2='right'; gui.solvemodel.linsolvernode.iluiter='1'; gui.solvemodel.linsolvernode.itrestart='50'; gui.solvemodel.linsolvernode.seconditer='1'; gui.solvemodel.linsolvernode.relax='1.0'; gui.solvemodel.linsolvernode.amgauto='3'; gui.solvemodel.linsolvernode.mglevels='6'; gui.solvemodel.linsolvernode.mgcycle='v'; gui.solvemodel.linsolvernode.maxcoarsedof='5000'; gui.solvemodel.linsolvernode.oocmemory='512.0'; gui.solvemodel.linsolvernode.oocfilename=''; gui.solvemodel.linsolvernode.modified='off'; gui.solvemodel.linsolvernode.fillratio='2.0'; gui.solvemodel.linsolvernode.respectpattern='on'; gui.solvemodel.linsolvernode.droptype='droptol'; gui.solvemodel.linsolvernode.vankavars=''; gui.solvemodel.linsolvernode.vankasolv='gmres'; gui.solvemodel.linsolvernode.vankatol='0.02'; gui.solvemodel.linsolvernode.vankarestart='100'; gui.solvemodel.linsolvernode.vankarelax='0.8'; gui.solvemodel.linsolvernode.vankablocked='on'; gui.solvemodel.linsolvernode.sorblocked='on'; gui.solvemodel.linsolvernode.sorvecdof=''; gui.solvemodel.linsolvernode.mgauto='shape'; gui.solvemodel.linsolvernode.rmethod='regular'; gui.solvemodel.linsolvernode.coarseassem='on'; gui.solvemodel.linsolvernode.meshscale='2'; gui.solvemodel.linsolvernode.mgautolevels='2'; gui.solvemodel.linsolvernode.mgkeep='off'; gui.solvemodel.linsolvernode.mggeom='Geom1'; gui.solvemodel.linsolvernode.mcase0='on'; gui.solvemodel.linsolvernode.mgassem0='on'; gui.solvemodel.solversegmodel.seggrps{1}.segcomp='Az'; gui.solvemodel.solversegmodel.seggrps{1}.ntol='1e-3'; gui.solvemodel.solversegmodel.seggrps{1}.timentol='1'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.currlinsolver='umfpack'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.type='linsolver'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.droptol='0.0'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.thresh='0.1'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.umfalloc='0.7'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.preorder='nd'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.preroworder='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.pivotstrategy='off'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.pardreorder='nd'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.pardrreorder='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.pivotperturb='1.0E-8'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.errorchk='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.errorchkd='off'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.termination='tol'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.iter='2'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.itol='1.0E-6'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.rhob='400.0'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.maxlinit='10000'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.prefuntype='left'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.prefuntype2='right'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.iluiter='1'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.itrestart='50'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.seconditer='1'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.relax='1.0'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.amgauto='3'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mglevels='6'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mgcycle='v'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.maxcoarsedof='5000'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.oocmemory='512.0'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.oocfilename=''; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.modified='off'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.fillratio='2.0'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.respectpattern='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.droptype='droptol'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.vankavars=''; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.vankasolv='gmres'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.vankatol='0.02'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.vankarestart='100'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.vankarelax='0.8'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.vankablocked='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.sorblocked='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.sorvecdof=''; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mgauto='shape'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.rmethod='regular'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.coarseassem='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.meshscale='2'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mgautolevels='2'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mgkeep='off'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mggeom='Geom1'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mcase0='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mgassem0='on'; gui.solvemodel.solversegmodel.seggrps{2}.segcomp='x y lm3 lm4'; gui.solvemodel.solversegmodel.seggrps{2}.ntol='1e-3'; gui.solvemodel.solversegmodel.seggrps{2}.timentol='1'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.currlinsolver='umfpack'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.type='linsolver'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.droptol='0.0'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.thresh='0.1'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.umfalloc='0.7'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.preorder='nd'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.preroworder='on'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.pivotstrategy='off'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.pardreorder='nd'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.pardrreorder='on'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.pivotperturb='1.0E-8'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.errorchk='on'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.errorchkd='off'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.termination='tol'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.iter='2'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.itol='1.0E-6'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.rhob='400.0'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.maxlinit='10000'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.prefuntype='left'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.prefuntype2='right'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.iluiter='1'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.itrestart='50'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.seconditer='1'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.relax='1.0'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.amgauto='3'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.mglevels='6'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.mgcycle='v'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.maxcoarsedof='5000'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.oocmemory='512.0'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.oocfilename=''; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.modified='off'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.fillratio='2.0'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.respectpattern='on'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.droptype='droptol'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