[IEEE 2013 3rd International Conference on Electric Power and Energy Conversion Systems (EPECS) -...

2013 3rd International Conference on Electric Power and Energy Conversion Systems, Yildiz Technical University, Istanbul, Turkey, October 2-4, 2013

CAD of Electrical Machines Using Coupled FEMMMATLAB Softwares

Tariq Benamimour Ammar Bentounsi and Hind Djeghloud Laboratory of Electrical Engineering

of Constantine ,LGEC University of Constantine 1 ,Algeria

Email:[email protected]

Laboratory of Electrical Engineering Laboratory of Electrical Engineering of Constantine ,LGEC of Constantine ,LGEC

University of Constantine I,Algeria University of Constantine 1 ,Algeria

Email: [email protected] Email:[email protected]

Abstract- This paper presents a software platform performed in

the laboratory of EE, LGEC, at University Constantine 1, Algeria,

dedicated to the CAD of electrical machines and based on an

interactive coupling of finite element free software FEMM with

MATLAB tool. The first step carried out under MATLAB is to

predetermine analytically the geometrical parameters of a given

machine from its specifications and to draw the structure by using

FEMM software. The second step allows to solve by FEM the

equations of the studied system and to determine its

electromagnetic characteristics. This methodology was

implemented for a 6/4 VRM prototype which characteristics will be

used in look-up tables under MA TLAB/Simulink for the dynamic

study of performance in a non-linear mode.

Keywords-CAD; electrical machine; FEMM; MATLAR; VRM.

I. INTRODUCTION

The problematic of designing an electromechanical system is to find a structure corresponding to a given need and expressed in a specification. A design process often requires several software tools to study all phenomena characterizing the operation of a given system. Reduction of costs and deadlines being a priority for the industrial sector, many approaches were developed in this direction. These include software platforms implementing multiphysics models through the coupling of dedicated software tools.

The work described in this paper focuses on developing a tool for the design and analysis of electromechanical converters. It is based on an original approach combining an analytical approach to pre-design according to specifications, performed in MATLAB software and coupled to a numerical finite element approach using FEMM software (Finite Element Modeling Method). Electromagnetic characteristics obtained by FEMM are either directly plotted under MA TLAB or used in look-up tables for dynamic simulation of non-linear mode of a variable reluctance machine (VRM) in MATLAB/Simulink. The numerical results of the FEA were then validated against the analytical solution using equivalent magnetic circuits to seven equiflux tubes according to an approach proposed by Krishnan and that we have implemented in a MA TLAB program called VRM.m. This CAD tool has been developed by a research team of the Laboratory of Electrical Engineering, LGEC, Faculty of Technology Science, University Constantinel, Algeria.

The idea of linking between several softwares to extract different characteristics is very interesting in order to reduce the time of analyzing and to get more exact results, but most of them are complicated and expensive sometimes because of the license agreement of the FEA used software, such as [1-5]. The originality of this paper shows how to link between MA TLAB and open source software called FEMM [6]. As never done before in similar works using this software classically [7-9], here FEMM is controlled remotely with MATLAB because of the large using and good manipulating of this last software by the students. For that, the first step was to find several geometric parameters using a Matlab*.m file, taking in account the desired specifications such as power, speed and the envelope size [10]. After that as a second part, a sub-program always under MA TLAB is calling automatically FEMM, which executes the orders given by the Matlab*.m file (draw, assign materials, excitations, boundaries, solve and analyze). When the analyze finished, the same Matlab*.m file recovered all needed data to plot any magnetic characteristic under MATLAB following the flowchart depicted in Fig.I.The geometric parameters of the studied 6/4 VRM are calculated with a sub-program under MATLAB, based on the approach developed in [II]. These parameters are used to model with FEM the considered prototype in order to extract its magnetic characteristics (flux, inductance ... ). From the obtained curves, the analytical study of the same machine presents results very close to the numerical one. The paper is organized as follows. Section II presents fundamentals of the studied variable reluctance machine. Section III explains the drawing process of the geometry. Section IV describes the interactive control of FEMM software from MA TLAB. Section V discusses the obtained results.

