Magnetostrictive Transducer 1

8/11/2019 Magnetostrictive Transducer 1

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Example:

Magnetostrictive Transducer


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Magnetostrictive Transducer

Steel housing

(for magnetic flux path)

Drive coil (homogenous

current carrying element)

Magnetostrictive rod

(active material)

Sectional view of a cylindrical transducer


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2D axial symmetry used to reduce computation time.

Non-linear constitutive relation between magnetostriction and

magnetic field is implemented. The material is assumed to be in

a pre-stressed state that would yield maximum magnetostriction.

Non-linear B-H curve is used to model realistic magnetic

behavior including saturation effect at high magnetic fields.

The drive coil is modeled as a homogenized current carrying

domain. Individual wires are not resolved.

Magnetostatic modeling is performed. A parametric sweep of

current density in the drive coil is used to demonstrate the non-

linear magnetostriction vs. magnetic field.

Model Features


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MagnetostrictionEffect of magnetic field

The free strain is often

modeled using linear

constitutive relation:

= dH

where dis called the piezo-

magnetic strain coefficient.

In reality, the free strain

(magnetostriction) has anon-linear dependence on

the applied magnetic field

and the mechanical stress

in the material.

Source:http://www.etrema-usa.com/documents/Terfenol.pdf

Pre-stress

Magnetostriction vs. Magnetic field at various pre-stresses


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AC/DC Module> Statics,

Magnetic> Azimuthal

Induction Currents,

Vector Potential

Calculates the azimuthal

magnetic potential (A) for

a given azimuthal current

density (J).

The magnetic problem issolved to find the spatial

distribution of

magnetization (Mr_emqa,

Mz_emqa).

Physics 1Electromagnetic


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Structural Mechanics

Module> Axial

Symmetry, Stress-Strain

> Static analysis

Magnetostriction

(Lambda_r, Lambda_z)

values are assigned as

initial strains (ri, zi) in the

magnetostrictive rod.

This creates a one-way

coupling of the structural

problem with the magnetic

problem.

Physics 2Structural


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Geometry

Steel housing

Air domain(required to view realistic

magnetic flux path)

Drive coil



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Steel housing

(Subdomain 2)

Dimensions Air(Subdomains 1, 4, 6)

Current-carrying coil(Subdomain 5)


(Subdomain 3)

Magnetostrictive rod- Radius = 3 mm

- Height = 50 mm

Coil

- Radius = 3 mm

- Height = 50 mm Steel housing

Head and base plates

- Radius = 20 mm

- Height = 5 mm

Side wall- Thickness = 5 mm

- Height = 50 mm

Air domain

- Radius = 90 mm

- Height = 180 mm


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Options > Constants


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Magnetostriction (i) along direction idepends on the magnetostriction

constant (s) and the magnetization direction cosine (

i).

The direction cosine is the ratio of magnetization along the required direction

(Mi) and the saturation magnetization (M

s) of the material.

The negative 1/3 term indicates that the magnetic moments are randomlyoriented in the material in the absence of any magnetic field.

We will not use this 1/3 term because we have assumed that the material is

sufficiently pre-stressed such that all magnetic moments are perpendicular to

the direction of magnetization at the beginning of the magnetization process.

Calculation of magnetostriction

3

1

M

M

2

3

3

1

2

32

s

i

s

2

isi

Ref: S. Chikazumi, Physics

of Ferromagnetism, 2nded.,

Clarendon Press.


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Options > Expressions > Subdomain Expressions

Note:Constitutive relation is applied only to subdomain 3

which represents the magnetostrictive material.


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Make sure the application mode emqais selected from

the Multiphysicsmenu.

Subdomains 1, 4, 6No changes are necessary.

Subdomain 2- Choose Library Materialas Soft iron

(with losses). Choose constitutive relation (HB) as H

= f(|B|)eB.

Go to Options > Materials/Coefficients library.

Expand Model(1) and click on Soft Iron (with

losses)(mat1). In the sigmaedit field, type 0.Click

Applyand OK.

Subdomain settings - Magnetic


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Subdomain 3Assume a non-linear but isotropic

magnetostrictive material. Choose constitutive

relation (HB) as H = f(|B|)eB. Type

HBFe(normB_emqa[1/T])[A/m]in the Hedit field.

HBFe is a user-defined function to model the non-

linear B-H curve in the magnetostrictive material.

The B-H curve function can be created by the userusing experimental material data. User-defined

functions are created from Options > Functions.



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Non-linear B-H Curve

Interpolation

table

B

H

H = HBFe(B)


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Subdomain 5 - Type J0in the Jeedit field.