.vankavars=''; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.vankasolv='gmres'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.vankatol='0.02'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.vankarestart='100'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.vankarelax='0.8'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.vankablocked='on'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.sorblocked='on'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.sorvecdof=''; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.mgauto='shape'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.rmethod='regular'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.coarseassem='on'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.meshscale='2'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.mgautolevels='2'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.mgkeep='off'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.mggeom='Geom1'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.mcase0='on'; gui.solvemodel.solversegmodel.seggrps{2}.linsolvernode.mgassem0='on'; gui.solvemodel.solversegmodel.segsteps{1}.segorder='1'; gui.solvemodel.solversegmodel.segsteps{1}.subterm='iter'; gui.solvemodel.solversegmodel.segsteps{1}.subdamp='0.5'; gui.solvemodel.solversegmodel.segsteps{1}.timesubdamp='1'; gui.solvemodel.solversegmodel.segsteps{1}.subiter='1'; gui.solvemodel.solversegmodel.segsteps{1}.maxsubiter='20'; gui.solvemodel.solversegmodel.segsteps{1}.timemaxsubiter='10'; gui.solvemodel.solversegmodel.segsteps{1}.subntol='1.0E-2'; gui.solvemodel.solversegmodel.segsteps{1}.subntolfact='1'; gui.solvemodel.solversegmodel.segsteps{1}.subdtech='const'; gui.solvemodel.solversegmodel.segsteps{1}.submandamp='off'; gui.solvemodel.solversegmodel.segsteps{1}.subinitstep='1.0'; gui.solvemodel.solversegmodel.segsteps{1}.subminstep='1.0E-4'; gui.solvemodel.solversegmodel.segsteps{1}.timesubminstep='1.0E-2'; gui.solvemodel.solversegmodel.segsteps{1}.subrstep='10.0'; gui.solvemodel.solversegmodel.segsteps{1}.timesubjtech='minimal'; gui.solvemodel.solversegmodel.segsteps{1}.subjtech='onevery'; gui.solvemodel.solversegmodel.segsteps{2}.segorder='2'; gui.solvemodel.solversegmodel.segsteps{2}.subterm='iter'; gui.solvemodel.solversegmodel.segsteps{2}.subdamp='0.5'; gui.solvemodel.solversegmodel.segsteps{2}.timesubdamp='1'; gui.solvemodel.solversegmodel.segsteps{2}.subiter='1'; gui.solvemodel.solversegmodel.segsteps{2}.maxsubiter='20'; gui.solvemodel.solversegmodel.segsteps{2}.timemaxsubiter='10'; gui.solvemodel.solversegmodel.segsteps{2}.subntol='1.0E-2'; gui.solvemodel.solversegmodel.segsteps{2}.subntolfact='1'; gui.solvemodel.solversegmodel.segsteps{2}.subdtech='const'; gui.solvemodel.solversegmodel.segsteps{2}.submandamp='off'; gui.solvemodel.solversegmodel.segsteps{2}.subinitstep='1.0'; gui.solvemodel.solversegmodel.segsteps{2}.subminstep='1.0E-4'; gui.solvemodel.solversegmodel.segsteps{2}.timesubminstep='1.0E-2'; gui.solvemodel.solversegmodel.segsteps{2}.subrstep='10.0'; gui.solvemodel.solversegmodel.segsteps{2}.timesubjtech='minimal'; gui.solvemodel.solversegmodel.segsteps{2}.subjtech='onevery'; gui.solvemodel.solversegmodel.manualsteps='off'; gui.solvemodel.solversegmodel.llimitdof=''; gui.solvemodel.solversegmodel.llimitval=''; gui.solvemodel.paramsweep.pname=''; gui.solvemodel.paramsweep.plist=''; gui.solvemodel.paramsweep.pdistrib='off'; gui.solvemodel.paramsweep.savefiles='off'; gui.solvemodel.paramsweep.varnames=''; gui.solvemodel.paramsweep.logfile=''; gui.solvemodel.defaults.ale_jtech='once'; gui.solvemodel.defaults.emqa_toutcomp='on'; gui.solvemodel.defaults.emqa_damp='1.0'; gui.solvemodel.defaults.emqa_timemaxiter='7'; gui.solvemodel.defaults.ale_damp='1.0'; gui.solvemodel.defaults.timemaxiter='7'; gui.solvemodel.defaults.nlsolver='manual'; gui.solvemodel.defaults.timentolfact='0.2'; gui.solvemodel.defaults.toutcomp='on'; gui.solvemodel.defaults.jtech='once'; gui.solvemodel.defaults.emqa_jtech='once'; gui.solvemodel.defaults.ale_timemaxiter='7'; gui.solvemodel.defaults.damp='1.0'; gui.solvemodel.defaults.ale_nlsolver='manual'; gui.solvemodel.defaults.ale_timentolfact='0.2'; gui.solvemodel.defaults.emqa_timentolfact='0.2'; gui.solvemodel.defaults.ale_toutcomp='on'; gui.solvemodel.defaults.emqa_nlsolver='manual'; gui.registry.general_currentmodel='Geom1'; gui.registry.general_currmeshcase='0'; gui.registry.general_savedonserver='off'; gui.registry.general_savedchanges='off'; gui.registry.general_rulingmode=''; gui.registry.general_incompletemfilehistory='off'; gui.registry.saved_license='123456789'; gui.registry.saved_version='COMSOL 3.5.0.494'; gui.registry.info_modelname=''; gui.registry.info_author=''; gui.registry.info_company=''; gui.registry.info_department=''; gui.registry.info_reference=''; gui.registry.info_url=''; gui.registry.info_saveddate='1265966976561'; gui.registry.info_creationdate='1265104321348'; gui.registry.info_modelresult=''; gui.registry.spice_netlist=''; gui.registry.spice_forceac='off'; gui.reportregistry.report_contents=''; gui.reportregistry.report_outputformat='html'; gui.reportregistry.report_filename=''; gui.reportregistry.report_autoopen='off'; gui.reportregistry.report_paperformat='a4'; gui.reportregistry.report_includedefaults='off'; gui.reportregistry.report_template='full'; gui.reportregistry.report_showemptysections='off'; gui.flmodel{1}.modelname='Geom1'; gui.flmodel{1}.currmode='post'; gui.flmodel{1}.currappl='0'; gui.flmodel{1}.axis.xmin='-0.12344727984269391'; gui.flmodel{1}.axis.xmax='0.11724077167557151'; gui.flmodel{1}.axis.ymin='-0.0614593594872952'; gui.flmodel{1}.axis.ymax='0.06854190290682964'; gui.flmodel{1}.axis.zmin='-1.0'; gui.flmodel{1}.axis.zmax='1.0'; gui.flmodel{1}.axis.xspacing='0.02'; gui.flmodel{1}.axis.yspacing='0.02'; gui.flmodel{1}.axis.zspacing='0.02'; gui.flmodel{1}.axis.extrax=''; gui.flmodel{1}.axis.extray=''; gui.flmodel{1}.axis.extraz=''; gui.flmodel{1}.camera.xmin='-1.2034402575913272'; gui.flmodel{1}.camera.xmax='1.2034402575913272'; gui.flmodel{1}.camera.ymin='-0.6500063119706243'; gui.flmodel{1}.camera.ymax='0.6500063119706243'; gui.flmodel{1}.camera.camposx='-0.03103254083561202'; gui.flmodel{1}.camera.camposy='0.035412717097672186'; gui.flmodel{1}.camera.camposz='12.03440257591327'; gui.flmodel{1}.camera.camtargetx='-0.03103254083561202'; gui.flmodel{1}.camera.camtargety='0.035412717097672186'; gui.flmodel{1}.camera.camtargetz='0.0'; gui.flmodel{1}.camera.camupx='0.0'; gui.flmodel{1}.camera.camupy='1.0'; gui.flmodel{1}.camera.camupz='0.0'; gui.flmodel{1}.lightmodel.headlight.type='point'; gui.flmodel{1}.lightmodel.headlight.name='headlight'; gui.flmodel{1}.lightmodel.headlight.enable='on'; gui.flmodel{1}.lightmodel.headlight.colorr='255'; gui.flmodel{1}.lightmodel.headlight.colorg='255'; gui.flmodel{1}.lightmodel.headlight.colorb='255'; gui.flmodel{1}.lightmodel.headlight.xpos='-0.031032542'; gui.flmodel{1}.lightmodel.headlight.ypos='0.035412718'; gui.flmodel{1}.lightmodel.headlight.zpos='12.034403'; gui.flmodel{1}.lightmodel.scenelight{1}.type='directional'; gui.flmodel{1}.lightmodel.scenelight{1}.name='light 1'; gui.flmodel{1}.lightmodel.scenelight{1}.enable='on'; gui.flmodel{1}.lightmodel.scenelight{1}.colorr='255'; gui.flmodel{1}.lightmodel.scenelight{1}.colorg='255'; gui.flmodel{1}.lightmodel.scenelight{1}.colorb='255'; gui.flmodel{1}.lightmodel.scenelight{1}.xdir='1.0'; gui.flmodel{1}.lightmodel.scenelight{1}.ydir='-1.0'; gui.flmodel{1}.lightmodel.scenelight{1}.zdir='1.0'; gui.flmodel{1}.lightmodel.scenelight{2}.type='directional'; gui.flmodel{1}.lightmodel.scenelight{2}.name='light 