A FEM Study of displacement sensor based on L-L ......OOO H Properties PMNβ28PT Ο, kg m-3 8060...
Transcript of A FEM Study of displacement sensor based on L-L ......OOO H Properties PMNβ28PT Ο, 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
βͺ 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:
βͺ Magnetostrictive effect is a property of
ferromagnetic materials that causes them
to change their shape or dimensions during
the process of magnetization.
βͺ Piezoelectric effect is the ability of certain
materials to generate an electric charge in
response to applied mechanical stress.
H
l
zΞ z
Magnetostrictive
layer
Piezoelectric
layer
Magnetostrictive
rod
Piezoelectric
plate
Ξ z Fixed boundary with
rigid frame
M
M
P
M P
0
l 1 l 2
r
βͺ 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
βͺ Piezoelectric linear constitutive equation
Modelling
e e ec eE
T
eD e E
Implementation with COMSOL
Implementation with COMSOL
βͺ Geometry
Implementation with COMSOL
Air block
NdFeB magnet
Magnetic pole
pieces
MS rod
PMN-PT plate
βͺ Realization of PZT material model
βͺ The linear constitutive equations for piezoelectric material
βͺ For solid mechanics, the elastic relations
βͺ 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
βͺ Realization of magnetostrictive material model
βͺ The elastic relations
Implementation with COMSOL
0( )Ec
0 ( , , )2 2 2
diag
Properties PMNβ28PT
Ο, kg m-3 8060ππππ¬ ,GPa 115.4ππππ¬ ,GPa 103.4ππππ¬ ,GPa 102.6ππππ¬ ,GPa 114.1ππππ¬ ,GPa 68.9ππππ¬ ,GPa 65.8πΊπππΊ /πΊπ 925πΊπππΊ /πΊπ 813
πππ,C m-2 -3.4πππ,C m-2 10.1πππ,C m-2 20.5
βͺ Boundary conditions & Mesh
Implementation with COMSOL
Results
Thanks.