Induced Voltage Moving Magnet

5/25/2018 Induced Voltage Moving Magnet

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Solved with COMSOL Multiphysics 4.3b

2 0 1 3 C O M S O L 1 | V O L TA G E I N D U C E D I N A C O I L B Y A M O V I N G M A G N E T

V o l t a g e I n du c e d i n a C o i l b y a

Mov i n g Magn e t

Introduction

A magnet moving axially through the center of a coil will induce a voltage across the

coil terminals. A practical application of this phenomenon is in shaker flashlights,

where the flashlight is vigorously shaken back and forth, thereby causing a magnet tomove through a multi-turn coil, which provides charge to the battery. This example

models the motion of a magnet through a coil and computes the induced voltages. The

displacement of the magnet is significant, so the model uses a moving and sliding

mesh.

Oscillating magnet

Multi-turn coil

Figure 1: Drawing showing a sinusoidally oscillating magnet and a multi-turn coil.

Model Definition

Figure 1illustrates the system setup, in which a magnet of strength 1.2 T is displaced

sinusoidally at 4 Hz with a peak displacement of 30 mm inside of an 800 turn coil.

This results in a 2D axisymmetric problem, where the modeling space is a rectangular

region in the rz-plane bounded by the Magnetic Insulation boundary condition,

which represents a metallic enclosure.


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2 | V O L T A G E I N D U C E D I N A C O I L B Y A M O V I N G M A G N E T 2 0 1 3 C O M S O L

Both the magnet and the multi-turn coil domains are represented by rectangles. The

magnet and coil corners are not rounded off, which leads to a simpler mesh and smaller

problem size. Although the sharp corners do introduce local singularities into themagnetic fields, it is not a concern for this type of model, whose single objective is to

determine the induced voltage across the coil. This voltage is computed by taking the

integral of the fields over the domains, which is quite insensitive to singularities in the

fields. The corners of these domains only need to be rounded if forces and field

strengths around the corners are of interest.

To define the displacement of the magnet and the surrounding air domains, the model

uses the moving mesh functionality. Because neither the coil nor the air domain

surrounding it needs to deform, it is sufficient to define the Moving Mesh physics in

the magnet and the air domains above and below it.

When the domain movement is significant, it is warranted to use the sliding mesh

functionality, introducing additional steps into the model setup. When drawing the

geometry, the Form Assembly functionality must be used to finalize the geometry.

This feature assumes that all objects are disjoint, and automatically creates an Identity

Pair at the touching boundaries between objects. The Identity Pair is used to define a

Pair Continuity boundary condition in the Magnetic Fields physics, which specifies

that the fields be continuous across the noncongruent meshes. For higher accuracy, the

model uses weak constraints and a smaller mesh size at these boundaries.

Solve the model in two steps. First, a stationary analysis of just the magnetic fields

computes the fields due to the magnet at its starting location. This is needed to provide

correct initial conditions for the subsequent transient analysis of the magnetic fields

and the moving mesh. The tolerances are tightened slightly from their defaults.

Results and Discussion

Figure 2shows the magnetic field and the mesh after 0.2 s, slightly less than the period

of oscillation of the magnet, T= 0.25 s. The mesh is stretched and compressed in the

air domains above and below the magnet. Although the mesh is noncongruent at the

Identity Pair boundary, the Pair Continuity boundary condition ensures that thesolution is continuous.

Figure 3displays the induced voltage for the open circuit configuration of the coil.


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Figure 2: Magnetic flux density and deformed mesh at the bottom of the stroke of themagnet.

Figure 3: Induced voltage in the coil over time.


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Model Library path:ACDC_Module/Motors_and_Actuators/

induced_voltage_moving_magnet

Modeling Instructions

M O D E L W I Z A R D

1 Go to the Model Wizardwindow.2 Click the 2D axisymmetricbutton.

3 Click Next.

4 In the Add physicstree, select AC/DC>Magnetic Fields (mf).

5 Click Add Selected.

6 In the Add physicstree, select Mathematics>Deformed Mesh>Moving Mesh (ale).

7 Click Add Selected.

8 Click Next.

9 Find the Studiessubsection. In the tree, select Preset Studies for Selected

Physics>Stationary.

10 Click Finish.

Define the frequency of a oscillating magnet.

G L O B A L D E F I N I T I O N S

Parameters

1 In the Model Builderwindow, right-click Global Definitionsand choose Parameters.

2 In the Parameterssettings window, locate the Parameterssection.

3 In the table, enter the following settings:

G E O M E T R Y 1

1 In the Model Builderwindow, under Model 1click Geometry 1.

2 In the Geometrysettings window, locate the Unitssection.

Name Expression Description

f0 4[Hz] Frequency of an oscillating magnet

T0 1/f0 Time period of an oscillating magnet


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3 From the Length unitlist, choose cm.

