Rotor-step straight skewing is a common method to reduce electromagnetic vibration of permanent magnet synchronous motors (PMSMs). However, the difference of the radial electromagnetic forces received by different axial positions of the stator caused by the elastic-plastic material is generally ignored in the theoretical analysis to determine the skewing structure, which makes the vibration suppression effect of the structure far less than expected in practical applications. Take a 48-slot 8-pole interior PMSM as an example, this paper compares the suppression effects of rotor-step straight skewing and rotor-step zigzag skewing when the elastoplasticity of the stator material is considered. It is pointed out that the rotor-step zigzag skewing can overcome the limitation of the straight skewing in restraining electromagnetic vibration in practical application. Based on the theoretical formula and multi-physical field simulation, the selection rules of the rotor-step zigzag skewing angle and segment number are summarized. Finally, the rationality and effectiveness of the simulation method are verified by experiments on the prototype.

The Halbach array permanent magnet (PM) spherical motor (PMSM) consists of a spherical rotor and a spherical-shell stator. The magnetic field distribution surrounding the rotor PMs is closely related to the spherical structure of the Halbach array PMSM. The Halbach array PM configuration characteristics lead to the end leakage magnetic field in the latitudinal direction of the spherical structure, which is end effect. Establishment of an accurate 3-D magnetic field analytical model containing the end leakage magnetic field of the Halbach array PMSM is the foundation of magnetic field distortion research with its influence on eddy-current loss. The magnetic field distribution of the Halbach array PMs in the air gap is calculated using the scalar magnetic potential. Laplace and Poisson equations of the scalar magnetic potential in the spherical coordinate system are derived. To analyze the end leakage magnetic field of the Halbach array PMSM in the latitudinal direction, concept of mechanical pseudo-cycle in the motor latitudinal direction is proposed, and the cycle of Fourier series is redefined. A completed 3-D analytical expression of the Halbach array PMSM magnetic field distribution is derived by the new Fourier series and spatial integral technology, in which the end leakage magnetic field is contained. The results obtained by the proposed analytical method are compared with the numerical results, i.e., the results obtained by the finite-element method, which verify the effectiveness of the analytical method. Magnetic field distribution containing the end leakage magnetic field in different magnetization methods is compared and analyzed, which shows that the Halbach array magnetization has a larger main air-gap magnetic field and a smaller end leakage magnetic field. The effect of motor structure parameters on the end leakage magnetic field is analyzed, and the effect of end leakage magnetic field on eddy-current loss is preliminarily discussed, which shows that eddy-current loss caused by end effect almost accounts for half of the total eddy-current loss. The research on end effect and the effect of motor parameters on end effect are of great significance. In the end, the leakage magnetic field results obtained by the proposed analytical method are verified by the experimental results.

The parameter mismatches affect the control performance of the model predictive current control. Aim at this problem, an incremental model predictive current control for permanent magnet synchronous motor with online compensation for parameter mismatches is proposed. Firstly, the incremental current prediction model is constructed to eliminate the rotor flux linkage. Secondly, the relationship between the incremental current prediction error and parameter mismatches are analyzed. Moreover, it is found that the resistance mismatch has almost no effect on the incremental prediction error. Ignoring the influence of resistance, the dq -axis incremental current errors and the incremental voltages are approximately linearly related, and the linear relationship is only determined by the inductance mismatch. Thirdly, the forgetting factor recursive least square method is used to identify the linear relationship. The parameter mismatches are compensated for the whole control system online. Using the idea of incremental current deadbeat, the incremental reference current is converted into the reference voltage vector. A single vector control strategy is used to compare the computational burden of switching quantity selection with the enumeration method and sectors judgment method. Finally, the proposed strategy is verified by simulation and experiment.

A double-layer permanent magnet spherical motor (PMSM) with same spatial distribution of stator poles and rotor poles is designed based on spherical harmonic theory in this paper. The stator coils are equivalent to permanent magnets to simplify the calculation, and the torque model based on virtual work method is derived. Firstly, the torque model of single pair of poles is derived on the premise of considering the fundamental component of the magnetic field. Then, the relative positions of stator poles and rotor poles, the direction angles of torque components are discussed. Finally, the torque model is obtained by space vector theory and superposition theorem. Moreover, the simulation and experiment are implemented to verify the feasibility and correctness of the proposed torque model. The obtained torque model in this paper has similar expression with that of traditional motor, which lays a theoretical foundation for the structure optimization and control strategy of PMSM.

The accurate identification of the rotor position of permanent magnet spherical motor (PMSM) is crucial to its closed-loop control. A novel method for rotor position identification of the PMSM based on compressive sensing is proposed, which can obtain accurate rotor position by a limited number of Hall sensors. First, the article designs a Hall sensor array based on the distribution characteristics of the rotor magnetic and the frequency domain characteristics of the air gap magnetic field, combined with the Fibonacci sequence. Then, an observation matrix construction method is proposed, used for compressed sensing of the radial magnetic field strength information in air gap. Finally, the position of the spherical rotor is identified according to the reconstructed information based on the sensor output value. The identification method is verified by experiments, which shows that the identification accuracy is about 1°.