II. BASIC THEORY OF VRM

For illustrative purposes, we use the basic three-phase machine with Ns=6 stator poles and Nr=4 rotor poles, a 6/4 VRM is shown in Fig. 2. The concentrated coils around each stator pole form the phase windings, while there are no windings or magnets on the rotor. The principle of operating is based on the change of reluctance (and hence the inductance seen by the stator winding) due to a geometrical salience (or magnetic anisotropy in the case of sheeted rotor or axially laminated rotor) during the displacement of the rotor.

978-1-4799-0688-8/13/$31.00 ©2013 IEEE


Start of the approximate design

� ---------- --------- - , / ,

/ , I Design specifications of the studied machine \ r (Power, speed . . . ) \

� � ..J E�

Specific electric and magnetic loadings ::;

\ \

... .. "0 = �

"". -------/

--------,

{ 1 1 1 1 1 1 1 1 1 \ '-

Calling FEMM and drawing the geometry

Assigning materials, boundaries and excitations

Plot results

To MA TLAB/Simulink lookup table bloc (for dynamic

simulation)

Figure I. Steps of linking between MA TLAB and FEMM. A

A' Figure 2. Diagram of the studied 6/4 VRM.

\ 1 I::; I::; I"" I ... 1 � 1"0 1.5 1

/

In the unaligned positlon corresponding to the maximum reluctance (or to the minimum inductance) if we apply a current in the stator winding, the torque will be produced by the tendency of the rotor to be aligned with the stator poles of the given phase according to the well known principle of "minimum reluctance or maximum flux", as shown in Fig. 3. If the energizing is stopped, the rotor will continue its movement until it reaches the next unaligned position. We repeat the operation by supplying the next phase of stator and so on. A continuous torque can be generated by the contribution of all phases. For each phase, the electromagnetic torque equation is given by

. _ (�) dL(�, 0 T - 2 ·' d�

While the average torque can be expressed as

(I)

(2)

where q is the number of phases, Nr is the number of rotor poles, Wa is the magnetic energy in the aligned position and Wu is the magnetic energy in the unaligned position.

III. GEOMETRY DRAW PROCESS

The draw process is the most important step of our work seen that it contains all geometric parameters of the prototype. In this step we must identify the unit of measurement, the minimum meshing angle, the current frequency ... etc. To get best results, the geometry should be drawn with a perfect accuracy under FEMM, so all points are depending on each other and on other geometric parameters with many mathematical expressions. The draw is based on projecting all points on a (x,y) plan and for that, we needed two new angles (angXr) and (angXs) expressed (in degrees) respectively by (3) and (4) according to Fig. 4.

R(Sin!!.!:)

Rsh R

Ro Yr Ys e

Bs Br

angXr=(90-2(asin(Yr+R:h ))) (3)

(R+e)sin(�) (4) angXs=(60-2(asin(

Ro-Ys 2 ))) where:

Shaft radius Rotor bore radius

Outer radius Rotor yoke thickness Stator yoke thickness

Air gap Stator tooth angle Rotor tooth angle

The final design of the machine under FEMM is shown in Fig. 5 and the geometric parameters are recorded in Table I. Because of the structural complexity of VRMs and highly saturated nature of the flux density, it is very difficult to accurately model the different characteristics analytically. Thus, a 2-D non-linear finite element model in FEMM must be used with a B(H) curve of the magnetic material illustrated in Fig. 6.


Such as in [12], the main steps of design for any selected geometry of VRM are the same. For that, the given results in Table 1 are obtained from the basic *.m file program under MA TLAB software as shown in Fig.7.

TABLE!. PARAMETERS OF THE STUDIED 6/4 VRM

Parameter Symbol Value Number of turns N 359 Rotor yoke thickness Yr 14.7 mm Stator yoke thickness Ys 14.8mm Air-gap length e 0.25 mm Outer radius Ro 114.2 mm Rotor bore radius R 57.1 mm Shaft Radius Rsh 20 mm

I Stator I Cu�nt(i)

Figure 3. Creation of the electromagnetic torque.

Figure 4. Angles (angXr) and (angXs).

Figure 5. The plotted 6/4 VRM under FEMM.

