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Rotating Machinery 3D Tutorial
Introduction
This application serves as a general introduction to the Rotating Machinery, Magnetic interface in 3D. The circular motion of a cylindrical copper rotor near a stationary permanent magnet generates induced eddy currents in the rotor. The rotor has an axial cut representing an optional lamination. Figure 1 shows the geometry with the rotor and stator.
Figure 1: Drawing showing how the rotor and stator with the permanent magnet are defined.
Model Definition
This COMSOL Multiphysics application is a time-dependent 3D problem. It is a true time-dependent model where the motion of the rotor is accounted for in the boundary condition between the stator and rotor geometries. For the solid (non-laminated) rotor the conducting part is modeled using Ampère’s law:
For the laminated rotor, the electric potential is introduced in order to set an insulating boundary condition. This is done by manually coupling two built-in formulations, effectively resulting in the following formulation:
In principle, there is also a displacement current density contribution but that is numerically negligible and is excluded in these equations.
The nonconducting parts of both the rotor and stator are modeled using a magnetic flux conservation equation for the scalar magnetic potential:
Rotation is modeled using a ready-made physics interface for rotating machinery. The central part of the geometry, containing the rotor and part of the air-gap, is modeled as rotating relative to the coordinate system of the stator. The rotor and the stator are created as two separate geometry objects, so it is possible to use an assembly (see the Geometry chapter in the COMSOL Multiphysics Reference Manual for details).
This has several advantages: the coupling between the rotor and the stator is done automatically, the parts can be meshed independently, and it allows for a controlled discontinuity in the scalar magnetic potential at the interface between the two geometry objects. The rotor problem is solved in a rotating coordinate system where the rotor is fixed (the rotor frame), whereas the stator problem is solved in a coordinate system that is fixed with respect to the stator (the stator frame). Using COMSOL terminology, they are both solved in the material frame. An identity pair connecting the rotating rotor frame with the fixed stator frame is created between the rotor and the stator. The identity pair enforces continuity for the magnetic scalar potential in the global fixed coordinate system (the stator frame relative to which the rotor rotates).
However, this means that in the frame on which continuity in the scalar magnetic potential is enforced, the meshes on either side of the rotor-stator interface cannot be made identical except for the case without any rotation so some interpolation between non-conforming meshes is involved. The resulting interpolation errors have little numerical impact if the assembly is created such that the resulting identity boundary pair only involves the scalar magnetic potential. In Ampère’s law for the magnetic vector potential, current conservation is an implicit requirement that is violated if the identity boundary pair would involve interpolation of the magnetic vector potential. The resulting interpolation errors unconditionally make such a model numerically unstable. Thus, special care has to be exercised when setting up the geometry using assemblies in an application like this.
Note: An additional intricacy when using a mixed potential formulation involving both scalar and vector magnetic potentials is that the domains using the scalar magnetic potential must be simply connected. A domain is simply connected if any closed line integration path does not link an external domain. An example of a not simply connected domain is a torus (as a closed loop may link the central hole). This is a requirement imposed by the integral form of Ampère’s law as, for example, the hole in the torus may carry a current linking the torus. In the scalar magnetic potential formulation, closed loop line integrals of the H field must evaluate to zero.
Results and Discussion
The eddy current loss in the rotor is shown for the laminated and non-laminated cases. The constant rotation speed is 3000 rpm. The finite rise time represents the inductive-resistive time constant of the rotor.
Figure 2: Eddy current loss comparison.
Application Library path: ACDC_Module/Motors_and_Actuators/rotating_machinery_3d_tutorial
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  3D.
2
In the Select Physics tree, select AC/DC>Electromagnetics and Mechanics>Rotating Machinery, Magnetic (rmm).
3
Click Add.
4
Click  Study.
Add a stationary study to compute initial conditions. The time-dependent study will be added later before solving.
5
In the Select Study tree, select General Studies>Stationary.
6
Click  Done.
Geometry 1
The geometry must be segmented in at least two parts, the stator and the rotor, to allow relative rotation. The geometry sequence for this tutorial can be imported from a separate mph file.
