A FEM Study of displacement sensor based on L-L ......OOO H Properties PMN–28PT ρ, kg m-3 8060...

Qingwei Lau, PhD candidate

School of ME, SJTU

A FEM Study of displacement sensor based on

L-L Magnetostrictive/Piezoelectric block

magnetoelectric composite material

Excerpt from the Proceedings of the 2016 COMSOL Conference in Shanghai

Contents

1 Introduction

2 Modelling of ME effect

3 Implementation with COMSOL

4 Simulation

5 Results

▪ Magnetoelectric effect (ME) is the phenomenon of inducing magnetic

(electric) polarization by applying an external electric (magnetic) field.

Introduction

Single Phase

MaterialCr2O3

Composite Material

Mech.

Strain

Magneti-

zation

Polarization

0-3 Type

2-2 Type

1-3 Type

0 for particle

1 for fiber

2 for layer

3 for matrix

H

magnetic mechanicalME effect

mechanical electric

E

electric mechanicalME effect

mechanical magnetic

Product Property:

▪ Magnetostrictive effect is a property of

ferromagnetic materials that causes them

to change their shape or dimensions during

the process of magnetization.

▪ Piezoelectric effect is the ability of certain

materials to generate an electric charge in

response to applied mechanical stress.

H

l

zΔ z

Magnetostrictive

layer

Piezoelectric

layer

Magnetostrictive

rod

Piezoelectric

plate

Δ z Fixed boundary with

rigid frame

M

M

P

M P

0

l 1 l 2

r

▪ Magnetostrictive nonlinear constitutive equation

Modelling

2m3 1(( ) )

2 3

ii s

iM

2 2( ) , ( )2

ss

s s

M M

M M

eH H M H

( ,H)E

0 0 ( ,H)B H M

2 2 2( ) , ( ) , ( )2 2

ys x s zx y z s

s s s

MM M

M M M

▪ Piezoelectric linear constitutive equation

Modelling

e e ec eE

T

eD e E

Implementation with COMSOL

Implementation with COMSOL

▪ Geometry

Implementation with COMSOL

Air block

NdFeB magnet

Magnetic pole

pieces

MS rod

PMN-PT plate

▪ Realization of PZT material model

▪ The linear constitutive equations for piezoelectric material

▪ For solid mechanics, the elastic relations

▪ For electrostatics, the electrical relations:

Implementation with COMSOL

0 0( ) eT

Es S c E

0( )rD D e E

1[( u) u]

2

T

s

VF

VD

E V

▪ Realization of magnetostrictive material model

▪ The elastic relations

Implementation with COMSOL

0( )Ec

0 ( , , )2 2 2

diag

Properties PMN–28PT

ρ, kg m-3 8060𝒄𝟏𝟏𝑬 ,GPa 115.4𝒄𝟏𝟐𝑬 ,GPa 103.4𝒄𝟏𝟑𝑬 ,GPa 102.6𝒄𝟑𝟑𝑬 ,GPa 114.1𝒄𝟒𝟒𝑬 ,GPa 68.9𝒄𝟔𝟔𝑬 ,GPa 65.8𝜺𝟏𝟏𝑺 /𝜺𝟎 925𝜺𝟑𝟑𝑺 /𝜺𝟎 813

𝒆𝟏𝟑,C m-2 -3.4𝒆𝟏𝟓,C m-2 10.1𝒆𝟑𝟑,C m-2 20.5

▪ Boundary conditions & Mesh

Implementation with COMSOL

Results

Thanks.