2'; gui.flmodel{1}.lightmodel.scenelight{2}.enable='on'; gui.flmodel{1}.lightmodel.scenelight{2}.colorr='255'; gui.flmodel{1}.lightmodel.scenelight{2}.colorg='255'; gui.flmodel{1}.lightmodel.scenelight{2}.colorb='255'; gui.flmodel{1}.lightmodel.scenelight{2}.xdir='-1.0'; gui.flmodel{1}.lightmodel.scenelight{2}.ydir='1.0'; gui.flmodel{1}.lightmodel.scenelight{2}.zdir='-1.0'; gui.flmodel{1}.lightmodel.scenelight{3}.type='directional'; gui.flmodel{1}.lightmodel.scenelight{3}.name='light 3'; gui.flmodel{1}.lightmodel.scenelight{3}.enable='on'; gui.flmodel{1}.lightmodel.scenelight{3}.colorr='255'; gui.flmodel{1}.lightmodel.scenelight{3}.colorg='255'; gui.flmodel{1}.lightmodel.scenelight{3}.colorb='255'; gui.flmodel{1}.lightmodel.scenelight{3}.xdir='-1.0'; gui.flmodel{1}.lightmodel.scenelight{3}.ydir='-1.0'; gui.flmodel{1}.lightmodel.scenelight{3}.zdir='1.0'; 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gui.flmodel{1}.postmodel.intdata{2}.intdata={'Az'}; gui.flmodel{1}.postmodel.intdata{2}.intrecover='off'; gui.flmodel{1}.postmodel.intdata{2}.intunit='Wb'; gui.flmodel{1}.postmodel.intdata{2}.phase='0'; gui.flmodel{1}.postmodel.intdata{2}.frame='ale'; gui.flmodel{1}.postmodel.intdata{2}.solnum='0'; gui.flmodel{1}.postmodel.intdata{2}.selectvia='stored'; gui.flmodel{1}.postmodel.intdata{3}.multiplyexpr='off'; gui.flmodel{1}.postmodel.intdata{3}.method='auto'; gui.flmodel{1}.postmodel.intdata{3}.order='4'; gui.flmodel{1}.postmodel.intdata{3}.autoorder='on'; gui.flmodel{1}.postmodel.intdata{3}.intdata={'normB_emqa'}; gui.flmodel{1}.postmodel.intdata{3}.intrecover='off'; gui.flmodel{1}.postmodel.intdata{3}.intunit='Wb'; gui.flmodel{1}.postmodel.intdata{3}.phase='0'; gui.flmodel{1}.postmodel.intdata{3}.frame='ale'; gui.flmodel{1}.postmodel.intdata{3}.solnum='0'; gui.flmodel{1}.postmodel.intdata{3}.selectvia='stored'; gui.flmodel{1}.postmodel.domainplot.colordata={'normB_emqa'}; gui.flmodel{1}.postmodel.domainplot.colorrangeauto='on'; gui.flmodel{1}.postmodel.domainplot.colorrangemin=''; gui.flmodel{1}.postmodel.domainplot.colorrangemax=''; gui.flmodel{1}.postmodel.domainplot.colorcont='on'; gui.flmodel{1}.postmodel.domainplot.colorrecover='off'; gui.flmodel{1}.postmodel.domainplot.colorunit='T'; gui.flmodel{1}.postmodel.domainplot.surfacesurfacemap='jet'; gui.flmodel{1}.postmodel.domainplot.surfacesurfacemapreverse='off'; gui.flmodel{1}.postmodel.domainplot.surfacesurfacebar='on'; gui.flmodel{1}.postmodel.domainplot.surfacesurfaceusemap='on'; gui.flmodel{1}.postmodel.domainplot.surfacesurfacecolor='255,0,0'; gui.flmodel{1}.postmodel.domainplot.surfacesurfacecoloring='interp'; gui.flmodel{1}.postmodel.domainplot.surfacesurfacefill='fill'; gui.flmodel{1}.postmodel.domainplot.extrusion='off'; gui.flmodel{1}.postmodel.domainplot.lineyaxisdata={'Az'}; gui.flmodel{1}.postmodel.domainplot.lineyaxiscont='on'; gui.flmodel{1}.postmodel.domainplot.lineyaxisrecover='off'; gui.flmodel{1}.postmodel.domainplot.lineyaxisunit='Wb/m'; gui.flmodel{1}.postmodel.domainplot.linexaxisxaxistype='arc'; gui.flmodel{1}.postmodel.domainplot.linexaxisuseexpr='off'; gui.flmodel{1}.postmodel.domainplot.linexaxisdata={'Az'}; gui.flmodel{1}.postmodel.domainplot.linexaxisunit='Wb/m'; gui.flmodel{1}.postmodel.domainplot.linelinestyle='solid'; gui.flmodel{1}.postmodel.domainplot.linelinecolor='cyclecolor'; gui.flmodel{1}.postmodel.domainplot.linelinemarker='none'; gui.flmodel{1}.postmodel.domainplot.linelegend='off'; gui.flmodel{1}.postmodel.domainplot.linelinelabels='off'; gui.flmodel{1}.postmodel.domainplot.linecolor='255,0,0'; gui.flmodel{1}.postmodel.domainplot.linesurfacemap='jet'; gui.flmodel{1}.postmodel.domainplot.linesurfacemapreverse='off'; gui.flmodel{1}.postmodel.domainplot.linesurfacebar='on'; gui.flmodel{1}.postmodel.domainplot.linesurfaceusemap='on'; gui.flmodel{1}.postmodel.domainplot.linesurfacecolor='255,0,0'; gui.flmodel{1}.postmodel.domainplot.linesurfacecoloring='interp'; gui.flmodel{1}.postmodel.domainplot.linesurfacefill='fill'; gui.flmodel{1}.postmodel.domainplot.pointyaxisdata={'Az'}; gui.flmodel{1}.postmodel.domainplot.pointyaxisrecover='off'; gui.flmodel{1}.postmodel.domainplot.pointyaxisunit='Wb/m'; gui.flmodel{1}.postmodel.domainplot.pointxxaxistype=''; gui.flmodel{1}.postmodel.domainplot.pointxuseexpr='off'; gui.flmodel{1}.postmodel.domainplot.pointxdata={'Az'}; gui.flmodel{1}.postmodel.domainplot.pointxunit='Wb/m'; gui.flmodel{1}.postmodel.domainplot.pointlinestyle='solid'; gui.flmodel{1}.postmodel.domainplot.pointlinecolor='cyclecolor'; gui.flmodel{1}.postmodel.domainplot.pointlinemarker='none'; gui.flmodel{1}.postmodel.domainplot.pointlegend='off'; gui.flmodel{1}.postmodel.domainplot.pointlinelabels='off'; gui.flmodel{1}.postmodel.domainplot.pointcolor='255,0,0'; gui.flmodel{1}.postmodel.domainplot.crossdispcolor='255,0,0'; gui.flmodel{1}.postmodel.domainplot.phase='0'; gui.flmodel{1}.postmodel.domainplot.frame='ale'; gui.flmodel{1}.postmodel.domainplot.solnum='0'; gui.flmodel{1}.postmodel.domainplot.selectvia='stored'; gui.flmodel{1}.postmodel.domainplot.autotitle='on'; gui.flmodel{1}.postmodel.domainplot.customtitle=''; gui.flmodel{1}.postmodel.domainplot.autolabelx='on'; gui.flmodel{1}.postmodel.domainplot.customlabelx=''; gui.flmodel{1}.postmodel.domainplot.autolabely='on'; gui.flmodel{1}.postmodel.domainplot.customlabely=''; gui.flmodel{1}.postmodel.domainplot.axistype={'lin','lin'}; gui.flmodel{1}.postmodel.domainplot.smoothinternal='on'; gui.flmodel{1}.postmodel.domainplot.autorefine='on'; gui.flmodel{1}.postmodel.domainplot.refine='1'; gui.flmodel{1}.postmodel.domainplot.plottypeind='0'; gui.flmodel{1}.postmodel.crossplot.extrusion='off'; gui.flmodel{1}.postmodel.crossplot.lineyaxisdata={'normB_emqa'}; gui.flmodel{1}.postmodel.crossplot.lineyaxisrecover='off'; gui.flmodel{1}.postmodel.crossplot.lineyaxisunit='T'; gui.flmodel{1}.postmodel.crossplot.linexaxisxaxistype='arc'; gui.flmodel{1}.postmodel.crossplot.linexaxisuseexpr='off'; gui.flmodel{1}.postmodel.crossplot.linexaxisdata={'normB_emqa'}; gui.flmodel{1}.postmodel.crossplot.linexaxisunit='T'; gui.flmodel{1}.postmodel.crossplot.linelinestyle='solid'; gui.flmodel{1}.postmodel.crossplot.linelinecolor='cyclecolor'; gui.flmodel{1}.postmodel.crossplot.linelinemarker='none'; gui.flmodel{1}.postmodel.crossplot.linelegend='off'; gui.flmodel{1}.postmodel.crossplot.linelinelabels='off'; gui.flmodel{1}.postmodel.crossplot.linecolor='255,0,0'; gui.flmodel{1}.postmodel.crossplot.linesurfacemap='jet'; gui.flmodel{1}.postmodel.crossplot.linesurfacemapreverse='off'; gui.flmodel{1}.postmodel.crossplot.linesurfacebar='on'; gui.flmodel{1}.postmodel.crossplot.linesurfaceusemap='on'; gui.flmodel{1}.postmodel.crossplot.linesurfacecolor='255,0,0'; gui.flmodel{1}.postmodel.crossplot.linesurfacecoloring='interp'; gui.flmodel{1}.postmodel.crossplot.linesurfacefill='fill'; gui.flmodel{1}.postmodel.crossplot.lineresolution='200'; gui.flmodel{1}.postmodel.crossplot.linecoord={'0','1','0','0'}; gui.flmodel{1}.postmodel.crossplot.linelevels='5'; gui.flmodel{1}.postmodel.crossplot.linevectorlevels=''; gui.flmodel{1}.postmodel.crossplot.lineisvector='off'; gui.flmodel{1}.postmodel.crossplot.lineactive='off'; gui.flmodel{1}.postmodel.crossplot.pointyaxisdata={'normB_emqa'}; gui.flmodel{1}.postmodel.crossplot.pointyaxisrecover='off'; gui.flmodel{1}.postmodel.crossplot.pointyaxisunit='T'; gui.flmodel{1}.postmodel.crossplot.pointxxaxistype=''; gui.flmodel{1}.postmodel.crossplot.pointxuseexpr='off'; gui.flmodel{1}.postmodel.crossplot.pointxdata={'normB_emqa'}; gui.flmodel{1}.postmodel.crossplot.pointxunit='Wb'; gui.flmodel{1}.postmodel.crossplot.pointlinestyle='solid'; gui.flmodel{1}.postmodel.crossplot.pointlinecolor='cyclecolor'; gui.flmodel{1}.postmodel.crossplot.pointlinemarker='none'; gui.flmodel{1}.postmodel.crossplot.pointlegend='off'; gui.flmodel{1}.postmodel.crossplot.pointlinelabels='off'; gui.flmodel{1}.postmodel.crossplot.pointcolor='255,0,0'; gui.flmodel{1}.postmodel.crossplot.pointcoord={'0','0'}; gui.flmodel{1}.postmodel.crossplot.crossdispcolor='255,0,0'; gui.flmodel{1}.postmodel.crossplot.phase='0'; gui.flmodel{1}.postmodel.crossplot.frame='ale'; gui.flmodel{1}.postmodel.crossplot.solnum='0'; gui.flmodel{1}.postmodel.crossplot.selectvia='stored'; gui.flmodel{1}.postmodel.crossplot.autotitle='on'; gui.flmodel{1}.postmodel.crossplot.customtitle=''; gui.flmodel{1}.postmodel.crossplot.autolabelx='on'; gui.flmodel{1}.postmodel.crossplot.customlabelx=''; gui.flmodel{1}.postmodel.crossplot.autolabely='on'; gui.flmodel{1}.postmodel.crossplot.customlabely=''; gui.flmodel{1}.postmodel.crossplot.axistype={'lin','lin'}; gui.flmodel{1}.postmodel.crossplot.smoothinternal='on'; gui.flmodel{1}.postmodel.crossplot.plottypeind='0'; gui.flmodel{1}.postmodel.dataexport.pntdata={'Az'}; gui.flmodel{1}.postmodel.dataexport.pntrecover='off'; gui.flmodel{1}.postmodel.dataexport.pntunit='Wb/m'; gui.flmodel{1}.postmodel.dataexport.pntlocation='element'; gui.flmodel{1}.postmodel.dataexport.pntlagorder='2'; gui.flmodel{1}.postmodel.dataexport.bnddata={'Az'}; gui.flmodel{1}.postmodel.dataexport.bndcont='off'; gui.flmodel{1}.postmodel.dataexport.bndrecover='off'; gui.flmodel{1}.postmodel.dataexport.bndunit='Wb/m'; gui.flmodel{1}.postmodel.dataexport.bndlocation='element'; gui.flmodel{1}.postmodel.dataexport.bndlagorder='2'; gui.flmodel{1}.postmodel.dataexport.subdata={'normB_emqa'}; gui.flmodel{1}.postmodel.dataexport.subcont='off'; gui.flmodel{1}.postmodel.dataexport.subrecover='off'; gui.flmodel{1}.postmodel.dataexport.subunit='T'; gui.flmodel{1}.postmodel.dataexport.subxspacing='10'; gui.flmodel{1}.postmodel.dataexport.subxvectorspacing=''; gui.flmodel{1}.postmodel.dataexport.subxisvector='off'; gui.flmodel{1}.postmodel.dataexport.subyspacing='10'; gui.flmodel{1}.postmodel.dataexport.subyvectorspacing=''; gui.flmodel{1}.postmodel.dataexport.subyisvector='off'; gui.flmodel{1}.postmodel.dataexport.sublocation='element'; gui.flmodel{1}.postmodel.dataexport.sublagorder='2'; gui.flmodel{1}.postmodel.dataexport.phase='0'; gui.flmodel{1}.postmodel.dataexport.frame='ale'; gui.flmodel{1}.postmodel.dataexport.solnum='0'; gui.flmodel{1}.postmodel.dataexport.selectvia='stored'; gui.flmodel{1}.postmodel.dataexport.smoothinternal='on'; gui.flmodel{1}.postmodel.dataexport.exportformat='ptd'; gui.flmodel{1}.postmodel.dataexport.struct='off'; gui.flmodel{1}.postmodel.dataexport.exportedim='2'; gui.flmodel{1}.postmodel.dataexport.plotexportformat='coorddata'; gui.flmodel{1}.postmodel.dataexport.plotstruct='off'; gui.flmodel{1}.postmodel.datadisplay.fullprecision='off'; gui.flmodel{1}.postmodel.datadisplay.smoothinternal='on'; gui.flmodel{1}.postmodel.datadisplay.phase='0'; gui.flmodel{1}.postmodel.datadisplay.frame='ale'; gui.flmodel{1}.postmodel.datadisplay.solnum='0'; gui.flmodel{1}.postmodel.datadisplay.selectvia='stored'; gui.flmodel{1}.postmodel.datadisplay.interpdata={'normB_emqa'}; gui.flmodel{1}.postmodel.datadisplay.interprecover='off'; gui.flmodel{1}.postmodel.datadisplay.interpunit='T'; gui.flmodel{1}.postmodel.datadisplay.coord={'0','0'}; gui.flmodel{1}.postmodel.globalplot.globalyaxisexprs={}; gui.flmodel{1}.postmodel.globalplot.globalyaxisexprsdisp={}; gui.flmodel{1}.postmodel.globalplot.linexaxisxaxistype=''; gui.flmodel{1}.postmodel.globalplot.linexaxisuseexpr='off'; gui.flmodel{1}.postmodel.globalplot.globallinestyle='solid'; gui.flmodel{1}.postmodel.globalplot.globallinecolor='cyclecolor'; gui.flmodel{1}.postmodel.globalplot.globallinemarker='none'; gui.flmodel{1}.postmodel.globalplot.globallegend='off'; gui.flmodel{1}.postmodel.globalplot.globallinelabels='off'; gui.flmodel{1}.postmodel.globalplot.globalcolor='255,0,0'; gui.flmodel{1}.postmodel.globalplot.autotitle='on'; gui.flmodel{1}.postmodel.globalplot.customtitle=''; gui.flmodel{1}.postmodel.globalplot.autolabelx='on'; gui.flmodel{1}.postmodel.globalplot.customlabelx=''; gui.flmodel{1}.postmodel.globalplot.autolabely='on'; gui.flmodel{1}.postmodel.globalplot.customlabely=''; gui.flmodel{1}.postmodel.globalplot.axistype={'lin','lin'}; gui.flmodel{1}.postmodel.globalplot.phase='0'; gui.flmodel{1}.postmodel.globalplot.solnum='0'; gui.flmodel{1}.postmodel.globalplot.selectvia='stored'; gui.flmodel{1}.geommodel.suppressed{1}=[]; gui.flmodel{1}.geommodel.suppressed{2}=[]; gui.flmodel{1}.geommodel.suppressed{3}=[]; gui.flmodel{1}.workplane.type='0'; gui.flmodel{1}.workplane.wrkpln='0,1,0,0,0,1,0,0,0'; gui.flmodel{1}.workplane.localsys='0,1,0,0,0,0,1,0,0,0,0,1'; gui.flmodel{1}.workplane.model2d='Geom1'; gui.flmodel{1}.workplane.quicktype='10'; gui.flmodel{1}.workplane.parameter='0'; gui.flmodel{1}.workplane.zdir='up'; gui.flmodel{1}.meshmodel.meshplot.subplot='on'; gui.flmodel{1}.meshmodel.meshplot.meshsubuseexpression='off'; gui.flmodel{1}.meshmodel.meshplot.meshsubcolor='128,128,128'; gui.flmodel{1}.meshmodel.meshplot.meshsubbordercheck='off'; gui.flmodel{1}.meshmodel.meshplot.meshwiresubplot='on'; gui.flmodel{1}.meshmodel.meshplot.meshwiresubcolor='192,192,192'; gui.flmodel{1}.meshmodel.meshplot.bndplot='on'; gui.flmodel{1}.meshmodel.meshplot.meshbndcolor='0,0,0'; gui.flmodel{1}.meshmodel.meshplot.useellogic='off'; gui.flmodel{1}.meshmodel.meshplot.ellogic=''; gui.flmodel{1}.meshmodel.meshplot.ellogictype='all'; 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JHH JH J JH JJHH JHHH J JHHHH J JH JHH J JH JJHJHHJJHJJH JHHJHHJJHJHHJJHJHHJJHJHHJJHJ JHJJHJJHHJJHHHJJHHHHJJHJHHJJHJHHJJHJJHJJHHJJHJHHJJHHJJHHJHJJHHJHJHJHJJHHJHJHJ JHH!JHH"J!JH"J"JH JHH#J#JH!JIH$JHH%J$JH%JHI&J%JH&JIH'J'JH#JII(J&JI(JII)J(JI)JII*J)JI*J*JI'J+JIII+JII+J,JII,JI,J-JII-JI.JII.J II-J/JII/JI/J.J.J0J I I0J I1JI I1J I I1J I I0J2J I I2J1J II3JI I3JI3J4JI4JIII5J3JI5JII6J5JI6J6JII6JI7J7JII7JI8J8JII8JI1J9J+JI9JI:JII;JII;JI}I;J:JIJI=J>JII?JI?JII?J@JI@JIIIAJIAJ?JI>JBJIIBJIBJAJI@JCJICJIICJ!ICJDJ!IDJ"I IDJ 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KII KII KII KI K K KII KIIII K K KI K KI KII KII KIIK KIKIIKII KKIKKIIIK KIKIIKIIKKIKIIKKIKIIKKIKKIKKKKIIKIIKKIKIIKKIKKIKKKKIIKKIIIKKIIKIIKKIIKIKIIKIJKIIKKIKKIKIIKIKKII KIK KII!KII!KKI!K!KI"KI K"KK!K#KI$KJ$KII%KII&K$KI&KII%K&KI%KI'K'KII'KIII(KI)K'KI*K)KI(K*KIJ+KII+K(K,KI K-K.KJ0KJII4J0K/K0K4J1KJJ0K1KJ2K0K/KJJ3K3KJJJJ4K4KJ3KJJ5K5KJ4KJJ6K JJ6KJJ7K6KJ7KJJ8K7KJ8KJ J9K8KJ9K JJ:K:KJ5K J J;K9K J;K;K J:K J JK>K 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DܸZS?05d?m0\&S?|so[l:7)B'Ba(MZXv s%ny:GI`mnQW}?6/?A[یz?`@* Ar`|?c|{?w y?l\"Nz?̂x?d*ciz?Uk>y?>bwy?~۔x?n!dw?+v?H,Kqw?G2?t? ^u?nt?Cs?}.s?M׌q?W$t?Ҥs?Ez!tr?zDUNL?T[Ks?%q?vȥb?>}kNl? qKj?ʒJ?6 D`?<ؑO{XF,s?25ڒű Gj[ $P]Q0BU8A59PXY7AހJ<z58+w -Q~ы2#f1gܪ#!9|x=>;zZM_sI``;GSdmKE>-"gI32yc7? bR|ɋTꏿ9$iյ|xv@߀ʪIvAU|(ja^5hHG :hqiWl6Vg? ,lRr?3-m 5aEmNAeN(u8^`HUaA٧efm7.u&K1w?vb'AaGht?d 3A;8:guv?|;pu?ysHs?aBt?ђ K&Qr?a1.+t?m6kr?깯q?LRDq?w$p?HZp?D.o?J>9l?lk?) 4p?jmo?!{}l? l_~+o?VbE7 k?kٺ Bf?WE#|d?S[?OQDew@?uh^V[B"8!ar{$FS@HMz|wL~ڋq.0 240H8KBˁ2ןc1 2vl*`5?m1$˸ijy!fHHt|skBЗ,jMqERΎog#IxQ,}Xv;v!:szX]2q?E&Aፓj?zV_p@Aɖ6lo?'u1n?_߈>vh?ѥkLl?aTl?'Fzi?_|C"f?pUmf?mÑ`?SB1g?juCL f?hb? lf?;i`?pJA_?t/HlY?z)d92GmS?2sTPRc! >NL?3 |aBպhc+5 yV(-⸐|c[A;`^";tZ"O>L]f/ꖿ Svh5AڒG3As:Ż^T\uʔ~L"dxKSH;v|Ç#T쨦ۧ⋿{ߟ|3mft]WՑzIƯmk֗[ڡԱ5kx?hW;%:+=ɁIi*%mMհsqĔLq%<Ax&~|bSC:p[U;K~.1Pus.n!\zgXu)m}' c?bBBA:sU?1{GAGof`?i[^^?`Q?FI\V?rl~eH?*"QO?AXM6Xڣh!?sW)>?IMtH?Fr @ߦl|\Cs\hXim(c6nFr[Tl4EWx8YBqdŴ$}fm յiDp@ТsDZTgb]]7fu1ATS\eK1AjI2 lXݑo4Ÿ[E& M+ $I-y-:H(M{>?