A Seminumerical Finite-Element Postprocessing Torque Ripple Analysis Technique for Synchronous Electric Machines Utilizing the Air-Gap Maxwell Stress Tensor

A novel method to calculate the harmonic torque components in synchronous machines is presented. Harmonic torque components create a torque ripple, which is undesirable in many applications. This torque ripple is a major cause of acoustic noise and vibration and can limit the machine´s application range. A seminumerical method is developed to calculate and analyze harmonic torque components based on Maxwell stress tensor theory. Development of the Maxwell stress expressions leads to a simple algebraic expression for the calculation. Finite-element (FE) analysis is used to determine the equation variables. It is shown that postprocessing of the FE solution provides valuable information regarding the composition of the torque waveform, based upon field harmonics, which was previously unavailable. A deeper insight can be gained into more direct electromagnetic design changes to reduce torque ripple in synchronous machines, improving their torque quality. As an example, the developed method is applied to a synchronous reluctance machine with fractional slot concentrated windings that is known to exhibit high torque ripple.