From f802cc7bfc193f75abc732483a3ddcefd0dab588 Mon Sep 17 00:00:00 2001 From: Giacomo Date: Sat, 7 Apr 2018 21:33:20 +0200 Subject: [PATCH] Python scripts available! Fixed #5 then I've added the Python scripts which replicate the same computations made in Matlab/Octave. --- README.md | 9 +- doc/doc.pdf | Bin 323835 -> 325063 bytes doc/doc.tex | 24 ++- fluid.py | 47 ++++++ fluid_functions.py | 371 +++++++++++++++++++++++++++++++++++++++++++++ test.m | 4 + 6 files changed, 444 insertions(+), 11 deletions(-) create mode 100644 fluid.py create mode 100644 fluid_functions.py diff --git a/README.md b/README.md index 095db8b..95b38f5 100644 --- a/README.md +++ b/README.md @@ -19,7 +19,7 @@ Synchronous Reluctance Rotor with *fluid* flux-barriers. ## Requirements -Matlab or Octave to compute the points. +Matlab or Octave or Python (NumPy + SciPy) to compute the points. The points calculation is general, so it could be implemented in any language, but I chose Matlab/Octave because it is my standard interface with [FEMM](http://www.femm.info) software. @@ -29,10 +29,3 @@ make a porting for your CAD engine or FEA software. If you do so, consider contributing to the project adding your interface scripting. - - -## ETA - -Already shipped! 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zuZ@1>R4PW+jXKn~6?dlY4f6a0`GMeKJIM7sok2U} z>XEZ**dd&J&Hm@U_ry3iVrfST?^34DFyC$qRG1xbDLF1n7E)SOW}4_5e+c_?cYkW7 z8J?#9&Jr>aGQJLPrvDmv(BygcG~xAb#@D9?9vLg5h`rii8XPJ*0m60jMP8dma4-!m z9XT|bPh%m2PRrCp;I zlh}eg*B>i)FxVC8SI|FffvypYd9-PKxoKcQ02k$K$kTUhdAYA(BT?th*VL~0B<&ih zn5iK3oMV@xA)Q8Amm`YddFAA;HLPe3%H^ofL)!d{N!M zGgw!-yekk+O?3OeHk?vNi8E3C6JV{4dQ2#mRC>&3k#zSwZZ=Z;~Vpk diff --git a/doc/doc.tex b/doc/doc.tex index 9cdfa2a..cee78c9 100644 --- a/doc/doc.tex +++ b/doc/doc.tex @@ -102,9 +102,10 @@ \section*{Goal} \section*{Requirements} -Matlab or Octave to compute the points. The points calculation is general, so -it could be implemented in any language, but I chose Matlab/Octave because it -is my standard interface with \href{http://www.femm.info/}{FEMM} software. +Matlab or Octave or Python (NumPy + SciPy) to compute the points. +The points calculation is general, so it could be implemented in any language, +but I chose Matlab/Octave because it is my standard interface with +\href{http://www.femm.info/}{FEMM} software. If you do not use FEMM, you can still use the calculation part and make a porting for your CAD engine or FEA software. If you do so, consider @@ -181,6 +182,23 @@ \section{Examples} \includegraphics[width=0.75\linewidth]{ex3} +\section{Files needed} + +For Matlab/Octave, the files needed for the computation are + +\texttt{fluid.m} and + +\texttt{calc\_fluid\_barrier.m} + +\noindent +while for Python they are + +\texttt{fluid.py} and + +\texttt{fluid\_functions.py}. + + + \clearpage \section{Theory} diff --git a/fluid.py