{G!䋿3%e39MCi1riuqʆtЦ\|Aʊvi : ? m1ywYH{3^"wZwr Q{^W`C<6!F3?x3FA;~I nDAB4WAd?8MV8>KְzSG+Ҙ`aǤ YCc`5hFell~q n+jm /h9psTAr5s;b-:n0AR4+ǥ/A:WFwkaАϑU_YIS:cT*{5'~qhF~gǂ}łDNj(%ҧM,a3$_/&;>Aa3i7i5A+2Re↿eUbkuaIilk󂶥kмYs{p'_?q˿sQ ۟uϲ|1y@þɟx<vrI齍k`/AU>:15/Aܵt/QB4rbݜՓ!u2Nʇ1~K R{"fLur0Am|< p;Ag$ix0A#9n7{P3A?awR؅Wc/Av{~1Q%GJQ$r3]hԆ; /!uq~/3xsrcom.femlab.xmesh.Xmesh[{ωI dofVersionZ initializedZuseInteriorBndLelemIndtLcom/femlab/util/FlIntList;Lelementsq~[geomMapt[ILgeomNumq~[L initElemIndq~[L initElementsq~[mcasesq~\[meGrpst[Lcom/femlab/xmesh/MEGrp;[meshNumt[[I[sorderq~\[ unitsystemst#[Lcom/femlab/api/client/UnitSystem;Lversionq~xpwq~ur[IM`&v겥xpuq~ 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g15=circ2('0.0028','base','center','pos',{'0.055','0.055'},'rot','0'); g16=circ2('0.0028','base','center','pos',{'0.055','0.05'},'rot','0'); g17=circ2('0.0028','base','center','pos',{'0.0055','0.05'},'rot','0'); g18=circ2('0.0028','base','center','pos',{'0.0055','0.056'},'rot','0'); g19=circ2('0.00028','base','center','pos',{'0.0055','0.056'},'rot','0'); g20=circ2('0.003','base','center','pos',{'0.0054','0.05'},'rot','0'); g21=circ2('0.0030','base','center','pos',{'0.004','0.05'},'rot','0'); g22=circ2('0.00150','base','center','pos',{'0.0040','0.05'},'rot','0'); g23=circ2('0.0025','base','center','pos',{'0.0040','0.05'},'rot','0'); g24=circ2('0.0025','base','center','pos',{'0.0040','0.053'},'rot','0'); g25=circ2('0.0025','base','center','pos',{'0.0030','0.053'},'rot','0'); g26=circ2('0.0023','base','center','pos',{'0.0030','0.053'},'rot','0'); g27=circ2('0.002','base','center','pos',{'0.0030','0.053'},'rot','0'); g28=circ2('0.02','base','center','pos',{'0.03','0.053'},'rot','0'); g29=circ2('0.002','base','center','pos',{'-0.03','0.053'},'rot','0'); g30=circ2('0.0020','base','center','pos',{'-0.003','0.053'},'rot','0'); [g31,g32]=geomcopy({g27,g30}); [g33,g34]=geomcopy({g31,g32}); g33=move(g33,[0,0]); g34=move(g34,[0,0]); g33=rotate(g33,0.5235987755982988,[0,0]); g34=rotate(g34,0.5235987755982988,[0,0]); [g35,g36]=geomcopy({g33,g34}); [g37,g38]=geomcopy({g35,g36}); g37=move(g37,[0,0]); g38=move(g38,[0,0]); g37=rotate(g37,0.5235987755982988,[0,0]); g38=rotate(g38,0.5235987755982988,[0,0]); [g39,g40]=geomcopy({g37,g38}); [g41,g42]=geomcopy({g39,g40}); g41=move(g41,[0,0]); g42=move(g42,[0,0]); g41=rotate(g41,0.5235987755982988,[0,0]); g42=rotate(g42,0.5235987755982988,[0,0]); [g43,g44]=geomcopy({g41,g42}); [g45,g46]=geomcopy({g43,g44}); g45=move(g45,[0,0]); g46=move(g46,[0,0]); g45=rotate(g45,0.5235987755982988,[0,0]); g46=rotate(g46,0.5235987755982988,[0,0]); [g47,g48]=geomcopy({g45,g46}); [g49,g50]=geomcopy({g47,g48}); g49=move(g49,[0,0]); g50=move(g50,[0,0]); g49=rotate(g49,0.5235987755982988,[0,0]); g50=rotate(g50,0.5235987755982988,[0,0]); [g51,g52]=geomcopy({g49,g50}); [g53,g54]=geomcopy({g51,g52}); g53=move(g53,[0,0]); g54=move(g54,[0,0]); g53=rotate(g53,0.5235987755982988,[0,0]); g54=rotate(g54,0.5235987755982988,[0,0]); [g55,g56]=geomcopy({g53,g54}); [g57,g58]=geomcopy({g55,g56}); g57=move(g57,[0,0]); g58=move(g58,[0,0]); g57=rotate(g57,0.5235987755982988,[0,0]); g58=rotate(g58,0.5235987755982988,[0,0]); [g59,g60]=geomcopy({g57,g58}); [g61,g62]=geomcopy({g59,g60}); g61=move(g61,[0,0]); g62=move(g62,[0,0]); g61=rotate(g61,0.5235987755982988,[0,0]); g62=rotate(g62,0.5235987755982988,[0,0]); [g63,g64]=geomcopy({g61,g62}); [g65,g66]=geomcopy({g63,g64}); g65=move(g65,[0,0]); g66=move(g66,[0,0]); g65=rotate(g65,0.5235987755982988,[0,0]); g66=rotate(g66,0.5235987755982988,[0,0]); [g67,g68]=geomcopy({g65,g66}); [g69,g70]=geomcopy({g67,g68}); g69=move(g69,[0,0]); g70=move(g70,[0,0]); g69=rotate(g69,0.5235987755982988,[0,0]); g70=rotate(g70,0.5235987755982988,[0,0]); [g71,g72]=geomcopy({g69,g70}); [g73,g74]=geomcopy({g71,g72}); g73=move(g73,[0,0]); g74=move(g74,[0,0]); g73=rotate(g73,0.5235987755982988,[0,0]); g74=rotate(g74,0.5235987755982988,[0,0]); g75=geomcomp({g12,g27,g30,g33,g34,g37,g38,g41,g42,g45,g46,g49,g50,g53,g54,g57,g58,g61,g62,g65,g66,g69,g70,g73,g74},'ns',{'g12','g27','g30','g33','g34','g37','g38','g41','g42','g45','g46','g49','g50','g53','g54','g57','g58','g61','g62','g65','g66','g69','g70','g73','g74'},'sf','g12+g27+g30+g33+g34+g37+g38+g41+g42+g45+g46+g49+g50+g53+g54+g57+g58+g61+g62+g65+g66+g69+g70+g73+g74','edge','none'); g76=circ2('0.04144','base','center','pos',{'0','0'},'rot','0'); g77=circ2('0.03050','base','center','pos',{'0','0'},'rot','22.5'); g78=circ2('0.00842','base','center','pos',{'0','0'},'rot','22.5'); g79=circ2('0.04167','base','center','pos',{'0','0'},'rot','0'); g80=rect2('0.011','1','base','center','pos',{'0','0'},'rot','22.5'); g81=rect2('0.011','1','base','center','pos',{'0','0'},'rot','-22.5'); g82=rect2('0.011','1','base','center','pos',{'0','0'},'rot','67.5'); g83=rect2('0.011','1','base','center','pos',{'0','0'},'rot','-67.5'); g85=rect2('0.012','1','base','center','pos',{'0','0'},'rot','-67.5'); g86=rect2('0.012','1','base','center','pos',{'0','0'},'rot','67.5'); g87=rect2('0.012','1','base','center','pos',{'0','0'},'rot','22.5'); g88=rect2('0.012','1','base','center','pos',{'0','0'},'rot','-22.5'); g89=geomcomp({g76,g77,g85,g86,g87,g88},'ns',{'C1','C2','R4','R3','R1','R2'},'sf','C2+C1*(R1+R2+R3+R4)','edge','all'); g90=geomcomp({g78,g79,g89},'ns',{'C3','C4','CO2'},'sf','CO2+C3+C4','edge','none'); % Create assembly and imprints clear s s.objs={g75,g90}; s.name={'CO1','CO3'}; s.tags={'g75','g90'}; fem.draw=struct('s',s); fem.geom=geomgroup(fem,'imprint','on',... 'paircand',{'CO1','CO3'}); % Geometry objects clear s s.objs={g75,g90}; s.name={'CO1','CO3'}; s.tags={'g75','g90'}; fem.draw=struct('s',s); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,2,2,2,2, ... 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,2, ... 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,2,2,2,2,2,2,2, ... 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, ... 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1, ... 2,2,2,2,2,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X'; ... 'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X'; ... 'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'},{'cos(omega)*X-sin(omega)*Y-X'; ... 'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X';'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','none','pres','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry % Analyzed geometry clear s s.objs={g75,g90}; s.name={'CO1','CO3'}; s.tags={'g75','g90'}; fem.draw=struct('s',s); fem.geom=geomgroup(fem,'imprint','off','paircand','none'); % Initialize mesh fem.mesh=meshinit(fem, ... 'hmaxfact',0.55, ... 'hcurve',0.25, ... 'hgrad',1.25, ... 'hcutoff',0.0005, ... 'hnarrow',2); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.Jez = {0,0,-350,350,350,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,150,150,150,0}; equ.ind = [1,2,3,4,5,3,3,5,5,3,3,5,5,3,3,5,5,3,3,5,5,3,3,5,5,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','6','7','10','11','14','15', ... '18','19','22','23','26'},{'4','5','8','9','12','13','16','17','20','21', ... '24','25'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; lib.matgroups{2}.name='Resistivity'; lib.matgroups{2}.variables={'alphares','T0','res0'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T]', ... 'axis',[-0.14428485437154293,0.12614923496809582,-0.06007423927391878,0.06580829540883218]); % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'triz',{'normB_emqa','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T] Height: Magnetic flux density, norm [T]', ... 'grid','on'); % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T]', ... 