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Static Field Modeling of a Halbach Rotor
Introduction
This example presents the static-field modeling of a flux-focusing magnetic rotor using permanent magnets, a magnetic rotor also known as a Halbach rotor. The use of permanent magnets in rotatory devices such as motors, generators, and magnetic gears is increasing due to their no-contact, frictionless operation. This model illustrates how to calculate and change the magnetic field of a Halbach rotor in 3D by changing the number of permanent magnet segments and the number of pole-pairs.
Figure 1: Illustration of a 16-segments, 4-pole pair Halbach rotor.
Model Definition
Set up the problem in a 3D modeling space. The model consists of a parameterized number of permanent magnet pieces arranged with a varying number of pole pairs. Figure 1 shows a 3D view of a 16-segments, 4-pole pair rotor with the magnetization direction of the magnets indicated. The black arrows show the radial and axial magnetization directions of the permanent magnets in the rotor. In this example, the permanent magnets are arranged in such a way that the magnetic flux density is minimized inside the rotor and maximized outside the rotor. The inner and outer rotor radii are 30 mm and 50 mm, respectively. The axial length of the rotor is 30 mm.
Results and Discussion
A steady-state study analysis is performed to calculate the magnetic field of a 16-segments Halbach rotor. This is done in a parametric sweep over the additional angle for each permanent magnet’s magnetization direction. The magnetic flux density for an 8-pole pair rotor is shown in Figure 2.
Figure 3 and Figure 4 illustrate the variations of the radial and azimuthal magnetic flux density as functions of rotor angle for the same rotor. The magnetic flux density is evaluated at a distance of 5 mm outside the rotor’s outer radius and 5 mm inside the rotor’s inside radius. Figure 5 shows the polar plot of the magnetic flux density norm at the same distances.
Another parametric sweep, this time over the number of segments, is then performed for an 8-pole pair rotor. The polar plot of the magnetic flux density norm for the 32-segments rotor is shown in Figure 6.
Figure 2: Magnetic flux density norm at the cross section of an 8-pole pair Halbach rotor (at z = 0 mm).
Figure 3: The radial magnetic flux density as a function of rotor angle measured at a distance of 5 mm inside and outside the rotor.
Figure 4: The azimuthal magnetic flux density as a function of rotor angle measured at a distance of 5 mm inside and outside the rotor.
Figure 5: Polar plot of the magnetic flux density norm measured at a distance of 5 mm inside and outside a 16-segments rotor.
Figure 6: Polar plot of the magnetic flux density norm measured at a distance of 5 mm inside and outside a 32-segments rotor.
Application Library path: ACDC_Module/Introductory_Magnetostatics/static_field_halbach_rotor_3d
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 > Magnetic Fields, No Currents > Magnetic Fields, No Currents (mfnc).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies > Stationary.
6
Click  Done.
Global Definitions
Parameters 1
Load the model parameters from the static_field_halbach_rotor_3d_parameters.txt file.
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file static_field_halbach_rotor_3d_parameters.txt.
Most of these parameters govern the geometry of the rotor, outer_analysis and inner_analysis determine the radius of two circular arcs where the magnetic flux density will later be analyzed. The parameter add_angle is related to the physics and requires some more explanation. This parameter changes the relative magnetization direction from one magnet segment in the rotor to the next. Figure 1 shows the magnetization directions for add_angle=-90[deg].
Geometry 1
Work Plane 1 (wp1)
1
In the Model Builder window, expand the Component 1 (comp1) > Geometry 1 node.
2
Right-click Geometry 1 and choose Work Plane.
3
In the Settings window for Work Plane, locate the Plane Definition section.
4
In the z-coordinate text field, type -height/2.
Work Plane 1 (wp1) > Plane Geometry
In the Model Builder window, click Plane Geometry.
Work Plane 1 (wp1) > Circle 1 (c1)
1
In the Work Plane toolbar, click  Circle.
2
In the Settings window for Circle, locate the Size and Shape section.
3
In the Radius text field, type Ro.
4
In the Sector angle text field, type alpha.
5
Locate the Rotation Angle section. In the Rotation text field, type -alpha/2.
Work Plane 1 (wp1) > Circle 2 (c2)
1
Right-click Component 1 (comp1) > Geometry 1 > Work Plane 1 (wp1) > Plane Geometry > Circle 1 (c1) and choose Duplicate.
