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AC Contactor with Shading Coil
Introduction
An AC contactor is a particular type of magnetic switch device, which is activated by a primary coil fed by an alternating current. Unlike DC switches, such devices can suffer from a tendency to reopen when the AC current crosses zero. The addition of a shading coil that supports retarded induced currents with respect to those of the feeding coil makes it possible to always have a nonzero pulling force, thus providing a more stable closure.
This example studies the closing dynamics of an AC contactor and consequent establishing of a mechanical contact. The changing distance between the moving and stationary parts of the device has an influence on the distribution of the magnetic field. This effect is accounted for using a moving mesh in the surrounding air. The model is set up using the Magnetomechanics multiphysics interface.
Model Definition
Figure 1 shows a cross section of the geometry of the device.
Figure 1: Full geometry of the contactor. The primary coil is shown in red, the shading coil is shown in black, the copper contacts are shown in orange, the iron core is shown in blue, and the plastic parts are shown in yellow.
The fixed part of the iron core is winded by the primary feeding coil, which together can act as a strong electric magnet that will pull down the moving part of the iron core. The moving part is suspended on springs known as return springs. When there is no current through the main coil, the return springs will keep the device opened. The electrical contact is made of copper and is split up into fixed parts, as well as a part that is attached to the moving part of the core. It is attached by another spring called the contact spring. The initial gap between the electrical contact parts is smaller than that between the iron pieces. When the core becomes fully closed, the contact spring will be slightly extended, thus providing an extra pulling force to keep the electrical contact closed.
The primary coil is fed by an AC voltage of 48 V at 50 Hz. Two shading coils (rings) made of aluminum are embedded into the side limbs of the fixed part of the iron core. The current induced in the shading coils will have a phase shift with respect to that in the primary coil. This will provide some pulling magnetic force even when the current in the primary coil is close to zero, preventing the contactor from opening.
The core is made of soft iron with nonlinear magnetization properties as specified by the BH curve shown in Figure 2.
Figure 2: The BH curve for soft iron.
Because of the two-fold mirror symmetry of the geometry along the vertical axis, it is sufficient to model only one half of the device. This will reduce the time needed to solve the model. In addition, the magnetic field needs to be computed in the air surrounding the contactor. This can be done by creating a bounding box for the geometry, as shown in Figure 3.
Figure 3: Model geometry, when cut in half and including the bounding box.
To include the effect of the changing distance between the parts, when the upper part of the device is deflected by the magnetic field, you set up a moving mesh in a domain surrounding the moving part. This is shown in Figure 3. The mesh is free to deform inside that domain, and it can also slide on the symmetry cut boundaries.
For the structural mechanics problem, the magnetic field, and the moving mesh, symmetry conditions are used at the symmetry cut plane. This allows you to retrieve the solution for the full geometry by mirroring that of the half that is being modeled.
Results and Discussion
Figure 4 shows how the sizes of the two different air gaps evolve in time. Here, it is shown that the initial air gap in the central limb is larger than that between the electrical contacts, even though both become zero after extending the contact spring. Figure 5 instead shows the current in the primary coil, along with the corresponding induced current in the shading coil. Figure 6 and Figure 7 show the magnetic fields generated by each coil.
Figure 4: Air gap evolution for the closing switch.
Figure 5: Currents in the primary and shading coils.
Figure 6: Magnetic flux density and magnetic flux streamlines at t = 50 ms. The magnetic field is generated by the primary coil.
Figure 7: Magnetic flux density and magnetic flux streamlines at t = 38.5 ms. The magnetic field is due to the induced current in the shading coil.
Figure 8 shows the contact forces acting on the electrical contact and the central limb, as evaluated by the Global Variable Probes. By comparing with the air gap sizes in Figure 4, it can be noted that the contact force on the central limb continues to oscillate even after the two parts initially made contact, while the force on the electrical contact remains zero due to the contact spring. Finally, Figure 9 shows how the vertical component of the total pulling electromagnetic force evolves in time, as evaluated by the Force Calculation feature. Comparing with the previous plot, it can be seen that this pulling force corresponds to the contact force on the central limb. However, due to the shading coil, the device never reopens.
Figure 8: Mechanical contact force variation in time.
Figure 9: The total pulling electromagnetic force (recomputed for the full geometry).
Notes About the COMSOL Implementation
The model is set up using the Magnetomechanics multiphysics interface. When this interface is added to a model, one Solid Mechanics and one Magnetic Fields physics interface are automatically added, along with a Magnetomechanical Forces multiphysics coupling feature. Two moving-mesh-related nodes are also added automatically: a Deforming Domain and a Symmetry/Roller boundary condition.
