A Generalized Theory to Predict the Torque Harmonics in Permanent Magnet Machines

The calculation of torque ripple in electric machines has been widely studied in the literature utilizing equivalent circuit approach and finite element approach. The objective of this paper is to have a deterministic set of mathematical equations consisting of basic properties such as space harmonics in the conductor distribution, space harmonics in the magnet flux distribution and time harmonics in the current to understand the creation of dc torque and torque ripple in permanent magnet machines. The physical quantities used in this study are the rotor magnetic flux density and the conductor distribution. These physical quantities are responsible for creating space harmonics. The time varying component is the inverter current harmonics. The torque is generated due to the interaction of the current density and the magnetic flux density in the air gap. The torque calculation method discussed in the paper highlights the contribution of each physical quantity in the final output torque of the machine. The set of equations presented in this paper shows the set of space and time based harmonic order components responsible for the creation of dc torque and torque ripple. This would enable in making broad system level design decisions for electric drive applications.