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Permanent Magnet Motor in 2D
Introduction
This tutorial model shows how to set up a 3-phase permanent magnet motor simulation in 2D, using motor parts that are available in the AC/DC Module Part Library. The model consists of three studies. First, a stationary study solves the problem at direct current, through the angular span of one pole pair, using Arkkio’s method to calculate the rotor torque. Then, by specifying the initial mechanical angle to yield maximum torque, a transient study solves the time-dependent problem for a complete electrical period, and calculates the results for torque ripple and radial magnetic flux density. Finally, using the results from the transient study, the loss density in the stator iron is calculated with a frequency domain study.
Modeling
This model is set up in 2D and simulates the cross section on the rotational axis of the PM motor. The relevant equation is
where A is the magnetic vector potential which defines the magnetic flux density B = ∇ × A, J is the current density, and μ is the magnetic permeability. The equation is solved for the out-of-plane vector component only, which implies that in-plane currents and out-of-plane magnetic fields are neglected. This is a justified assumption for the 2D model which greatly simplifies and stabilizes the problem.
The separate rotor and stator objects are built as an assembly, and the relative rotation between rotor and stator is handled by the Rotating Domain node of the Moving Mesh feature, which includes all effects of relative motion between the parts. The domains are connected in the physics via boundary conditions on the continuity pair boundary, which resides in the air gap between them. This continuity pair allows for mesh discontinuities across the boundary where variables can be interpolated between the two independent meshes, ensuring continuity in the magnetic vector potential.
The torque is computed with the Arkkio Torque Calculation feature, which is automatically applied on the air gap domain adjacent to the continuity pair. The losses in the rotor and stator iron are calculated using a Loss Calculation subnode and a Time to Frequency Losses study. In the coils, the losses are Ohmic, while the losses in the iron are computed with the Steinmetz loss model.
Results and Discussion
The objective of the first study is to find the initial mechanical angle which produces the maximum torque on the rotor. As seen in Figure 1, the parametric sweep of the initial angle yields a curve displaying two extremes: one corresponding to accelerating torque, and the other corresponding to deceleration, in the direction of the prescribed counter-clockwise rotation. For the maximum accelerating torque, the former is chosen for the initial angle. The subsequent transient study solves the synchronous rotation of the stator field and the rotor. Figure 2 plots the rotor torque ripple as a function of time for one electrical period. Finally, a Time to Frequency Losses study calculates the loss density using the results of the previous transient study. Figure 4 shows the resulting loss density in the stator as well as the rotor iron.
Figure 1: Rotor torque plotted as a function of the initial mechanical angle.
Figure 2: Rotor torque plotted as a function of time for a complete electrical period.
Figure 3: Radial magnetic flux density plotted versus the arc length of the continuity pair boundary, for time t = 0.
Figure 4: Loss density.
Application Library path: ACDC_Module/Motors_and_Actuators/pm_motor_2d_introduction
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  2D.
2
In the Select Physics tree, select AC/DC>Electromagnetics and Mechanics>Rotating Machinery, Magnetic (rmm).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Stationary.
6
Click  Done.
Begin by specifying a number of general parameters that will be used by the model.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
L
200[mm]
0.2 m
Out-of-plane thickness of motor
init_ang
0[deg]
0 rad
Initial mechanical angle
Np
10
10
Number of poles
w_rot
60[rpm]
1 1/s
Rotational speed
f_el
w_rot*(Np/2)
5 1/s
Electrical frequency
I0
10[A]
10 A
Peak current
Nturn
10
10
Number of wire turns in slot
ff_slot
0.8
0.8
Slot filling factor
Next, build the motor using rotor and stator parts from the geometry part library. Initialize the parts, and tick the selections that are pre-defined to make it convenient to assign material properties and magnetization direction.
Part Libraries
1
In the Home toolbar, click  Windows and choose Part Libraries.
2
In the Part Libraries window, select AC/DC Module>Rotating Machinery 2D>Rotors>Internal>surface_mounted_magnet_internal_rotor_2d in the tree.
3
Click  Add to Geometry.
Geometry 1
Internal Rotor – Surface Mounted Magnets 1 (pi1)
1
In the Model Builder window, under Component 1 (comp1)>Geometry 1 click Internal Rotor – Surface Mounted Magnets 1 (pi1).