'axis',[-0.06975000351667404,0.06975000351667404,-0.06975000351667404,0.06975000351667404]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.Jez = {0,0,-500,-500,500,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,150,150,150,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; lib.matgroups{2}.name='Resistivity'; lib.matgroups{2}.variables={'alphares','T0','res0'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T]', ... 'axis',[-0.1481145310179648,0.1299789116145177,-0.06007423927391878,0.06580829540883218]); % Plot solution postplot(fem, ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'title','Arrow: Magnetic field', ... 'axis',[-0.1442848543715429,0.1261492349680958,-0.06372591560576979,0.06945997174068319]); % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T]', ... 'axis',[-0.1481145310179648,0.1299789116145177,-0.06007423927391878,0.06580829540883218]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.Jez = {0,0,-500,-500,500,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-150,-150,150,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; lib.matgroups{2}.name='Resistivity'; lib.matgroups{2}.variables={'alphares','T0','res0'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T]', ... 'axis',[-0.1481145310179648,0.1299789116145177,-0.06007423927391878,0.06580829540883218]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.Jez = {0,0,-1000,-1000,1000,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-200,-200,200,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; lib.matgroups{2}.name='Resistivity'; lib.matgroups{2}.variables={'alphares','T0','res0'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T]', ... 'axis',[-0.1481145310179651,0.129978911614518,-0.06367469312607393,0.062207841556677274]); % Plot solution postplot(fem, ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'title','Arrow: Magnetic field', ... 'axis',[-0.14428485437154315,0.12614923496809605,-0.06690040180116656,0.0654335502317699]); % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T]', ... 'axis',[-0.1481145310179651,0.129978911614518,-0.06367469312607393,0.062207841556677274]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = t`{'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.L = {1,1,0.5,0.5,0.5,1}; equ.Jez = {0,0,-3000,-3000,3000,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-400,-400,400,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; lib.matgroups{2}.name='Resistivity'; lib.matgroups{2}.variables={'alphares','T0','res0'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T]', ... 'axis',[-0.1481145310179651,0.129978911614518,-0.06367469312607393,0.062207841556677274]); % Plot solution postplot(fem, ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'title','Arrow: Magnetic field', ... 'axis',[-0.14428485437154315,0.12614923496809605,-0.06732636945792493,0.06585951788852827]); % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T]', ... 'axis',[-0.1481145310179651,0.129978911614518,-0.06367469312607393,0.062207841556677274]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.L = {1,1,0.11,0.11,0.11,1}; equ.Jez = {0,0,-3000,-3000,3000,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-400,-400,400,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; lib.matgroups{2}.name='Resistivity'; lib.matgroups{2}.variables={'alphares','T0','res0'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T]', ... 'axis',[-0.1481145310179651,0.129978911614518,-0.06367469312607393,0.062207841556677274]); % Constants fem.const = {'t','0[s]', ... 'rpm','60[1/min]', ... 'A','pi*(0.028[cm])^2', ... 'L','0.1196', ... 'NN','300'}; % Constants fem.const = {'t','0[s]', ... 'rpm','60[1/min]', ... 'A','pi*(0.028[cm])^2', ... 'L','0.1196', ... 'NN','300'}; % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.L = {1,1,0.11,0.11,0.11,1}; equ.Jez = {0,0,-3000,-3000,3000,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-400,-400,400,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; lib.matgroups{2}.name='Resistivity'; lib.matgroups{2}.variables={'alphares','T0','res0'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T]', ... 'axis',[-0.14428485437154315,0.12614923496809605,-0.06775785721390695,0.06629100564451029]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.L = {1,1,0.11,0.11,0.11,1}; equ.Jez = {0,0,-3000,-3000,3000,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-400,-400,400,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; lib.matgroups{2}.name='Resistivity'; lib.matgroups{2}.variables={'alphares','T0','res0'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.14428485437154315,0.12614923496809605,-0.06775785721390697,0.0662910056445103]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.L = {1,0.1196,0.11,0.11,0.11,0.1196}; equ.Jez = {0,0,-3000,-3000,3000,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-400,-400,400,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elem.maxvars = {}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.15713485429696872,0.13899923489352162,-0.06775785721390695,0.06629100564451029]); % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.11040209716543953,0.09227617458366909,0.0045107095830158594,0.10497434536362155]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.L = {1,0.11t`96,0.11,0.11,0.11,0.1196}; equ.Jez = {0,0,-30,-30,30,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-400,-400,400,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elem.maxvars = {}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.11979594289200242,0.11358943472488008,-0.054022129060345536,0.06048938799466691]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.magconstrel = {'mur','Br','mur','mur','mur','Br'}; equ.L = {1,0.1196,0.11,0.11,0.11,0.1196}; equ.Jez = {0,0,-30,-30,30,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-400,-400,400,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elem.maxvars = {}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.11979594289200242,0.11358943472488008,-0.054022129060345536,0.06048938799466691]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.magconstrel = {'mur','Br','mur','mur','mur','Br'}; equ.L = {1,0.1196,0.11,0.11,0.11,0.1196}; equ.Jez = {0,0,-5000,-5000,5000,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-400,-400,400,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elem.maxvars = {}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.11979594289200242,0.11358943472488008,-0.054022129060345536,0.06048938799466691]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.magconstrel = {'mur','Br','mur','mur','mur','Br'}; equ.L = {1,0.1196,0.11,0.11,0.11,0.1196}; equ.Jez = {0,0,-5,-5,5,0}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-400,-400,400,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elem.maxvars = {}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.11979594289200242,0.11358943472488008,-0.054022129060345536,0.06048938799466691]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.magconstrel = {'mur','Br','mur','mur','mur','Br'}; equ.L = {1,0.1196,0.11,0.11,0.11,0.1196}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-400,-400,400,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elem.maxvars = {}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.11979594289200242,0.11358943472488008,-0.054022129060345536,0.06048938799466691]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.magconstrel = {'mur','Br','mur','mur','Br'}; equ.L = {1,0.1196,0.11,0.11,0.1196}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.ind = [1,2,3,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,2,5]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omegtKa)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elem.maxvars = {}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.11979594289200242,0.11358943472488008,-0.054022129060345536,0.06048938799466691]); % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'title','Surface: Magnetic flux density, norm [T]', ... 