With development of electrical machines, traditional machine theory can no longer explain the operation principles of some new type machines, such as vernier machine, stator PM machine, etc. The principle of flux-modulation (FM) provides an important direction for development of machine theory. This study overviews the development of the FM machine regarding its principle and topology. According to the studies on FM effect of different types of electrical machines, it can be found that FM principle is universal in electrical machines. However, the researches of FM principle are still limited to some specific machines at present and it leads to the fragmentation of theory. A new general air-gap FM theory is introduced and it can be expected to be the unified theory for electrical machines. To verify the correctness of the new theory, some electrical machines, including induction machine and non-salient pole machine, are analyzed by the general air-gap FM theory. In addition, the design and engineering application of FM machine and theory is analyzed. To verify the inherent unity of electrical machine, the topology evolutions of FM machine are also discussed. Based on the new general air-gap FM theory, the innovative methods of topology can be summarized while the development prospects of FM machine are subsequently discussed.

Permanent-magnet vernier machine has an excellent potential for electric vehicles due to its desirable features of a simple mechanical structure and high-torque density, while the poor power factor is its main drawback. In this paper, a spoke-type permanent-magnet vernier machine is designed and optimized for torque density and power factor improvement. First, the machine structure, operation principle and sizing equation are introduced. Then, the machine is optimized by a multi-objective genetic algorithm. To enhance the optimization efficiency and accuracy, multi-level, sensitivity analysis and approximate model technologies are employed in the optimization. It is shown that improved torque density and power factor are achieved in the optimized machine as compared to the initial one. Finally, a prototype machine is built, and the experiments on the prototype machine are carried out to verify the design optimization.

This article investigates rotor losses in permanent magnet Vernier machines. By analyzing air-gap field, the harmonic distribution and frequency of modulated open-circuit flux density and armature reaction flux density are obtained. Then, rotor losses production principle is revealed and the influence of each harmonic on the loss is analyzed. Meanwhile, the influence of each harmonic on torque is also studied. It is found that some harmonics have no contribution to torque but produce additional losses. On this basis, a new rotor structure is proposed to suppress the rotor losses. Comparison results indicate that by suppressing nonworking harmonics, the rotor losses can be reduced effectively without affecting the effective torque. Finally, the theoretical and finite-element analysis results are verified by prototype tests.

In this paper, a modular linear permanent-magnet (PM) vernier machine is presented and optimized for high-precision and safety-critical direct-drive applications. The novelty of this paper is to not only propose a multi-objective optimization method, but also present a modular linear PM vernier machine. The presented machine has the merit of desired fault-tolerant capability and improved force performances by mainly adopting the modular mover structure. To realize low detent force, high thrust force, low force ripple and good fault tolerance, modular mover structure, PM array with flux-intensifying effect and six-phase structure are adopted in machine design. Furthermore, a new multi-objective optimization method is proposed to obtain a set of tradeoff solutions among multiple optimization objectives in machine optimization. First, to decompose the high dimension design space, the design variables are stratified into non-sensitive and sensitive levels by utilizing a comprehensive sensitivity analysis. Second, combined approximation models are implemented to decrease the large amount of computations. Then, to enhance the efficiencies of two multi-objective optimization processes, multi-objective differential evolution algorithm with ranking-based mutation operator is employed. After the optimization by the proposed multi-objective optimization method, the desired comprehensive performances with high optimization efficiency and accuracy can be obtained. Finally, to verify the results of theoretical analysis, a prototype machine is fabricated.

This article proposes a new hybrid analytical model combining subdomain model and equivalent magnetic network for permanent magnet vernier machines, which are easy to get saturated due to the air-gap field modulation effect. The key is representing saturation effect by iterating equivalent surface current as part of interface conditions in the proposed subdomain model. First, five subdomains are divided to calculate magnetic field distribution. The equivalent surface current is utilized as the boundary constraint between subdomains and iron core. Second, the equivalent magnetic network is established based on stator structure, and the fluxes flowing into flux modulation poles are equivalent as the magnetic flux sources. Node magnetic potentials can be achieved with the application of Kirchhoff's law of current. Then, the equivalent surface current is updated for convergence by node magnetic potential to accurately predict saturated performance. Finally, a prototype is manufactured, and the effectiveness of the proposed hybrid model is verified by the finite-element analysis (FEA) and experimental results. The hybrid model combines the subdomain model and the equivalent magnetic network model to complement each other and it is demonstrated to be more efficient than the FEA model while maintaining high accuracy.

Permanent magnet (PM) vernier machine has excellent prospects because of its high torque density, whereas its power factor is lower than conventional PM counterpart. At present, power factor of PM vernier machine is mainly analyzed and improved from the perspective of either PM magnetic field or armature magnetic field individually. Also, synergetic effect of both PM and armature fields is rarely considered, thus limiting the power factor improvement. In this article, a synergetic optimization approach considering both PM and armature airgap harmonics simultaneously is proposed to improve the power factor of PM vernier machine. First, the power factor is analyzed from the both PM and armature airgap harmonics. Second, the proposed optimization framework is interpreted and implemented. Meanwhile, a PM vernier machine with rotor flux barriers is selected as a design example to investigate the effectiveness of the proposed optimization approach. Finally, a prototype machine is manufactured and experimented to verify the effectiveness of the proposed optimization approach.