magnetostrictive transducer 1
TRANSCRIPT
-
8/11/2019 Magnetostrictive Transducer 1
1/34
Example:
Magnetostrictive Transducer
-
8/11/2019 Magnetostrictive Transducer 1
2/34
-
8/11/2019 Magnetostrictive Transducer 1
3/34
Magnetostrictive Transducer
Steel housing
(for magnetic flux path)
Drive coil (homogenous
current carrying element)
Magnetostrictive rod
(active material)
Sectional view of a cylindrical transducer
-
8/11/2019 Magnetostrictive Transducer 1
4/34
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
-
8/11/2019 Magnetostrictive Transducer 1
5/34
-
8/11/2019 Magnetostrictive Transducer 1
6/34
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
-
8/11/2019 Magnetostrictive Transducer 1
7/34
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
-
8/11/2019 Magnetostrictive Transducer 1
8/34
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
-
8/11/2019 Magnetostrictive Transducer 1
9/34
Geometry
Steel housing
Air domain(required to view realistic
magnetic flux path)
Drive coil
Magnetostrictive rod
-
8/11/2019 Magnetostrictive Transducer 1
10/34
Steel housing
(Subdomain 2)
Dimensions Air(Subdomains 1, 4, 6)
Current-carrying coil(Subdomain 5)
Magnetostrictive rod
(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
-
8/11/2019 Magnetostrictive Transducer 1
11/34
Options > Constants
-
8/11/2019 Magnetostrictive Transducer 1
12/34
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.
-
8/11/2019 Magnetostrictive Transducer 1
13/34
Options > Expressions > Subdomain Expressions
Note:Constitutive relation is applied only to subdomain 3
which represents the magnetostrictive material.
-
8/11/2019 Magnetostrictive Transducer 1
14/34
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
-
8/11/2019 Magnetostrictive Transducer 1
15/34
Subdomain settings - Magnetic
-
8/11/2019 Magnetostrictive Transducer 1
16/34
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.
Subdomain settings - Magnetic
-
8/11/2019 Magnetostrictive Transducer 1
17/34
Subdomain settings - Magnetic
-
8/11/2019 Magnetostrictive Transducer 1
18/34
Non-linear B-H Curve
Interpolation
table
B
H
H = HBFe(B)
-
8/11/2019 Magnetostrictive Transducer 1
19/34
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.
Subdomain settings - Magnetic
-
8/11/2019 Magnetostrictive Transducer 1
20/34
Subdomain settings - Magnetic
-
8/11/2019 Magnetostrictive Transducer 1
21/34
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.
-
8/11/2019 Magnetostrictive Transducer 1
22/34
-
8/11/2019 Magnetostrictive Transducer 1
23/34
Subdomain settings - Structural
-
8/11/2019 Magnetostrictive Transducer 1
24/34
Subdomain 3Add the magnetostriction (Lambda_r andLambda_z) using the Initial Stress and Straintab.
Subdomain settings - Structural
-
8/11/2019 Magnetostrictive Transducer 1
25/34
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
-
8/11/2019 Magnetostrictive Transducer 1
26/34
-
8/11/2019 Magnetostrictive Transducer 1
27/34
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
-
8/11/2019 Magnetostrictive Transducer 1
28/34
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.
-
8/11/2019 Magnetostrictive Transducer 1
29/34
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)
-
8/11/2019 Magnetostrictive Transducer 1
30/34
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.
-
8/11/2019 Magnetostrictive Transducer 1
31/34
Solve > Solver Parameters
Use the settings
shown here and
click OK.
Click the =
button to solve.
It will probably
take a fewminutes.
-
8/11/2019 Magnetostrictive Transducer 1
32/34
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.
-
8/11/2019 Magnetostrictive Transducer 1
33/34
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.
-
8/11/2019 Magnetostrictive Transducer 1
34/34
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/