## Sources and Effects of Torque Ripple

Electrical excitation of the machine contributes to the torque ripple because the torque of the machine will follow the current. The most extreme example of this is the single-phase machine where there will be cyclical torque at two-times the fundamental frequency, and a zero-torque element. By increasing the phases, you can eliminate the zero cross and amplitude of the ripple, but you will increase the frequency. The typical machine will have three phases, which is advantageous for torque ripple, but will not eliminate it.

Since the torque is created by the sinusoidal excitation, the torque ripple from excitation will be at the same frequency as the electrical signal, which means as speed increases, so will the torque ripple frequency. In addition, other elements of torque ripple will be present, because excitation is not a perfect sine wave. Inverters which operate at a high frequency are often employed, and the machine winding will affect the distribution of current. As a result, these issues will create additional torque ripple.

Construction is another example of a contributing factor which can impact torque ripple. In all machines torque ripple is driven by the machine winding function, and each machine type has a contribution of torque ripple form the rotor magnetics interacting with the stator iron. In induction machines, the torque ripple is smaller in amplitude and could be managed with the skew of the rotor bars. With an increase in the utilization of permanent magnet machines, you need to account for the effects of the magnets on the rotor, in addition to the winding function and skew. The magnets on the rotor will attract to the iron on the stator, and as the machine spins, the magnets will attract to each stator tooth. Since there are a fixed number of rotor magnets and stator slots, this element of torque ripple will also be proportional to speed. The high amplitude, and potentially high frequencies due to the speed of the machine make torque ripple from permanent magnets a difficult problem to characterize and reduce.

Given that excitation and the construction of the machine create torque ripple, you can also use these two features in combination to alleviate it. Different construction patterns combined with different types of machine control can be used to reduce torque ripple. Advances in feedback and inverter technology allow us to push the envelope of torque ripple mitigation. In order to validate that these methods of torque ripple mitigation work, engineers need to validate their designs with measurements.