models.acdc.magnetic damping

7/27/2019 Models.acdc.Magnetic Damping

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Solved with COMSOL Multiphysics 4.3b

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

Magne t i c Damp i n g o f V i b r a t i n g

Condu c t i n g S o l i d s

Introduction

When a conductive solid material moves through a static magnetic field, an eddy

current is induced. The current that flows through the conductor, which is itself

moving through the magnetic field, induces a Lorentz force back on the solid.Therefore, a conducting solid that is vibrating in a static magnetic field will experience

a structural damping.

This example computes the effect on the magnetic field when a cantilever beam is

harmonically excited across a range of frequencies and placed in a strong magnetic

field. The approach presented here assumes that the relative magnitude of the

structural displacements are small, that the material has isotropic and linear properties,

and that the magnetic field is static.

Note: This model requires the AC/DC Module and either the Structural Mechanics

Module or the MEMS Module.


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Wire

Cantileverbeam

Current

Magnetic field


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

Figure 1: A vibrating beam next to a current carrying wire experiences magneticdamping.

Model Definition

For a solid material experiencing a time-harmonic forced excitation, the displacementfield is of the form

which can also be written in the frequency domain as a phasor:

Thus, the velocity field is given by

Next, consider the effect of a spatially non-uniform but static magnetic field, B(r).

Under the assumption that the local displacements are small enough so that each

u r t,( ) u r( ) t( )sin=

u r t,( ) Re u

r( )eit

( )=

v r t,( ) Re iu

r( )eit

( )=


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moving point in the solid sees only the magnetic field in the undeformed state, the

induced current density is given by

where is the material conductivity. The body forces experienced by a

current-carrying domain moving through a magnetic field are given by

These body forces can be applied to the frequency domain structural mechanics

problem and act as a damping on the system.

This model first computes the static magnetic field due to a current-carrying wire

which is next to an aluminum beam. In the second solution step, the beam experiences

a forced harmonic vibration. The strength of the magnetic field is varied, and the effect

of the magnetic damping on the response of the system is observed.

Results and Discussion

Figure 2shows the magnetic field computed for the structure at rest. Figure 3displays

the magnitude of the displacement of the tip of the beam versus excitation frequency

for two different magnetic field intensities for the frequency-domain structural

dynamics problem. The magnetic field provides significant additional damping.

Figure 4plots the body forces due to the induced currents.

Ji

v B r( )=

FB

Ji

B r( )=


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Figure 2: The magnetic field around a current carrying wire.

Figure 3: Displacement of the tip of the beam versus excitation frequency for differingmagnetic field strengths.


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Figure 4: The body forces on the beam due to the induced currents.

Notes About the COMSOL Implementation

Solve this model with two physics interfaces: Magnetic and Electric Fields and Solid

Mechanics. Use a Stationary study for the Magnetic and Electric Fields and a

Frequency Domain study for Solid Mechanics.

Model Library path:ACDC_Module/Motors_and_Actuators/magnetic_damping

Modeling Instructions

M O D E L W I Z A R D

1 Go to the Model Wizardwindow.

2 Click Next.

3 In the Add physicstree, select AC/DC>Magnetic and Electric Fields (mef).

4 Click Add Selected.


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5 In the Add physicstree, select Structural Mechanics>Solid Mechanics (solid).

6 Click Add Selected.

7 Click Next.

8 Find the Studiessubsection. In the tree, select Custom Studies>Empty Study.

9 Click Finish.

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:

You will use the applied current as a sweep parameter later.

G E O M E T R Y 1

Block 1

First, create a block for the simulation domain.

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

Block 2

Add a block describing the cantilever beam.

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

2 In the Blocksettings window, locate the Size and Shapesection.

3 In the Widthedit field, type 0.9.

4 In the Depthedit field, type0.025

.5 In the Heightedit field, type 0.1.

6 Locate the Positionsection. In the yedit field, type 0.575.

7 In the zedit field, type 0.45.

Cylinder 1

Next, add a cylinder for the wire generating the static magnetic field.

Name Expression Description

sigma 3.774e7[S/m] Material conductivity

a_c 50000[A] Applied current on the wire


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1 Right-click Geometry 1and choose Cylinder.

2 In the Cylindersettings window, locate the Size and Shapesection.

3 In the Radiusedit field, type 0.05.

4 Locate the Positionsection. In the xedit field, type 0.5.

5 In the yedit field, type 0.5.

6 Click the Build Allbutton.

7 Click the Wireframe Renderingbutton on the Graphics toolbar.

D E F I N I T I O N S

Add variables for the induced current density and body force on the cantilever beam.

Variables 1

1 In the Model Builderwindow, under Model 1right-click Definitionsand choose

Variables.

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

3 From the Geometric entity levellist, choose Domain.

4 Select Domain 2 only.


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5 Locate the Variablessection. In the table, enter the following settings:

Here, the mef.and solid.prefixes are for the physics interfaces Magnetics and

Electric Fields and Solid Mechanics, respectively.

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

Ampre's Law 11 In the Model Builderwindow, right-click Magnetic and Electric Fieldsand choose

Ampre's Law.