Note that the electrical conductivity in subdomain 5 is

set to zero because in reality the turns of wires in adrive coil are insulated from each other so that the

current only flows along the circumferential direction ()

and not along the axial (z) and radial (r) directions.



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Boundary settings - Magnetic

Axial Symmetry(Boundaries 1, 3, 5, 7, 9)

Magnetic Insulation(Boundaries 2, 11, 26)

All other boundaries

- Continuity

This boundary conditionsets the magnetic vector

potential A= zero. This is

an approximation for a

boundary at infinity. The

user may also use infinite

elementsfor a more high

fidelity model. See the

AC/DC Module User's

Guide for information on

infinite elements.


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Subdomain settings - Structural


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Subdomain 3Add the magnetostriction (Lambda_r andLambda_z) using the Initial Stress and Straintab.

Subdomain settings - Structural


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Why initial strain?

ii

C

Generalized Hookes Law

Magnetostriction does not produce stress in the material

unless it is constrained.

Modeling magnetostriction as an initial strain ensures

that the material remains stress-free when the strain in

the body is the same as the magnetostriction.

[]Stress

[C]Stiffness

[]Strain

[i] - Initial strain

[i] - Initial stress


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It is desired to calculate the magneticquantities in the magnetostrictive rod

and steel housing with high accuracy.

Go to the Subdomaintab under Mesh

> Free Mesh Parameters. Type 1e-3inthe Maximum element sizeedit field

for subdomains 2 and 3.

Go to the Boundarytab under Free

Mesh Parameters. Type 1e-4in theMaximum element sizeedit field for

boundaries 6 and 8.

Click the Remeshbutton followed by

OKbutton.

Meshing


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Results

Uniform magnetic flux

density inside the

magnetostrictive rod along

the centerline (r = 0).

Flux density tapers off

sharply through the steel

head and base plates.

Magnetic flux concentration through

the magnetostrictive rod and steel

housing depicted by the streamlines.


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Results

Uniform axial strain (~ 1.47e-4)

in the magnetostrictive rod due

to magnetostriction.

Zero axial stress in the

magnetostrictive rod due

to free strain.

Uniform axial strain in the

magnetostrictive rod along

the centerline (r = 0)


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Creating the non-linear vs.Hcurve

It is desired to find out the free strain of the

magnetostrictive material or displacement obtained from

the transducer as a function of the input current or input

magnetic field for most applications.

To find this out we need to perform a parametric

analysis.

Assume J0 varies quasi-statically so that there is no

inductive effect and no skin-effect.


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Solve > Solver Parameters

Use the settings

shown here and

click OK.

Click the =

button to solve.

It will probably

take a fewminutes.


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Plotting the non-linear vs.Hcurve

Postprocessing > Plot Parameters> Domain Plot Parameters.

In the Generaltab, make sure all the

solutions are selected in the

Solutions to usearea.

Select the Pointtab and choose

point 4.

In the y-axis dataarea, type

Lambda_zin the Expressionedit

field.

In the x-axis dataarea, select the

Expression radio button and then

click on the Expression button. Type

Hz_emqa.

Non-linear magnetostriction vs.

magnetic field curve along the

axial direction.


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Plotting the displacement vs. input current density

Postprocessing > Plot Parameters> Domain Plot Parameters.

In the Generaltab, make sure all the

solutions are selected in the

Solutions to usearea.

Select the Pointtab and choose

point 4.

In the y-axis dataarea, type win the

Expressionedit field.

In the x-axis dataarea, select the

Expression radio button and then

click on the Expression button. Type

J0.

Non-linear axial displacement vs.

input current density.


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References

1. C. Mudivarthi, S. Datta, J. Atulasimha and A. B. Flatau, A bidirectionally

coupled magnetoelastic model and its validation using a Galfenol

unimorph sensor, Smart Materials and Structures, 17035005 (8pp),

2008.

http://www.iop.org/EJ/abstract/0964-1726/17/3/035005/

2. F. Graham, Development and Validation of a Bidirectionally Coupled

Magnetoelastic FEM Model for Current Driven Magnetostrictive Devices,

M.S. Thesis, Aerospace Engineering, University of Maryland, College

Park, USA, 2009.

http://www.lib.umd.edu/drum/handle/1903/9354
http://www.iop.org/EJ/abstract/0964-1726/17/3/035005/http://www.lib.umd.edu/drum/handle/1903/9354http://www.lib.umd.edu/drum/handle/1903/9354http://www.iop.org/EJ/abstract/0964-1726/17/3/035005/http://www.iop.org/EJ/abstract/0964-1726/17/3/035005/http://www.iop.org/EJ/abstract/0964-1726/17/3/035005/

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Magnetostrictive Transducer 1

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