1
In the Geometry toolbar, click  Insert Sequence.
2
Browse to the model’s Application Libraries folder and double-click the file rotating_machinery_3d_tutorial_geom_sequence.mph.
3
In the Geometry toolbar, click  Build All.
4
Click the  Go to Default View button in the Graphics toolbar.
5
Click the  Wireframe Rendering button in the Graphics toolbar.
A boundary pair is automatically created between rotor and stator.
Next, add explicit selections for the source and destination sides of the boundary pair.
Definitions
Identity Boundary Pair 1 (ap1)
1
In the Model Builder window, expand the Component 1 (comp1)>Definitions node, then click Identity Boundary Pair 1 (ap1).
2
In the Settings window for Pair, locate the Source Boundaries section.
3
Click  Create Selection.
4
In the Create Selection dialog box, type src in the Selection name text field.
5
Click OK.
6
In the Settings window for Pair, locate the Destination Boundaries section.
7
Click  Create Selection.
8
In the Create Selection dialog box, type dst in the Selection name text field.
9
Click OK.
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
omega
3000[rpm]
50 1/s
Rotational velocity
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>Copper.
6
Click  Add to Component 1 (comp1).
7
In the tree, select AC/DC>Hard Magnetic Materials>Sintered NdFeB Grades (Chinese Standard)>N35 (Sintered NdFeB).
8
Click  Add to Component 1 (comp1).
9
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Copper (mat2)
1
Select Domains 4 and 5 only.
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
Click  Create Selection.
4
In the Create Selection dialog box, type Rotating disk in the Selection name text field.
5
Click OK.
N35 (Sintered NdFeB) (mat3)
1
In the Model Builder window, click N35 (Sintered NdFeB) (mat3).
2
Select Domain 2 only.
Rotating Machinery, Magnetic (rmm)
Use Magnetic Flux Conservation in the nonconducting domains and Ampère’s Law in the conducting domains. Set up the permanent magnet as a domain described by remanent flux and recoil permeability.
Air, formulation for nonconducting domain
1
In the Model Builder window, under Component 1 (comp1) right-click Rotating Machinery, Magnetic (rmm) and choose Magnetic Flux Conservation.
2
In the Settings window for Magnetic Flux Conservation, type Air, formulation for nonconducting domain in the Label text field.
3
Select Domains 1 and 3 only.
Permanent magnet, formulation for nonconducting domain
1
In the Physics toolbar, click  Domains and choose Magnetic Flux Conservation.
2
In the Settings window for Magnetic Flux Conservation, type Permanent magnet, formulation for nonconducting domain in the Label text field.
3
Select Domain 2 only.
4
Locate the Constitutive Relation B-H section. From the Magnetization model list, choose Remanent flux density.
Rotating machinery in 3D needs explicit gauge fixing of the vector potential.
Gauge Fixing for A-field 1
1
In the Physics toolbar, click  Domains and choose Gauge Fixing for A-field.
2
In the Settings window for Gauge Fixing for A-field, locate the Domain Selection section.
3
From the Selection list, choose Rotating disk.
The gauge fixing needs to be constrained in at least one point. Explicitly enforce a constraint on the value.
4
Click the  Show More Options button in the Model Builder toolbar.
5
In the Show More Options dialog box, in the tree, select the check box for the node Physics>Advanced Physics Options.
6
Click OK.
7
In the Settings window for Gauge Fixing for A-field, click to expand the Advanced Settings section.
8
Select the Ensure constraint on value check box.
Specify the rotation of the rotor domain.
Definitions
Rotating Domain 1
1
In the Definitions toolbar, click  Moving Mesh and choose Rotating Domain.
2
Select Domains 3–5 only.
3
In the Settings window for Rotating Domain, locate the Rotation section.
4
From the Rotation type list, choose Specified rotational velocity.
5
In the ω text field, type omega.
Rotating Machinery, Magnetic (rmm)
The scalar and vector potentials are connected via a special boundary condition, which is applied by default at the interface between the two formulations.
A continuity feature has to be added to specify the coupling across the pair. Note that pair features can be applied only if the same formulation is active on both sides of the pair. Pairs with moving (nonconforming) mesh are allowed only between Magnetic Flux Conservation domains.