The magnetic body and surface forces acting on the plate are applied automatically by the coupling feature on its selection. Later on in the modeling, you will also add a Force Calculation node under the Magnetic Fields physics interface. This node is only used in postprocessing for computing the total force acting on the plate.
Model the return springs by using a Spring Foundation feature in the domain representing the moving part of the core. For the contact spring, use a special Spring-Damper feature that connects the moving part of the electrical contact with the plastic cover attached to the moving core.
Use an offset on the mechanical Contact feature to prevent the complete closing of the air gaps, because such a change in the topology would be incompatible with the moving mesh in the air gaps. Furthermore, since the mesh will be more and more distorted when the gaps are closing, you need to activate the automatic remeshing option on the study step node.
Application Library path: Structural_Mechanics_Module/Magnetomechanics/contactor_shading_coil
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 Structural Mechanics>Electromagnetics-Structure Interaction>Magnetomechanics>Magnetomechanics.
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Time Dependent.
6
Click  Done.
First, define some parameters that are used when creating 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
em_w
100[mm]
0.1 m
Width, electromagnet
em_h
60[mm]
0.06 m
Height, electromagnet
core_w
20[mm]
0.02 m
Width, core
pl_h
30[mm]
0.03 m
Height, plunger
plunger_travel
6[mm]
0.006 m
Total stroke, plunger
N
500
500
Number of turns, primary coil
d
1.35[N*s/m]
1.35 N·s/m
Damping constant, return spring
kr
24.2[N/m]
24.2 N/m
Spring constant, return spring
l0
plunger_travel*0.1
6E-4 m
Undeformed length, contact spring
op
plunger_travel*0.7
0.0042 m
Opening, electrical contact
dc
2.7[mm]
0.0027 m
Diameter, shading coil
kc
255[N/m]
255 N/m
Spring constant, contact spring
c
7[N*s/m]
7 N·s/m
Damping coefficient, contact spring
Now, start building the geometry of the model.
Geometry 1
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, locate the Units section.
3
From the Length unit list, choose mm.
Rectangle 1 (r1)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type em_w/2.
4
In the Height text field, type em_h.
Rectangle 2 (r2)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type em_w/2.
4
In the Height text field, type pl_h.
5
Locate the Position section. In the y text field, type em_h.
Rectangle 3 (r3)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type (em_w-2*core_w)/2.
4
In the Height text field, type em_h+pl_h -core_w.
5
Locate the Position section. In the x text field, type core_w/2.
6
In the y text field, type core_w/2.
Difference 1 (dif1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Difference.
2
Select the objects r1 and r2 only.
3
In the Settings window for Difference, locate the Difference section.
4
Find the Objects to subtract subsection. Click to select the  Activate Selection toggle button.
5
Select the object r3 only.
Split 1 (spl1)
1
In the Geometry toolbar, click  Conversions and choose Split.
2
Select the object dif1 only.
Rectangle 4 (r4)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 20.
4
In the Height text field, type 44.
5
Locate the Position section. In the x text field, type 12.
6
In the y text field, type 12.
Rectangle 5 (r5)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 50.
4
In the Height text field, type 5.
5
Locate the Position section. In the y text field, type 90.
Rectangle 6 (r6)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 10.
4
In the Height text field, type 20.
5
Locate the Position section. In the y text field, type 95.
Rectangle 7 (r7)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 24.
4
In the Height text field, type 3.
5
Locate the Position section. In the y text field, type 115.
6
Click to expand the Layers section. Select the Layers to the left check box.
7
Clear the Layers on bottom check box.
8
In the table, enter the following settings:
Layer name
Thickness (mm)
Layer 1
10
Rectangle 8 (r8)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 6.
4
Locate the Position section. In the x text field, type 18.
5
In the y text field, type 114.
Rectangle 9 (r9)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 6.
4
Locate the Position section. In the x text field, type 18.
5
In the y text field, type 113.
Rectangle 10 (r10)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 40.
4
In the Height text field, type 3.
5
Locate the Position section. In the x text field, type 18.
6
In the y text field, type 110.
Move 1 (mov1)
1
In the Geometry toolbar, click  Transforms and choose Move.
2
In the Settings window for Move, locate the Displacement section.
3
In the y text field, type l0.
4
Select the objects r10, r7, r8, and r9 only.
Move 2 (mov2)
1
In the Geometry toolbar, click  Transforms and choose Move.