Follow these instructions to construct the model geometry.

Rectangle 1

1 Right-click Model 1>Geometry 1and choose Rectangle.

2 In the Rectanglesettings window, locate the Sizesection.

3 In the Heightedit field, type 2.

4 Locate the Positionsection. In the zedit field, type -1.

5 Click the Build Selectedbutton.

Rectangle 2

1 In the Model Builderwindow, right-click Geometry 1and choose Rectangle.



4 Locate the Positionsection. In the redit field, type 1.1.

5 In the zedit field, type -4.


7 Click the Zoom Extentsbutton on the Graphics toolbar.

Rectangle 3

1 Right-click Geometry 1and choose Rectangle.


3 In the Heightedit field, type 12.4 Locate the Positionsection. In the zedit field, type -6.


6 Click the Zoom Extentsbutton on the Graphics toolbar.

Rectangle 4

1 Right-click Geometry 1and choose Rectangle.

2 In the Rectanglesettings window, locate the Sizesection.3 In the Widthedit field, type 3.


5 Locate the Positionsection. In the redit field, type 1.

6 In the zedit field, type -6.



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Form a union of a Rectangle 1and Rectangle 3.

Union 1

1 Right-click Geometry 1and choose Boolean Operations>Union.

2 Select the objects r1and r3only.


Next, form a union of a Rectangle 2and Rectangle 4.

Union 2

1 Right-click Geometry 1and choose Boolean Operations>Union.

2 Select the objects r4and r2only.


Finish the geometry creation by using an assembly.

Form Union

1 In the Model Builderwindow, under Model 1>Geometry 1click Form Union.

2 In the Finalizesettings window, locate the Finalizesection.3 In the Relative repair toleranceedit field, type 1e-6.

4 From the Finalization methodlist, choose Form an assembly.


The final geometry looks as shown in the figure above.


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D E F I N I T I O N S

Define boundary selections for the magnet and continuity pair.

Explicit 1

1 In the Model Builderwindow, right-click Definitionsand choose Selections>Explicit.

2 In the Explicitsettings window, locate the Input Entitiessection.

3 From the Geometric entity levellist, choose Boundary.

4 Select Boundaries 3, 4, 6, and 9 only.

5 Right-click Model 1>Definitions>Explicit 1and choose Rename.

6 Go to the Rename Explicitdialog box and type Magnet Boundariesin the New name

edit field.

7 Click OK.

Explicit 2

1 Right-click Definitionsand choose Selections>Explicit.

2 In the Explicitsettings window, locate the Input Entitiessection.


4 Select Boundaries 810 only.

5 Right-click Model 1>Definitions>Explicit 2and choose Rename.

6 Go to the Rename Explicitdialog box and type Continuity Boundariesin the New

nameedit field.


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7 Click OK.

Now, assign air for all the domains.

M A T E R I A L S

Material Browser

1 In the Model Builderwindow, under Model 1right-click Materialsand choose Open

Material Browser.

2 In the Material Browsersettings window, In the tree, select Built-In>Air.

3 In the Material_browserwindow, click Add Material to Model.

Now set up the physics for the magnetic field. Apply Ampres law in the magnet and

the air domain.

M A G N E T I C F I E L D S

Ampre's Law 2

1 In the Model Builderwindow, under Model 1right-click Magnetic Fieldsand chooseAmpre's Law.

2 Select Domain 2 only.

3 In the Ampre's Lawsettings window, locate the Magnetic Fieldsection.

4 From the Constitutive relationlist, choose Remanent flux density.


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5 In the Brtable, enter the following settings:

Next, add the Multi-Turn Coil Domain feature to model the coil.

Multi-Turn Coil 1

1 In the Model Builderwindow, right-click Magnetic Fieldsand choose Multi-Turn Coil.

2 Select Domain 5 only.

3 In the Multi-Turn Coilsettings window, locate the Multi-Turn Coilsection.

4 In the Nedit field, type 800.

5 In the acoiledit field, type pi*(0.5[mm])^2.

6 In the Icoiledit field, type 0.

7 In the Model Builderwindows toolbar, click the Showbutton and select AdvancedPhysics Optionsin the menu.

Add a continuity boundary condition and enable the weak constraints features.

Continuity 1

1 Right-click Magnetic Fieldsand choose Pairs>Continuity.

2 In the Continuitysettings window, locate the Pair Selectionsection.

0 r0 phi

1.2 z


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3 In the Pairslist, select Identity Pair 1.

