Analytical calculation of 6k order electromagnetic torque of permanent magnet synchronous motors for electric vehicles

The electromagnetic torque ripple of permanent magnet synchronous motors in electric vehicles, which causes the vehicle body's structural order vibration and noise, was studied theoretically, and a new method for analytical calculation of the electromagnetic torque of permanent magnet synchronous motors based on the air-gap magnetic field's rectangle distribution was presented under the consideration of the air-gap magnetic field's non-sinusoidal distribution. Then, the frequency and order of electromagnetic torque ripple were analyzed. The results show that a permanent magnetic synchronous motor's electromagnetic toque ripple caused by the air-gap magnetic field's non-sinusoidal distribution has a 6k order (k∈N) ripple characteristic, and the frequency of torque ripple is directly proportional to pole pairs and rotate speed, which can theoretically explain the order vibration of permanent magnet synchronous motors and provide scientific basis for modal frequency planning of electric vehicles. When harmonic current is ignored, the results show that the harmonic flux linkages (Ψ_6k-1 and Ψ_6k+1) can cause 6k order harmonic electromagnetic torque. The obtained torque waveforms were approximately the same as that calculated by the 2D finite element method, which proved the accuracy and efficiency of the method.