Eddy Current Loss
Eddy Current Loss: Theoretical Foundations
Fundamentals of Eddy Current Loss
Professor, how do you calculate eddy current loss?
It's the Joule loss caused by eddy currents induced in a conductor within an alternating magnetic field. For a single thin sheet:
$d$: sheet thickness, $f$: frequency, $B_m$: magnetic flux density amplitude, $\rho$: resistivity. Since it's proportional to $d^2$, laminating to reduce sheet thickness is fundamental for loss reduction.
That's the reason for laminating electrical steel sheets.
Eddy current loss decreases as thickness is reduced: 0.5 mm → 0.35 mm → 0.2 mm. However, the number of laminations increases and the space factor (volume ratio of iron) decreases. For high-frequency applications, amorphous alloys (25 μm) and nanocrystalline alloys (18 μm) are also used.
Summary
- $P_e \propto d^2 f^2 B_m^2$ — Proportional to the square of thickness and frequency
- Laminated Core — Reduces thickness and interrupts eddy current paths
- Amorphous Alloy — Significantly reduces high-frequency loss with ultra-thin sheets
The Secret of 0.35mm Silicon Steel Sheet—The Thickness-Squared Law Governs Core Design
Have you ever wondered why transformer cores are made of hundreds of thin laminated sheets? Since eddy current loss is proportional to the square of the thickness d, slicing a single iron sheet (35mm thick) into 1/100th thickness (0.35mm) and laminating them reduces the loss per sheet to 1/10000. Even with 100 sheets laminated, the total loss is 1/100 of the original. Modern hybrid vehicle motors use high-strength non-oriented silicon steel sheets with thicknesses of 0.20mm or 0.15mm, with thickness uniformity within ±5μm. Balancing rolling technology and magnetic properties is where material manufacturers show their skill, and this "thinness competition" is still ongoing.
Computational Methods for Eddy Current Loss
Eddy Current Loss Calculation with FEM
How do you calculate eddy current loss with FEM?
There are two approaches.
1. Direct Method — Solve the eddy current equation and integrate loss via $P = \int \mathbf{J}^2/\sigma \, dV$. Requires meshing each steel sheet, leading to high computational cost.
2. Iron Loss Formula Method — Obtain magnetic flux density distribution via FEM, then calculate via post-processing using iron loss formulas (e.g., modified Steinmetz equation).
Term 1: Hysteresis loss, Term 2: Classical eddy current loss, Term 3: Anomalous eddy current loss.
Which method is used in JMAG?
The iron loss formula method is standard in JMAG. It enables high-precision iron loss prediction without meshing each sheet individually. It can also account for iron loss increase due to harmonic magnetic fields.
Summary
- Direct Method — Accurate but computationally expensive
- Iron Loss Formula Method — Practical. Fast calculation via post-processing
- Harmonic Consideration — Harmonic iron loss can become dominant in PWM drives
Amorphous Metal—The "Ultra-Low Loss" Core Born from a Cooling Rate of 10⁶℃/s
You may have encountered the material "amorphous alloy" in numerical analysis of eddy current loss. This is a non-crystalline metal obtained by spraying molten metal onto a roll and rapidly quenching it at a rate of one million degrees Celsius per second. The lack of crystal structure makes magnetic domain movement extremely smooth. Its thickness is also 25μm, over 10 times thinner than silicon steel sheets. Using it for distribution transformer cores can theoretically reduce iron loss by about 70%, leading major Japanese transformer manufacturers to start mass production in the 2010s. However, it has drawbacks: "brittle," "difficult to cut," and "expensive." Care is also needed when handling its material constants in analysis.