Demagnetization Curve
Demagnetization Curve: Theoretical Foundations
What is a Demagnetization Curve?
Professor, a demagnetization curve is part of the B-H curve, right?
The second quadrant of the B-H hysteresis loop is called the demagnetization curve (demag curve). It is the most critical characteristic for determining the operating point of a permanent magnet.
Key parameters:
- $B_r$ (Remanent Flux Density): Magnetic flux density at H=0. For NdFeB magnets, 1.0 to 1.4 T
- $H_{cB}$ (Coercivity): Magnetic field strength where B=0
- $H_{cJ}$ (Intrinsic Coercivity): Magnetic field strength where magnetization J=0. An indicator of heat resistance
- $(BH)_{max}$: Maximum energy product. A comprehensive indicator of magnet performance
A magnet with high $B_r$ and high $H_{cJ}$ is ideal, isn't it?
Yes. However, both decrease as temperature rises. For NdFeB, the temperature coefficient is approximately $-0.12$%/°C for $B_r$ and about $-0.6$%/°C for $H_{cJ}$. It is essential to use the demagnetization curve at the operating temperature.
Summary
- B-H curve in the second quadrant — Operating characteristics of permanent magnets
- $B_r$, $H_{cJ}$, $(BH)_{max}$ — The three major parameters for magnet selection
- Temperature dependence — Risk of irreversible demagnetization at high temperatures
Why Neodymium Magnets are the "Strongest" – The Exquisite Balance of Br and Coercivity
The shape of the demagnetization curve is determined by two factors: remanent flux density Br and coercivity Hc. Ferrite magnets have relatively high Hc but low Br. Alnico magnets have high Br but very low Hc, making them prone to demagnetization even with a small reverse field. Neodymium magnets (Nd₂Fe₁₄B), discovered in 1984 by Dr. Masato Sagawa and others at Sumitomo Special Metals, achieved the ideal combination of both high Br and high Hc. Their BHmax (maximum energy product) exceeds 400 kJ/m³, allowing them to store about 10 times the energy of ferrite magnets of the same volume—this is the theoretical basis for calling them the "strongest magnets."
Computational Methods for Demagnetization Curve
Handling Demagnetization Curves in FEM
How do you incorporate a demagnetization curve into FEM?
Permanent magnets are handled using an equivalent current model. Constitutive relation for magnets:
$\mathbf{M}_0$: Remanent magnetization vector. The slope of the demagnetization curve is the recoil permeability $\mu_r$ (approx. 1.05 for NdFeB).
How do you determine irreversible demagnetization?
Irreversible demagnetization occurs when the operating point falls below the knee point of the demagnetization curve. In JMAG or Maxwell, the operating point of each element can be plotted on the demagnetization curve to visualize regions below the knee point. For demagnetization analysis including temperature distribution, a temperature-dependent demagnetization curve is assigned to each element.
Summary
- Equivalent current model — $\mathbf{B} = \mu_0(\mathbf{H} + \mathbf{M}_0)$
- Knee point determination — Evaluation criterion for irreversible demagnetization
- Temperature coupling — Use temperature-corresponding demagnetization curves for each element
How to Obtain Demagnetization Curve Data – Don't Blindly Trust Manufacturer Catalogs
Demagnetization curve data input into FEA is often taken from manufacturer datasheets, but actual magnets can deviate from catalog values due to lot variations and manufacturing temperature history. Particularly for high-grade products with BHmax (maximum energy product) above 50 MGOe, cases have been reported where in-house measurements of small samples are 5-10% lower than catalog values. For critical designs, it is more reliable to perform in-house measurements using a VSM (Vibrating Sample Magnetometer) and feed the data, including temperature dependence, back into the FEA. Designs based solely on catalog data can lead to unexpected demagnetization issues during mass production.
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