2
In the Settings window for Part Instance, locate the Input Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
number_of_poles
Np
10
Number of magnetic poles in rotor
number_of_modeled_poles
Np
10
Number of magnetic poles included in the geometry
4
Click to expand the Domain Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Shaft
√
√
None
Rotor iron
√
√
None
Odd magnets
√
√
None
Even magnets
√
√
None
Rotor magnets
√
√
None
Rotor solid domains
√
√
None
Rotor air
√
√
None
All
√
√
None
Part Libraries
1
In the Home toolbar, click  Windows and choose Part Libraries.
2
In the Model Builder window, click Geometry 1.
3
In the Part Libraries window, select AC/DC Module>Rotating Machinery 2D>Stators>External>slotted_external_stator_2d in the tree.
4
Click  Add to Geometry.
Geometry 1
External Stator – Slotted 1 (pi2)
Select a radial partition for the slot winding type.
1
In the Model Builder window, under Component 1 (comp1)>Geometry 1 click External Stator – Slotted 1 (pi2).
2
In the Settings window for Part Instance, locate the Input Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
slot_winding_type
2
2
Slot winding type: 1-No partition, 2-Radial partition, 3-Azimuthal partition, 4-Radial and azimuthal partition.
4
Locate the Domain Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Stator iron
√
√
None
Stator slots
√
√
None
Stator air
√
√
None
All
√
√
None
Create an assembly from the two geometry objects, connected by a pair boundary.
Form Union (fin)
1
In the Model Builder window, under Component 1 (comp1)>Geometry 1 click Form Union (fin).
2
In the Settings window for Form Union/Assembly, locate the Form Union/Assembly section.
3
From the Action list, choose Form an assembly.
4
In the Home toolbar, click  Build All.
5
Click the  Zoom Extents button in the Graphics toolbar.
In order to follow the rotor poles, the stator field completes a period in the time it takes the rotor to move the angular span of two magnetic poles. Thus, the electrical frequency is scaled by Np/2 with respect to the rotor frequency. In the next step, define the time dependent angle, and the electrical and mechanical angle, where the latter are offset by the initial angle, init_ang, that you will choose to produce the maximum rotor torque.
Definitions
Electrical and Mechanical Angle
1
In the Model Builder window, expand the Component 1 (comp1)>Definitions node.
2
Right-click Definitions and choose Variables.
3
In the Settings window for Variables, type Electrical and Mechanical Angle in the Label text field.
4
Locate the Variables section. In the table, enter the following settings:
Name
Expression
Unit
Description
angle
2*pi*w_rot*if(isdefined(t),t,0[s])
 
Rotation angle
ang_e
Np/2*(angle-init_ang)
rad
Electrical angle
ang_m
angle
 
Mechanical angle
Next, define the cross section area of the slots, and the three phase currents of the stator coils.
Integration Over Half Slot
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type Integration Over Half Slot in the Label text field.
3
In the Operator name text field, type halfslot_int.
4
Locate the Source Selection section. Click  Paste Selection.
5
In the Paste Selection dialog box, type 14 in the Selection text field.
6
Click OK.
Coil variables
1
Right-click Definitions and choose Variables.
2
In the Settings window for Variables, type Coil variables in the Label text field.
3
Locate the Variables section. In the table, enter the following settings:
Name
Expression
Unit
Description
coil_area
halfslot_int(1)
m²
Coil area
IA
I0*cos(ang_e)
A
Phase A current
IB
I0*cos(ang_e-120[deg])
A
Phase B current
IC
I0*cos(ang_e-240[deg])
A
Phase C current
wire_cross_section
halfslot_int(1)*ff_slot/Nturn
m²
Coil wire cross section
Now, define a cylindrical coordinate system in order to specify a radial direction for the remanent magnetic flux density of the rotor magnets.
Cylindrical System 2 (sys2)
In the Definitions toolbar, click  Coordinate Systems and choose Cylindrical System.
Create union selections for the motor air and iron parts, respectively.
Air
1
In the Definitions toolbar, click  Union.
2
In the Settings window for Union, type Air in the Label text field.
3
Locate the Input Entities section. Under Selections to add, click  Add.
4
In the Add dialog box, in the Selections to add list, choose Rotor air (Internal Rotor – Surface Mounted Magnets 1) and Stator air (External Stator – Slotted 1).
5
Click OK.
Iron
1
In the Definitions toolbar, click  Union.
2
In the Settings window for Union, type Iron in the Label text field.
3
Locate the Input Entities section. Under Selections to add, click  Add.
4
In the Add dialog box, in the Selections to add list, choose Rotor iron (Internal Rotor – Surface Mounted Magnets 1) and Stator iron (External Stator – Slotted 1).
5
Click OK.
Next, add materials and assign them to their appropriate domain selections.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in>Air.
4
Click Add to Component in the window toolbar.
