Permanent Magnet Analysis
Permanent Magnet: Theoretical Foundations
Permanent Magnet
Professor, how are permanent magnets handled in FEM?
A permanent magnet is a material with remanent flux density $B_r$. It generates a magnetic field without an external current.
Or equivalently:
$\mathbf{M}_r$: Remanent magnetization, $\mathbf{H}_c$: Coercivity. In FEM, $B_r$ and the magnetization direction are specified for the magnet region.
Major Permanent Magnet Materials
| Material | $B_r$ [T] | $H_{cJ}$ [kA/m] | $(BH)_{max}$ [kJ/m³] | Applications |
|---|---|---|---|---|
| NdFeB (Sintered) | 1.2 to 1.5 | 800 to 2500 | 300 to 450 | Motors, Generators |
| SmCo | 0.9 to 1.1 | 600 to 2000 | 150 to 250 | High-temperature applications |
| Ferrite | 0.3 to 0.4 | 200 to 400 | 25 to 40 | Low-cost, Speakers |
| Alnico | 0.7 to 1.3 | 40 to 160 | 10 to 80 | Instruments, Sensors |
NdFeB is overwhelmingly strong.
NdFeB is essential for EV/HEV motors. However, there is a risk of price volatility for rare earth elements, and research on the resurgence of ferrite motors is also underway.
Summary
- Set $B_r$ and magnetization direction in FEM — The basics of permanent magnets
- NdFeB: $B_r = 1.2$ to 1.5 T — The strongest permanent magnet
- $(BH)_{max}$ — An indicator of the magnet's energy density
The Birth of Neodymium Magnets—How Masato Sagawa Changed the World of Electromagnetic Devices in 1982
The neodymium magnet (Nd₂Fe₁₄B), indispensable for modern high-performance motors, speakers, and MRI, was invented in 1982 by Dr. Masato Sagawa of Sumitomo Special Metals. Its maximum energy product (BHmax) was more than double that of the previous samarium-cobalt magnets, making the "miniaturization and high output" of EV motors possible at once. Its only weakness is the decrease in coercivity at high temperatures, leading to rapid demagnetization above 120-150°C. Accurately evaluating this "temperature characteristic" with CAE has become an essential task in motor design for EVs and hybrid vehicles.
Computational Methods for Permanent Magnet
Permanent Magnets in FEM
A permanent magnet can be treated as an equivalent current source:
For uniform magnetization, the volume current is zero, and only the surface current exists. FEM solvers perform this conversion internally and automatically.
Solver Settings
Summary
- Permanent magnet = Equivalent surface current — Automatically converted internally in FEM
- Only need to specify $B_r$ and magnetization direction — Simple user setup
Demagnetization Analysis of Permanent Magnets—Checking if the Operating Point Crosses the "Knee" of the BH Curve
In demagnetization analysis of permanent magnets, it is checked whether the "operating point (B, H)" of each magnet element is above the knee point of the demagnetization curve. By calculating B and H for all magnet elements in FEM and plotting the operating points on the demagnetization curve, demagnetization risk is evaluated. The combination of high temperature, high current, and reverse magnetic field constitutes the worst-case scenario. The analysis procedure is: ① Perform FEM calculation under worst-case current and temperature, ② Extract B-H for each element, ③ Compare with temperature-specific demagnetization curves and calculate the margin. Both JMAG and ANSYS Maxwell support this Demagnetization analysis workflow as standard.