Continuity 1
1
In the Physics toolbar, click  Pairs and choose Continuity.
2
In the Settings window for Continuity, locate the Pair Selection section.
3
Under Pairs, click  Add.
4
In the Add dialog box, select Identity Boundary Pair 1 (ap1) in the Pairs list.
5
Click OK.
The scalar potential also needs a point constraint, which is readily available as a standard point feature.
Zero Magnetic Scalar Potential 1
1
In the Physics toolbar, click  Points and choose Zero Magnetic Scalar Potential.
2
Select Point 1 only.
Mesh 1
Some extra care is needed for the meshing of source and destination boundaries for the pair; the destination side needs a finer mesh than the source side. To get full control, mesh these surfaces separately. Use a boundary layer mesh for the copper domain to better resolve the expected velocity skin effect.
Free Triangular 1
1
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose More Operations>Free Triangular.
2
In the Settings window for Free Triangular, locate the Boundary Selection section.
3
From the Selection list, choose src.
Size 1
1
Right-click Free Triangular 1 and choose Size.
2
In the Settings window for Size, locate the Element Size section.
3
Click the Custom button.
4
Locate the Element Size Parameters section. Select the Maximum element size check box.
5
In the associated text field, type 2e-3.
Free Triangular 2
1
In the Model Builder window, right-click Mesh 1 and choose More Operations>Free Triangular.
2
In the Settings window for Free Triangular, locate the Boundary Selection section.
3
From the Selection list, choose dst.
Size 1
1
Right-click Free Triangular 2 and choose Size.
2
In the Settings window for Size, locate the Element Size section.
3
Click the Custom button.
4
Locate the Element Size Parameters section. Select the Maximum element size check box.
5
In the associated text field, type 7e-4.
Free Tetrahedral 1
In the Model Builder window, right-click Mesh 1 and choose Free Tetrahedral.
Size 1
1
In the Model Builder window, right-click Free Tetrahedral 1 and choose Size.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
Select Boundaries 5–10, 21–27, and 29–32 only.
5
Locate the Element Size section. Click the Custom button.
6
Locate the Element Size Parameters section. Select the Maximum element size check box.
7
In the associated text field, type 7e-4.
Free Tetrahedral 1
1
In the Model Builder window, click Free Tetrahedral 1.
2
In the Settings window for Free Tetrahedral, locate the Domain Selection section.
3
From the Geometric entity level list, choose Domain.
4
Select Domains 1, 2, 4, and 5 only.
Boundary Layers 1
1
In the Mesh toolbar, click  Boundary Layers.
2
In the Settings window for Boundary Layers, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Rotating disk.
Boundary Layer Properties 1
1
In the Model Builder window, expand the Boundary Layers 1 node, then click Boundary Layer Properties 1.
2
Select Boundary 26 only.
3
In the Settings window for Boundary Layer Properties, locate the Boundary Layer Properties section.
4
From the Thickness of first layer list, choose Manual.
5
In the Thickness text field, type 1.0E-4.
6
In the Number of boundary layers text field, type 2.
7
In the Thickness text field, type 7.0E-5.
8
In the Boundary layer stretching factor text field, type 1.3.
Free Tetrahedral 2
1
In the Mesh toolbar, click  Free Tetrahedral.
2
In the Settings window for Free Tetrahedral, click  Build All.
Solid copper disk
1
In the Model Builder window, click Study 1.
2
In the Settings window for Study, type Solid copper disk in the Label text field.
Add some stability improvement such as linear discretization and a tuning of time-dependent study. When computing, the stationary solution is automatically used as initial condition.
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(0,1e-5,1.5e-4) range(3e-4,1.5e-4,0.015).
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.
Continuity 1
1
In the Model Builder window, under Component 1 (comp1)>Rotating Machinery, Magnetic (rmm) click Continuity 1.
2
In the Settings window for Continuity, click to expand the Constraint Settings section.
3
Select the Use weak constraints check box.
Solid copper disk
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node, then click Dependent Variables 2.
