Electric Motor Simulation — Torque, Losses & Efficiency Map
PMSM and induction motor FEM, Maxwell stress tensor torque calculation, torque ripple, iron losses (Steinmetz), thermal coupling, and efficiency mapping.
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Quick Explainer
How does FEM compute torque in an electric motor?
The Maxwell Stress Tensor (MST) method integrates electromagnetic stress over a closed surface in the air gap: torque = integral of (r x T) dot dA. Alternatively, the Virtual Work method computes torque as dW/d_theta, the derivative of stored magnetic energy with respect to rotor angle. MST is more commonly implemented in commercial codes.
What causes torque ripple in a PMSM and how does simulation help reduce it?
Torque ripple comes from cogging torque (magnet-slot interaction even with no current) and commutation ripple (current waveform harmonics). FEM computes torque vs. rotor angle over a full electrical cycle. Design variables like magnet pole arc width, skewing angle, and slot/pole combination are optimized in FEM to minimize ripple while maintaining average torque.