# Iron Loss Calculations in Laminated Structures

Motors & generators with MagNet
Machine designers today wish to design more efficient electromagnetic and, electromechanical devices. Traditionally, the designer would use the Loss Curves provided by the material supplier at the appropriate frequency. These curves are based on Epstein frame measurements of a small sample, at various frequencies of a sinusoidal magnetic field.

Most modern core loss calculation approaches apply Epstein frame data neglecting a number of significant factors such as drive types, differences between flux density evolution in various parts of the model, etc. These approximations have various shortcomings and many other methods have been attempted to accurately account for iron losses. Ultimately, FEA based numerical schemes that take into account the histories of flux density in various parts of the machine, as well as drive type, are likely to be best. In MagNet, some novel approaches for computing iron losses have been implemented. The new techniques allow the user to separate the loss sources at the component level. Using the example of an interior permanent magnet motor, this novel approach is introduced and demonstrated below.

### METHODS and RESULTS

## CALCULATING IRON LOSSES with SIMULATION SOFTWARE

Traditionally, analysis software has used the manufacturer’s loss data in a very simple fashion. The method is to simply calculate the magnetic flux density at many points throughout the structure. This field is considered to be the peak flux density and the loss is simply read off of the Loss as a function of flux density curve for the appropriate frequency.

This method is fine for magnetostatic or harmonic analysis, since the field displayed can be assumed to be the peak field. In general, this is not the case. In a motor for example, the time-varying flux density field can be induced by motion such as in the rotor of a motor or by time-varying fields produced by currents in a motor stator. The frequencies in both cases are not the same for the rotor and stator. For time domain analysis a more sophisticated method of estimating the losses is required.

## CALCULATING IRON LOSSES in MAGNET

The method used to calculate iron losses in MagNet for magneto-static and time-harmonic analysis is the traditional method. For the time domain solutions, a new method is used to get much better estimates of the losses. This method is still based on the Epstein Frame loss measurements but uses the Steinmetz equation augmented with an eddy current term to split the total iron loss into 2 components; hysteresis with anomalous losses and eddy current losses. The Loss curve data from the manufacturer at several frequencies is used to get the coefficients for the Steinmetz and eddy current loss terms. This way, both loss quantities can be calculated individually. The new loss page for the material is shown in the figure to the left.

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## BLDC MODEL

The loss calculations were performed on a BLDC model shown in this figure. For the purposes of the analysis, only one quarter of the motor was modeled. This reduces the solution time required and also the post-processing time as well.

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## COMPARING |B| WAVEFORMS in the ROTOR and STATOR

The flux density in the stator and rotor do not have the same frequency content. As shown in the figure on the left, the stator has much less harmonic content than the rotor. With MagNet, the averaging interval for the stator and rotor are set independently or, globally, by the user. This adds more flexibility to the iron loss analysis.

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## HYSTERESIS LOSS COMPONENT

Hysteresis loss component

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## EDDY CURRENT LOSS

Eddy current loss

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## LOSSES in the ROTOR

The high frequency content in the magnetic flux density in the rotor leads to higher losses in the rotor. This is shown in more detail in the two following figures for the rotor.

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## SECOND LOSSES in the ROTOR

Second view of losses in the rotor

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## LOSSES in the STATOR

The opposite is shown in more detail in the two following figures for the stator.We have shown the example of a BLDC motor where the iron losses were split into hysteresis and eddy current loss components. It was shown that the flux density shows higher frequencies seen in the rotor. From the results it can be seen that the losses are higher in the rotor; in particular, the eddy current losses are much higher in the rotor than in the stator.

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