How does Motor-CAD calculate the Hysteresis losses?

Motor-CAD provides analytical–empirical formulations for laminated steel core losses while Ansys Maxwell resolves hysteresis directly from nonlinear B–H curves using time-domain FEA.

A. Iron and Hysteresis Loss Modeling in Motor-CAD

Motor-CAD includes three selectable analytical methods for iron (core) loss estimation: 

1. Bertotti (Classical) Iron-Loss Model

The total core loss is divided into three physical components—hysteresis, classical eddy-current, and excess losses—represented by: 

where: 

Ph: Hysteresis loss 

Pe: Classical eddy-current loss 

Pexc: Excess (anomalous) loss 

Kh,Ke,Kexc: Empirical curve-fitted coefficients 

f: Excitation frequency (Hz) 

B: Flux density (T) 

t: Lamination thickness (m) 

α: Exponent fitted from measured data 

These coefficients are typically obtained from Epstein frame test data provided by lamination manufacturers under sinusoidal excitation. 

 

2.Bertotti (Maxwell) Variant

To ensure compatibility with Ansys Maxwell, Motor-CAD also provides a Maxwell-adjusted Bertotti formulation. This includes a 2π^2

scaling factor in the eddy-current term: 

This approach ensures consistency between Motor-CAD design-stage predictions and Maxwell FEA results, particularly in co-simulation and export workflows. 

3. Modified Steinmetz Method (MSE)

The Modified Steinmetz Equation provides an alternative that separates hysteresis and eddy-current contributions: 

where  Kh,Keddy,α,βK are empirically derived from multiple test curves (at least three data points). 

This model is especially effective for non-sinusoidal flux waveforms, such as those found in BLDC and PMSM drives.

B. Adjustments for Non-Sinusoidal and Transient Conditions

For rotating machines operating under non-sinusoidal flux conditions, Motor-CAD enhances the loss calculation by incorporating the time derivative of flux density: 

To account for minor hysteresis loops in transient simulations, Motor-CAD applies an empirical correction factor Kc: 

This correction captures intra-cycle magnetization phenomena that occur when the B–H trajectory deviates from the major loop—effects that are not represented in standard Epstein tests. 

 

References 

1. G. Bertotti, “General Properties of Power Losses in Soft Ferromagnetic Materials,” IEEE Transactions on Magnetics, vol. 24, no. 1, pp. 621–630, 1988. 
2. D. M. Ionel et al., “Computation of Core Losses in Electrical Machines Using Improved Models for Laminated Steel,” IEEE Transactions on Industry Applications, vol. 43, no. 6, 2007.