The Use of Multiphysics Models in the Design and Simulation of Magnetostrictive Transducers

Dr. Julie Slaughter ETREMA Products, Inc

Ames, IA

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Designer and manufacturer of technology driven, high value systems based on electromagnetics.

• Small business • Started in 1990 as a foundry for

TERFENOL-D • Developed engineering capability

in the 90’s to grow the market • Shifted to system approach in

2000’s

ETREMA Products, Inc.

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Today’s Talk • What is magnetostriction? • Magnetostrictive devices • Modeling magnetostriction

• Tools & how they are used • Three examples of using COMSOL in various phases of a

product development • Design example • Validation of modeling tools • Diagnosis of a design flaw

• Future modeling efforts • Summary

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What is magnetostriction? • Inherent property of

ferromagnetic materials where the magnetic and mechanical domains are coupled • Applied magnetic field results

in a change in the mechanical state of the material (Joule)

• Applied stress or strain results in a change in the magnetic state of the material (Villari)

• Magnetostrictive materials • Nickel, iron, transformer steels:

strain <50 µε • Iron-gallium alloys (Galfenol):

strain 150-450 µε • Rare earth-iron alloys (Terfenol-

D): strain >1000 µε 4

Characteristics of magnetostrictive materials

• Nonlinear material behavior

• Material properties are not constant (Young’s modulus, magnetic permeability)

• Response is highly dependent on mechanical and magnetic states

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-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-160 -80 0 80 160

Mag

netic

Flu

x D

ensit

y (

Tesla

)

Magnetic Field (kA/m)

Magnetic Flux Density As A Function Of Applied Stress

7.2 MPa

14.1 MPa

20.9 MPa

27.8 MPa

34.6 MPa

41.4 MPa

48.3 MPa

55.1 MPa

Figure from: R.A. Kellogg , The Delta-E Effect in Terfenol-D and Its Application in a Tunable Mechanical Resonator, M.S. Thesis, 2000. p. 45

Data for Terfenol-D produced by ETREMA

Linear magnetostrictive equations

HdTBHdTsS

Tt

H

µ+=

+=

Field Variable

Description

S Strain (m/m)

T Stress (Pa)

B Magnetic flux density (Tesla)

H Magnetic field (A/m)

Material property

Description

sH Compliance matrix at constant H

d, dt Magnetostrictive coefficients (δB/δT, δS/δH)

µT Magnetic permeability at constant stress

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Magnetostrictive transducers • Used in a wide array of

applications and industries • End application drives the device

design

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AMS – Small Engine Piston Turning

Navy Active SONAR

Standard actuators – DC to 25 kHz

STARS – Law enforcement

What is in a transducer?

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• Magnetostrictive material

• Permanent magnets • Coil • Magnetic flux

carrying components

• Structural components

• Thermal transfer components

Transducer design process

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Definition of performance requirements

Basic sizing and

feasibility

Detailed design

Design validation

Tools: 1D models (equivalent

circuits, equation

based) “Hand”

calculations

Tools: 2D & 3D COMSOL models, single

physics

Tools: 2D & 3D COMSOL

models, fully coupled

Design example • Small SONAR source

• Broad bandwidth • High SPL • Compact

• The intent is to package it with integrated electronics • Stray magnetic flux can interfere with electronics • Heating/cooling of both the transducer and electronics is a concern

• Eventual use is in a close-packed array

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Magnetic models

AC magnetics • Size the coil and other components to

generate the alternating magnetic fields needed to produce the appropriate mechanical output

• Match the transducer electrical requirements with available power amplifiers

• Evaluate losses due to eddy currents

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DC magnetics • Size permanent magnets to appropriately

bias the material at the design prestress • Size additional magnetic circuit

components to carry the magnetic flux - avoid saturation

Mechanical models

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Thermal models

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Magnetostrictive FEA models • Coupled linear

magnetostrictive model • Assumes a

magnetically biased design

• Small signal analysis • Coupled to a water load

to calculate acoustic output

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Model validation • ETREMA Terfenol-D transducer -

CU18A • 18 kHz nominal resonant frequency • 5 um (0-pk) displacement

• Significant amounts of performance data exist for this transducer • 100’s have been built and tested

Terfenol-D Coil

Magnets

Housing

Flexure

Tail mass

Threaded output interface

“washer”

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Z-axis

Magnetic fields and displacements

• Magnetic fields and displacements look quite reasonable • Magnetic fields are confined to the magnetic circuit • Flexure and output interface have the largest deflections for the transducer

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Comparison with actual data

• Models of impedance and displacement were very similar to experimental results

• Two main sources of error • Material properties • Damping

0.0

50.0

100.0

150.0

200.0

250.0

300.0

10000 15000 20000 25000

Abso

lute

val

ue o

f im

peda

nce

(ohm

)

Frequency (Hz)

ExperimentCOMSOL

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

10000 15000 20000 25000

Phas

e of

impe

danc

e (o

hm)

Frequency (Hz)

ExperimentCOMSOL

0.00.51.01.52.02.53.03.54.04.55.0

10000 15000 20000 25000

Disp

lace

men

t (um

)

Frequency (Hz)

ExperimentCOMSOL

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Design diagnosis • SONAR projector

• Three “modes” of operation: omnipole, dipole, quadrupole • One of the three modes, dipole, had very low acoustic output (-20 dB)

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omni- di- quad- Head mass

Driver

Center mass

FEA models • Coupled structural-acoustic models • Single ring plus surrounding water • No magnetostriction – too time

intensive to solve • Revealed a problem in the design

Water

Perfectly Matched Layer

Projector

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Expt FEA

Expt FEA

Expt FEA

Problem resolution • FEA showed the cause of the low

dipole output • The design was modified to

improve the response • Experiments verified that the

improved design operated as expected

20 omni- di- quad- cardioid

Flawed hardware

Corrected hardware

Future modeling efforts • Nonlinear fully-coupled magnetostrictive models

• Some models have already been developed – need verification and additional material properties

• Transducers which are not magnetically biased • Large-signal transducers which include hysteresis • Aid in developing closed-loop controls for specific applications

• Couple thermal effects with magnetostrictive models • Include temperature dependent material properties • Different time scale than magnetostrictive process

• Computer-driven optimization of designs • Optimize the amount of high-cost materials in transducers

(magnetostrictive materials, permanent magnets, flux path materials, coils, etc.)

• Improve performance, decrease cost, improve manufacturability 21

Summary • Fully coupled multiphysics simulation is a powerful tool for

transducer design, evaluation, and optimization • Focus was on magnetostriction but all transducer technologies

have coupled multiphysics (piezoelectric, electrostatic, electromagnetic, etc.)

• Finite element models can be used at different stages of product development • Design development • Existing product evaluation • Troubleshooting performance issues

• Resolving differences between models and experimental data is critical to continuous model improvement

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