2
In the Settings window for Circle, locate the Size and Shape section.
3
In the Radius text field, type Ri.
4
Click  Build Selected.
Work Plane 1 (wp1) > Difference 1 (dif1)
1
In the Work Plane toolbar, click  Booleans and Partitions and choose Difference.
2
Select the object c1 only.
3
In the Settings window for Difference, locate the Difference section.
4
Click to select the  Activate Selection toggle button for Objects to subtract.
5
Select the object c2 only.
6
Click  Build Selected.
Work Plane 1 (wp1) > Rotate 1 (rot1)
1
In the Work Plane toolbar, click  Transforms and choose Rotate.
2
Select the object dif1 only.
3
In the Settings window for Rotate, locate the Rotation section.
4
In the Angle text field, type range(alpha,alpha,360).
5
Click  Build Selected.
6
Click the  Zoom Extents button in the Graphics toolbar.
Magnets
1
In the Model Builder window, right-click Geometry 1 and choose Extrude.
2
In the Settings window for Extrude, type Magnets in the Label text field.
3
Locate the Distances section. In the table, enter the following settings:
Distances (m)
height
4
Locate the Selections of Resulting Entities section. Select the Resulting objects selection checkbox.
5
Click  Build Selected.
6
Click the  Zoom Extents button in the Graphics toolbar.
Cylinder 1 (cyl1)
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type r_system.
4
In the Height text field, type height_system.
5
Locate the Position section. In the z text field, type -height_system/2.
Arcs
1
In the Geometry toolbar, click  Work Plane.
2
In the Settings window for Work Plane, type Arcs in the Label text field.
3
Locate the Selections of Resulting Entities section. Select the Resulting objects selection checkbox.
4
From the Show in physics list, choose Edge selection.
5
Find the Selections from plane geometry subsection. Select the Show in physics checkbox.
Arcs (wp2) > Plane Geometry
In the Model Builder window, click Plane Geometry.
Inner Arc
1
In the Work Plane toolbar, click  Circle.
2
In the Settings window for Circle, type Inner Arc in the Label text field.
3
Locate the Object Type section. From the Type list, choose Curve.
4
Locate the Size and Shape section. In the Radius text field, type inner_analysis.
5
Locate the Selections of Resulting Entities section. Select the Resulting objects selection checkbox.
6
From the Show in 3D list, choose Boundary selection.
Outer Arc
1
Right-click Inner Arc and choose Duplicate.
2
In the Settings window for Circle, type Outer Arc in the Label text field.
3
Locate the Size and Shape section. In the Radius text field, type outer_analysis.
Form Union (fin)
1
In the Geometry toolbar, click  Build All.
2
Click the  Zoom Extents button in the Graphics toolbar.
3
Click the  Wireframe Rendering button in the Graphics toolbar.
4
In the Model Builder window, under Component 1 (comp1) > Geometry 1 click Form Union (fin).
Create selections for the north and south boundaries of one magnet segment. This will later, by extension, help define all magnets’ magnetization direction.
Definitions
North Boundary
1
In the Definitions toolbar, click  Cylinder.
2
In the Settings window for Cylinder, type North Boundary in the Label text field.
3
Locate the Geometric Entity Level section. From the Level list, choose Boundary.
4
Locate the Size and Shape section. In the Outer radius text field, type Ri.
5
In the Inner radius text field, type Ri.
6
In the Start angle text field, type -alpha/2.
7
In the End angle text field, type alpha/2.
8
Locate the Output Entities section. From the Include entity if list, choose All vertices inside cylinder.
South Boundary
1
Right-click North Boundary and choose Duplicate.
2
In the Settings window for Cylinder, type South Boundary in the Label text field.
3
Locate the Size and Shape section. In the Outer radius text field, type Ro.
4
In the Inner radius text field, type Ro.
Next, create a cylindrical coordinate system and a Vector Transform feature to define variables for the radial and azimuthal magnetic flux densities.
Cylindrical System 2 (sys2)
1
In the Definitions toolbar, click  Coordinate Systems and choose Cylindrical System.
2
Click the  Show More Options button in the Model Builder toolbar.
3
In the Show More Options dialog, select General > Variable Utilities in the tree.
4
In the tree, select the checkbox for the node General > Variable Utilities.
5
Click OK.
