Download Characterization of a ferromagnetic material for static application

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Example
Creation
date
Characterization of a ferromagnetic material
2009
Author : Pascal Ferran - Université Claude Bernard Lyon
Ref. FLU2_MS_MAG_06
Program
Dimension
Version
Physics
Application
Work area
Flux
2D
10.3
Magnetic
Static
Magnetic
FRAMEWORK
Presentation
General remarks
In this example, we’ll see the characterization of materials with the method of the
torus. To do so, we’ll consider a coil torus with 2 coils (primary and secondary).
The torus material is characterized by a model defined by the combination of a
straight line and a curve with tangent arc. Js and µr are the parameters of this model.
A sinusoidal current is injected in the primary coil, an induced voltage is measured at
the secondary coil. The magnetic field H corresponds to the current, the magnetic
induction field corresponds to the voltage. Th B(H) curve enables us to characterize
the material.
We’ll consider the original B(H) curve and the one « measured » via the torus.
Objective
- Computation of the magnetic induction in the torus from the voltage at the
terminals of the secondary coil.
- Computation of the magnetic field H in the ferromagnetic torus
The parameters the user can change are:
Average relative permeability of the magnetic material (MUR)
Magnetic polarization at material saturation (JS)
Maximum current (I_MAX) injected in the primary coil
Number of spires of the primary and secondary coils (NP, NS)
Theoretical
reminders
See Annex
Properties
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Flux
- Rated average radius of the torus: R_MOY =
28.75 mm
- Rated number of spires in the primary and
secondary coils : Np = 4000 spires and Ns = 1000
spires
-Rated characteristics of the torus material :
Js = 1.2 T and µr = 500
- Maximal value of the direct current injected in the
primary coil : I_MAX = 1 A
- Measurements are made in direct mode
Illustration
Main characteristics
Some results …
Curv B(H) of the material considering the different computation modes (all parameters are rated)
PAGE 2
Characterization of a ferromagnetic material
Flux
FRAMEWORK
Distribution of the surface density of the magnetic flux (I = 1A, Np = 4000, Ns= 1000,
r = 500 et Js = 1,2T)
(all parameters are rated)
To go further …
-
Impact of the airgap in a magnetic circuit with toric shape
Study of current sensors
Characterization of material via the method of the torus in 3D
…
Characterization of a ferromagnetic material
PAGE 3
MODEL IN FLUX
Flux
MODEL IN FLUX
Domain
Dimension
2D
Depth
THICKNESS
Infinite Box
Disk
Length unit.
mm
Angle unit.
degrees
Size
Out. Radius : 150mm
Periodicity
In. radius : 100mm
Symmetry
Characteristics
none
Repetition number :
Offset angle :
Even/odd periodicity
Application
Properties
Geometry / Mesh
Full model in the FLUX environment
Mesh
2nd order type
Mesh
Number of nodes
10133
Input Parameters
Name
Type
Description
Rated value
THICKNESS
ALPHA
I_MAX
Js
Geometrical
Physical
Physical
Physical
7 mm
1
1A
1.2 T
MUR
Physical
Np
Physical
Ns
Physical
Problem’s depth
Current variation coefficient
Current maximal intensity
Magnetic
polarization
at
material saturation
Average relative permeability
of the material
Number of spires of the
primary coil
Number of spires of the
secondary coil
PAGE 4
500
4000
1000
Characterization of a ferromagnetic material
Flux
MODEL IN FLUX
Material Base
NAME
B(H) model
Magnetic property
J(H) model
Electrical property
D(E) model
Dielectric property
K(T) model
K(T) characteristics
RCP(T) model
RCP(T) characteristics
MATERIAL
Analytical isotropic saturation
MUR - Js
Regions
NAME
AIR
INFINITE
Nature
Surface region
Air region or
vacuum
-
Surface region
Air region or
vacuum
-
MAGNETIC_CIRCUI
T
Surface region
Non
conductive
magnetic region
MATERIAL
-
-
-
-
-
-
-
-
-
-
Np spires – Negative
orientation of the current
-
-
-
-
-
-
-
-
-
Type
Material
Mechanical Set
Corresponding
circuit component
Electrical
characteristics
Current source
Thermal
characteristics
