Download Characterization of a ferromagnetic material for steady state application

Flux
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Example
Creation
date
Characterization of a ferromagnetic material
2009
Author : Pascal Ferran - Université Claude Bernard Lyon
Ref. FLU2_MH_MAG_01
Program
Dimension
Version
Physics
Application
Work area
Flux
2D
10.3
Magnetic
Steady state
Magnetic
FRAMEWORK
Presentation
General remarks
In this example, we determine the characterization of materials with the method of
the torus. To do so, we’ll consider a coil torus with 2 (primary and secondary) coils.
The torus is made of a material characterized by a model defined by a combination of
a straight line and a curve in tangent arc. Js and µr are the parameters of this model.
A sinusoidal current is injected in the primary coil and an induced voltage is measured
at secondary coil.
The magnetic field H corresponds to the current, the magnetic induction field B
corresponds to the voltage. With the resulting B(H) curve, we can characterize the
material.
We will compare the original B(H) curve with the one “measured” with 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
The number of spires of the primary and secondary coils (NP, NS)
Theoretical
reminders
See Annex
CEDRAT S.A. 15, Chemin de Malacher Inovallée – 38246 MEYLAN Cedex (France) – Tél : +33 (0)4 76 90 50 45 – Email : [email protected]
Flux
Properties
- Average rated radius of the torus: R_MOY =
28.75 mm
- Rated number of spires of the primary and
secondary coild: Np = 4000 spires and Ns = 1000
spires
- Rated characteristics of the torus material :
Js = 1.2 T and µr = 500
- Maximal peak value of the current injected in the
primary coil : I_MAX = 1 A
- Current source frequency = 1 Hz
Illustration
Main characteristics
Some results …
Material B(H) curve (all the parameters are rated)
PAGE 2
Title
Flux
FRAMEWORK
Evolution of the Vs (V) voltage according to the inducting current (A) (all the parameters are rated)
To go further …
-
Title
Impact of an airgap in a magnetic circuit with a toric shape
Study of current sensors
Characterization of materials with the method of the torus in 3D
…
PAGE 3
MODEL IN FLUX
Flux
MODEL IN FLUX
Domain
Dimension
2D
Depth
DEPTH
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
Steady magnetic
Properties
Geometry / Mesh
Full model in the FLUX environment
2nd order type
Mesh
Mesh
Number of nodes
10055
Input Parameters
Name
DEPTH
ALPHA
I_MAX
Js
MUR
Np
Ns
FREQ
PAGE 4
Type
Geometrical
Physical
Physical
Physical
Physical
Physical
Physical
Physical
Description
Problem’s depth
Current variation coefficient
Current maximale intensity
Magnetic polarization at material saturation
Material Average relative permeability
Number of spires of the primary coil
Number of spires of the secondary coil
Injected current frequency
Rated value
7 mm
1
1A
1.2 T
500
4000 spires
1000 spires
1 Hz
Title
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
Nature
AIR
Surface region
Air region or
vacuum
-
INFINITE
Surface region
Air region or
vacuum
-
COMPONENT
Surface region
Non conductive
magnetic region
MATERIAL
-
PN
Surface region
Coil conductor type
region
-
-
-
-
COILCONDUCTOR_1
Electrical characteristics
-
-
-
Current source
-
-
-
Np spires –
Negative current
orientation
-
Thermal characteristics
-
-
-
-
Possible thermal source
-
-
-
-
NAME
Nature
PP
Surface region
SN
Line region
Type
Coil conductor type region
Coil conductor type region
Material
Mechanical Set
Corresponding circuit
component
-
-
SP
Line region
Coil conductor type
region
-
COILCONDUCTOR_1
COILCONDUCTOR_2
COILCONDUCTOR_2
Current source
Np spires – Positive
current orientation
-
Ns spires – Negative
current orientation
-
Ns – Positive current
orientation
-
Thermal characteristics
-
-
-
Possible thermal source
-
-
-
Type
Material
Mechanical Set
Corresponding circuit
component
Electrical characteristics
Title
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
COILCONDUCTOR_1
Coil conductor
COILCONDUCTOR_2
Coil conductor
RESISTOR
Resistance
Characteristics
Imposed current :
I_MAX x ALPHA
Coil conductor associated to a
circuit
1 M Ohms
Associated Region
PN
PP
SN
SP
-
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
PAGE 6
Title
Flux
Scenario
SCENARIO_1
MODEL IN FLUX
Name of
parameter
ALPHA
Duration of the solving
Title
Controllable
parameter
Physical
1 min 30s
Variation
method
Steps list
Interval definition
Step selection
0.0 to 1.0
0.000
0.020
0.075
0.200
0.400
0.600
0.800
1.000
Operating System
-
0.010
0.050
0.100
0.300
0.500
0.700
0.900
-
Windows XP 32 bits
PAGE 7
ANNEX
Flux
ANNEX
Theoretical reminders
Magnetic
induction
measurement
In the magnetic circuit, the voltage at the terminals of the secondary coil can be
measured. Then we can deduct the average flux in the magnetic circuit from the
below relation:
vs  NS 
d
dt
avec   B  S
Then :
B  vs 
H computation
1
NS  2    f  S
Let’s calculate H with the Amoere theorem formula :
 H  dl  
j
Nj  ij
c
In this case, the current circulating in the secondary coil is 0 and we integrate H along
the average contour of the torus (average radius = R_MOY).
Obtained result:
ALPHA  I _ MAX  NP  H  2    R _ MOY
From which we get :
H
Magnetic material
characterization
ALPHA  I _ MAX  NP
2    R _ MOY
In Flux, a material can be characterized by the following magnetic property:
« Analytical isotropic saturation (arctg, 2 coef.) ».
The corresponding mathematical expression of the B(H) is :
PAGE 8
Title
Flux
Notations and
symbols
ANNEX
symbol
description
unit
Voltage at the secondray coil
terminals
Average Flux in the magnetic circuit
Magnetic induction field
Torus section
Inductive current signal frequency
Magnetic field
Peak value of the current circulating
in the primary coil
Average radius of the torus
Number of spires of the primary coil
Number of spires of the secondary
coil
Coefficient to adapt the current
value to its maximal value
vs

B
S
f
H
I_MAX
R_MOY
NP
NS
ALPHA
V
Wb
T
m²
Hz
A/m
A
m
Numerical applications
Presentation
Analytical computation of different magnitudes seeked for the following
working point :
-
Determination of
H
Js = 1.2 T - µr = 500
R_MOY = 28.75 mm
Np = 4000 spires – Np = 1000 spires
I_MAX = 1 A
ALPHA = 0.05
It is now possible to determine the value of H for the working point defined by
applying the Ampere theorem.
H
Determination
of B (Flux
formula)
Magnetic material property :
Torus average radius :
Number of spires :
Maximale intensity :
Adjustment coefficient :
ALPHA  I _ MAX  NP
0.05  1  4000

 1107 A / m
2    R _ MOY
2    28.75  10 3
From the H value, it is possible to determine the corresponding value of 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
Title
PAGE 9