Transcript PEPM-2016-Poster
Demagnetizing factors and load lines for rectangular prisms determined using FEA for NdFeB and other magnets Christina H. Chen and Michael S. Guthrie
Quadrant Solutions, Inc., 2387 Bering Rd., San Jose, CA 95131, USA
Abstract:
MagNet FEA software is used to determine the demag factors (
N
) for rectangular prisms of varying dimensions. The load lines are also calculated based on the
N
values. The results show that the
N
depends not only on the magnet shape, but also related to the
B-H
curve shape. Six equations are generated for the magnets in certain dimension ranges. The FEA results are compared to other reported data, and it is believed that the 3D computer simulations employing the actual magnetic hysteresis data enable a better accuracy.
Introduction & Experiment:
Open-circuit measurements are always subject to a demagnetizing correction. The accuracy of the factor N has yet to be improved. 3D FEA simulations, employing the actual magnetic hysteresis data, enable a better accuracy.
Table 1 Spherical materials were first verified using the FEA
N
values were first verified
Results:
The FEA generated filed plots are shown in the figure below, and the results were used to create the following 6 equations.
π (
π π
= 1) = π (
π π
= 2) =
0.487
πΏ π +0.51
0.659
πΏ π +0.70
β¦Linearβ¦..β¦.....β¦.(4) β¦Linearβ¦..β¦β¦..β¦.(5)
π (
π π
= 4) =
0.95
0.791
πΏ +0.87
π β¦Linear β¦.β¦.β¦.(6)
π
π
= 1 =
π 1.2
0.450
πΏ π +0.51
β¦β¦Alnico 9β¦.β¦..(7)
π π (
π
= 2 =
π π π
= 4) =
0.510
πΏ π +0.60
β¦β¦Alnico 9β¦..β¦....(8) 0.78
0.502
πΏ π +0.65
β¦Alnico 9β¦..β¦.(9) Different
B-H
curves (linear/non-linear) for the same shape resulting in different demagnetizing factors, a different concept compared to other reports. The comparison can be seen in the plots.
Comparison of the N values resulting from FEA with those from other reports [4,5] for πΎ π» = 4
The Load Line:
π© The
N
value is used to calculate , the slope of π― the load lines, for determine the operating points for various applications:
π΅ =
π β π π© π― β¦β¦β¦β¦β¦β¦β¦β¦(10) π© π―
=
π π΅
β π
β¦β¦β¦β¦.β¦β¦β¦β¦.(11)
3 steps
determining the demagnetizing factor
N
: 1) Simulate the sample employing the actual
B-H
curve in FEA software for the material without any applied field; 2) Integrate the field
H
d
the sampleβs volume; and the induction
B
over 3) Calculate the demagnetizing factor
N
based on the magnetization
4
ο°
M
and the demagnetizing field
H
, using the equations (1-3):
π
ο°
π΄ = π© β π―
β¦β¦β¦β¦β¦β¦..(1)
H = H
a
+ H
d
= 0 + H
d
= H
d
β¦.(2)
π΅ =
π π― π ο° π΄
β¦(0 <
N
< 1)β¦
.β¦(3) Demagnetizing factors (N) from FEA and fitted equations for NdFeB and Alnico 9 with πΎ π»
=
1 Magnetic field plots for the Alnico 9 & N48SH π³ magnets with π» = 0.2, 0.5, 1, 2 & 5 and πΎ π» =1.
Demagnetizing factors (N) from FEA and fitted equations for NdFeB and Alnico 9 with πΎ π»
= 4
The load lines and operating points with corresponding shapes with πΎ π» =1 for ten magnets
Conclusions & discussion
1.
N not only depends on the shape of the magnet, but also the shape of the
B-H
curve.
2. Alnico with non-linear 2 nd
Q B-H
has smaller
N
3. Six
N
equations have been generated for magnets in certain dimensional ranges for both linear and non-linear demagnetization curves, such as NdFeB and Alnico.
4. The results are compared to other reports: the 3D FEA simulations employing the actual magnetic hysteresis data enable better accuracy.
5. It is also possible to develop a single equation to determine the β
N
β for all the permanent πΎ magnets with various ; for which more effort π» is needed.
6. Four tables are presented with FEA demag netizing factors and calculated load lines for rectangular prisms with the length to a side ratio in the range of 0.04 to 20.