# Application Catalog

## 191 - Torque Analysis of Three-Phase Induction Motors Accounting for the Skew Using the Multi-slice Method

2014-12

Module: DP

### Overview

An induction motor can utilize skew easily because the cage is constructed by metallic casting such as die casting. When skew is applied, it arranges the variations in the magnetic flux that links to the cage in a sinusoidal wave. This makes it possible to eliminate the harmonic components from the induction current that cause negative torque and constrain things like the torque variations caused by influence from the slots.
Generally when skew is applied, magnetic flux also flows in the axis direction, and this requires that a 3D analysis is performed in order to thoroughly evaluate skew effect. However, 3D analyses tend to cause an inordinate amount of calculation costs. The multi-slice method, representing skew approximately with a 2D cross-section superimposition, is effective.
In this document, the multi-slice method is used to compare torque waveforms of a cage three-phase induction motor with and without skew, and is then used to verify the effects of using skew to reduce torque variations.

### Torque Characteristic

The torque waveform is indicated in fig. 1, and the torque characteristics are indicated in table 1.
The harmonics of torque are significantly deleted due to skewing, showing that this is connected to a decrease in vibration and noise.

### Current in the Secondary Conductor

Average current density distribution in one period of electric angle in the secondary conductor is shown in fig. 2 and 3, a section graph is shown in fig. 4, and current waveform and frequency components for the secondary conductor are shown in fig. 5 and 6.
As shown in fig. 2, 3 and 4, bar current without skewing is concentrated on the rotor surface, and with skewing, bar current enters almost to the inside. As shown in fig. 5 and 6, it is believed that this is due to the harmonic components in the secondary current decreases due to skewing, and the skin depth then becomes thicker. Slot harmonic components around 420(Hz), determined by the number of revolutions and slots, are greatly reduced.