5
In the tree, select AC/DC>Soft Iron (Without Losses).
6
Click Add to Component in the window toolbar.
7
In the tree, select AC/DC>Copper.
8
Click Add to Component in the window toolbar.
9
In the tree, select AC/DC>Hard Magnetic Materials>Sintered NdFeB Grades (Chinese Standard)>N54 (Sintered NdFeB).
10
Click Add to Component in the window toolbar.
11
In the tree, select Built-in>Iron.
12
Click Add to Component in the window toolbar.
13
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Soft Iron (Without Losses) (mat2)
1
In the Model Builder window, under Component 1 (comp1)>Materials click Soft Iron (Without Losses) (mat2).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Iron.
Iron (mat5)
1
In the Model Builder window, click Iron (mat5).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Shaft (Internal Rotor – Surface Mounted Magnets 1).
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
4000
1
Basic
Electrical conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0
S/m
Basic
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
1
1
Basic
Coefficient of thermal expansion
alpha_iso ; alphaii = alpha_iso, alphaij = 0
12.2e-6[1/K]
1/K
Basic
Heat capacity at constant pressure
Cp
440[J/(kg*K)]
J/(kg·K)
Basic
Density
rho
7870[kg/m^3]
kg/m³
Basic
Thermal conductivity
k_iso ; kii = k_iso, kij = 0
76.2[W/(m*K)]
W/(m·K)
Basic
Young’s modulus
E
200e9[Pa]
Pa
Young’s modulus and Poisson’s ratio
Poisson’s ratio
nu
0.29
1
Young’s modulus and Poisson’s ratio
Copper (mat3)
1
In the Model Builder window, click Copper (mat3).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Stator slots (External Stator – Slotted 1).
N54 (Sintered NdFeB) (mat4)
1
In the Model Builder window, click N54 (Sintered NdFeB) (mat4).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Rotor magnets (Internal Rotor – Surface Mounted Magnets 1).
Rotating Machinery, Magnetic (rmm)
In the Definitions toolbar, click  Moving Mesh and choose Domains>Rotating Domain.
Moving Mesh
Rotating Domain 1
1
In the Settings window for Rotating Domain, locate the Domain Selection section.
2
From the Selection list, choose All (Internal Rotor – Surface Mounted Magnets 1).
3
Locate the Rotation section. In the α text field, type ang_m.
Rotating Machinery, Magnetic (rmm)
1
In the Model Builder window, under Component 1 (comp1) click Rotating Machinery, Magnetic (rmm).
2
In the Settings window for Rotating Machinery, Magnetic, locate the Thickness section.
3
In the d text field, type L.
B-H Iron Regions
1
In the Physics toolbar, click  Domains and choose Ampère’s Law.
2
In the Settings window for Ampère’s Law, type B-H Iron Regions in the Label text field.
3
Locate the Domain Selection section. From the Selection list, choose Iron.
4
Locate the Constitutive Relation B-H section. From the Magnetization model list, choose B-H curve.
Loss Calculation 1
1
In the Physics toolbar, click  Attributes and choose Loss Calculation.
2
In the Settings window for Loss Calculation, locate the Loss Model section.
3
From the Loss model list, choose Steinmetz.
Odd Magnets
1
In the Physics toolbar, click  Domains and choose Ampère’s Law.
2
In the Settings window for Ampère’s Law, type Odd Magnets in the Label text field.
3
Locate the Domain Selection section. From the Selection list, choose Odd magnets (Internal Rotor – Surface Mounted Magnets 1).
4
Locate the Coordinate System Selection section. From the Coordinate system list, choose Cylindrical System 2 (sys2).
5
Locate the Constitutive Relation B-H section. From the Magnetization model list, choose Remanent flux density.
6
Locate the Constitutive Relation Jc-E section. From the σ list, choose User defined.
Even Magnets
1
Right-click Odd Magnets and choose Duplicate.
2
In the Settings window for Ampère’s Law, type Even Magnets in the Label text field.
3
Locate the Domain Selection section. From the Selection list, choose Even magnets (Internal Rotor – Surface Mounted Magnets 1).
4
Locate the Constitutive Relation B-H section. Specify the e vector as
-1
r
0
phi
0
a
Phase A
1
In the Physics toolbar, click  Domains and choose Coil.
2
In the Settings window for Coil, type Phase A in the Label text field.
3
Locate the Domain Selection section. Click  Paste Selection.
4
In the Paste Selection dialog box, type 9,11,13-16,18,20 in the Selection text field.
5
Click OK.
6
In the Settings window for Coil, locate the Coil section.