'axis',[-0.11979594289200242,0.11358943472488008,-0.054022129060345536,0.06048938799466691]); % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.11697623108064603,0.11076972291352369,-0.055666186220986645,0.06213344515530802]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.magconstrel = {'mur','Br','mur','mur','mur','Br'}; equ.L = {1,0.1196,0.11,0.11,0.11,0.1196}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-100,-100,100,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elem.maxvars = {}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.11979594289200242,0.11358943472488008,-0.054022129060345536,0.06048938799466691]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.magconstrel = {'mur','Br','Br','Br','Br','Br'}; equ.L = {1,0.1196,0.11,0.11,0.11,0.1196}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-100,-100,100,0}; equ.ind = [1,2,3,4,5,5,5,5,3,3,3,3,5,5,5,5,3,3,3,3,5,5,5,5,3,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elem.maxvars = {}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.12642722714720575,0.12022071898008338,-0.056968154326133155,0.06405069774566759]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.magconstrel = {'mur','Br','Br','Br','Br','Br'}; equ.L = {1,0.1196,0.11,0.11,0.11,0.1196}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-240,240,240,0}; equ.ind = [1,2,3,4,5,3,3,5,5,3,3,5,5,3,3,5,5,3,3,5,5,3,3,5,5,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elem.maxvars = {}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.12642722714720575,0.12022071898008338,-0.056968154326133155,0.06405069774566759]); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Constants fem.const = {'t','0[s]', ... 'rpm','60[1/min]', ... 'A','pi*(0.028[cm])^2', ... 'L','1', ... 'NN','300'}; % Constants fem.const = {'t','0[s]', ... 'rpm','60[1/min]', ... 'A','pi*(0.028[cm])^2', ... 'L','1', ... 'NN','300'}; % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''lm1'')','shlag(2,''Az'')'}; appl.gporder = {30,4}; appl.assignsuffix = '_emqa'; clear prop clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.wcshape = 1; bnd.type = {'cont','A0'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2, ... 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]; clear pair pair.type = 'cont'; pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.magconstrel = {'mur','Br','Br','Br','Br','Br'}; equ.L = {1,1,0.11,0.11,0.11,1}; equ.gporder = 2; equ.sigma = {'mat3_sigma','mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma', ... 'mat4_sigma'}; equ.epsilonr = {1,'mat2_epsilonr','mat1_epsilonr','mat1_epsilonr','mat1_epsilonr', ... 'mat4_epsilonr'}; equ.mur = {1,'mat2_MUR(normB_emqa[1/T])','mat1_mur','mat1_mur','mat1_mur', ... 'mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... 'mat2_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa','1/mu0_emqa*normB_emqa'}; equ.shape = 2; equ.deltaV = {0,0,-240,240,240,0}; equ.ind = [1,2,3,4,5,3,3,5,5,3,3,5,5,3,3,5,5,3,3,5,5,3,3,5,5,3,1,2,6]; appl.equ = equ; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'MovingMesh'; appl.sdim = {'X','Y','Z'}; appl.shape = {'shlag(2,''lm3'')','shlag(2,''lm4'')','shlag(2,''x'')','shlag(2,''y'')'}; appl.gporder = {30,4}; appl.cporder = 2; appl.assignsuffix = '_ale'; clear prop prop.analysis='transient'; clear weakconstr weakconstr.value = 'on'; weakconstr.dim = {'lm3','lm4'}; prop.weakconstr = weakconstr; appl.prop = prop; clear bnd bnd.defflag = {{1;1},{1;1},{1;1},{1;1},{1;1},{0;0}}; bnd.wcshape = [1;2]; bnd.name = {'fixed','rotate_CCW','rotate_CW','angle_CCW','angle_CW',''}; bnd.deform = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'},{0;0}}; bnd.ind = [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6, ... 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]; clear pair pair.pair = 'Pair 1'; bnd.pair = pair; appl.bnd = bnd; clear equ equ.gporder = 2; equ.presexpr = {{0;0},{'cos(2*pi*rpm*t)*X-sin(2*pi*rpm*t)*Y-X';'sin(2*pi*rpm*t)*X+cos(2*pi*rpm*t)*Y-Y'}, ... {0;0},{'cos(-2*pi*rpm*t)*X-sin(-2*pi*rpm*t)*Y-X';'sin(-2*pi*rpm*t)*X+cos(-2*pi*rpm*t)*Y-Y'}, ... {'cos(omega)*X-sin(omega)*Y-X';'sin(omega)*X+cos(omega)*Y-Y'},{'cos(-omega)*X-sin(-omega)*Y-X'; ... 'sin(-omega)*X+cos(-omega)*Y-Y'}}; equ.name = {'default','rotate_CCW','fixed','rotate_CW','angle_CCW','angle_CW'}; equ.shape = [3;4]; equ.type = {'none','pres','none','pres','pres','pres'}; equ.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2]; appl.equ = equ; fem.appl{2} = appl; fem.sdim = {{'X','Y'},{'x','y'}}; fem.frame = {'ref','ale'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Boundary settings clear bnd bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; bnd.dim = {'Az','lm1','x','y','lm3','lm4'}; % Boundary pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [54,55,91,92]; pair{1}.src.operator = 'src2dst_ip2'; pair{1}.dst.dl = [169,170,183,184]; pair{1}.dst.operator = 'dst2src_ip2'; bnd.pair = pair; fem.bnd = bnd; % Point settings clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az','x','y'}; % Point pairs clear pair pair{1}.type= 'identity'; pair{1}.name= 'Pair 1'; pair{1}.src.dl = [32,76,77,121]; pair{1}.src.operator = 'src2dst_ip1'; pair{1}.dst.dl = [153,172,173,192]; pair{1}.dst.operator = 'dst2src_ip1'; pnt.pair = pair; fem.pnt = pnt; % Coupling variable elements clear elemcpl % Integration coupling variables clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{{},'-L*NN*Ez_emqa/A','L*NN*Ez_emqa/A'}}; equ.ipoints = {{{},'4','4'}}; equ.frame = {{{},'ref','ref'}}; equ.ind = {{'1','2','27','28','29'},{'3','4','9','10','11','12','17', ... '18','19','20','25','26'},{'5','6','7','8','13','14','15','16','21','22', ... '23','24'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {'Vi'}; elem.global = {'1'}; elem.maxvars = {}; elemcpl{1} = elem; fem.elemcpl = elemcpl; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.alphares='3.9e-3[1/K]'; lib.mat{1}.variables.mur='1'; lib.mat{1}.variables.sigma='5.998e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.C='385[J/(kg*K)]'; lib.mat{1}.variables.epsilon='0.5'; lib.mat{1}.variables.res0='1.72e-8[ohm*m]'; lib.mat{1}.variables.rho='8700[kg/m^3]'; lib.mat{1}.variables.k='400[W/(m*K)]'; lib.mat{1}.variables.T0='273.15[K]'; lib.mat{2}.name='Soft Iron (without losses)'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{2}.variables.mur='MUR(normB[1/T])'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{2}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Air'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{3}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{3}.variables.gamma='1.4'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{3}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{3}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{3}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Aluminum'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.33'; lib.mat{4}.variables.E='70e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.C='900[J/(kg*K)]'; lib.mat{4}.variables.nMurn='-3.5e11[Pa]'; lib.mat{4}.variables.mMurn='-3.3e11[Pa]'; lib.mat{4}.variables.muLame='2.6e10[Pa]'; lib.mat{4}.variables.k='160[W/(m*K)]'; lib.mat{4}.variables.lMurn='-2.5e11[Pa]'; lib.mat{4}.variables.sigma='3.774e7[S/m]'; lib.mat{4}.variables.alpha='23e-6[1/K]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.lambLame='5.1e10[Pa]'; lib.mat{4}.variables.rho='2700[kg/m^3]'; lib.matgroups{1}.name='Electromagnetic (AC/DC)'; lib.matgroups{1}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femstatic(fem, ... 