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Acta Technica Jaurinensis Vol. 5. No. 1. 2012 77 Simulation of a PMSM Motor in COMSOL Environment G. Kovács Széchenyi István University, Regional University Knowledge Center for Vehicle Industry, 9026 Győr, Egyetem tér 1. e-mail: kovacsg@maxwell.sze.hu Abstract: The paper presents simulation results of a two-dimensional Permanent Magnet Synchronous Motor (PMSM, PMS motor), which were calculated by the help of the Infolytica MotorSolve and of the COMSOL Mu
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   Acta Technica Jaurinensis Vol. 5. No. 1. 2012  77 Simulation of a PMSM Motor in COMSOL Environment G. Kovács Széchenyi István University, Regional University Knowledge Center for Vehicle Industry, 9026 Gy ő r, Egyetem tér 1. e-mail: kovacsg@maxwell.sze.hu Abstract: The paper presents simulation results of a two-dimensional Permanent Magnet Synchronous Motor (PMSM, PMS motor), which were calculated  by the help of the Infolytica MotorSolve and of the COMSOL Multiphysics, as well. The simulation results were compared with each other focusing on the torque, the magnetic flux density and the magnetic  potential of the PMSM motor.  Keywords: Permanent Magnet Synchronous Motor, Finite Element Method, Infolytica  MotorSolve, Comsol Multiphysics 1.   Introduction The computer-aided design is one of the most important parts of the electric engine development. The development of the electric motor is at the Széchenyi István University, as well. My part of this development is to design a PMSM [1] family and calculate their parameters by the help of finite element method [2-8]. These developed motors will be applied with bicycles and smaller motors. The main essential of the PMSM development is to reduce the weight and the size of the engine but the torque and losses of the motor not to change. The aim of the development of the engine was to design PMSM which in low-speed case has about 10Nm torque. The Figure 1. shows the scheme of the developed permanent magnet synchronous motor which is designed by the help with Infolytica MotorSolve [9]. This motor was developed moreover it is under construction. The outer diameter of the motor is 205 mm furthermore the inner diameter of the motor is 187 mm. The rotor type is exterior and it has 28 Neodymium magnets. The stator has 36 slots with three  phase double layers windings. The type of the rotor and the stator material is M19. The maximum power of the PMSM is 1200 W, as well as the maximum rotational speed of the motor is 1000 RPM. In this case the delivered torque is about –64 Nm. When the rotational speed is about 100RPM then the delivered torque is 11.8 Nm and the motor has 200 W power. The aim of this work is to reproduce the MotorSolve simulation results in the COMSOL [10-11] environment focusing the torque, the magnetic potential and the  Vol. 5. No. 1. 2012 Acta Technica Jaurinensis  78 magnetic flux density of the developed permanent magnet synchronous motor in the case of 1000 RPM rotational speed.  Figure 1. The scheme of the PMS motor 2.   Simulation of the PMSM with Infolytica MotorSolve The computer-aided design is usually the first parts of the electric engine development. There are more ways for the electric motor design, as well. For instance the Infolytica MotorSolve is an electric motor design software for brushless DC motor. In this case the motor design is made by the help with different templates. By the help of the change of the sizes of the schemes can have been designed the electric motor furthermore the Figure 2. shows some templates of the magnets of the rotor.  Figure 2. Templates for the rotor magnets  Figure 3. Templates for the stator slots   Acta Technica Jaurinensis Vol. 5. No. 1. 2012  79 The Figure 3. shows some templates of the slots of the stator. The parameters of the electric motor are calculated by the help of an automated-FEA (Finite Element Analysis) solver, for example torque, losses, power, and the others. The disadvantage of the program that the motor designing is possible by the help only with some defined templates, which means that there is no way to design a motor with optional geometry. The easy applicability is the advantage of the program. 3.   Simulation of the PMS motor with Comsol Multiphysics The COMSOL Multiphysics is a Finite Element Based software for the modelling and simulation of any physics-based system. In this case calculations on optional geometry have been able to make with the program; however the preprocessing is more difficult for instance to draw the model, or to set the boundary conditions. The Figure 4. shows some possibility of settings.  Figure 4. The graphical user interface of COMSOL The simulated model has been modelled as a static magnetic field problem, where the following Maxwell's equations [2-8] can be used , ΩΩ in , m00  ∪=×∇  J   Η   (1) . ΩΩ in ,0 m0 ∪=⋅∇  Β  (2) Here  Η   is the magnetic field intensity, 0  J   is the source current density,  Β  is the magnetic flux density. The  Η   magnetic field intensity can be expressed as ⎩⎨⎧= . Ω  material,magneticin ,  ν ν , Ω  air,in ,  ν m000  B B H    r   (3)  Vol. 5. No. 1. 2012 Acta Technica Jaurinensis  80 Here 0  ν  is the reluctivity of vacuum and r   ν  is the relative reluctivity. The air region is denoted by 0 Ω  and the magnetically region is denoted by m Ω . The magnetic flux density can be expressed as ,  A  Β  ×∇=  (4) where  Α  is the magnetic vector potential [2, 8]. This expression is satisfied (2), because of the identity 0 ≡×∇⋅∇  v  for any vector function  ( ) r vv  = . Substituting (4) to the (1) and (2) and using the (3) constitutive relations can be obtained by the following partial differential equations: ( ) , Ω in , 000  J  A  =×∇×∇  ν  (5) and ( ) . Ω in , 00 mr  νν  J  A  =×∇×∇  (6) The divergence of the magnetic vector potential can be selected according to Coulomb gauge, ,0 =⋅∇  Α  (7) which is satisfied automatically in two dimensional problems [2, 8]. In two dimensional case the source current density has only  z   component, moreover the magnetic field intensity vector and the magnetic flux density vector have  x  and  y  components, ( ) ,, ,00  z  z   y x J   e J   =  (8) ( ) ,),(,  y y x x  y x H  y x H   ee H   +=  (9) ( ) .),(,  y y x x  y x B y x B  ee B  +=  (10) The magnetic vector potential has only  z   component ( ) ,,  z  z  z   y x A  e A  =  (11) and the  x  and  y  components of the magnetic flux density can be described as ( ) ,,  y y x  z  x ∂∂=  A B  (12) and ( ) .,  x y x  z  y ∂∂−=  A B  (13) The boundary conditions of a two dimensional static magnetic field problem can be formulated as ( ) , Γ on , H 0n A  =××∇ ν  (14) and . Γ on , B 0 An  =×  (15)
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