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C Programming Language Based Finite Element Analysis of ...

Here H is the magnetic field intensity, J 0 is the sourcecurrent density, B is the magnetic flux density. The Hmagnetic field intensity can be expressed as[5-10]⎧νB,in air, Ω ,00H = ⎨(3)⎩νν B,in magnetic material, Ω .0 rmHere ν is the reluctivity **of** vacuum and ν is the relative0rreluctivity. The air region is denoted by Ω and the0magnetically region is denoted by Ω . The magnetic fluxmdensity can be expressed asΒ = ∇ × A,(4)where is the magnetic vector potential [2, 8]. This expressionis satised (2), because **of** the identity ∇ ⋅∇ × v ≡ 0 for anyvector function v = v ( r). Substituting (4) to the (1) and (2)and using the (3) constitutive relations can be obtained by thefollowing partial differential equations:andn × A = 0 on Γ .(15),BThe problem was calculated by the help with the (5) and (6)partial differential equations and the (13) and (14) boundaryconditions.The main advantage **of** the COMSOL, that solution **of**optional geometry is possible but the preprocessing andpostprocessing period is more difficult and for example thesolution the transient analysis to calculate the torque **of** themotor is very slow. The static magnetic field problem wascalculated by the help with these partial differential equationsand boundary conditions.IV. COMPARING THE TWO DIFFERENT DEVELOPMENTSOFTWAREThe Fig.4, shows the scheme **of** the developed permanentmagnet synchronous motor which is designed by the helpwith Infolytica MotorSolve [9].and( ∇ × A ) = J , in Ω ,ν00 0∇ ×(5)( ν ν ∇ × A) J , in Ω .∇ ×(6)0r=0mThe divergence **of** the magnetic vector potential can beselected according to Coulomb gauge,∇ ⋅ Α = 0,(7)which is satisfied automatically in two dimensional problems[2, 8]. In two dimensional case the source current density hasonly z component, moreover the magnetic field intensityvector and the magnetic flux density vector have x and ycomponents,J = J x,y(8)( ) ,e0 0,zz( x, y) e H (x, y) e ,H = H +(9)xx( x, y) e B (x, y) e .yB = B +(10)xxyyyThe magnetic vector potential has only z component( x, y) e ,A = A(11)zzand the x and y components **of** the magnetic flux densitycan be described asandz∂zB ( x,y) = A ,(12)x∂y∂AzB ( x,y) = − .(13)y∂xThe boundary conditions **of** a two dimensional staticmagnetic field problem can be formulated as( ν × A ) × n = 0,on Γ ,∇ (14)HFig. 4. The scheme **of** the PMSM motor.The outer diameter **of** the motor is 205mm furthermore theinner diameter **of** the motor is 187mm. The rotor type isexterior and it has 28 Neodymium magnets. The stator has 36slots with three phase double layers windings. The type **of** therotor and the stator material is M19. The maximum power **of**the PMSM is 1200W, as well as the maximum rotationalspeed **of** the motor is 1000RPM. In this case the deliveredtorque is about -64Nm. When the rotational speed is about100RPM then the delivered torque is 11.8Nm and the motorhas 200W power.The simulation results were compared focusing themagnetic potential, and the magnetic flux density **of** the PMSmotor in the case **of** 1000 RPM rotational speed. The sameplace were chosen for the calculation **of** the magnitude **of** themagnetic potential and the magnetic flux density119

The Fig. 5, shows the simulation result **of** the magneticpotential calculated by the Infolytica MotorSolve.Fig. 5.The simulation results **of** the magnetic potential with the helpInfolytica MotorSolve.The Fig. 6, shows the simulation result **of** the magneticpotential by the help **of** COMSOL Multiphysics.Fig. 6. The simulation results **of** the magnetic potential with the helpCOMSOL Multiphysics.Comparing the simulation results which were calculatedtwo different design s**of**tware tools they are similar in the case**of** 1000RPM rotational speed.The simulation results **of** the magnetic flux density **of** thePMSM were compared along the same line as well. The Fig.7, shows the simulation result **of** the magnetic flux densitycalculated by the Infolytica MotorSolve.Fig. 8. The simulation results **of** the magnetic magnetic flux densiy with thehelp COMSOL Multiphysics.Comparing the simulation results which were calculatedtwo different design s**of**tware tools they are similar in the case**of** 1000RPM rotational speed.The simulation results **of** the PMSM were compared witheach other focusing the delivered torque in the case **of**1000RPM rotational speed, as well. Calculating the deliveredtorque with Infolytica MotorSolve is - 68,4 Nm and withCOMSOL Multiphysics is - 67,25 Nm in the case **of** maximalrotational speed.Comparing the simulation results are similar to each otherwhich means the two different design s**of**tware tools areconvenient to design PMS motors. The main advantage **of** theInfolytica MotorSolve is that the development **of** the motor iseasier than with COMSOL Multiphysics. Disadvantage **of** thefirst program is that the motor design is possible by the helpwith only some predefined templates. The main advantage **of**the COMSOL Multyphisics is the possibility **of** designing thePMS motors with optional geometries; however the method**of** this development is more difficult with COMSOLMultiphysics.A C programming language based developmentenvironment is decided to develop due to the disadvantages **of**the other two different development s**of**tware tools.V. C PROGRAMMING LANGUAGE BASED DEVELOPMENTENVIRONMENTThe new development is actually a finite element basedsolver for calculate parameters **of** induction motors and PMSmotors. The Fig. 9, shows the structure **of** the developmentenvironment.Fig. 7. The simulation results **of** the magnetic flux density with the help twodifferent design s**of**tware tools.The Fig. 8, shows the simulation result **of** the magnetic fluxdensity by the help **of** COMSOL Multiphysics.Fig. 8. The scheme **of** the development environment.The structure **of** the environment consists three parts.120