7
From the Conductor model list, choose Homogenized multiturn.
8
Select the Coil group check box.
9
In the Icoil text field, type IA.
10
Locate the Homogenized Multiturn Conductor section. In the N text field, type Nturn.
11
In the acoil text field, type wire_cross_section.
Loss Calculation 1
In the Physics toolbar, click  Attributes and choose Loss Calculation.
Phase A
In the Model Builder window, click Phase A.
Reversed Current Direction 1
1
In the Physics toolbar, click  Attributes and choose Reversed Current Direction.
2
In the Settings window for Reversed Current Direction, locate the Domain Selection section.
3
Click  Paste Selection.
4
In the Paste Selection dialog box, type 11,13,14,20 in the Selection text field.
5
Click OK.
Phase B
1
Right-click Phase A and choose Duplicate.
2
In the Settings window for Coil, type Phase B in the Label text field.
3
Locate the Domain Selection section. Click  Clear Selection.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 5,7,10,12,17,19,21,23 in the Selection text field.
6
Click OK.
7
In the Settings window for Coil, locate the Coil section.
8
In the Icoil text field, type IB.
Reversed Current Direction 1
1
In the Model Builder window, expand the Phase B node, then click Reversed Current Direction 1.
2
In the Settings window for Reversed Current Direction, locate the Domain Selection section.
3
Click  Clear Selection.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 7,10,17,23 in the Selection text field.
6
Click OK.
Phase C
1
In the Model Builder window, right-click Phase B and choose Duplicate.
2
In the Settings window for Coil, type Phase C in the Label text field.
3
Locate the Domain Selection section. Click  Clear Selection.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 1,3,4,6,22,24-26 in the Selection text field.
6
Click OK.
7
In the Settings window for Coil, locate the Coil section.
8
In the Icoil text field, type IC.
Reversed Current Direction 1
1
In the Model Builder window, expand the Phase C node, then click Reversed Current Direction 1.
2
In the Settings window for Reversed Current Direction, locate the Domain Selection section.
3
Click  Clear Selection.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 3,6,24,26 in the Selection text field.
6
Click OK.
Next, implement the Arkkio Torque Calculation feature for calculating the torque on the rotor. The node is automatically applied to the air gap. The Arkkio force integrand is multiplied with a support function which is nonzero in the correct radial extent, between the rotor magnets and stator iron.
Arkkio Torque Calculation 1
In the Physics toolbar, click  Domains and choose Arkkio Torque Calculation.
Mesh 1
Free Triangular 1
In the Mesh toolbar, click  Free Triangular.
Size
1
In the Model Builder window, click Size.
2
In the Settings window for Size, locate the Element Size section.
3
From the Predefined list, choose Coarser.
4
Click the Custom button.
5
Locate the Element Size Parameters section. In the Maximum element size text field, type 5[mm].
6
In the Minimum element size text field, type 0.5[mm].
7
In the Model Builder window, right-click Mesh 1 and choose Build All.
Study 1: Initial angle parametric sweep at DC current
1
In the Model Builder window, click Study 1.
2
In the Settings window for Study, type Study 1: Initial angle parametric sweep at DC current in the Label text field.
Step 1: Stationary
1
In the Model Builder window, under Study 1: Initial angle parametric sweep at DC current click Step 1: Stationary.
2
In the Settings window for Stationary, click to expand the Results While Solving section.
3
Select the Plot check box.
4
Click to expand the Study Extensions section. Select the Auxiliary sweep check box.
5
Click  Add.
6
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
init_ang (Initial mechanical angle)
range(0,4[deg],360[deg]/(Np/2))
deg
7
In the Home toolbar, click  Compute.
Results
Streamline 1
1
In the Model Builder window, expand the Magnetic Flux Density Norm (rmm) node.
2
Right-click Streamline 1 and choose Disable.
Contour 1
1
In the Model Builder window, click Contour 1.
2
In the Settings window for Contour, locate the Levels section.
3
In the Total levels text field, type 16.
4
Locate the Coloring and Style section. From the Color list, choose Black.
5
In the Magnetic Flux Density Norm (rmm) toolbar, click  Plot.
Torque
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Torque in the Label text field.
3
Locate the Plot Settings section. Select the x-axis label check box.
4
In the associated text field, type Angle [deg].
5
Select the y-axis label check box.
6
In the associated text field, type Torque [N*m].
Global 1
1
Right-click Torque and choose Global.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
rmm.Tark_1
N*m
Axial torque
4
In the Torque toolbar, click  Plot.