Vector Transform 1 (vectr1)
1
In the Definitions toolbar, click  Variable Utilities and choose Vector Transform.
2
In the Settings window for Vector Transform, type B_cyl in the Name text field.
3
Locate the Geometric Entity Selection section. From the Selection list, choose All domains.
4
Click Replace Expression in the upper-right corner of the Input section. From the menu, choose Component 1 (comp1) > Magnetic Fields, No Currents > Magnetic > Magnetic flux density > mfnc.B - Magnetic flux density - T.
5
Locate the Output section. From the Coordinate system list, choose Cylindrical System 2 (sys2).
6
Locate the Transform Settings section. From the Transform as list, choose Flux vector.
View 1
Hide a few boundaries to view the results only in the inner part of the model domain.
Hide for Physics 1
1
In the Model Builder window, right-click View 1 and choose Hide for Physics.
2
In the Settings window for Hide for Physics, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
Select Boundaries 1, 2, 4, and 49 only.
5
Click the  Transparency button in the Graphics toolbar.
Magnetic Fields, No Currents (mfnc)
Now, set up the physics interface
Magnet 1
1
In the Physics toolbar, click  Domains and choose Magnet.
2
In the Settings window for Magnet, locate the Domain Selection section.
3
From the Selection list, choose Magnets.
4
Locate the Magnet section. From the Pattern type list, choose Circular pattern.
5
From the Type of periodicity list, choose User defined.
6
In the α text field, type add_angle.
North 1
1
In the Model Builder window, click North 1.
2
In the Settings window for North, locate the Boundary Selection section.
3
From the Selection list, choose North Boundary.
South 1
1
In the Model Builder window, click South 1.
2
In the Settings window for South, locate the Boundary Selection section.
3
From the Selection list, choose South Boundary.
The final addition to the physics interface is a point constraint for the magnetic scalar potential. Without this addition, there will be no unique solution which can cause problems in the solver.
Zero Magnetic Scalar Potential 1
1
In the Physics toolbar, click  Points and choose Zero Magnetic Scalar Potential.
2
Select Point 1 only.
Add Material
1
In the Materials 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 the Add to Component button in the window toolbar.
5
In the tree, select AC/DC > Hard Magnetic Materials > Sintered NdFeB Grades (Chinese Standard) > N50 (Sintered NdFeB).
6
Click the Add to Component button in the window toolbar.
7
In the Materials toolbar, click  Add Material to close the Add Material window.
Materials
N50 (Sintered NdFeB) (mat2)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Magnets.
Mesh 1
Next, the mesh will be constructed. Now it becomes clear why the inner and outer arcs were included in the geometry. These will be given very fine meshes to allow a highly resolved analysis of the magnetic field. First, however, specify the mesh size of the magnets.
Size 1
1
In the Model Builder window, under Component 1 (comp1) right-click Mesh 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 Domain.
4
From the Selection list, choose Magnets.
5
Locate the Element Size section. From the Predefined list, choose Finer.
Specify a customized fine mesh on the curves where the magnetic flux density is to be evaluated. This helps to obtain a smooth curve for the magnetic flux density.
Size 2
1
In the Model Builder window, right-click Mesh 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 Edge.
4
From the Selection list, choose Arcs.
5
Locate the Element Size section. Click the Custom button.
6
Locate the Element Size Parameters section.
7
Select the Maximum element size checkbox. In the associated text field, type 0.5[mm].
Free Tetrahedral 1
1
In the Mesh toolbar, click  Free Tetrahedral.
2
In the Settings window for Free Tetrahedral, click  Build All.
Compare the mesh with the figure shown below.
Study 1 - Additional Angle Sweep
Now, create a Parametric Sweep for the stationary study. This will sweep over different values for the additional angle parameter to look at the resulting magnetic fields.
1
In the Model Builder window, click Study 1.
2
In the Settings window for Study, type Study 1 - Additional Angle Sweep in the Label text field.
3
Locate the Study Settings section. Clear the Generate default plots checkbox.
Parametric Sweep
1
In the Study toolbar, click  Parametric Sweep.
2
In the Settings window for Parametric Sweep, locate the Study Settings section.
3
Click  Add.
4
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
add_angle (Additional angle for magnetization pattern)
range(-90,45,90)
deg
5
In the Study toolbar, click  Compute.
Results
In the Model Builder window, expand the Results node.