2
In the Settings window for Move, locate the Displacement section.
3
In the y text field, type plunger_travel.
4
Select the objects mov1(1), mov1(2), mov1(3), mov1(4), r5, r6, and spl1(2) only.
Move 3 (mov3)
1
In the Geometry toolbar, click  Transforms and choose Move.
2
In the Settings window for Move, locate the Displacement section.
3
In the y text field, type -op.
4
Select the objects mov2(1) and mov2(4) only.
Fillet 1 (fil1)
1
In the Geometry toolbar, click  Fillet.
2
In the Settings window for Fillet, locate the Radius section.
3
In the Radius text field, type core_w*0.1.
4
On the object mov2(7), select Points 3, 5, and 7 only.
5
On the object spl1(1), select Points 4, 6, and 8 only.
Fillet 2 (fil2)
1
In the Geometry toolbar, click  Fillet.
2
In the Settings window for Fillet, locate the Radius section.
3
In the Radius text field, type 1.
4
On the object mov2(3), select Points 1 and 2 only.
5
On the object mov3(2), select Points 3 and 4 only.
To finish the building of the geometry, set up a bounding box for it, which will define the surrounding air domains.
Rectangle 11 (r11)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 3*em_w/2.
4
In the Height text field, type 3*em_w.
5
Locate the Position section. In the y text field, type -em_w.
Next, define domains representing the shading coil cross section.
Rectangle 12 (r12)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type dc.
4
In the Height text field, type 2.
5
Locate the Position section. From the Base list, choose Center.
6
In the x text field, type 44.
7
In the y text field, type 59.
8
Locate the Layers section. Clear the Layers on bottom check box.
9
Select the Layers to the right check box.
10
Select the Layers to the left check box.
11
In the table, enter the following settings:
Layer name
Thickness (mm)
Layer 1
0.8
Delete Entities 1 (del1)
1
In the Model Builder window, right-click Geometry 1 and choose Delete Entities.
2
On the object r12, select Boundary 5 only.
Finally, define a domain where the moving mesh will be used.
Rectangle 13 (r13)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 58.
4
In the Height text field, type 90.
5
Locate the Position section. In the y text field, type 50.
6
Click  Build All Objects.
In order to treat the boundaries that start off separated but eventually come into contact, create two contact pairs. One of them is for the copper electrical contact, while the other one is for the iron pieces in the core.
Definitions
Contact Pair 1 (p1)
1
In the Definitions toolbar, click  Pairs and choose Contact Pair.
2
Select Boundaries 44, 78, and 80 only.
3
In the Settings window for Pair, locate the Destination Boundaries section.
4
Click to select the  Activate Selection toggle button.
5
Select Boundaries 45, 79, and 81 only.
6
Locate the Advanced section. From the Search distance list, choose Manual.
7
In the Distance text field, type 6.
Contact Pair 2 (p2)
1
In the Definitions toolbar, click  Pairs and choose Contact Pair.
2
Select Boundaries 8, 55, 59, 61, 64, 66, 76, 82, and 84 only.
3
In the Settings window for Pair, locate the Destination Boundaries section.
4
Click to select the  Activate Selection toggle button.
5
Select Boundaries 10, 56, 77, 83, and 85 only.
6
Locate the Advanced section. From the Search distance list, choose Manual.
7
In the Distance text field, type 6.
In order to account for the distance between the parts decreasing, moving mesh functionality will be used.
Moving Mesh
Deforming Domain 1
1
In the Model Builder window, under Component 1 (comp1)>Moving Mesh click Deforming Domain 1.
2
Select Domain 4 only.
Symmetry/Roller 1
1
In the Model Builder window, click Symmetry/Roller 1.
2
Select Boundaries 7, 15, 19, 72, and 74 only.
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
Right-click and choose Add to Component 1 (comp1).
5
In the tree, select AC/DC>Soft Iron (Without Losses).
6
Right-click and choose Add to Component 1 (comp1).
Materials
Soft Iron (Without Losses) (mat2)
1
In the Model Builder window, under Component 1 (comp1)>Materials click Soft Iron (Without Losses) (mat2).
2
Select Domains 2, 3, 5, and 16 only.
Add Material
1
Go to the Add Material window.
2
In the tree, select Built-in>Copper.
3
Right-click and choose Add to Component 1 (comp1).
Materials
Copper (mat3)
1
In the Model Builder window, under Component 1 (comp1)>Materials click Copper (mat3).
2
Select Domains 8, 10, and 13–15 only.