b/fluid.py new file mode 100644 index 0000000..765456a --- /dev/null +++ b/fluid.py @@ -0,0 +1,47 @@ +# -*- coding: utf-8 -*- +""" +Created on Thu Apr 5 21:31:31 2018 + +@author: Giacomo +""" + +from fluid_functions import * + +deb = 0; + +## DATA +rotor = structtype(); +rotor.p = 2; # number of pole pairs +mm = 1e-3; # millimeters +rotor.De = 200*mm; # [m], rotor outer diameter + +rotor.Nb = 3; # number of flux-barriers +rotor.tb = np.array([4, 8, 15])*mm; # flux-barrier widths +rotor.wc = np.array([3, 7, 12, 10])*mm; # flux-carrier widths +rotor.Nstep = np.array([2, 4, 6]); # number of steps to draw the flux-barrier side +rotor.wrib_t = 1*mm; # [m], tangential iron rib width + +# you can input flux-barrier angles or let the program compute them +#rotor.barrier_angles_el = np.array([14,26,38])*2; # [deg], electrical flux-barrier angles +#rotor.barrier_end = 'rect'; # choose 'rect' or comment + +# you can define the rib width or comment +rotor.wrib = np.array([1,2,4])*mm; # [m], radial iron rib widths +# You can define the magnet width or comment +#rotor.wm = np.array([10,20,40])*mm; + + +## barrier points computation +barrier = structtype(); +barrier = calc_fluid_barrier(rotor, deb); + + + +## simple matlab plot +for bkk in range(0,np.size(barrier.X)): + plt.plot(np.squeeze(barrier.X[bkk]), np.squeeze(barrier.Y[bkk]), '.-') + +plt.axis('equal') +plt.show() + + diff --git a/fluid_functions.py b/fluid_functions.py new file mode 100644 index 0000000..cd62fcb --- /dev/null +++ b/fluid_functions.py @@ -0,0 +1,371 @@ +# -*- coding: utf-8 -*- +""" +Created on Thu Apr 5 21:49:54 2018 + +@author: Giacomo +""" + +import numpy as np +import scipy as sp +from matplotlib import pyplot as plt + +# I define a dummy class for Matlab structure like objects +class structtype(): + pass + + +def psi_fluid(rho,xi,rho0): + return (rho**2 - rho0**2)/rho*np.sin(xi); +# return (np.power(rho,2) - rho0**2)/rho*np.sin(xi); + +def phi_fluid(rho,xi,rho0): + return (np.power(rho,2) + rho0**2)/rho*np.cos(xi); + +def xi_fluid(psi,rho,rho0): + return np.arcsin(psi*rho/(np.power(rho,2) - rho0**2)); + +def rho_fluid(psi,xi,rho0): + return ( psi + np.sqrt(np.power(psi,2) + 4*np.power(np.sin(xi),2)*rho0**2) )/(2*np.sin(xi)); + +def r_map(rho): + return np.power(rho, 1/p); + +def th_map(xi): + return xi/p; + +def rho_map(r): + return np.power(r, p); + +def xi_map(th): + return th*p; + +def vr(r,th,R0): + return p*(np.power(r,(p-1)) - R0**(2*p)/np.power(r,(p+1)))*np.cos(p*th); + +def vt(r,th,R0): + return -p*( np.power(r,(p-1)) + R0**(2*p)/np.power(r,(p+1)) )*np.sin(p*th); + +def vx(vr_v,vth_v,th): + return vr_v*np.cos(th) - vth_v*np.sin(th); + +def vy(vr_v,vth_v,th): + return vr_v*np.sin(th) + vth_v*np.cos(th); + + +def CentralPt_Eq(th, *args): + psiCentralPt, rho0, mCentral, qCentral = args; + return