Irreversible Demagnetization Analysis for Permanent Magnet Motors
Theoretical Fundamentals of Permanent Magnet Motor Demagnetization
Irreversible Demagnetization
Professor, once demagnetization occurs, does the magnetization never return?
Good question. There are two types of demagnetization: "reversible" and "irreversible." Reversible demagnetization returns to normal when temperature drops. The problem is irreversible demagnetization. When the B-H curve operating point falls below the knee point (inflection point), the permanent magnet's magnetic force decreases permanently. Even if you remove the external cause, it doesn't recover.
What?! Permanently?! What's the mechanism behind that?
In simple terms, permanent magnets have internal "magnetic domains" — tiny regions. In normal conditions, these all point in the same direction, creating strong magnetism. But when exposed to strong reverse magnetic fields or high temperatures, some domains flip to random directions. When pushed below the knee point, these reversed domains can't flip back — this is irreversible demagnetization.
In actual motor operation, when does this happen?
The most dangerous is the combination of high temperature and large current. Specifically: when an EV climbs a steep hill at high torque (large current), during inverter short-circuit failure, or during prolonged low-speed high-torque operation. When magnet temperature rises to 180°C or 200°C due to copper losses, coercivity drops dramatically and crosses below the knee point rapidly.
B-H Curve and Knee Point
Specifically, where on the B-H curve is the knee point? Could you explain with equations?
The demagnetization curve (second quadrant B-H curve) of a permanent magnet normally decreases linearly, but beyond a certain magnetic field strength, it suddenly bends and flux density drops sharply. This "corner" is the knee point. Mathematically:
where $B_r(T)$ is the residual flux density at temperature $T$, $\mu_{\text{rec}}$ is the recoil permeability, and $H_k(T)$ is the knee point magnetic field strength. The irreversible demagnetization condition is:
where $H_{\text{op}}$ is the magnetic field strength at the magnet's operating point (including demagnetizing field).
So if the operating point drops below the knee point, it's failure. But the knee point itself changes with temperature, right?
Exactly. Moreover, when temperature rises, the knee point shifts upward-right — meaning even weaker reverse magnetic fields cause irreversible demagnetization. At high temperatures, magnets become "more fragile." That's why using temperature-dependent B-H curves in demagnetization analysis is absolutely essential.
Temperature Coefficients and Magnet Grades
How much do magnet properties change with temperature? I want to know the numbers.
NdFeB (neodymium) magnet temperature dependence is expressed by these equations:
Typical temperature coefficients look like this:
| Magnet Type | $\alpha_B$ (%/°C) | $\alpha_H$ (%/°C) | Max Operating Temp |
|---|---|---|---|
| NdFeB (N series) | -0.10 to -0.12 | -0.55 to -0.65 | 80°C |
| NdFeB (SH series) | -0.10 to -0.12 | -0.50 to -0.58 | 150°C |
| NdFeB (UH/EH series) | -0.10 to -0.12 | -0.45 to -0.55 | 180-200°C |
| SmCo | -0.03 to -0.04 | -0.15 to -0.30 | 300°C |
| Ferrite | -0.18 to -0.20 | +0.30 to +0.40 | 250°C |
NdFeB's $\alpha_H$ of -0.5 to -0.6%/°C means coercivity drops by 50-60% for every 100°C rise?!
Exactly. That's why in EV motor design where magnet temperature reaches 150°C, high-coercivity SH or UH grades are mandatory. Cheaping out with low-cost N-grade magnets leads to output dropping on summer hills due to demagnetization.
Ferrite's positive $\alpha_H$ is interesting. Temperature increases coercivity?
Good catch. Ferrite gets stronger at high temperature, but loses coercivity at low temperature. Risk of demagnetization during cold-start in winter. So ferrite motor demagnetization analysis needs to check "lowest temperature × maximum current" condition — opposite to NdFeB.
Demagnetization Margin Definition
How much safety margin should we maintain to avoid crossing the knee point?