Create a cut plane to analyze the magnetic field.
Cut Plane - Additional Angle Sweep
1
In the Model Builder window, expand the Results > Datasets node.
2
Right-click Results > Datasets and choose Cut Plane.
3
In the Settings window for Cut Plane, type Cut Plane - Additional Angle Sweep in the Label text field.
4
Locate the Data section. From the Dataset list, choose Study 1 - Additional Angle Sweep/Parametric Solutions 1 (sol2).
5
Locate the Plane Data section. From the Plane list, choose xy-planes.
Magnetic Flux Density, Additional Angle Sweep
1
In the Results toolbar, click  2D Plot Group.
2
In the Settings window for 2D Plot Group, type Magnetic Flux Density, Additional Angle Sweep in the Label text field.
Surface 1
1
In the Magnetic Flux Density, Additional Angle Sweep toolbar, click  Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type mfnc.normB.
4
Locate the Coloring and Style section. From the Color table list, choose Prism.
Magnetic Flux Density, Additional Angle Sweep
In the Magnetic Flux Density, Additional Angle Sweep toolbar, click  Arrow Surface.
Arrow Surface 1
1
In the Settings window for Arrow Surface, locate the Arrow Positioning section.
2
Find the x grid points subsection. In the Points text field, type 30.
3
Find the y grid points subsection. In the Points text field, type 30.
4
Locate the Coloring and Style section. From the Color list, choose Black.
5
In the Magnetic Flux Density, Additional Angle Sweep toolbar, click  Plot.
Compare the plots corresponding to the different parameter values by clicking Plot Previous or Plot Next. Note how the magnetic flux density changes from being predominantly inside the rotor for positive values of add_angle to predominantly outside for negative values. Recreate the figure below for add_angle=-45[deg].
Radial Magnetic Flux Density
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Radial Magnetic Flux Density in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 1 - Additional Angle Sweep/Parametric Solutions 1 (sol2).
4
From the Parameter selection (add_angle) list, choose From list.
5
In the Parameter values (add_angle (deg)) list box, select -90.
6
Click to expand the Title section. From the Title type list, choose Manual.
7
In the Title text area, type Radial magnetic flux density.
8
In the Parameter indicator text field, type add_angle = eval(add_angle*180/pi) deg.
9
Locate the Plot Settings section.
10
Select the x-axis label checkbox. In the associated text field, type Angle (rad/2\pi).
11
Select the y-axis label checkbox. In the associated text field, type Radial magnetic flux density (T).
Outer Arc
1
In the Radial Magnetic Flux Density toolbar, click  Line Graph.
2
In the Settings window for Line Graph, type Outer Arc in the Label text field.
3
Locate the Selection section. From the Selection list, choose Outer Arc (Arcs).
4
Locate the y-Axis Data section. In the Expression text field, type B_cyl.vr.
5
Locate the x-Axis Data section. Select the Normalize checkbox.
6
Click to expand the Legends section. Select the Show legends checkbox.
7
Find the Include subsection. Select the Label checkbox.
8
Clear the Solution checkbox.
Inner Arc
1
Right-click Outer Arc and choose Duplicate.
2
In the Settings window for Line Graph, type Inner Arc in the Label text field.
3
Locate the Selection section. From the Selection list, choose Inner Arc (Arcs).
4
In the Radial Magnetic Flux Density toolbar, click  Plot.
Note how the radial magnetic flux density changes on the two arcs for all parameter values by clicking Plot Next or Plot Previous. Compare the plot for add_angle=-45[deg] with the figure below.
Azimuthal Magnetic Flux Density
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Azimuthal Magnetic Flux Density in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 1 - Additional Angle Sweep/Parametric Solutions 1 (sol2).
4
From the Parameter selection (add_angle) list, choose From list.
5
In the Parameter values (add_angle (deg)) list box, select -90.
6
Locate the Title section. From the Title type list, choose Manual.
7
In the Title text area, type Azimuthal magnetic flux density.
8
In the Parameter indicator text field, type add_angle = eval(add_angle*180/pi) deg.
9
Locate the Plot Settings section.
10
Select the x-axis label checkbox. In the associated text field, type Angle (rad/2\pi).
11
Select the y-axis label checkbox. In the associated text field, type Azimuthal magnetic flux density (T).
Outer Arc
1
In the Azimuthal Magnetic Flux Density toolbar, click  Line Graph.
