Iron Loss (Core Loss) Analysis
Theory: three components of iron loss
Overview
After raising our EV motor's speed, iron loss jumped and efficiency dropped. Will a different steel grade help?
The fix depends on which component grew. Iron loss is split into hysteresis loss (cycling magnetisation back and forth), eddy-current loss (currents circulating in the core) and excess loss that neither explains. Hysteresis scales with frequency and eddy loss with its square, so higher speed and frequency make eddy loss dominant — in which case thinner or higher-resistivity steel helps.
Loss separation (Bertotti)
$f$ is frequency, $B$ peak flux density, $\sigma$ sheet conductivity, $d$ thickness and $\rho$ density; $k_h, k_{ex}$ are fitted from material measurements. The middle classical eddy term scales with the square of both thickness and frequency. The hysteresis exponent deviates somewhat from 2 depending on the material.
Where the formula holds
The classical eddy formula assumes the sheet is much thinner than the skin depth, with uniform flux through the thickness. As frequency rises and skin depth approaches thickness, flux crowds to the surface and the formula overestimates loss.
Silicon steel transformed transformers
Late-19th-century transformer cores were ordinary iron — lossy, and plagued by ageing as losses rose with use. Around 1900 Hadfield and colleagues in Britain found that adding a few percent silicon raised resistivity, cut eddy loss and suppressed ageing. In the 1930s Goss in the US invented grain-oriented electrical steel with aligned crystals, sharply lowering transformer core loss. Japanese steelmakers have since produced world-leading low-loss grades with techniques such as domain refinement.
Worked examples
Example 1: frequency and component shares
Illustrative coefficients (0.35 mm; at 50 Hz and 1.5 T, hysteresis 1.6 W/kg and excess 0.3 W/kg; conductivity 2.0×10⁶ S/m):
| Condition | Hysteresis | Eddy | Excess | Total | Eddy share |
|---|---|---|---|---|---|
| 50 Hz, 1.5 T | 1.6 | 0.3 | 0.3 | 2.2 W/kg | 13% |
| 400 Hz, 1.0 T | 5.7 | 8.4 | 3.7 | 17.8 W/kg | 47% |
| 1 kHz, 1.0 T | 14.2 | 52.7 | 14.6 | 81.5 W/kg | 65% |
Example 2: effect of thickness
| Condition | 0.35 mm | 0.20 mm | Reduction |
|---|---|---|---|
| 50 Hz, 1.5 T | 2.2 W/kg | 2.0 W/kg | −9% |
| 400 Hz, 1.0 T | 17.8 W/kg | 12.1 W/kg | −32% |
| 1 kHz, 1.0 T | 81.5 W/kg | 46.0 W/kg | −44% |
At 50 Hz thinner sheet barely helps, but at high frequency it helps a lot.
Right. In a 50 Hz transformer hysteresis dominates, so easily magnetised grain-oriented or well-textured steel helps. At hundreds of hertz, as in high-speed motors, eddy loss dominates and thin or high-resistivity steel helps; a 10 kg motor core goes from 178 W to 121 W at 400 Hz. At 1 kHz, though, skin depth (about 0.21 mm assuming μr 3,000) is below 0.35 mm, so the classical formula overstates loss. For real evaluation use the steel maker's frequency-specific measured data.
How to approach the analysis
Computing it in FEA
- Obtain each element's flux-density waveform from magnetic analysis (transient with rotation for motors).
- Decompose waveforms into harmonics and sum the loss of each; for rotating fields consider both directions.
- Fit coefficients to material data (loss measured at each frequency and flux density).
- Apply degradation factors for punching and assembly, and pass the loss distribution to thermal analysis.
Cautions
- PWM harmonics: inverter switching harmonics can add 10–30% to iron loss.
- Processing damage: punched edges degrade magnetic properties, strongly affecting narrow teeth.
- Stress effects: compressive stress from shrink fits and press fits raises iron loss.
“Iron loss 1.5 times the datasheet”
A prototype motor's measured iron loss came out nearly 1.5 times the value calculated from datasheet figures — not unusual. Datasheets use sinusoidal fields on undamaged test samples. In a real motor, inverter harmonics, punched-edge degradation, housing press-fit stress and rotating fields each add loss. Build correction factors in from the start of design, and calibrate them on prototype measurements to improve predictions for the next design.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Using datasheet values directly | Iron loss underestimated | Correct for processing and harmonics |
| Classical formula at high frequency | Eddy loss overstated | Compare with skin depth |
| Sinusoidal-only evaluation | Harmonic loss missed | Decompose the waveform |
| Acting without separating components | Ineffective material choice | Identify the dominant component |
| Not passing loss to thermal analysis | Local hot spots missed | Couple as a distribution |
I'd like to try iron-loss and magnetic-material calculations myself.
Try the magnetic hysteresis simulator for hysteresis, the skin depth calculator for skin depth and the transformer efficiency tool for transformer efficiency. Related topics are covered in the Steinmetz equation, high-frequency transformers, winding loss and motor efficiency maps.
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