IV. REMOTE CONTROL OF FEMM FROM MA TLAB

FEMM offers a scripting property which enables to control the software remotely by using its inner script "LUA" or by using a MATLAB.m file. Both" LUA" scripts and the *.m file contain a list of its inner functions nouns used for calling and commanding FEMM. The m file includes commands used to perform the drawing, assigning materials and excitation, running the simulation, updating rotor position, data values recovering ... etc.

The sample algorithm given below can create a 2D model of a simple magnetic circuit, after the algorithm is written and compiled under MATLAB, FEMM starts automatically.

openfemm;%calling FEMM create(O);%select a magnetic problem L=IO;%Depth of the problem mi�robdef(0,'millimeters','planar',le8,L,30,0);%(problem definition, units .. ) main _ maximize;%open in a window mi_ addboundprop(,boundry',O,O,O,O,O,O,O,O,O);%creat a new boundary'Dirichlet' mi_ addnode( -100,-100); mi_ addnode(200,-1 00); mi_ addnode(200,200); mi_ addnode(-l 00,200); mi_ addsegment(-l 00,-1 00,200,100); mi_ addsegment(200,-1 00,200,200); mi_ addsegment(200,200,-1 00,200); mi_ addsegment( -100,200,-100,-100); z=mi_selectsegment(O,-IOO); mi_setsegmentprop('boundary', 1, 1, 1, 1); z=mi_selectsegment(200,0); mi_setsegmentprop('boundary', 1, 1, 1, 1); z=mi_selectsegment(0,200); mi_setsegmentpropCboundary', 1,1,1,1); z=mi_selectsegment( -100,0); mi_setsegmentpropCboundary', 1,1,1,1) %exterior core mi_ addnode(O,O); mi_ addnode(100,0); mi_ addnode(O, 100); mi_ addnode(l 00, 100); mi_ addnode(l 00,49.5); mi_ addnode( 100,50.5); mi_ addsegment(O,O, 1 00,0); mi_ addsegment(O,O,O, 1 00);

Figure 6. B(H) curve of the used ferromagnetic material.


mi_ addsegment( 1 00,0,100,49.5); mi_ addsegment( 1 00,100,0,100); mi_ addsegment( 1 00,50.5,100,100); %interior core mi_addnode(1 0, I 0); mi_ addnode(90, I 0); mi_ addnode(90,49.S); mi_ addnode(90,SO.S); mi_ addnode(90, 90); mi_ addnode(l 0,90); mi_ addsegment( 1 0, 1 0,90,10); mi_ addsegment(90, 1 0,90,49.5); mi_ addsegment(90,SO.S,90,90); mi_ addsegment(90,90, I 0,90); mi_addsegment(1 0,90, I 0, I 0); mi_addsegment(90,49.S, I 00,49.5); mi_ addsegment(90,SO.S, 1 00,50.5) %coils mi_ drawrectang1e( 1 0,20,20,80); mi_ drawrectang1e(-1 0,20,0,80); i= 10; %excitation mi_ addcircprop('current',i, I); %materials mi_getmateriaICCopper');

Fil, Edit Text Go C.II Tooh D.b�9 O"ktop Window Help

mi _ .. dd"�llfl"I"nt (10,10,90, WI ;mi _ .. dd"�llfll"nt (90, 10, 90, �g. 5) ;",i _ .. dd"�,""",nt 190.50.5,90,90) ; 101_ add""'lJIl1"nt (90, 90, la, 9

mi_add""!JT!I"nt (lO,90, 10, WI ;mi_add""!JT!I"nt IgO.�9.5.100. qg.S) ;mi_add""!lf!I"nt 190,50.5,100, 50. 5)

lcoil!!