3
In the Settings window for Dependent Variables, locate the Scaling section.
4
From the Method list, choose Initial value based.
5
In the Model Builder window, under Solid copper disk>Solver Configurations>Solution 1 (sol1) click Time-Dependent Solver 1.
6
In the Settings window for Time-Dependent Solver, click to expand the Time Stepping section.
7
From the Steps taken by solver list, choose Intermediate.
8
From the Maximum BDF order list, choose 2.
9
Find the Algebraic variable settings subsection. From the Error estimation list, choose Exclude algebraic.
10
Click to expand the Output section. Locate the General section. From the Times to store list, choose Steps taken by solver.
11
In the Model Builder window, expand the Solid copper disk>Solver Configurations>Solution 1 (sol1)>Time-Dependent Solver 1 node, then click Fully Coupled 1.
12
In the Settings window for Fully Coupled, click to expand the Method and Termination section.
13
From the Jacobian update list, choose Minimal.
14
In the Model Builder window, under Solid copper disk>Solver Configurations>Solution 1 (sol1)>Time-Dependent Solver 1 click Direct.
15
In the Settings window for Direct, locate the General section.
16
From the Solver list, choose PARDISO.
17
In the Study toolbar, click  Compute.
Results
Magnetic Flux Density Norm (rmm)
In the Magnetic Flux Density Norm (rmm) toolbar, click  Plot.
Now plot the induced eddy currents in the copper disk.
Currents and solid domain boundaries representation
1
In the Home toolbar, click  Add Plot Group and choose 3D Plot Group.
2
In the Settings window for 3D Plot Group, locate the Plot Settings section.
3
Clear the Plot dataset edges check box.
4
In the Label text field, type Currents and solid domain boundaries representation.
5
Locate the Plot Settings section. Click  Go to Source.
Definitions
View 1
1
In the Model Builder window, under Component 1 (comp1)>Definitions click View 1.
2
In the Settings window for View, locate the View section.
3
Clear the Show grid check box.
Results
Surface 1
1
In the Model Builder window, right-click Currents and solid domain boundaries representation and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type 1.
4
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
5
From the Color list, choose Gray.
Selection 1
1
Right-click Surface 1 and choose Selection.
2
Select Boundaries 5–10, 23, and 29–32 only.
Arrow Volume 1
1
In the Model Builder window, right-click Currents and solid domain boundaries representation and choose Arrow Volume.
2
In the Settings window for Arrow Volume, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Rotating Machinery, Magnetic (Magnetic Fields)>Currents and charge>rmm.Jx,...,rmm.Jz - Current density (spatial frame).
3
Locate the Arrow Positioning section. Find the x grid points subsection. In the Points text field, type 10.
4
Find the y grid points subsection. In the Points text field, type 10.
5
Find the z grid points subsection. In the Points text field, type 10.
6
Locate the Coloring and Style section. From the Arrow length list, choose Logarithmic.
7
In the Range quotient text field, type 10.
Selection 1
1
Right-click Arrow Volume 1 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Rotating disk.
Color Expression 1
1
In the Model Builder window, right-click Arrow Volume 1 and choose Color Expression.
2
In the Settings window for Color Expression, locate the Expression section.
3
In the Expression text field, type rmm.normJ.
4
In the Currents and solid domain boundaries representation toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
Compute the dissipated power in the copper disk.
Volume Integration 1
1
In the Results toolbar, click  More Derived Values and choose Integration>Volume Integration.
2
In the Settings window for Volume Integration, locate the Selection section.
3
From the Selection list, choose Rotating disk.
4
Locate the Expressions section. In the table, enter the following settings:
Expression
Unit
Description
rmm.Qh
W
Volumetric loss density, electromagnetic
5
Clicknext to  Evaluate, then choose New Table.
Table
1
Go to the Table window.
Plot the tabulated dissipated power for the bulk copper disc.
2
Click Table Graph in the window toolbar.
Results
Table Graph 1
1
Click the  x-Axis Log Scale button in the Graphics toolbar.
2
Click the  y-Axis Log Scale button in the Graphics toolbar.
