## 157 – Analysis of Eddy Currents in an IPM Motor Using the Gap Flux Boundary

### Overview It is becoming increasingly common for permanent magnet motors to use rare earth magnets in order to achieve higher output density because they have a high energy product. Neodymium rare earth magnets have a high electric conductivity because they contain a great deal of iron, so when a varying magnetic field is applied to them they produce joule loss from eddy currents. IPM structure adoption and field weakening controls have become prevalent in recent years in order to allow faster rotation. This has led to an increase in the frequencies and fluctuation ranges of the varying fields applied to magnets, resulting in a corresponding increase in joule losses. By dividing the magnet like one would a laminated core to control eddy currents, one can obtain a method of raising the apparent electric conductivity while lowering the eddy currents. Armature reactions in the stator occur before the eddy currents produced in the magnet, so the eddy currents are determined by: The slot geometry of the stator core, the geometry of the rotor, the nonlinear magnetic properties of the core material, and the current waveform that flows through the coil.
In order to examine these kinds of magnet eddy currents ahead of time, one has to be precise when accounting for things like these various geometries and material properties. This is why a magnetic field simulation using the finite element method (FEM), which can account for them, would be the most effective.
This Application Note explains how to use the gap flux boundary condition to evaluate the eddy current loss in the magnet by changing the number of magnet divisions. This will make it possible to obtain effective results in a shorter period of time than with a normal transient response analysis.

### Change in the Losses of the Divided Magnet

Fig. 1 shows the magnet’s eddy current losses and fig. 2 shows the eddy current loss density distribution.
From fig. 1, it is apparent that the losses are largest at 2880 Hz. This is caused by the effects from the slot harmonic components, which are decided by multiplying the rotation speed by the number of slots. From fig. 1 and 2, it is also apparent that the eddy current losses decrease as the number of magnet divisions increases.
By increasing the number of divisions in the magnet, the magnetic flux that links the individual magnets is reduced. Because of this, the eddy current density in each divided magnet is reduced as well, making it so that the total amount of eddy current loss decreases.  ### Eddy Current Density Distribution in the Magnet Fig. 3 shows the eddy current density distribution in the magnet at 2880 Hz. It is apparent that dividing the magnet causes the eddy currents to decrease.