31 - 1-10;mi_addc:1repr<>p (' curr"nr;'. i, 11 ;

n mi_ll"u .... t"rial (' C"�p",,, ) ;mi_II"t""","'!"i<l11' .\.1,,' I ; mi_'""t=t""i .. 11 'US St",,1 Typo: 2-5 0.018 inch thicJo::n""", );

mi_getmaterialCAir'); mi_getmaterialCUS Steel Type 2-S 0.018 inch thickness'); mi_ addb1ock1abe1( 15,50); mi_se1ect1abe1( 15,50); mi_setblockprop('Copper', I ,30,'current',0, I ,24/2); mi_ clearselected; mi_ addblocklabel(-S,SO); mi_selectlabel(S,SO); mi_setblockpropCCopper', 1 ,30,'current',0, 1 ,-24/2); mi_ c1earse1ected: mi_ addb1ock1abe1( 50,50); mi_se1ect1abe1(SO,SO); mi_setblockprop('Air', I ,30,0,0, I ,0); mi_ clearselected; mi_ addblocklabel(SO,S); mi_selectlabel(SO,S); mi_setblockpropCUS Steel Type 2-S 0.018 inch thickness', 1,30,0,0,1,0); mi_ c1earse1ected: %view and analyze mi_ zoomnatura10; mi_saveas('c:\ \femm42\ \sample. fern'); mi_ analyze(O);%analze miJoadsolutionO;%get results %end

F,I. �drt V..- P,,,bl,.,,, fid � ... tion PfOpmin �n An.ty..r. Window H�p

Figure 7. Screenshots of FEMM window after the compilation of the above algorithm.

V. VRM SIMULATIONS UNDER FEMM

The main program of the VRM is more complicated and contains almost six subprograms, each one of them calculates many specialized variables, as an example, the first subprogram initializes several geometric coefficients and parameters. The last subprogram is the most important one, it contains almost 320 lines of command and it calls all of the other subprograms, for that different VRM configurations can be optimized using its plan of calculating not only the 6/4 VRM topology.

The rotation step of any iteration had selected 5° as shown in Fig. 8. So when FEMM starts automatically, draws the

geometry, assigns different materials, defines several boundaries, meshes (Fig. 9) and analyzes the problem for the current rotor position, the torque value and other desired variables are saved in a separated matrix in MATLAB. The next stage is refreshing the rotor position with the above selected step (5°). The material labels must be separated in any loop, or must be fixed with its bloc. The value of the current can be modified in any loop of simulation and the using of all library materials is possible too; it aims to realize a material optimization as easily as possible.

When the FEA simulation is over, FEMM is closed automatically and the simulation results are plotted under MATLAB. The obtained results of torque, inductance and flux


vs. stator excitation at different rotor positions are shown in Fig. 10, Fig. 11 and Fig. 12, respectively.

To validate the results, we have represented the analytical flux-current characteristics corresponding to the two extreme rotor positions (aligned and unaligned) performed under MA TLAB subprogram depicted in Fig 13 on the same graph of FEMM numerical results, as shown in Fig. 14. We note a small difference between the curves of the two approaches. For example, we needed the two look-up tables (for torque and flux) to simulate one phase of a VRM under MA TLAB/Simulink as shown in Fig.lS.

Figure 9. Screenshot for FEMM analysis in the 2nd rotor position (+5°)

GOO,oode<1 •• to<1.poy Figure 10. Meshing under FEMM in the 3th rotor position (+10°)

torque vs poslhon 0

-lOA 5 V � 8A

0 ....----- -6A

/!, � � 4A r-5 .Jf � O�

f 5 � i:'--- --Ijj 0 "" '------------'I 5 -.../

0 10 20 30 40 50 60 70 80 90 posmon ['[

Figure II. Torque vs. rotor position for different stator excitations.

10 20 30

flux vs position

40 50 pOSition ['I 60 70 80

Figure 12. Inductance vs. rotor position for different stator excitations.

indt.Olance vs position

O, � '1 r\

'\ /

90

r-�� " 1 - 6A '-------"

: ------- \ / � 0---'" "" 1/ ---,- �" \ /// ---

� �\ // // 0 �\ Ih � r

0 w " ro 00 position ['I

Figure 13. Flux vs. rotor position for different stator excitations.