4 Click to expand the Constraint Settingssection. Select the Use weak constraintscheck

box.

Magneti c Insulation 1

1 In the Model Builderwindow, expand the Continuity 1node, then click Magnetic

Insulation 1.

2 In the Magnetic Insulationsettings window, click to expand the Constraint Settings

section.

3 Select the Use weak constraintscheck box.Use the Moving Mesh physics interface only in the domains left to the continuity pair.

M O V I N G M E S H

1 In the Model Builderwindow, under Model 1click Moving Mesh.

2 In the Moving Meshsettings window, locate the Domain Selectionsection.

3 From the Selectionlist, choose Manual.

4 Select Domains 13 only.

Free Deformation 1

1 Right-click Model 1>Moving Meshand choose Free Deformation.

2 Select Domains 13 only.


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Prescribed Mesh Displacement 2

1 In the Model Builderwindow, right-click Moving Meshand choose Prescribed Mesh

Displacement.2 In the Model Builderwindow, click Prescribed Mesh Displacement 2.

3 In the Prescribed Mesh Displacementsettings window, locate the Boundary Selection

section.

4 From the Selectionlist, choose Magnet Boundaries.

5 Locate the Prescribed Mesh Displacementsection. In the dzedit field, type

30[mm]*sin(2*pi*f0*t).

Prescribed Mesh Displacement 3

1 In the Model Builderwindow, right-click Moving Meshand choose Prescribed Mesh

Displacement.

2 Select Boundaries 1, 5, 8, and 10 only.

3 In the Prescribed Mesh Displacementsettings window, locate the Prescribed Mesh

Displacementsection.

4 Clear the Prescribed z displacementcheck box.

M E S H 1

1 In the Model Builderwindow, under Model 1click Mesh 1.

2 In the Meshsettings window, locate the Mesh Settingssection.


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3 From the Element sizelist, choose Fine.

Size 1

1 Right-click Model 1>Mesh 1and choose Size.

2 In the Sizesettings window, locate the Geometric Entity Selectionsection.


4 From the Selectionlist, choose Continuity Boundaries.

5 Locate the Element Sizesection. Click the Custombutton.

6 Locate the Element Size Parameterssection. Select the Maximum element sizecheck

box.

7 In the associated edit field, type 3[mm].

Free Triangular 1

1 In the Model Builderwindow, right-click Mesh 1and choose Free Triangular.

2 In the Settingswindow, click Build All.

The mesh should look like that shown in the figure below.

S T U D Y 1

Step 1: Stationary

Solve for the Magnetic Fields physics only in the stationary case.

1 In the Model Builderwindow, under Study 1click Step 1: Stationary.


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2 In the Stationarysettings window, locate the Physics and Variables Selectionsection.

3 In the table, enter the following settings:

Now, add the Time Dependent study step and solve the problem in the time domain.

The Time Dependent study automatically takes the initial values for the vector

potential from the stationary solution.

Step 2: Time Dependent1 In the Model Builderwindow, right-click Study 1and choose Study Steps>Time

Dependent.

2 In the Time Dependentsettings window, locate the Study Settingssection.

3 In the Timesedit field, type range(0,T0/100,T0).

4 Select the Relative tolerancecheck box.

5 In the associated edit field, type 0.0001.

6 Right-click Study 1and choose Compute.

R E S U L T S

Magnetic Flux Density Norm (mf)

Use the following steps to generate a plot of the magnetic flux density norm and

deformed mesh as shown in Figure 2.

1 In the 2D Plot Groupsettings window, locate the Datasection.

2 From the Timelist, choose 0.2.

3 In the Model Builderwindow, right-click Magnetic Flux Density Norm (mf)and choose

Mesh.

4 In the Meshsettings window, locate the Colorsection.

5 From the Element colorlist, choose None.

6 From the Wireframe colorlist, choose White.

7 Click the Plotbutton.

Finally, reproduce the plot for an induced voltage in the coil.

1D Plot Group 3

1 In the Model Builderwindow, right-click Resultsand choose 1D Plot Group.

2 Right-click 1D Plot Group 3and choose Global.

Physics Solve for

Moving Mesh


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3 In the Globalsettings window, click Replace Expressionin the upper-right corner of

the y-Axis Datasection. From the menu, choose Magnetic Fields>Coil parameters>Coil

voltage (mf.VCoil_1).4 Click the Plotbutton.

5 In the Model Builderwindow, right-click 1D Plot Group 3and choose Rename.

6 Go to the Rename 1D Plot Groupdialog box and type Coil Induced Voltagein

the New nameedit field.

7 Click OK.

Compare the plot with Figure 3.

Documents

Induced Voltage Moving Magnet