Synthesis of cogging-torque waveform from analysis of a single stator slot

A simple analytical technique is proposed to synthesize the cogging-torque waveform of a permanent-magnet brushless machine from the cogging torque, which is associated with a single stator slot. An analytical expression is derived, which reveals the relationship between the two. It is then applied to two motors, which have a fractional number of slots per pole. It is shown that the resultant cogging-torque waveform can be synthesized to a high accuracy, as confirmed by both finite-element analysis and measurements. It is also shown that not all the cogging-torque harmonies that exist in the cogging-torque waveform due to a single slot will be present in the resultant cogging torque, and that the most significant components can be identified analytically.