2 Select Domains 1 and 2 only.

Name Expression DescriptionJi_x sigma*(solid.u_tY*mef.B

z-solid.u_tZ*mef.By)

Induced current density,

x-component

Ji_y sigma*(solid.u_tZ*mef.B

x-solid.u_tX*mef.Bz)


y-component

Ji_z sigma*(solid.u_tX*mef.B

y-solid.u_tY*mef.Bx)


z-component

F_B_x Ji_y*mef.Bz-Ji_z*mef.By Body force, x-component

F_B_y Ji_z*mef.Bx-Ji_x*mef.Bz Body force, y-component

F_B_z Ji_x*mef.By-Ji_y*mef.Bx Body force, z-component


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Magnetic Insulation 2

1 Right-click Magnetic and Electric Fieldsand choose Magnetic Insulation.

2 Select Boundaries 13 and 14 only.

Ground 1

1 Right-click Model 1>Magnetic and Electric Fields>Magnetic Insulation 2and choose

Ground.

2 Select Boundary 13 only.

Terminal 1

1 Right-click Magnetic Insulation 2and choose Terminal.


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3 In the Terminalsettings window, locate the Terminalsection.

4 In the I0edit field, type a_c.

S O L I D M E C H A N I C S

Solid Mechanics analyzes only the cantilever beam.

1 In the Model Builderwindow, under Model 1click Solid Mechanics.


Linear Elastic Material 1

Add a damping factor on Linear Elastic Material Model 1.

1 In the Model Builderwindow, expand the Solid Mechanicsnode.

Damping 1

2 Right-click Linear Elastic Material 1and choose Damping.

3 In the Dampingsettings window, locate the Damping Settingssection.

4 From the Damping typelist, choose Isotropic loss factor.

5 From the slist, choose User defined. In the associated edit field, type 0.1.

Fixed Constraint 1

1 In the Model Builderwindow, right-click Solid Mechanicsand choose Fixed Constraint.


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Boundary Load 1

1 Right-click Solid Mechanicsand choose Boundary Load.


3 In the Boundary Loadsettings window, locate the Forcesection.


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4 In the FAtable, enter the following settings:

Body Load 1

1 Right-click Solid Mechanicsand choose Body Load.


3 In the Body Loadsettings window, locate the Forcesection.

4 In the FVtable, enter the following settings:

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>Aluminum .

0 x1e4 y

0 z

F_B_x x

F_B_y y

F_B_z z


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3 Click Add Material to Model.

Aluminum

1 In the Model Builderwindow, under Model 1>Materialsclick Aluminum.

2 Select Domains 2 and 3 only.

Material Browser

1 In the Model Builderwindow, right-click Materialsand choose Open Material Browser.

2 In the Material Browsersettings window, In the tree, select Built-In>Air.3 Click Add Material to Model.

Air

1 In the Model Builderwindow, under Model 1>Materialsclick Air.


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M E S H 1

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

2 In the Meshsettings window, locate the Mesh Settingssection.

3 From the Element sizelist, choose Coarser.

S T U D Y 1

Parametric Sweep

1 In the Model Builderwindow, right-click Study 1and choose Parametric Sweep.

2 In the Parametric Sweepsettings window, locate the Study Settingssection.

3 Click Add.

4 In the table, enter the following settings:

Step 1: Stationar y

1 Right-click Study 1and choose Study Steps>Stationary.

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

3 Select the Modify physics tree and variables for study stepcheck box.

Parameter names Parameter value list

a_c 0[A] 50000[A]


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4 In the Physics and variables selectiontree, select Model 1>Solid Mechanics.

5 Click Disable.

Step 2: Frequency Domain

1 Right-click Study 1and choose Study Steps>Frequency Domain.

2 In the Frequency Domainsettings window, locate the Study Settingssection.

3 In the Frequenciesedit field, type range(5,0.5,50).

4 In the Model Builderwindow, click Step 2: Frequency Domain.

5 In the Frequency Domainsettings window, locate the Physics and Variables Selection

section.

6 Select the Modify physics tree and variables for study stepcheck box.

7 In the Physics and variables selectiontree, select Model 1>Magnetic and Electric Fields.

8 Click Provide Degrees of Freedom.

9 In the Model Builderwindow, right-click Study 1and choose Compute.

R E S U L T S

Magnetic Flux Density Norm (mef)

The first default plot group shows the he magnetic field around a current carrying

wire; compare with Figure 2.


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Stress (solid)

The second default plot shows the von Mises stress.

3D Plot Group 3

Add a third plot group with an arrow plot of the body force on the cantilever beam

(Figure 4).

1 In the Model Builderwindow, right-click Resultsand choose 3D Plot Group.2 Right-click 3D Plot Group 3and choose Arrow Volume.

3 In the Arrow Volumesettings window, locate the Expressionsection.

4 In the X componentedit field, type F_B_x.

5 In the Y componentedit field, type F_B_y.

6 In the Z componentedit field, type F_B_z.

7 Locate the Arrow Positioningsection. Find the X grid pointssubsection. In the Pointsedit field, type 40.

8 Find the Y grid pointssubsection. In the Pointsedit field, type 40.

9 Find the Z grid pointssubsection. In the Pointsedit field, type 1.

10 Click the Plotbutton.

11 Click the Zoom Inbutton on the Graphics toolbar.


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1D Plot Group 4

Finish by adding the displacement plot of the tip of the beam.

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

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

3 From the Data setlist, choose Solution 3.

4 Click to expand the Axissection. Select the y-axis log scalecheck box.

5 Right-click Results>1D Plot Group 4and choose Point Graph.

6 Select Point 18 only.

7 In the Point Graphsettings window, click Replace Expressionin the upper-right

corner of the y-Axis Datasection. From the menu, choose Solid

Mechanics>Displacement>Displacement, RMS (solid.disp_rms).

8 Click to expand the Legendssection. Select the Show legendscheck box.

9 Click the Plotbutton.

Compare the resulting plot with that shown in Figure 3.


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