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.
Results:
The FEA generated filed plots are
shown in the figure below, and the results were
used to create the following 6 equations.
𝑁(
𝑊
𝑇
𝑁(
𝑊
𝑇
= 2) =
𝑁(
𝑊
𝑇
= 4) =
𝑁
𝑊
𝑇
=1 =
𝑁
𝑊
𝑇
=2 =
𝑁(
𝑊
𝑇
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
= 1) =
= 4) =
0.487
…Linear…..….....….(4)
𝐿
+0.51
𝑇
0.659
𝐿
+0.70
𝑇
…Linear…..……..….(5)
0.791
0.95
…Linear ….….….(6)
𝐿
+0.87
𝑇
0.450
𝐿
1.2 +0.51
𝑇
0.510
𝐿
+0.60
𝑇
……Alnico 9….…..(7)
……Alnico 9…..…....(8)
0.502
0.78
𝐿
+0.65
𝑇
…Alnico 9…..….(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
𝑾
=
𝑻
4
The Load Line:
𝑩
𝑯
The N value is used to calculate
, the slope of
the load lines, for determine the operating points
for various applications:
𝑵=
𝑩
𝑯
=
𝟏
𝟏−
𝟏
𝑵
𝑩
𝑯
……………………(10)
− 𝟏 ………….………….(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 Hd and the induction B over
the sample’s volume;
3) Calculate the demagnetizing factor N
based on the magnetization 4M and the
demagnetizing field H, using the equations (1-3):
𝟒𝑴 = 𝑩 − 𝑯………………..(1)
The load lines and operating points with
𝑾
corresponding shapes with =1 for ten magnets
H = Ha + Hd = 0 + Hd = Hd….(2)
𝑵=
𝑯𝒅
𝟒 𝑴
…(0 < N < 1)….…(3)
𝑻
Magnetic field plots for the Alnico 9 & N48SH
𝑳
𝑾
magnets with = 0.2, 0.5, 1, 2 & 5 and =1.
𝑻
𝑻
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 2nd 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 “N” for all the permanent
𝑾
magnets with various ; for which more effort
𝑻
is needed.
Demagnetizing factors (N) from FEA and fitted equations
𝑾
for NdFeB and Alnico 9 with =1
𝑻
Demagnetizing factors (N) from FEA and fitted
𝑾
equations for NdFeB and Alnico 9 with = 4
𝑻
6. Four tables are presented with FEA demagnetizing factors and calculated load lines for
rectangular prisms with the length to a side
ratio in the range of 0.04 to 20.