Add Material
1
Go to the Add Material window.
2
In the tree, select Built-in>Acrylic plastic.
3
Right-click and choose Add to Component 1 (comp1).
Materials
Acrylic plastic (mat4)
1
In the Model Builder window, under Component 1 (comp1)>Materials click Acrylic plastic (mat4).
2
Select Domains 6 and 7 only.
Add Material
1
Go to the Add Material window.
2
In the tree, select Built-in>Aluminum.
3
Right-click and choose Add to Component 1 (comp1).
4
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Aluminum (mat5)
Select Domains 17 and 18 only.
Now, it is time to add the physics to the model, using the Solid Mechanics interface and the Magnetic Fields interface. Both of these were added automatically when the multiphysics coupling was added.
Solid Mechanics (solid)
1
In the Model Builder window, under Component 1 (comp1) click Solid Mechanics (solid).
2
In the Settings window for Solid Mechanics, locate the Thickness section.
3
In the d text field, type 30[mm].
4
Select Domains 2, 3, 5–8, 10, and 13–18 only.
Fixed Constraint 1
1
In the Physics toolbar, click  Boundaries and choose Fixed Constraint.
2
Select Boundaries 4, 41, and 73 only.
Spring Foundation 1
1
In the Physics toolbar, click  Domains and choose Spring Foundation.
2
Select Domain 5 only.
3
In the Settings window for Spring Foundation, locate the Spring section.
4
From the Spring type list, choose Total spring constant.
5
In the ktot text field, type kr.
6
Click to expand the Viscous Damping section. From the Damping type list, choose Total damping constant.
7
In the dtot text field, type d.
Roller 1
1
In the Physics toolbar, click  Boundaries and choose Roller.
2
Select Boundaries 47, 67, 68, 70, and 71 only.
Attachment 1
1
In the Physics toolbar, click  Boundaries and choose Attachment.
2
Select Boundary 18 only.
Attachment 2
1
In the Physics toolbar, click  Boundaries and choose Attachment.
2
Select Boundary 16 only.
Spring-Damper 1
1
In the Physics toolbar, click  Global and choose Spring-Damper.
2
In the Settings window for Spring-Damper, locate the Attachment Selection section.
3
From the Source list, choose Attachment 1.
4
From the Destination list, choose Attachment 2.
5
Locate the Spring-Damper section. In the k text field, type kc.
6
In the c text field, type c.
Symmetry 1
1
In the Physics toolbar, click  Boundaries and choose Symmetry.
2
Select Boundaries 3, 5, 9, 11, 13, and 17 only.
Contact 1
1
In the Model Builder window, click Contact 1.
2
In the Settings window for Contact, click to expand the Contact Surface Offset and Adjustment section.
3
In the doffset,d text field, type 0.05[mm].
Magnetic Fields (mf)
1
In the Model Builder window, under Component 1 (comp1) click Magnetic Fields (mf).
2
In the Settings window for Magnetic Fields, locate the Thickness section.
3
In the d text field, type 30[mm].
Ampère’s Law 2, Iron
1
In the Physics toolbar, click  Domains and choose Ampère’s Law.
2
In the Settings window for Ampère’s Law, type Ampère's Law 2, Iron in the Label text field.
3
Select Domains 2, 3, 5, and 16 only.
4
Locate the Material Type section. From the Material type list, choose Solid.
5
Locate the Constitutive Relation B-H section. From the Magnetization model list, choose B-H curve.
Ampère’s Law 3, Air
1
In the Physics toolbar, click  Domains and choose Ampère’s Law.
2
In the Settings window for Ampère’s Law, type Ampère's Law 3, Air in the Label text field.
3
Select Domains 1, 4, and 9 only.
Coil 1, primary
1
In the Physics toolbar, click  Domains and choose Coil.
2
In the Settings window for Coil, type Coil 1, primary in the Label text field.
3
Select Domains 11 and 12 only.
4
Locate the Coil section. From the Conductor model list, choose Homogenized multiturn.
5
From the Coil excitation list, choose Voltage.
6
In the Vcoil text field, type 48[V]*sin(2*pi*50[Hz]*t)/2.
7
Locate the Homogenized Multiturn Conductor section. In the N text field, type N.
8
From the Coil wire cross-section area list, choose From round wire diameter.
9
In the dcoil text field, type 1.5[mm].
Coil 2, shading
1
In the Physics toolbar, click  Domains and choose Coil.
2
In the Settings window for Coil, type Coil 2, shading in the Label text field.