np.multiply( r_map( rho_fluid(psiCentralPt, xi_map(th), rho0) ), + ( np.sin(th) - mCentral*np.cos(th) ) ) - qCentral; + + +def BarrierEndSystem(X, *args): +# th,xd,yd,xo,yo,R = X; + th = X[0:Nb]; + xd = X[1*Nb:2*Nb]; + yd = X[2*Nb:3*Nb]; + xo = X[3*Nb:4*Nb]; + yo = X[4*Nb:5*Nb]; + R = X[5*Nb:6*Nb]; + + psiA, rho0, xE, yE = args; + R0 = r_map(rho0); + firstEq = xd - np.multiply( r_map(rho_fluid(psiA, p*th, rho0)), np.cos(th) ); + seconEq = yd - np.multiply( r_map(rho_fluid(psiA, p*th, rho0)), np.sin(th) ); + thirdEq = (xd - xo)**2 + (yd - yo)**2 - R**2; +# thirdEq = (xE - xo)**2 + (yE - yo)**2 - R**2; + fourtEq = (xE - xo)**2 + (yE - yo)**2 - R**2; + fifthEq = np.multiply( (xo - xd), vx( vr( r_map(rho_fluid(psiA, p*th, rho0)),th,R0 ), vt( r_map(rho_fluid(psiA, p*th, rho0)) ,th,R0 ), th) ) + np.multiply( (yo - yd), vy( vr( r_map(rho_fluid(psiA, p*th, rho0)),th,R0 ), vt( r_map(rho_fluid(psiA, p*th, rho0)) ,th,R0 ), th) ); + sixthEq = np.multiply(xo - xE,yE) - np.multiply(yo - yE,xE); + return np.concatenate([firstEq, + seconEq, + thirdEq, + fourtEq, + fifthEq, + sixthEq]) + +def PsiPhi(X, *args): + psi, phi, rho0, N = args; + rho = X[0:N]; + xi = X[N:2*N]; + return np.concatenate( [psi - psi_fluid(rho, xi, rho0), + phi - phi_fluid(rho, xi, rho0)] ) + + +# MAIN function definition +def calc_fluid_barrier(r, deb): + "CALC_FLUID_BARRIER computes the flux-barrier points along the streamline function." + + Dr = r.De; # [m], rotor outer diameter + ScalingFactor = 1/( 10**(round(np.log10(Dr))) ); + # ScalingFactor = 1; + Dr = Dr*ScalingFactor; + + pi = np.pi; + global p, Nb # I have been lazy here... + p = r.p; # number of pole pairs + Nb = r.Nb; # number of flux-barriers + tb = r.tb*ScalingFactor; # flux-barrier widths + wc = r.wc*ScalingFactor; # flux-carrier widths + Nstep = r.Nstep; # number of steps to draw the flux-barrier side + + wrib_t = r.wrib_t*ScalingFactor; # [m], tangential iron rib width + + + if hasattr(r,'barrier_angles_el'): + barrier_angles_el = r.barrier_angles_el; # [deg], electrical flux-barrier angles + AutoBarrierEndCalc = 0; + else: + barrier_angles_el = np.zeros([1,Nb]); + AutoBarrierEndCalc = 1; + + if hasattr(r,'wm'): + wm = r.wm*ScalingFactor; + else: + wm = 0; + + if hasattr(r,'wrib'): + wrib = r.wrib*ScalingFactor + wm; # [m], radial iron rib widths + else: + wrib = np.zeros([1,Nb]) + wm; + + Dend = Dr - 2*wrib_t; # [m], flux-barrier end diameter + Dsh = Dend - 2*( np.sum(tb) + np.sum(wc) ); # [m], shaft diameter + R0 = Dsh/2; # [m], shaft radius + barrier_angles = barrier_angles_el/p; # [deg], flux-barrier angles + if hasattr(r,'barrier_end'): + barrier_end = r.barrier_end; + else: + barrier_end = ''; + + ## Precomputations + rho0 = rho_map(R0); + + ## Central base points + RAprime = Dend/2 - np.concatenate( (np.array([0]), np.cumsum( tb[0:-1]) ) ) - np.cumsum( wc[0:-1] ); # top + RBprime = RAprime - tb; # bottom + te_qAxis = pi/(2*p); # q-axis angle in rotor reference frame + + # get A' and B' considering rib and magnet widths + mCentral = np.tan(te_qAxis); # slope + qCentral = np.tile( -wrib/2/np.cos(te_qAxis), 2); # intercept + + psiCentralPtA = psi_fluid(rho_map(RAprime), xi_map(te_qAxis), rho0); + psiCentralPtB = psi_fluid(rho_map(RBprime), xi_map(te_qAxis), rho0); + psiCentralPt = np.array( np.concatenate( (psiCentralPtA, psiCentralPtB) ) ); + psiA = psiCentralPtA; + psiB = psiCentralPtB; + + + FunctionTolerance = 10*np.spacing(1); + StepTolerance = 1e4*np.spacing(1); + + X0 = np.repeat(te_qAxis, 2*Nb); + data = (psiCentralPt,rho0,mCentral,qCentral); + # test function +# print( CentralPt_Eq(X0, *data ) ) + + teAB = sp.optimize.fsolve(CentralPt_Eq, X0, args=data, xtol=StepTolerance, epsfcn=FunctionTolerance); + teA = teAB[0:Nb]; + teB = teAB[Nb:]; + RA = r_map( rho_fluid(psiA, xi_map(teA), rho0) ); + RB = r_map( rho_fluid(psiB, xi_map(teB), rho0) ); + + # 1st test --> OK! +# print(RA,teA,RB,teB) + + # Outer base points C,D preparation + RCprime = Dend/2; + teCprime = th_map( xi_fluid(psiA, rho_map(RCprime), rho0) ); + xCprime = Dend/2*np.cos(teCprime); + yCprime = Dend/2*np.sin(teCprime); + + RDprime = Dend/2; + teDprime = th_map( xi_fluid(psiB, rho_map(RDprime), rho0) ); + xDprime = Dend/2*np.cos(teDprime); + yDprime = Dend/2*np.sin(teDprime); + + if AutoBarrierEndCalc: + teE = (teCprime + teDprime)/2; + aphE = pi/2/p - teE; + barrier_angles = 180/np.pi*aphE; + barrier_angles_el = p*barrier_angles; + else: + aphE = barrier_angles*pi/180; + teE = pi/2/p - aphE; + + xE = Dend/2*np.cos(teE); + yE = Dend/2*np.sin(teE); + + # 2nd test --> OK! +# print(xE,yE) + + + + + + + + + + + + ## Outer base points C (top) + if barrier_end == 'rect': + RC = RCprime; + teC = teCprime; + xC = xCprime; + yC = yCprime; + xOC = xC; + yOC = yC; + + else: + X0 = [ 1.5*teE, 0.9*xE, 0.9*yE, 0.8*xE, 0.8*yE, 0.25*xE]; + X0 = np.reshape(X0, Nb*6); + + data = (psiA, rho0, xE, yE); + X = sp.optimize.fsolve( BarrierEndSystem, X0, args=data); + + xOC = X[3*Nb:4*Nb]; + yOC = X[4*Nb:5*Nb]; + xC = X[1*Nb:2*Nb]; + yC = X[2*Nb:3*Nb]; + RC = np.sqrt(xC**2 + yC**2); + teC = np.arctan2(yC, xC); + + # 3rd test --> OK! +# print(xOC) +# print(yOC) +# print(xC) +# print(yC) +# print(RC) +# print(teC) + + + ## Outer base points D (bottom) + if barrier_end == 'rect': + RD = RDprime; + teD = teDprime; + xD = xDprime; + yD = yDprime; + xOD = xD; + yOD = yD; + + else: + X0 = [ 0.8*teE, 0.8*xE, 0.8*yE, 0.9*xE, 0.9*yE, 0.2*xE]; + X0 = np.reshape(X0, Nb*6); + + data = (psiB, rho0, xE, yE); + X = sp.optimize.fsolve( BarrierEndSystem, X0, args=data); + + xOD = X[3*Nb:4*Nb]; + yOD = X[4*Nb:5*Nb]; + xD = X[1*Nb:2*Nb]; + yD = X[2*Nb:3*Nb]; + RD = np.sqrt(xD**2 + yD**2); + teD = np.arctan2(yD, xD); + + # 4th test --> OK! +# print(xOD) +# print(yOD) +# print(xD) +# print(yD) +# print(RD) +# print(teD) + + + ## Flux-barrier points + # We already have the potentials of the two flux-barrier sidelines + phiA = phi_fluid( rho_map(RA), xi_map(teA), rho0); + phiB = phi_fluid( rho_map(RB), xi_map(teB), rho0); + + phiC = phi_fluid( rho_map(RC), xi_map(teC), rho0); + phiD = phi_fluid( rho_map(RD), xi_map(teD), rho0); + + barrier = structtype(); + + + + + + + + + + + + + XX = []; + YY = []; + + for bkk in range(0,Nb): + dphiAC = np.divide(phiC[bkk] - phiA[bkk], Nstep[bkk]); + dphiBD = np.divide(phiD[bkk] - phiB[bkk], Nstep[bkk]); + # we create the matrix of potentials phi needed for points intersections + PhiAC = phiA[bkk] + np.cumsum( np.tile(dphiAC, Nstep[bkk] - 1) ); + PhiBD = phiB[bkk] + np.cumsum( np.tile(dphiBD, Nstep[bkk] - 1) ); + PsiAC = np.tile( psiA[bkk], Nstep[bkk]-1); + PsiBD = np.tile( psiB[bkk], Nstep[bkk]-1); + + X0 = np.concatenate( [np.linspace(rho0, Dend/2, np.size(PhiAC)), np.linspace(pi/4, xi_map(teE[bkk]), np.size(PhiAC))] ); + + data = (PsiAC, PhiAC, rho0, Nstep[bkk]-1); + RhoXi_AC = sp.optimize.fsolve( PsiPhi, X0, args=data ); + + data = (PsiBD, PhiBD, rho0, Nstep[bkk]-1); + RhoXi_BD = sp.optimize.fsolve( PsiPhi, X0, args=data ); + + R_AC = r_map( RhoXi_AC[0:Nstep[bkk]-1] ); + te_AC = th_map( RhoXi_AC[Nstep[bkk]-1:] ); + R_BD = r_map( RhoXi_BD[0:Nstep[bkk]-1] ); + te_BD = th_map( RhoXi_BD[Nstep[bkk]-1:] ); + + # 5th test --> OK! +# print(R_AC, te_AC) +# print(R_BD, te_BD) + + Zeta = np.concatenate( [[ + # top side + xE[bkk] + 1j*yE[bkk], + xOC[bkk] + 1j*yOC[bkk], + xC[bkk] + 1j*yC[bkk] ], + np.flipud( np.multiply(R_AC, np.exp(1j*te_AC)) ), + [RA[bkk]*np.exp(1j*teA[bkk]), + # bottom side + RB[bkk]*np.exp(1j*teB[bkk])], + np.multiply( R_BD, np.exp(1j*te_BD) ), + [xD[bkk] + 1j*yD[bkk], + xOD[bkk] + 1j*yOD[bkk], + xE[bkk] + 1j*yE[bkk]] + ] )/ScalingFactor; + + X = Zeta.real; + Y = Zeta.imag; + + XX.append([X]); + YY.append([Y]); + + + barrier.X = XX; + barrier.Y = YY; + + + if deb == 1: + Apt = np.multiply(RA/ScalingFactor, np.exp(1j*teA) ); + Bpt = np.multiply(RB/ScalingFactor, np.exp(1j*teB) ); + Cpt = np.multiply(RC/ScalingFactor, np.exp(1j*teC) ); + Dpt = np.multiply(RD/ScalingFactor, np.exp(1j*teD) ); + plt.plot( [Apt.real,Cpt.real], [Apt.imag,Cpt.imag], "ro" ) + plt.plot( [Bpt.real,Dpt.real], [Bpt.imag,Dpt.imag], "bo" ) + plt.plot( xE/ScalingFactor, yE/ScalingFactor, "ko" ) + + for bkk in range(0,Nb): + plt.plot(np.squeeze(barrier.X[bkk]), np.squeeze(barrier.Y[bkk])) + + plt.axis('equal') + plt.show() + + + + + + return barrier \ No newline at end of file diff --git a/test.m b/test.m index ff42dfe..559f981 100644 --- a/test.m +++ b/test.m @@ -14,6 +14,7 @@ end %% DATA +try openfemm(1) mm = 1e-3; % millimeters rotor.De = 200*mm; % [m], rotor outer diameter @@ -72,4 +73,7 @@ end closefemm; +catch + disp('FEMM not available.'); +end toc