## 15 – Cogging Torque Analysis of an SPM Motor with a Step Skewed Magnet

### Overview Reductions in vibration and noise are being sought after because they are a cause of torque variations in motors, and demands for reduction are particularly strong with motors that are used in machine tools and power steering. Cogging torque, which is a torque variation that is produced when there is no current, is generated because the electromagnetic force, which is produced in the gap, changes in relation to the rotor’s rotation, making it necessary to apply skew to the stator and rotor and improvise with the magnet and stator’s geometry in order to limit said variations in electromagnetic force as a countermeasure for reducing the torque variations. When applying skew, force in the thrust direction is produced in exchange for a reduction in the cogging torque, meaning that there is the disadvantage of producing eddy currents from the magnetic flux that links in the lamination direction.
Consequently, in order to accurately evaluate a motor that has skew applied, one needs a magnetic field analysis simulation that uses the finite element method (FEM), which can account for a detailed 3D geometry, instead of studies that use the magnetic circuit method or a 2D magnetic field analysis.
This Application Note presents the use of magnetic field analysis to evaluate the magnetic flux density distribution and cogging torque in each part of an SPM motor with a step skewed magnet.

### Magnetic Flux Density Distribution

Fig. 1 shows the magnetic flux density distribution at the rotation angle of 60 degrees, and fig. 2 shows the frequency component of the magnetic flux density waveform in the gap. The upper limit of the frequency component is 1440 Hz, and the primary component of the frequency is 120 Hz because there are 4 poles and the rotation speed is 30 rps.
As shown in fig. 1, the magnetic circuit is changed by the application of the step skew. As shown in fig. 2, the ratio of the frequency component at 360 Hz, which is the fundamental frequency of the cogging torque, is 13 % when the magnet is not step skewed and 4 % when the magnet is step skewed, so the cogging torque may be reduced by applying the step skew.  ### Cogging Torque Waveform Fig. 3 shows the cogging torque waveforms of Model A and Model B. When the magnet is step skewed, the peak value of the cogging torque is reduced by about 50 percent.