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C Programming Language Based Finite Element Analysis of ...

C Programming Language Based Finite Element Analysis of ...

Here H is the magnetic

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 ofoptional 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 ofthe 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 software tools they are similar in the caseof 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 software tools they are similar in the caseof 1000RPM rotational speed.The simulation results of the PMSM were compared witheach other focusing the delivered torque in the case of1000RPM 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 software 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 ofthe COMSOL Multyphisics is the possibility of designing thePMS motors with optional geometries; however the methodof this development is more difficult with COMSOLMultiphysics.A C programming language based developmentenvironment is decided to develop due to the disadvantages ofthe other two different development software 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 software 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

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