That's quantified by Demagnetization Margin (DM). Definition:
$H_{\text{op}}$ is the minimum magnetic field strength inside the magnet (most critical location), $H_k(T)$ is the knee point field at that temperature. If DM is positive, it's safe; negative means demagnetization occurs.
Practical guidelines:
| DM Value | Assessment | Application |
|---|---|---|
| DM > 30% | Ample margin | Consumer products, low reliability demands |
| DM 20-30% | Standard margin | Automotive (normal driving) |
| DM 10-20% | Limited margin | Requires caution, sensitivity analysis essential |
| DM < 10% | Danger zone | Consider magnet grade change |
So 20% minimum is standard for automotive. But the result must change a lot depending on how you set conditions…
That's the real challenge of demagnetization analysis. Whether we assume 150°C or 170°C, 100A or 150A, and how we treat magnet tolerances all significantly affect results. That's why "worst-case stacking" becomes critical.
Actual Operating Conditions for Demagnetization
What are the specific risky scenarios in actual motor operation?
Ranked by danger level:
- Inverter short-circuit fault: Over-current 5-10× rated current flows, creating massive demagnetizing field in d-axis. Most severe condition.
- Low-speed high-torque continuous operation: EV climbing steep grades, towing. Large copper losses, rapid magnet temperature rise.
- Flux-weakening control: High-speed operation injects negative d-axis current to weaken flux. Demagnetizing field increases directly.
- Low-temperature ferrite operation: Cold-start at -40°C as mentioned earlier.
Flux-weakening is also risky? Like continuous highway cruising…
Right. At highway speeds, motor temperature is already elevated, then add flux-weakening — double jeopardy. Design validation includes maximum-speed × continuous operation × maximum coolant temperature condition.
Magnet "Memory" and "Forgetting" — Domain Wall Pinning Effects
Permanent magnet magnetization is maintained by aligned magnetic domains. External reverse field causes domain wall displacement, starting to flip domains. Below the knee point, domain walls overcome pinning sites (at grain boundaries and precipitates) and can't return. This is the microscopic mechanism of irreversible demagnetization. High-coercivity NdFeB grades (SH/UH/EH) add Dy (dysprosium) and Tb (terbium) to strengthen domain wall pinning. Rare-earth element price volatility directly impacts motor design costs.
Numerical Computation Methods for Permanent Magnet Motor Demagnetization
Electromagnetic Field FEM Formulation
What equations does the computer actually solve for demagnetization analysis?
The foundation is Maxwell's equations using magnetic vector potential $\mathbf{A}$. For 2D motor cross-section analysis, the governing equation is:
where $\nu = 1/\mu$ is magnetic reluctivity, $\mathbf{J}_s$ is applied current density, $\sigma \frac{\partial \mathbf{A}}{\partial t}$ is the eddy current term, and $\mathbf{M}_r$ is the permanent magnet's remanent magnetization vector.
The $\mathbf{M}_r$ term represents the permanent magnet. When demagnetization happens, does this value change?
Exactly. When demagnetization occurs, $\mathbf{M}_r$ decreases. But the magnet doesn't demagnetize uniformly — "partial demagnetization" occurs. Magnet edges and corners experience concentrated demagnetizing field, so demagnetization starts there.
FEM calculates B and H operating points element-by-element, judging whether each element falls below the knee point.
Handling Nonlinear B-H Curves
How is nonlinear B-H curve handled numerically?
Newton-Raphson iteration updating permeability $\mu$ each cycle. In magnet regions, the constitutive relation is:
where $\mu_{\text{rec}}$ is recoil permeability (typically 1.02–1.10). Below the knee point:
$\mu_{\text{demag}}$ is the nonlinear permeability below knee point, interpolated from B-H curve slope.