3
Select Domains 17 and 18 only.
4
Locate the Material Type section. From the Material type list, choose Solid.
5
Locate the Coil section. In the Icoil text field, type 0[A].
Magnetic Insulation 2
1
In the Physics toolbar, click  Boundaries and choose Magnetic Insulation.
2
Select Boundaries 18, 20, 33, 34, 40, 41, 44–47, 73, and 78–81 only.
Symmetry Plane 1
1
In the Physics toolbar, click  Boundaries and choose Symmetry Plane.
2
Select Boundaries 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, and 21 only.
Finally, the selection for the multiphysics coupling between the two physics interfaces needs to be specified.
Multiphysics
Magnetomechanical Forces 1 (mmf1)
1
In the Model Builder window, under Component 1 (comp1)>Multiphysics click Magnetomechanical Forces 1 (mmf1).
2
Select Domains 2, 3, 5, and 16–18 only.
Materials
Acrylic plastic (mat4)
1
In the Model Builder window, under Component 1 (comp1)>Materials click Acrylic plastic (mat4).
2
In the Settings window for Material, locate the Material Contents section.
3
In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electrical conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0
S/m
Basic
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
3.5
1
Basic
Soft Iron (Without Losses) (mat2)
1
In the Model Builder window, click Soft Iron (Without Losses) (mat2).
2
In the Settings window for Material, locate the Material Contents section.
3
In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Young’s modulus
E
204e9
Pa
Young’s modulus and Poisson’s ratio
Poisson’s ratio
nu
0.39
1
Young’s modulus and Poisson’s ratio
Density
rho
7840
kg/m³
Basic
In order to show the results during the computation, prepare some probes. The first two of these are point probes, which are placed in the air gaps between the electrical contact and the core, where they evaluate certain variables.
Definitions
Air gap, electrical contact
1
In the Definitions toolbar, click  Probes and choose Point Probe.
2
In the Settings window for Point Probe, type Air gap, electrical contact in the Label text field.
3
In the Variable name text field, type gap_p1.
4
Select Point 30 only.
5
Locate the Expression section. In the Expression text field, type solid.gap_p1.
6
Select the Description check box. In the associated text field, type Electrical contact air gap.
7
Click to expand the Table and Window Settings section. Click  Add Plot Window.
Air gap, central limb
1
Right-click Air gap, electrical contact and choose Duplicate.
2
In the Settings window for Point Probe, type Air gap, central limb in the Label text field.
3
In the Variable name text field, type gap_p2.
4
Select Point 4 only.
5
Locate the Expression section. In the Expression text field, type solid.gap_p2.
6
In the Description text field, type Central limb air gap.
Contact force, electrical contact
1
In the Definitions toolbar, click  Probes and choose Global Variable Probe.
2
In the Settings window for Global Variable Probe, type Contact force, electrical contact in the Label text field.
3
In the Variable name text field, type T_toty_p1.
4
Locate the Expression section. In the Expression text field, type solid.dcnt1.T_toty_p1*(solid.dcnt1.T_toty_p1<500[N])+500[N]*(solid.dcnt1.T_toty_p1>500[N]).
5
Select the Description check box. In the associated text field, type Contact force, electrical contact.
6
Click to expand the Table and Window Settings section. Click  Add Plot Window.
Contact force, central limb
1
Right-click Contact force, electrical contact and choose Duplicate.
2
In the Settings window for Global Variable Probe, type Contact force, central limb in the Label text field.
3
In the Variable name text field, type T_toty_p2.
4
Locate the Expression section. In the Description text field, type Contact force, central limb.
5
In the Expression text field, type solid.dcnt1.T_toty_p2*(solid.dcnt1.T_toty_p2<500[N])+500[N]*(solid.dcnt1.T_toty_p2>500[N]).
Integration 1 (intop1)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
Select Domain 18 only.
Total current, coil
1
In the Definitions toolbar, click  Probes and choose Global Variable Probe.
2
In the Settings window for Global Variable Probe, type I_coil in the Variable name text field.
3
In the Label text field, type Total current, coil.
4
Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Magnetic Fields>Coil parameters>mf.ICoil_1 - Coil current - A.
5
Locate the Table and Window Settings section. Click  Add Plot Window.
Total current, shading coil
1
Right-click Total current, coil and choose Duplicate.
2
In the Settings window for Global Variable Probe, type I_shading_coil in the Variable name text field.
3
In the Label text field, type Total current, shading coil.
4
Locate the Expression section. In the Expression text field, type intop1(abs(mf.Jz)).