Adding an internal insulating layer as a boundary condition.
In an electromagnetic formulation using the vector potential A only, the interior electric insulation boundary condition is not available. This limitation is overcome by introducing the scalar electric potential V by adding a properly coupled Electric Currents physics interface which has a built-in electric insulation boundary condition.
Add Physics
1
In the Home toolbar, click  Add Physics to open the Add Physics window.
2
Go to the Add Physics window.
3
In the tree, select AC/DC>Electric Fields and Currents>Electric Currents (ec).
4
Click Add to Component 1 in the window toolbar.
Electric Currents (ec)
1
In the Settings window for Electric Currents, locate the Domain Selection section.
2
From the Selection list, choose Rotating disk.
3
Click to expand the Discretization section. From the Electric potential list, choose Linear.
Current Conservation 1
1
In the Model Builder window, under Component 1 (comp1)>Electric Currents (ec) click Current Conservation 1.
2
In the Settings window for Current Conservation, locate the Material Type section.
3
From the Material type list, choose Solid.
External Current Density 1
1
In the Physics toolbar, click  Domains and choose External Current Density.
2
In the Settings window for External Current Density, locate the Domain Selection section.
3
From the Selection list, choose Rotating disk.
4
Locate the External Current Density section. Specify the Je vector as
rmm.Jix
x
rmm.Jiy
y
rmm.Jiz
z
Electric Insulation 2
1
In the Physics toolbar, click  Boundaries and choose Electric Insulation.
2
Select Boundary 26 only.
In the absence of boundary conditions on the electrical potential, its level has to be fixed by point conditions on both sides.
Electric Potential 1
1
In the Physics toolbar, click  Points and choose Electric Potential.
2
Select Points 27 and 29 only.
Rotating Machinery, Magnetic (rmm)
In the Model Builder window, under Component 1 (comp1) click Rotating Machinery, Magnetic (rmm).
External Current Density 1
1
In the Physics toolbar, click  Domains and choose External Current Density.
2
In the Settings window for External Current Density, locate the Domain Selection section.
3
From the Selection list, choose Rotating disk.
4
Locate the External Current Density section. Specify the Je vector as
ec.Jx-rmm.Jix
x
ec.Jy-rmm.Jiy
y
ec.Jz-rmm.Jiz
z
Set up a second study for the solution with the insulating layer in the copper disk.
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.
Solid copper disk
Step 2: Time Dependent
In the Model Builder window, under Solid copper disk right-click Step 2: Time Dependent and choose Copy.
Laminated copper disk
1
In the Model Builder window, click Study 2.
2
In the Settings window for Study, type Laminated copper disk in the Label text field.
3
Right-click Laminated copper disk and choose Paste Time Dependent.
Solid copper disk
Disable in the newly added physics in the first study so that it, when run, will reproduce the same results.
Step 1: Stationary
1
In the Model Builder window, under Solid copper disk click Step 1: Stationary.
2
In the Settings window for Stationary, locate the Physics and Variables Selection section.
3
Select the Modify model configuration for study step check box.
4
In the Physics and variables selection tree, select Component 1 (comp1)>Rotating Machinery, Magnetic (rmm), Controls spatial frame>External Current Density 1.
5
Click  Disable.
6
In the Physics and variables selection tree, select Component 1 (comp1)>Electric Currents (ec).
7
Click  Disable in Model.
Step 2: Time Dependent
1
In the Model Builder window, click Step 2: Time Dependent.
2
In the Settings window for Time Dependent, locate the Physics and Variables Selection section.
3
Select the Modify model configuration for study step check box.
4
In the Physics and variables selection tree, select Component 1 (comp1)>Rotating Machinery, Magnetic (rmm), Controls spatial frame>External Current Density 1.
5
Click  Disable.
6
In the Physics and variables selection tree, select Component 1 (comp1)>Electric Currents (ec).
7
Click  Disable in Model.
Laminated copper disk
Generate the solver sequence and perform modifications similar to those of the first study.
Solution 3 (sol3)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 3 (sol3) node.