2
In the Settings window for Line Graph, type Outer Arc in the Label text field.
3
Locate the Selection section. From the Selection list, choose Outer Arc (Arcs).
4
Locate the y-Axis Data section. In the Expression text field, type B_cyl.vphi.
5
Locate the x-Axis Data section. Select the Normalize checkbox.
6
Locate the Legends section. Select the Show legends checkbox.
7
Find the Include subsection. Select the Label checkbox.
8
Clear the Solution checkbox.
Inner Arc
1
Right-click Outer Arc and choose Duplicate.
2
In the Settings window for Line Graph, type Inner Arc in the Label text field.
3
Locate the Selection section. From the Selection list, choose Inner Arc (Arcs).
4
In the Azimuthal Magnetic Flux Density toolbar, click  Plot.
Once again, compare the plots corresponding to the different parameter values by Clicking Plot Next or Plot Previous. Make sure the plot for add_angle=-45[deg] looks like the figure below.
Magnetic Flux Density Norm
1
In the Results toolbar, click  Polar Plot Group.
2
In the Settings window for Polar Plot Group, type Magnetic Flux Density Norm in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 1 - Additional Angle Sweep/Parametric Solutions 1 (sol2).
4
From the Parameter selection (add_angle) list, choose From list.
5
In the Parameter values (add_angle (deg)) list box, select -90.
6
Click to expand the Title section. From the Title type list, choose Manual.
7
In the Title text area, type Magnetic flux density norm.
8
In the Parameter indicator text field, type add_angle = eval(add_angle*180/pi) deg.
9
Locate the Axis section. Select the Manual axis limits checkbox.
10
In the r maximum text field, type 0.85.
Outer Arc
1
In the Magnetic Flux Density Norm toolbar, click  Line Graph.
2
In the Settings window for Line Graph, type Outer Arc in the Label text field.
3
Locate the Selection section. From the Selection list, choose Outer Arc (Arcs).
4
Locate the r-Axis Data section. In the Expression text field, type mfnc.normB.
5
Locate the θ Angle Data section. From the Parameter list, choose Expression.
6
In the Expression text field, type sys2.phi.
7
Click to expand the Legends section. Select the Show legends checkbox.
8
Find the Include subsection. Select the Label checkbox.
9
Clear the Solution checkbox.
Inner Arc
1
Right-click Outer Arc and choose Duplicate.
2
In the Settings window for Line Graph, type Inner Arc in the Label text field.
3
Locate the Selection section. From the Selection list, choose Inner Arc (Arcs).
4
In the Magnetic Flux Density Norm toolbar, click  Plot.
5
Click  Plot Next.
Compare the plot for add_angle=-45[deg] with the figure below.
3D Magnetic Flux Density
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, type 3D Magnetic Flux Density in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 1 - Additional Angle Sweep/Parametric Solutions 1 (sol2).
4
From the Parameter value (add_angle (deg)) list, choose -45.
5
Locate the Plot Settings section. Clear the Plot dataset edges checkbox.
6
Click to expand the Title section. From the Title type list, choose Label.
7
Click to collapse the Title section. Locate the Color Legend section. Select the Show maximum and minimum values checkbox.
Volume 1
1
In the 3D Magnetic Flux Density toolbar, click  Volume.
2
In the Settings window for Volume, locate the Expression section.
3
In the Expression text field, type mfnc.normB.
4
Locate the Coloring and Style section. From the Color table list, choose Prism.
Selection 1
1
Right-click Volume 1 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Magnets.
Filter 1
1
In the Model Builder window, right-click Volume 1 and choose Filter.
2
In the Settings window for Filter, locate the Element Selection section.
3
In the Logical expression for inclusion text field, type z<-1[mm].
3D Magnetic Flux Density
In the 3D Magnetic Flux Density toolbar, click  More Plots and choose Streamline Surface.
Streamline Surface 1
1
In the Settings window for Streamline Surface, locate the Data section.
2
From the Dataset list, choose Cut Plane - Additional Angle Sweep.
3
From the Solution parameters list, choose From parent.
4
Locate the Streamline Positioning section. From the Positioning list, choose Magnitude controlled.
5
In the Minimum density level text field, type 2.
6
In the Maximum density level text field, type 11.
Color Expression 1
1
Right-click Streamline Surface 1 and choose Color Expression.