'solcomp',{'lm1','Az'}, ... 'outcomp',{'lm1','Az'}, ... 'blocksize','auto'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'title','Contour: Magnetic flux density, norm [T]', ... 'axis',[-0.13148645565251452,0.12527994748539212,-0.060406717686533065,0.0674892611060675]); uq~ t% COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) flclear fem % COMSOL version clear vrsn vrsn.name = 'COMSOL 3.5'; vrsn.ext = ''; vrsn.major = 0; vrsn.build = 494; vrsn.rcs = '$Name: $'; vrsn.date = '$Date: 2008/09/19 16:09:48 $'; fem.version = vrsn; % Constants fem.const = {'t','0[s]', ... 'rpm','60[1/min]', ... 'A','pi*(0.028[cm])^2', ... 'L','0.1196', ... 'NN','1'}; % Geometry g1=circ2('0.05725','base','center','pos',{'0','0'},'rot','15'); g2=circ2('0.04190','base','center','pos',{'0','0'},'rot','0'); g3=circ2('0.04167','base','center','pos',{'0','0'},'rot','0'); g4=circ2('0.06975','base','center','pos',{'0','0'},'rot','0'); g5=rect2('0.011','1','base','center','pos',{'0','0'},'rot','0'); g6=rect2('0.011','1','base','center','pos',{'0','0'},'rot','30'); g7=rect2('0.011','1','base','center','pos',{'0','0'},'rot','60'); g8=rect2('0.011','1','base','center','pos',{'0','0'},'rot','90'); g9=rect2('0.011','1','base','center','pos',{'0','0'},'rot','120'); g10=rect2('0.011','1','base','center','pos',{'0','0'},'rot','150'); g11=geomcomp({g1,g2,g5,g6,g7,g8,g9,g10},'ns',{'C1','C2','R1','R2','R3','R4','R5','R6'},'sf','C2+C1*(R1+R2+R3+R4+R5+R6)','edge','all'); g12=geomcomp({g3,g4,g11},'ns',{'C3','C4','CO1'},'sf','C4+CO1-C3','edge','none'); g13=circ2('0.028','base','center','pos',{'0.005','0.02'},'rot','0'); g14=circ2('0.00028','base','center','pos',{'0.0050','0.02'},'rot','0'); g15=circ2('0.0028','base','center','pos',{'0.055','0.055'},'rot','0'); g16=circ2('0.0028','base','center','pos',{'0.055','0.05'},'rot','0'); g17=circ2('0.0028','base','center','pos',{'0.0055','0.05'},'rot','0'); g18=circ2('0.0028','base','center','pos',{'0.0055','0.056'},'rot','0'); g19=circ2('0.00028','base','center','pos',{'0.0055','0.056'},'rot','0'); g20=circ2('0.003','base','center','pos',{'0.0054','0.05'},'rot','0'); g21=circ2('0.0030','base','center','pos',{'0.004','0.05'},'rot','0'); g22=circ2('0.00150','base','center','pos',{'0.0040','0.05'},'rot','0'); g23=circ2('0.0025','base','center','pos',{'0.0040','0.05'},'rot','0'); g24=circ2('0.0025','base','center','pos',{'0.0040','0.053'},'rot','0'); g25=circ2('0.0025','base','center','pos',{'0.0030','0.053'},'rot','0'); g26=circ2('0.0023','base','center','pos',{'0.0030','0.053'},'rot','0'); g27=circ2('0.002','base','center','pos',{'0.0030','0.053'},'rot','0'); g28=circ2('0.02','base','center','pos',{'0.03','0.053'},'rot','0'); g29=circ2('0.002','base','center','pos',{'-0.03','0.053'},'rot','0'); g30=circ2('0.0020','base','center','pos',{'-0.003','0.053'},'rot','0'); [g31,g32]=geomcopy({g27,g30}); [g33,g34]=geomcopy({g31,g32}); g33=move(g33,[0,0]); g34=move(g34,[0,0]); g33=rotate(g33,0.5235987755982988,[0,0]); g34=rotate(g34,0.5235987755982988,[0,0]); [g35,g36]=geomcopy({g33,g34}); [g37,g38]=geomcopy({g35,g36}); g37=move(g37,[0,0]); g38=move(g38,[0,0]); g37=rotate(g37,0.5235987755982988,[0,0]); g38=rotate(g38,0.5235987755982988,[0,0]); [g39,g40]=geomcopy({g37,g38}); [g41,g42]=geomcopy({g39,g40}); g41=move(g41,[0,0]); g42=move(g42,[0,0]); g41=rotate(g41,0.5235987755982988,[0,0]); g42=rotate(g42,0.5235987755982988,[0,0]); [g43,g44]=geomcopy({g41,g42}); [g45,g46]=geomcopy({g43,g44}); g45=move(g45,[0,0]); g46=move(g46,[0,0]); g45=rotate(g45,0.5235987755982988,[0,0]); g46=rotate(g46,0.5235987755982988,[0,0]); [g47,g48]=geomcopy({g45,g46}); [g49,g50]=geomcopy({g47,g48}); g49=move(g49,[0,0]); g50=move(g50,[0,0]); g49=rotate(g49,0.5235987755982988,[0,0]); g50=rotate(g50,0.5235987755982988,[0,0]); [g51,g52]=geomcopy({g49,g50}); [g53,g54]=geomcopy({g51,g52}); g53=move(g53,[0,0]); g54=move(g54,[0,0]); g53=rotate(g53,0.5235987755982988,[0,0]); g54=rotate(g54,0.5235987755982988,[0,0]); [g55,g56]=geomcopy({g53,g54}); [g57,g58]=geomcopy({g55,g56}); g57=move(g57,[0,0]); g58=move(g58,[0,0]); g57=rotate(g57,0.5235987755982988,[0,0]); g58=rotate(g58,0.5235987755982988,[0,0]); [g59,g60]=geomcopy({g57,g58}); [g61,g62]=geomcopy({g59,g60}); g61=move(g61,[0,0]); g62=move(g62,[0,0]); g61=rotate(g61,0.5235987755982988,[0,0]); g62=rotate(g62,0.5235987755982988,[0,0]); [g63,g64]=geomcopy({g61,g62}); [g65,g66]=geomcopy({g63,g64}); g65=move(g65,[0,0]); g66=move(g66,[0,0]); g65=rotate(g65,0.5235987755982988,[0,0]); g66=rotate(g66,0.5235987755982988,[0,0]); [g67,g68]=geomcopy({g65,g66}); [g69,g70]=geomcopy({g67,g68}); g69=move(g69,[0,0]); g70=move(g70,[0,0]); g69=rotate(g69,0.5235987755982988,[0,0]); g70=rotate(g70,0.5235987755982988,[0,0]); [g71,g72]=geomcopy({g69,g70}); [g73,g74]=geomcopy({g71,g72}); g73=move(g73,[0,0]); g74=move(g74,[0,0]); g73=rotate(g73,0.5235987755982988,[0,0]); g74=rotate(g74,0.5235987755982988,[0,0]); g75=geomcomp({g12,g27,g30,g33,g34,g37,g38,g41,g42,g45,g46,g49,g50,g53,g54,g57,g58,g61,g62,g65,g66,g69,g70,g73,g74},'ns',{'g12','g27','g30','g33','g34','g37','g38','g41','g42','g45','g46','g49','g50','g53','g54','g57','g58','g61','g62','g65','g66','g69','g70','g73','g74'},'sf','g12+g27+g30+g33+g34+g37+g38+g41+g42+g45+g46+g49+g50+g53+g54+g57+g58+g61+g62+g65+g66+g69+g70+g73+g74','edge','none'); g76=circ2('0.04144','base','center','pos',{'0','0'},'rot','0'); g77=circ2('0.03050','base','center','pos',{'0','0'},'rot','22.5'); g78=circ2('0.00842','base','center','pos',{'0','0'},'rot','22.5'); g79=circ2('0.04167','base','center','pos',{'0','0'},'rot','0'); g80=rect2('0.011','1','base','center','pos',{'0','0'},'rot','22.5'); g81=rect2('0.011','1','base','center','pos',{'0','0'},'rot','-22.5'); g82=rect2('0.011','1','base','center','pos',{'0','0'},'rot','67.5'); g83=rect2('0.011','1','base','center','pos',{'0','0'},'rot','-67.5'); g85=rect2('0.012','1','base','center','pos',{'0','0'},'rot','-67.5'); g86=rect2('0.012','1','base','center','pos',{'0','0'},'rot','67.5'); g87=rect2('0.012','1','base','center','pos',{'0','0'},'rot','22.5'); g88=rect2('0.012','1','base','center','pos',{'0','0'},'rot','-22.5'); g89=geomcomp({g76,g77,g85,g86,g87,g88},'ns',{'C1','C2','R4','R3','R1','R2'},'sf','C2+C1*(R1+R2+R3+R4)','edge','all'); g90=geomcomp({g78,g79,g89},'ns',{'C3','C4','CO2'},'sf','CO2+C3+C4','edge','none'); % Create assembly and imprints clear s s.objs={g75,g90}; s.name={'CO1','CO3'}; s.tags={'g75','g90'}; fem.draw=struct('s',s); fem.geom=geomgroup(fem,'imprint','on',... 'paircand',{'CO1','CO3'}); % Geometry objects clear s s.objs={g75,g90}; s.name={'CO1','CO3'}; s.tags={'g75','g90'}; fem.draw=struct('s',s); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry % Analyzed geometry clear s s.objs={g75,g90}; s.name={'CO1','CO3'}; s.tags={'g75','g90'}; fem.draw=struct('s',s); fem.geom=geomgroup(fem,'imprint','off','paircand','none'); % Constants fem.const = {'t','0[s]', ... 'rpm','60[1/min]', ... 'A','pi*(0.028[cm])^2', ... 'L','0.1196', ... 'NN','300'}; % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Constants fem.const = {'t','0[s]', ... 'rpm','60[1/min]', ... 'A','pi*(0.028[cm])^2', ... 'L','1', ... 'NN','300'}; tclear mfile clear vrsn vrsn.name = 'COMSOL 3.5'; vrsn.ext = ''; vrsn.major = 0; vrsn.build = 494; vrsn.rcs = '$Name: $'; vrsn.date = '$Date: 2008/09/19 16:09:48 $'; mfile.version=vrsn; mfile.fem='fem'; mfile.stored={'fem0','fem1'}; mfile.tags={}; mfile.types={}; x