Design of High-speed High Power Density Single-phase Permanent Magnet Brushless DC Motor Considering Control Performance

Shichong Xia1, Shanming Wang2 

1 Tsinghua University, Department of Electrical Engineering, Beijing 100084, China

2 Tsinghua University, Department of Electrical Engineering, Beijing 100084, China

Abstract—This paper point out that asymmetric air gap cause phase shift of cogging torque and EMF, which will affect motor performance. The method of adding phase compensation in control is proposed. In addition, a new structure of asymmetric air gap that can reduce torque ripple is used in design of high-speed high power density single-phase permanent magnet brushless direct current (SPPMBLDC) motor. Finally, a 500 W, 100 000 rpm SPPMBLDC motor is designed and verified by finite element method. And the power density of this motor is calculated to be 32.15kW/L (37.59kW/kg).

Index Terms—cogging torque, EMF, high power density, high speed, phase shift.

I.      Introduction

When the power is 500W, the number of pole pairs is four and the rated speed is 100000 rpm, the electromagnetic torque is calculated to be 0.0477Nm. However, the amplitude of cogging torque also is about 0.04Nm. Cogging torque is a constant and only related to structure of motor, so it has a great effect on the motor torque and the performance of motor. Therefore, the way improving the performance of SPPMBLDC motor is proposed in the paper.

II.     Theory Analysis

According to the size formula in motor design, the relationship between motor power and volume can be expressed as

When the volume of the motor is constant, increasing speed can increase power of the motor. Therefore, increasing speed can increase power density. In SPPMBLDC motor, asymmetric air gap structure can increase starting torque and eliminate the start dead point of motor. In addition, asymmetric air gap can cause the phase shift of cogging torque and the EMF. The electromagnetic torque Te generated by sinusoidal current and cogging torque Tcog generated by the inherent structure of stator and rotor can be expressed as

Therefore, the torque of motor can be expressed as

III.     Verification

The tapered air gap is adopted to overcome startup dead point of SPPMBLDC motor. Different tapered air gaps produce different offset angles of cogging torque and EMF.

Fig. 1 Motor stator tooth structures with different tapered air gap.

Fig. 2 The waveforms of cogging torque, EMF, control voltage and torque.


TABLE I The results of motor with different tapered air gap

Motor structure



Control compensation angle (°)

Effective torque (Nm)

Peak torque (Nm)

A tapered air gap






B tapered air gap







From the results of Fig. 2 and TABLE I, different tapered air gaps produce different offset angle of cogging and EMF. In order to achieve a better control performance, a proper compensation angle is necessary in the control of SPPMBLDC motor. The peak torque with the structure of A tapered air gap is obviously greater than the structure of B tapered air gap. So the correctness of theoretical analysis is proved. Finally, a 500W/100000 rpm SPPMBLDC motor with B tapered air gap is designed. And the power density of this motor is calculated to be 32.15kW/L (37.59kW/kg).


M. Andriollo, M. De Bortoli, G. Martinelli, A. Morini and A. Tortella, "Design Improvement of a Single-Phase Brushless Permanent Magnet Motor for Small Fan Appliances," in IEEE Transactions on Industrial Electronics, vol. 57, no. 1, pp. 88-95, Jan. 2010.

Posted by: Shicong Xia, student, Tsinghua University, China (12-Sep-2019)