The model switches before and after the knee point, so convergence must be tricky…
Sharp insight. The B-H slope changes abruptly at knee point, making NR convergence poor. Countermeasures:
- Spline-interpolate B-H curve smoothly near knee point
- Apply NR damping (under-relaxation: 0.3–0.7)
- Set convergence criterion to residual norm $\|R\|/\|R_0\| < 10^{-4}$
- Subdivide field increments into small steps
Thermal-Electromagnetic Coupled Analysis
Since temperature is critical, do we need both thermal and electromagnetic analysis?
For accurate demagnetization assessment, thermal-electromagnetic coupling is necessary. The workflow:
- Electromagnetic analysis: Calculate torque, loss distribution (iron + copper + magnet eddy)
- Thermal analysis: Feed loss distribution as heat source, calculate temperature
- Update B-H curve: Modify magnet B-H at new temperature by element
- Re-run EM analysis: Use updated B-H curves → return to step 1
Iterate until temperature converges. Typically 2–5 iterations suffice in practice.
That must take forever to compute…
True. Industry often uses "one-way coupling": predict max magnet temperature from steady-state thermal analysis, then run EM once with that temperature's B-H curve. Full two-way coupling is reserved for final validation.
Partial Demagnetization Modeling
Earlier you mentioned "partial demagnetization." How do we model only part of the magnet demagnetizing?
Two main approaches:
- Element-wise remanence update: Judge each finite element's operating point; if below knee point, reduce $B_r$ only in that element. JMAG's "Demagnetization Analysis" uses this method.
- Recoil line tracking: Post-demagnetization magnet follows recoil line (slope $\mu_0 \mu_{\text{rec}}$) from knee point. New recoil line intercept becomes $B_r'$.
To properly evaluate motor characteristics after partial demagnetization, run EM analysis once more using demagnetized $B_r'$ values. Torque ripple and cogging torque waveforms change after demagnetization, affecting NVH (noise/vibration).
Practical Application of Permanent Magnet Motor Demagnetization Analysis
Analysis Workflow
Walk me through demagnetization analysis from the beginning.
Typical workflow:
- Create motor model: Build 2D cross-section. Use rotational periodicity — e.g., for 8-pole, model just 45°.
- Input material data: Set magnet B-H curves from 20°C to 200°C in 20°C increments. Include steel B-H (with iron loss curves).
- Set driving conditions: Speed, current amplitude/phase (d-q axes), commutation pattern.
- Set temperature condition: Direct magnet temperature input. One-way coupling: use predicted peak; two-way: link to thermal model.
- Run EM analysis: Transient analysis covering at least one electrical period (e.g., 60° for example).
- Judge demagnetization: Extract operating points of all magnet elements each timestep, compare to knee point.
- Re-analyze if needed: Update demagnetized element $B_r$, rerun. Evaluate torque drop rate.
Check all timesteps? Why not just the worst moment?
Demagnetizing field varies with rotor angle. Maximum field differs by rotor position and magnet location. Different magnet regions hit worst conditions at different rotor angles. Checking all timesteps is safest.
Mesh Strategy
Any meshing cautions for demagnetization analysis?
Magnet mesh quality is critical. Key points:
| Region | Recommended Element Size | Reason |
|---|---|---|
| Magnet (overall) | 0.3–0.5 mm | Capture partial demagnetization distribution |
| Magnet edge/corner | 0.1–0.2 mm | Demagnetizing field concentrates; demagnetization initiates here |
| Air gap | Gap length / 3 to 1/5 | Torque accuracy |
| Stator tooth tip | 0.3–0.5 mm | Capture magnetic saturation effects |
| Back yoke | 1.0–2.0 mm | Coarse okay (relatively uniform flux density) |
Magnet meshing like stress concentration in structural analysis?
Exactly parallel. "Demagnetizing field concentration" in magnets ≡ "stress concentration" in structures. Coarse mesh misses field peak, overlooking demagnetization. Minimum 3–5 element layers across magnet thickness recommended.
Worst-Case Condition Setup
What exactly is "worst case"?
Typical automotive worst-case conditions:
- Magnet temperature: Maximum operating (e.g., 180°C), with some OEMs adding +10–20°C margin for cooling failure.