Initial value of stator mmf (FO�ni) or pole flux density (BsO)

For path 1 calculate • The flux density in the different machine parts (Bk)

• Corresponding fields (Hk) and penneability (jJk) from B-H

• Mean lengths of fields circulation (lk)

• Reluctance (Rl � L Rk)

• Total mmf: FI�RI*¢o

yes Bs�Bs±LjBs

From the [mal Bsk compute the inductance of flux path 1

Likewise compute inductance contributed by the other paths and sum them: Lu � L Lk

Figure 14. Flowchart of sub-program for the analytic calculation.

00


flux inkages vs excitabon 4

2

1

8 -/I

r=--6 V;I Cc nvert d en rgy ( Wa-V u) 4

2 /; --

J'- -I-:::: 5 10

rurentlAI

Analytical results Numerical results

Figure 15. Comparison between half-numerical and numerical results.

Figure 16. Insertion of the look-up tables blocs in MATLAB/Simulink.

III. CONCLUSIONS AND PROSPECTS

The study developed in this paper focused around linking two softwares for fmding best simulation results. A hybrid methodology was made from the design to the FEA, ending with a non-linear simulation of the studied prototype. The proposed work allows to economize time of initializing design process of any structure of electrical machines under FEMM environment, to command FEMM remotely with MATLAB, to design and extract electromagnetic characteristics perfectly by using simple tools. In the future works, we will try to realize an optimization study and add other subprograms which may make it easy to estimate losses, efficiency ... etc.

REFERENCES

[1] B. Bilgin and M. Krishnamurthy, "An FEAlMATLAB Based Machine Design Tool for Switched Reluctance Motors", in Proc. IEEE Vehicle Power and Propulsion Conference, 6-9 Sept. 2011, pp. 1-6.

[2] Z. Tang, P. Pillay, Y. Chen and A.M. Omekanda, "Prediction of Electromagnetic Forces and Vibrations in VRMs Operating at Steady State and Transient Speeds", IEEE Trans. On Industry Applications Conference, Vo1.41, No.4, 2005, pp. 927-934.

[3] M. Leroy, "Etude et mise au point de motoventilateurs a hautes performances pour I'aeronautique",(study and control of motoventilators in high performances for the aerospace), doctorate thesis, UMR CNRS N°5828,2006.

[4] A. Matveev, PJ. Van Dutisen , "Novel Caspoc-Based Software For Multilevel Simulation Of Switched Reluctance Drives", in Proc. of PCIM, Nuremberg, Germany, May 20-22, 2003.

[5] Z. Cheng, D. Liang, "Simulation of Switched Reluctance Starter/Generator System Based on Simplorer", in Proc. of the 81h Int. Con! on Electrical Machines and Systems (ICEMS), 2005,VoLI, pp.564-567.

[6] D. Meeker, "FEMM42.exe software". http://www.femm.info. [7] M.B Rego, L.c. Gomes and ai, "Survey of Inductance Curves in Switched

Reluctance Machine Using Finite Elements", International Conference on Renewable Energies and Power Quality (ICREPQ' 12), Spain, March 2012.

[8] D. Uygun, C. Akuner, M. Yumutraci, "A New Construction of Switched Reluctance Motor Improving Magnetic Field and Torque Production", in Proceding of the 6th WSEAS, Istanbul, Turkey, 2006.

[9] M. Kowol, P. Mynarek, D. Mrochen, "The Electromagnetic Field Calculation of the Switched Reluctance Motor", 1"'1 Int. Students Conference on Electrodynamic and Mechatronic (SCE]] '09), 19-21 May 2001, pp.13-14.

[10] R. Krishnan, R. Arumugam and IF. Lindsay, "Design Procedure for Switched - Reluctance Motor", IEEE Transactions on Industry Applications, Vol.24, No. 3, pp. 456-461, May-June 1988.

[II] R. Krishnan, "Switched Reluctance Motor Drives: Modeling, Simulation, Analysis, Design, and Applications ", Industrial Electronics Series 2001, CRC Press.

[12] M.N. Anwar, 1. Husain and V. Radun, "A Comprehensive Design Methodology for Switched Reluctance Machine", IEEE Transactions on Industry Application, Vol. 37, No. 6, pp. 1684-1692, Nov.lDec. 2001.

[IEEE 2013 3rd International Conference on Electric Power and Energy Conversion Systems (EPECS) -...

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