Possible
source
thermal
PRIMARY_COIL_MINUS
Surface region
Coil conductor type region
PRIMARY_FIELD
NOM
Nature
PRIMARY_COIL_PLUS
Surface region
SEC_MINUS
Line region
Type
Coil conductor type region
Coil conductor type region
Matériau associé
Ens. mécanique
Composant
circuit associé
-
-
SEC_PLUS
Line region
Coil
conductor
region
-
PRIMARY_FIELD
SECONDARY_COIL
SECONDARY_COIL
Caractéristiques
électriques
Np
spires
–
Positive
orientation of the current
Ns
spires
–
Negative
orientation of the current
Source de courant
Caractéristiques
thermiques
-
-
Ns spires
orientation
current
-
-
-
-
-
-
-
Source de
éventuelle
chaleur
Characterization of a ferromagnetic material
–
type
Positive
of
the
PAGE 5
MODEL IN FLUX
Flux
Mechanical Set
Fixed part :
Compressible part :
Type
Characteristics
Miscellaneous
Mobile part :
Type of kinematics
Internal characteristics:
External characteristics :
Mechanical stops
Electrical circuit
Component
Type
PRIMARY_FIELD
Coil conductor
SECONDARY_COIL
Coil conductor
Characteristics
Imposed current :
I_MAX x ALPHA
Imposed current : 0
Associated Region
PRIMARY_COIL_MINUS
PRIMARY_COIL_PLUS
SEC_MINUS
SEC_PLUS
Electric scheme
Solving process options
Type of linear system solver
Type of non-linear system
solver
Automatically
chosen
Parameters
Precision
Newton Raphson
Automatically defined
0.0001
Method for computing the
relaxation factor
Nb iterations
100
Automatically defined
Thermal coupling
Advanced characteristics
Solving
Scenario
SCENARIO_1
Name
of
parameter
ALPHA
Duration of the solving
PAGE 6
Controllable
parameter
Physical
40 seconds
Variation
method
Steps list
Interval definition
Step selection
0.0 to 1.0
0.01, 0.02, 0.05,
0.075, 0.1, 0.2,
0.3, 0.4, 0.5, 0.6,
0.7, 0.8, 0.9, 1.0
Operating System
Windows XP 32 bits
Characterization of a ferromagnetic material
Flux
ANNEX
ANNEX
Theoretical reminders
Magnetic
induction
measurement
We can measure the voltage at the terminals of the secondary coil and deduct from it
the average flux in the magnetic circuit from the following relation :
vs  NS 
d
dt
avec   B  S
From which we get :
B  vs 
H Computation
1
NS  2    f  S
Let’s calculate H with the Ampere’s theorem formula :
 H  dl  
j
Nj  ij
c
In this case, the current circulating in the secondary coil is equal to 0 and we
integrate H along the average contour of the torus (average radius = = R_MOY).
Result:
ALPHA  I _ MAX  NP  H  2    R _ MOY
Coming from :
H
Characterization
of the magnetic
material used
ALPHA  I _ MAX  NP
2    R _ MOY
In Flux, a material can be characterized by having the following magnetic property:
Isotropic analytical saturation (arctg, 2 coef.) ».
The corresponding mathematical expression of the B(H) model is :
Characterization of a ferromagnetic material
PAGE 7
ANNEX
Notations and
symbols
Flux
symbol
description
vs
unit
Voltage at the terminals of secondary c
Average flux in the magnetic circuit
Magnetic induction field
Torus section
Magnetic field
Peak value of the current carried by
the primary coil
Torus average radius
Number of spires of the primary coil
Number of spires of the secondary coil
Coefficient allowing the adjustment of
the of the current value to its maximal
value

B
S
H
I_MAX
R_MOY
Np
Ns
ALPHA
V
Wb
T
m²
A/m
A
m
Numerical applications
Presentation
Analytical computation of the different values seeked for the below working
point :
-
Determination of
H
It is now possible of determine the value of H at the defined working point by
applying the Ampere theorem :
H
Determination
of B (Flux
formula)
Property of the magnetic material : Js = 1.2 T - µr = 500
Torus average radius :
R_MOY = 28.75 mm
Number of spires :
Np = 4000 spires – Np = 1000 spires
Maximal intensity :
I_MAX = 1 A
Current ratio:
ALPHA = 0.05
ALPHA  I _ MAX  NP
0.05  1  4000

 1107 A / m
2    R _ MOY
2    28.75  10 3
From the determined H value, it is possible to find the corresponding value of the B :
  ( µr  1 ) µ0 H 
arctg 


2 Js


  (500  1) 4  10 7  1107 
2  1.2
7

B  4  10  1107 
arctg 


2
1
.
2


B  µ0 H 
2 Js
B  0.56 T
PAGE 8
Characterization of a ferromagnetic material