Analytic determination of cogging torque harmonics of brushless permanent magnet machines

In this paper a new analytic method for the determination of possibly arising cogging torque harmonics of brushless permanent magnet machines is presented. Cogging torque is caused by a change of the system's total magnetic energy concerning a rotor revolution for no stator coil(s) excitation. Usually, this change in magnetic energy is very low compared to the torque values for nominal load. The cogging torque calculation using finite element software is very sensitive regarding the quality of the used mesh. Therefore, an analytic consideration of possibly arising cogging torque harmonics is advantageous. Cogging torque harmonics only arising from calculation errors can be determined and the comparison of the calculated and the analytically determined cogging torque spectrum can be used for a qualitative evaluation of the calculation accuracy. With the presented generalized method, it is further even possible to calculate cogging torque harmonics resulting from unbalances, manufacturing errors, etc. Finally, application examples are presented to effectively reduce cogging torque without a decrease of the machine's efficiency by analyzing the cogging torque harmonics depending on the magnetic field harmonics of the permanent magnet excitation.