## 124 – Cogging Torque Analysis of an SPM Motor Accounting for Uneven Stator Diameter

### Overview

When a motor is assembled, the inner diameter of the stator can become uneven because of fabrication errors, shrink fitting, press fitting, etc. Cogging torque increases due to this unevenness, causing vibration and noise.
When a frame is pressed onto a stator core, and when the frame thickness is not uniform in the circumferential direction, the fitting pressure has a distribution in the circumferential direction, and the inner diameter of the stator can become uneven. In order to deal with vibration and noise, it is necessary to accurately grasp the amount of unevenness and evaluate the cogging torque in relation to this unevenness. The stator’s inner-diameter unevenness due to press fitting depends on the frame’s geometry, so it can be accurately grasped using the finite element method (FEM).
This Application Note presents how to obtain the cogging torque with and without uneven displacement in the stator teeth, based on the displacement obtained in an analysis of stress from press fitting.

### Displacement of the Teeth

A contour plot of the displacement is indicated in fig. 1. When the thickness of the frame is even, the displacement is even in all of the teeth. However, if the thickness of the frame is uneven, the displacement is also uneven. The displacement is larger in the thicker parts of the frame.
Here, the case with uniform frame thickness is referred to as even and the case with varying frame thickness is referred to as uneven.

### Cogging Torque

The cogging torque waveform is shown in fig. 2, and the frequency components of the cogging torque are shown in figures 3, 4, and 5. Fig. 2 shows that the amplitude of the cogging torque is larger for an uneven frame than for an even frame. Further, figures 3, 4, and 5 show that the amplitude is larger with an uneven frame at 720 Hz, the frequency component of the cogging torque, and also at 120 Hz, the frequency of the indented parts of the teeth every 90 deg.