5
Select the Description check box. In the associated text field, type Shading coil current (absolute value).
Study 1
Step 1: Time Dependent
1
In the Model Builder window, under Study 1 click Step 1: Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
From the Time unit list, choose ms.
4
In the Output times text field, type range(0,0.2,20) range(20.5,0.5,50).
5
Click to expand the Study Extensions section. Select the Automatic remeshing check box.
6
In the Study toolbar, click  Show Default Plots.
Results
Stress (solid)
Set up a dataset to visualize the results for the full geometry. Since only half of the geometry was modeled due to the symmetry, a mirror operation is required to retrieve the full model. Also, create a view that can be used for the different plots.
Mirror 2D 1
1
In the Model Builder window, expand the Results>Datasets node.
2
Right-click Results>Datasets and choose More 2D Datasets>Mirror 2D.
3
In the Settings window for Mirror 2D, locate the Data section.
4
From the Dataset list, choose Study 1/Remeshed Solution 1 (sol2).
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
Select the Lock axis check box.
Axis
1
In the Model Builder window, expand the View 1 node, then click Axis.
2
In the Settings window for Axis, locate the Axis section.
3
In the x minimum text field, type -90.
4
In the x maximum text field, type 90.
5
In the y minimum text field, type -20.
6
In the y maximum text field, type 160.
Also, set up the plots and the study so that the full contactor is shown when solving.
Results
Magnetic Flux Density Norm (mf)
1
In the Model Builder window, under Results click Magnetic Flux Density Norm (mf).
2
In the Settings window for 2D Plot Group, locate the Data section.
3
From the Dataset list, choose Mirror 2D 1.
4
Locate the Plot Settings section. From the View list, choose View 1.
Study 1
Step 1: Time Dependent
1
In the Model Builder window, expand the Study 1>Solver Configurations node, then click Study 1>Step 1: Time Dependent.
2
In the Settings window for Time Dependent, click to expand the Results While Solving section.
3
Select the Plot check box.
4
From the Plot group list, choose Magnetic Flux Density Norm (mf).
5
In the Home toolbar, click  Compute.
Results
Air Gap
1
In the Model Builder window, under Results click Probe Plot Group 4.
2
In the Settings window for 1D Plot Group, type Air Gap in the Label text field.
Probe Table Graph 1
1
In the Model Builder window, expand the Air Gap node, then click Probe Table Graph 1.
2
In the Settings window for Table Graph, click to expand the Legends section.
3
From the Legends list, choose Manual.
4
In the table, enter the following settings:
Legends
Air gap, electrical contact (mm)
Air gap, central limb (mm)
Contact Force
1
In the Model Builder window, under Results click Probe Plot Group 5.
2
In the Settings window for 1D Plot Group, type Contact Force in the Label text field.
Coil Current
1
In the Model Builder window, under Results click Probe Plot Group 6.
2
In the Settings window for 1D Plot Group, type Coil Current in the Label text field.
Calculate the total electromagnetic force acting on the moving part, by adding a Force Calculation feature to the model. This feature is only used for postprocessing.
Magnetic Fields (mf)
Force Calculation, for Postprocessing
1
In the Physics toolbar, click  Domains and choose Force Calculation.
2
In the Settings window for Force Calculation, type Force Calculation, for Postprocessing in the Label text field.
3
Select Domain 5 only.
Study 1
In the Study toolbar, click  Update Solution.
Results
1D Plot Group 7
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
Global 1
Right-click 1D Plot Group 7 and choose Global.
Total Electromagnetic Force
1
In the Settings window for 1D Plot Group, type Total Electromagnetic Force in the Label text field.
2
Locate the Data section. From the Dataset list, choose Study 1/Remeshed Solution 1 (sol2).
3
Locate the Legend section. Clear the Show legends check box.
Global 1
1
In the Model Builder window, click Global 1.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
2*mf.Forcey_0
N
Total electromagnetic force, y component
4
In the Total Electromagnetic Force toolbar, click  Plot.
Contact Force, Electrical Contact
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Contact Force, Electrical Contact in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 1/Remeshed Solution 1 (sol2).
4
From the Time selection list, choose Interpolated.
5
In the Times (ms) text field, type range(15,0.2,50).
6
Locate the Legend section. Clear the Show legends check box.
Global 1
1
Right-click Contact Force, Electrical Contact and choose Global.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Definitions>T_toty_p1 - Contact force, electrical contact - N.
3
In the Contact Force, Electrical Contact toolbar, click  Plot.