- Current: Maximum current (1.5–3× rated). For short-circuit faults: 5–10× rated.
- Magnet tolerance: Lower-bound $B_r$ (-3% to -5%), lower-bound $H_{cj}$ (-5% to -10%).
- Magnet thickness: Minimum from dimensional tolerances (thinner → larger demagnetizing field).
All conditions simultaneously worst? Seems overly conservative?
Statistically, simultaneous worst is unlikely. Modern "Six-Sigma robust design" uses statistical distributions. But safety-critical functions still demand conservative worst-case stacking. OEM preference varies — check your spec.
Result Evaluation and Judgment Criteria
How do we judge pass/fail from analysis results?
Three-level evaluation:
- Demagnetization ratio: Average $B_r$ drop across magnet. Usually ≤5% acceptable.
- Demagnetized area ratio: Percentage of elements below knee point. Goal: ≤10%.
- Torque drop rate: Pre vs. post-demagnetization torque. Target: ≤2–3%.
Torque drop rate is the practical pass/fail criterion — even localized magnet corner demagnetization may be tolerable if torque impact is small.
EV's "Hill-Climb Test" — When Demagnetization Analysis Saved a Design
A Japanese OEM's EV prototype failed durability test: "long hills at low speed cause acceleration loss on flat roads afterward." Root cause: irreversible magnet demagnetization. Low-speed high-torque continuous operation pushed magnet temperature past design limit, crossing the knee point at magnet edges. Demagnetization sim reproduced the failure: corners of magnet fell below knee point with 2mm-deep partial demagnetization. Switching from N42SH to N42UH grade and adding C0.5 corner radii solved it. 15% magnet cost increase vs. recall avoidance — clearly worth it.
Irreversible Demagnetization Analysis for Permanent Magnet: Software & Solver Comparison for Permanent Magnet Motor Demagnetization Analysis
JMAG-Designer
Which software is best for demagnetization analysis?
JMAG is JSOL Corp's (Japan) electromagnetic EM software specialized for motor design. Demagnetization analysis strengths:
- Dedicated demagnetization GUI: Select "Demagnetization Analysis" — auto element-wise knee point judgment and partial-demagnetization recalculation.
- Magnet material database: Direct integration with magnet makers (Shin-Etsu, TDK, Hitachi Metals). Temperature-dependent B-H curves included.
- Demagnetization contour display: Color-map showing demagnetization ratio distribution. Instantly see which regions demagnetized and by how much.
- Parametric study: Auto-generate demagnetization margin maps varying temperature and current.
Ansys Maxwell
What about Ansys Maxwell?
Ansys Maxwell is world-leading general EM software. For demagnetization:
- Icepak thermal coupling: Single Ansys Workbench platform enables Maxwell (EM) → Icepak (thermal-fluid) two-way coupling. Detailed coolant-flow-included temperature prediction.
- Demagnetization Module: Set temperature-dependent B-H curves; auto element-wise partial demagnetization update.
- Script automation (IronPython): Batch-run many parameter cases automatically.
- 3D analysis: End effects and skewed magnets in 3D demagnetization assessment.
Altair Flux
Heard of Flux too. Is it strong in demagnetization?
Altair Flux (formerly Cedrat, France) emphasizes mathematical rigor:
- Partial demagnetization accuracy: Element-wise independent recoil line tracking. Precision demagnetization algorithm.
- FEM-BEM coupling: Open region (rotor exterior) handled by BEM → no external air mesh needed. Efficient.
- FluxMotor: Motor-dedicated pre-post processor. Quick motor geometry from templates.