2
In the Settings window for Color Expression, locate the Expression section.
3
In the Expression text field, type mfnc.normB.
4
Locate the Coloring and Style section. Clear the Color legend checkbox.
5
From the Color table transformation list, choose Nonlinear.
6
In the Color calibration parameter text field, type -0.8.
7
In the 3D Magnetic Flux Density toolbar, click  Plot.
8
Click the  Transparency button in the Graphics toolbar.
Compare the 3D magnetic flux density plot with the figure below.
Create a new stationary study with its own parametric sweep over the parameter n_segments. This allows for a comparison of how the number of segments changes the magnetic field.
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 the Add Study button in the window toolbar.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 2 - Number of Segments Sweep
1
In the Settings window for Study, type Study 2 - Number of Segments Sweep in the Label text field.
2
Locate the Study Settings section. Clear the Generate default plots checkbox.
Parametric Sweep
1
In the Study toolbar, click  Parametric Sweep.
2
In the Settings window for Parametric Sweep, locate the Study Settings section.
3
Click  Add.
4
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
n_segments (Number of magnet segments)
8 16 24 32
 
Keep in mind that the number of segments is constrained such that n_segments*add_angle is an integer multiple of 360 degrees. This is to make sure a full rotation around the rotor results in the magnetization vector returning to its original orientation.
5
In the Study toolbar, click  Compute.
Results
Create a new cut plane for the new parametric sweep.
Cut Plane - Number of Segments Sweep
1
In the Results toolbar, click  Cut Plane.
2
In the Settings window for Cut Plane, type Cut Plane - Number of Segments Sweep in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 2 - Number of Segments Sweep/Parametric Solutions 2 (sol9).
4
Locate the Plane Data section. From the Plane list, choose xy-planes.
Magnetic Flux Density, Number of Segments Sweep
1
In the Model Builder window, right-click Magnetic Flux Density, Additional Angle Sweep and choose Duplicate.
2
In the Settings window for 2D Plot Group, type Magnetic Flux Density, Number of Segments Sweep in the Label text field.
3
Locate the Data section. From the Dataset list, choose Cut Plane - Number of Segments Sweep.
4
In the Magnetic Flux Density, Number of Segments Sweep toolbar, click  Plot.
Compare the magnetic flux densities corresponding to the different parameter values by clicking Plot Previous or Plot Next. Recreate the one-dimensional plot groups and the polar plot group for the new study.
Radial Magnetic Flux Density - Number of Segments Sweep
1
In the Model Builder window, right-click Radial Magnetic Flux Density and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Radial Magnetic Flux Density - Number of Segments Sweep in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 2 - Number of Segments Sweep/Parametric Solutions 2 (sol9).
4
Locate the Title section. In the Parameter indicator text field, type n_segments = eval(n_segments).
5
In the Radial Magnetic Flux Density - Number of Segments Sweep toolbar, click  Plot.
Compare the radial magnetic flux densities corresponding to the different parameter values by clicking Plot Previous or Plot Next.
Azimuthal Magnetic Flux Density - Number of Segments Sweep
1
In the Model Builder window, right-click Azimuthal Magnetic Flux Density and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Azimuthal Magnetic Flux Density - Number of Segments Sweep in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 2 - Number of Segments Sweep/Parametric Solutions 2 (sol9).
4
Locate the Title section. In the Parameter indicator text field, type n_segments = eval(n_segments).
5
In the Azimuthal Magnetic Flux Density - Number of Segments Sweep toolbar, click  Plot.
Compare the azimuthal magnetic flux densities corresponding to the different parameter values by clicking Plot Previous or Plot Next.
Magnetic Flux Density Norm - Number of Segments Sweep
1
In the Model Builder window, right-click Magnetic Flux Density Norm and choose Duplicate.
2
In the Settings window for Polar Plot Group, type Magnetic Flux Density Norm - Number of Segments Sweep in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 2 - Number of Segments Sweep/Parametric Solutions 2 (sol9).
4
Locate the Title section. In the Parameter indicator text field, type n_segments = eval(n_segments).
5
In the Magnetic Flux Density Norm - Number of Segments Sweep toolbar, click  Plot.
Look through the magnetic flux density norms for the different parameters and note how the difference between the inner and outer arcs changes. Compare the polar plot for n_segments=32 with the figure below.