3
In the Model Builder window, expand the Laminated copper disk>Solver Configurations>Solution 3 (sol3)>Time-Dependent Solver 1 node, then click Laminated copper disk>Solver Configurations>Solution 3 (sol3)>Dependent Variables 2.
4
In the Settings window for Dependent Variables, locate the Scaling section.
5
From the Method list, choose Initial value based.
6
In the Model Builder window, under Laminated copper disk>Solver Configurations>Solution 3 (sol3) click Time-Dependent Solver 1.
7
In the Settings window for Time-Dependent Solver, locate the Time Stepping section.
8
From the Maximum BDF order list, choose 2.
9
Find the Algebraic variable settings subsection. From the Error estimation list, choose Exclude algebraic.
10
From the Steps taken by solver list, choose Intermediate.
11
Locate the General section. From the Times to store list, choose Steps taken by solver.
12
Right-click Laminated copper disk>Solver Configurations>Solution 3 (sol3)>Time-Dependent Solver 1 and choose Fully Coupled.
13
In the Settings window for Fully Coupled, locate the General section.
14
From the Linear solver list, choose Direct.
15
In the Model Builder window, under Laminated copper disk>Solver Configurations>Solution 3 (sol3)>Time-Dependent Solver 1 click Direct.
16
In the Settings window for Direct, locate the General section.
17
From the Solver list, choose PARDISO.
18
In the Home toolbar, click  Add Physics to close the Add Physics window.
19
In the Home toolbar, click  Add Study to close the Add Study window.
20
In the Home toolbar, click  Compute.
Results
Magnetic Flux Density Norm (rmm) 1
In the Magnetic Flux Density Norm (rmm) 1 toolbar, click  Plot.
Add a plot representing the z component of the current which is zero on the insulating gap. It should reproduce figure below.
Current perpendicular to the insulating plane
1
In the Home toolbar, click  Add Plot Group and choose 3D Plot Group.
2
In the Settings window for 3D Plot Group, type Current perpendicular to the insulating plane in the Label text field.
3
Locate the Data section. From the Dataset list, choose Laminated copper disk/Solution 3 (sol3).
Volume 1
1
Right-click Current perpendicular to the insulating plane and choose Volume.
2
In the Settings window for Volume, locate the Expression section.
3
In the Expression text field, type rmm.Jz.
4
In the Unit field, type A/mm^2.
5
Locate the Coloring and Style section. From the Color table list, choose WaveLight.
6
Select the Symmetrize color range check box.
7
In the Current perpendicular to the insulating plane toolbar, click  Plot.
8
Click  Plot.
Verify that for the nonlaminated case, the z component of the current is high on the midplane as shown in the plot below.
Current perpendicular to the insulating plane
1
In the Model Builder window, click Current perpendicular to the insulating plane.
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Dataset list, choose Solid copper disk/Solution 1 (sol1).
4
In the Current perpendicular to the insulating plane toolbar, click  Plot.
Add a new column to the previously generated table and update the corresponding plot with the losses for the laminated disk. The latter case, features decreased losses as expected.
Volume Integration 2
1
In the Model Builder window, under Results>Derived Values right-click Volume Integration 1 and choose Duplicate.
2
In the Settings window for Volume Integration, locate the Data section.
3
From the Dataset list, choose Laminated copper disk/Solution 3 (sol3).
4
Click  Evaluate (Table 1 - Volume Integration 1).
Finalize the addition of the plot and verify that it is similar to the one below.
Table Graph 1
1
In the Model Builder window, click Table Graph 1.
2
In the Settings window for Table Graph, click to expand the Legends section.
3
Select the Show legends check box.
4
From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
Solid copper disk
Laminated copper disk
Losses in the copper disk
1
In the Model Builder window, click 1D Plot Group 3.
2
In the Settings window for 1D Plot Group, click to expand the Title section.
3
In the Label text field, type Losses in the copper disk.
4
Locate the Title section. From the Title type list, choose Manual.
5
In the Title text area, type Losses in the copper disk with and without an insulating layer (W).
6
Locate the Legend section. From the Position list, choose Lower right.
7
In the Losses in the copper disk toolbar, click  Plot.