Feature Comparison Matrix
Can you compare them side-by-side?
| Feature | JMAG | Maxwell | Flux | COMSOL |
|---|---|---|---|---|
| Demagnetization dedicated GUI | ◎ | ○ | ○ | △ (manual) |
| Partial demagnetization model | ◎ | ○ | ◎ | △ |
| Magnet maker database | ◎ (Japan-focused) | ○ | ○ | △ |
| Thermal coupling | ○ | ◎ (Icepak) | ○ | ◎ (built-in) |
| 3D capability | ○ | ◎ | ○ | ◎ |
| Script automation | ○ | ◎ | ○ | ◎ (Java API) |
| Japanese support | ◎ | ○ | △ | ○ |
| Price range | Medium | High | Medium | Medium-High |
Japanese motor companies seem to prefer JMAG. Why?
JMAG dominates Japanese OEM/Tier-1 market. Reason: rich magnet material partnerships with domestic makers, matching design needs. Globally, Maxwell and MotorCAD dominate. China shows JMAG-Maxwell parity. Ultimately, "magnet data availability in your software" is the selection driver.
Demagnetization Analysis: "Material Data Quality" Is King
The analysis accuracy bottleneck isn't the solver algorithm — it's magnet material data quality. Temperature-dependent B-H curves, especially near knee point curvature, depend on magnet maker's measured data. Catalog values often have only 20°C and 100°C; intermediate temperatures require interpolation. In reality, knee point temperature dependence is nonlinear, causing ±10% errors in demagnetization margin if interpolation is crude. JMAG's direct magnet-maker partnerships provide fine-grained temperature data, explaining its advantage.
Irreversible Demagnetization Analysis for Permanent Magnet: Common Issues & Debugging Permanent Magnet Motor Demagnetization Analysis
Overestimated Demagnetization Assessment
Professor, analysis says half the magnet demagnetized, but hardware doesn't show that. What's wrong?
Demagnetization over-assessment has typical patterns:
| Root Cause | Symptom | Fix |
|---|---|---|
| Coarse mesh | Magnet edge demagnetizing field spreads globally | Refine magnet to 0.2 mm or less |
| B-H curve extrapolation | Missing below-knee-point data, linear extrapolation | Get actual measured data from magnet maker |
| Temperature too high | Assumed higher temp than actual | Confirm via thermal coupled analysis |
| Magnet magnetization direction wrong | Local demagnetizing field falsely concentrated | Input correct magnetization orientation from maker data |
Nonlinear Convergence Failure
Demagnetization analysis won't converge. Help!
Convergence failure near knee point is demagnetization-specific. Try:
- Under-relaxation: Apply 0.3–0.5 damping to NR step updates (JMAG: "relaxation factor," Maxwell: "Damping Factor")
- Current ramp-up: Don't jump to full current; step through 10%→50%→100%
- B-H curve smoothing: Add extra data points near knee point, spline-interpolate smoothly
- Better initial conditions: Use prior timestep solution as initial guess
Deviation from Measured Results
Sim says no demagnetization, but hardware fails. Why?
Sim-test mismatch root causes:
- Magnet temperature underestimated: Surface temperature measured, but interior (especially in IPM motors surrounded by iron) is hotter.
- Transient temperature spikes: Short-circuit fault lasts seconds — peak temperature may exceed steady-state by far.
- Magnet batch variation: Same lot has ±10% coercivity spread. Catalog "typ." must be replaced with "min." for design.
- Assembly damage: Impact during magnet insertion, magnetization defects.
So simulation alone isn't enough — material data quality and manufacturing matter too.
Exactly. Demagnetization analysis requires total engineering: trustworthy material data, accurate temperature prediction, design margins, and manufacturing control.
Design Checklist
Before finalizing analysis, what must we check?
Demagnetization analysis checklist:
- B-H curves temperature-dependent? (Not single 20°C curve!)
- Below-knee-point B-H data available? (No crude linear extrapolation)
- Magnet temperature from worst-case?
- Current includes maximum + fault scenarios?
- Magnet tolerance (Br, Hcj lower bounds) applied?
- Mesh convergence verified? (Triple mesh size, check result stability)
- Demagnetization margin (DM) meets internal standard?
- Torque drop post-demagnetization evaluated?
- Ferrite: low-temperature condition checked?
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