The maximum torque on the rotor is found at an initial angle offset of 20°. Select this angle for the parameter init_ang to start off the transient study.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
init_ang
20[deg]
0.34907 rad
Initial mechanical angle
Definitions
Global Variable Probe 1 (var1)
1
In the Definitions toolbar, click  Probes and choose Global Variable Probe.
2
In the Settings window for Global Variable Probe, locate the Expression section.
3
In the Expression text field, type rmm.Tark_1.
4
Select the Description check box.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select General Studies>Stationary.
4
Click Add Study in the window toolbar.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 2: Synchronous rotation
1
In the Model Builder window, click Study 2.
2
In the Settings window for Study, type Study 2: Synchronous rotation in the Label text field.
Time Dependent
1
In the Study toolbar, click  Study Steps and choose Time Dependent>Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
In the Output times text field, type range(0,2/Np/6/6,1)/f_el.
In order for the transient solver to achieve a stable solution of the nonlinear problem, you need to apply two settings:
- setting Update Jacobian to On every iteration. This will make the convergence more robust within each time step.
- using Linear elements for the discretization. This will yield a more reliable solution near regions of magnetic saturation.
Solution 2 (sol2)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 2 (sol2) node.
3
In the Model Builder window, expand the Study 2: Synchronous rotation>Solver Configurations>Solution 2 (sol2)>Time-Dependent Solver 1 node, then click Fully Coupled 1.
4
In the Settings window for Fully Coupled, click to expand the Method and Termination section.
5
From the Jacobian update list, choose On every iteration.
Rotating Machinery, Magnetic (rmm)
1
In the Model Builder window, under Component 1 (comp1) click Rotating Machinery, Magnetic (rmm).
2
In the Settings window for Rotating Machinery, Magnetic, click to expand the Discretization section.
3
From the Magnetic vector potential list, choose Linear.
4
From the Magnetic scalar potential list, choose Linear.
Study 2: Synchronous rotation
In the Study toolbar, click  Compute.
Results
Probe Plot Group 4
1
In the Model Builder window, under Results click Probe Plot Group 4.
2
In the Probe Plot Group 4 toolbar, click  Plot.
Now plot the radial component of the magnetic flux density in the air gap. To do that, define a suitable boundary within the air gap, and plot the quantity along its arc length.
Geometry 1
Internal Rotor – Surface Mounted Magnets 1 (pi1)
1
In the Model Builder window, under Component 1 (comp1)>Geometry 1 click Internal Rotor – Surface Mounted Magnets 1 (pi1).
2
In the Settings window for Part Instance, click to expand the Boundary Selections section.
3
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Exterior
√
√
None
4
In the Home toolbar, click  Build All.
Results
Air Gap Radial Magnetic Flux Density
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Air Gap Radial Magnetic Flux Density in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 2: Synchronous rotation/Solution 2 (sol2).
4
From the Time selection list, choose First.
Line Graph 1
1
Right-click Air Gap Radial Magnetic Flux Density and choose Line Graph.
2
In the Settings window for Line Graph, locate the Selection section.
3
From the Selection list, choose Exterior (Internal Rotor – Surface Mounted Magnets 1).
4
Locate the y-Axis Data section. In the Expression text field, type rmm.ark1.Brad.
5
In the Air Gap Radial Magnetic Flux Density toolbar, click  Plot.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select Preset Studies for Selected Physics Interfaces>Time to Frequency Losses.
4
Click Add Study in the window toolbar.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 3: Loss calculation over full rotation
1
In the Model Builder window, click Study 3.
2
In the Settings window for Study, type Study 3: Loss calculation over full rotation in the Label text field.
Step 1: Time to Frequency Losses
1
In the Model Builder window, under Study 3: Loss calculation over full rotation click Step 1: Time to Frequency Losses.
2
In the Settings window for Time to Frequency Losses, locate the Study Settings section.
3
From the Input study list, choose Study 2: Synchronous rotation, Time Dependent.
4
In the Electrical period text field, type 1/f_el.
5
In the Number of harmonics text field, type 10*6.
Solution 4 (sol4)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 4 (sol4) node, then click FFT Solver 1.
3
In the Settings window for FFT Solver, locate the General section.
4
From the Defined by study step list, choose User defined.
5
In the Study toolbar, click  Compute.
Results
Selection 1
1
In the Model Builder window, expand the Results>Cycle Averaged Losses (rmm) node.
2
Right-click Surface 1 and choose Selection.
3
In the Settings window for Selection, locate the Selection section.
4
From the Selection list, choose Iron.
5
In the Cycle Averaged Losses (rmm) toolbar, click  Plot.