## [JAC039] Torque Analysis of a Three Phase Induction Motor Accounting for the Skew

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### 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 contain things like the torque variations caused by influence from the slots.
Applying skew generally affects the flow of magnetic flux in the axial direction, making it complex. This is why an analysis that can correctly verify the three dimensional magnetic flux flow is necessary to obtain an advance evaluation of the skew’s effects.
This Application Note presents a comparison of the torque waveforms of three phase squirrel cage induction motors with and without torque, and introduces the effects of using skew to reduce torque variations. Changes in the higher components caused by skew are also displayed by separating the frequencies of the secondary current, which causes the torque variations.

### Torque Variations

The torque waveform with and without a cage that has skew is indicated in fig. 1, fig. 2, and fig. 3, and the size of the torque variations is indicated in Table 1. The results in fig. 1 are obtained with a 3D analysis. The results in fig. 2 are obtained with a 2D analysis. The results in fig. 3 combine the 2D analysis results with the skew angle. An induction motor produces torque from the rotating magnetic field of the stator coil and the induction current of the rotor. The torque variations can be reduced by using a cage that has skew. Fig. 3 shows that the superimposition of the 2D analysis and the skew angle makes it easy to display the reductions in torque ripple from skew and the approximate generated torque.

### Current Density Distribution

Fig. 4 shows the secondary current density versus frequency, and fig. 5 shows the current density distribution of the cage. The harmonic components of the current produced by the harmonic magnetic flux in the stator are reduced by using a cage with skew as indicated by the secondary current density versus frequency. This is why the torque variations have been reduced as described above.