## 93 – Cogging Torque Analysis of a Motor with 8 Poles and 9 Slots Accounting for Eccentricity

### Overview

Eccentricity can occur on the center axis or the rotation axis of a motor. It is advantageous to evaluate the effects of eccentricity because it can cause vibrations and noise and break the symmetry of the magnetic flux density distribution and the electromagnetic force.
This example presents the use of a magnetic field analysis to obtain the cogging torque and electromagnetic force with and without eccentricity.

### Cogging Torque

The cogging torque is indicated in Fig. 1, the frequency components of the cogging torque with eccentricity are indicted in Fig. 2, and the frequency components of the cogging torque without eccentricity are indicated in Fig. 3.
The periodicity worsens as the cogging torque gets larger when there is eccentricity, as indicated in Fig. 1. The dominate frequency components are 240 Hz with eccentricity and 2160 Hz without eccentricity, as indicated in Fig. 2 and Fig. 3. For this reason, the periodicity of the cogging torque is 5 degrees and 45 degrees. Furthermore, the frequency component at 2160 Hz originates in the slot combination while the frequency component at 240 Hz originates in the poles.

### Electromagnetic Force Acting on the Rotor and Teeth

The direction component (X component) of the eccentricity for the electromagnetic force acting on the rotor with and without eccentricity is indicated in Fig. 4 and the orthogonal direction component (Y component) of the eccentricity is indicated in Fig. 5. The X and Y direction components of the electromagnet force acting in the teeth as the gap thins when there is eccentricity is indicated in Fig. 6 and Fig. 7. The -X axis direction component of the electromagnetic force acting on the teeth is indicated as positive values.
The X direction component of the electromagnetic force for the rotor as well as the teeth gets larger with eccentricity as indicated in Fig. 4 and Fig. 6. This is caused by the increasing effects of the magnet poles when the gap thins because of the eccentricity in the X-axis direction. Therefore, the periodicity of the cogging torque is effected.
The force without eccentricity has a periodicity of 45 degrees produced by the slot combination. Eccentricity occurs in the magnetic flux and the electromagnetic force can not be eliminated because the geometry and magnetic field do not have symmetry.