Robust optimization design for PMBL machine considering permanent magnet material uncertainties

Abstract

I. IntroductionIn recent years, permanent magnet brushless machines (PMBL) have been widely applied in various applications thanks to the merits of high efficiency, high power density, and free maintenance. For this type of machine, PMs are crucial components, whose quality has a significant influence on motor performance. However, there are many uncertainty factors in the PM material characteristic and manufacturing, which often lead to machine performance deviate from the design results. For example, for PM magnetic characteristics, there exists inconsistency between different batches of PM on magnetization magnitude and direction, which leads to PMs remanence and magnetization angle slightly deviate from a given reference. On the other hand, since some PM material machining precision is relatively lower, there is often a discrepancy between the actual and nominal size. During the assembly, this discrepancy might cause a gap between PM and core, which will seriously influence machine performance. Thus, how to design PMBL machines in a robust way to resist PM material uncertainty factor has attracted much attention.To address this problem, researchers have paid plenty of effort, proposing multiple optimization design methods. In reference [1], a robust optimization method is proposed for transverse flux PM motor, in which the influence of inconsistency of magnetic characteristics of PM material is considered. Then, in order to reduce the influence of PM machining error during the motor manufacturing process, a robust optimization method is utilized for a novel double-sides air-core PM linear synchronous motor. [2]. Besides, many engineering probability uncertainty analysis methods are employed to improve PM machine design robustness.[3] Yet, it is noted that these researches generally treated uncertainties as single random variables, lacking the consideration about the specific influence of uncertainties on PM material.In this paper, a robust optimization method is proposed to improve PMBL machine design reliability, where PM material uncertainty factors are sufficiently considered. To better clarify the optimization method, a double PM brushless machine (DPMBL) is investigated as a design example, where NdFeB-PM and ferrite-PM are adopted together to improve machine torque density and reduce the Rare-earth PM usage. The detailed design process and optimized results are presented specifically. By implementing the proposed optimization method, it can be found that the performance and design reliability of the DPMBL machine can be improved.II. Design case and design methodFig.1(a) gives the configuration of the investigated DPMBL machine. It can be seen that the machine adopts a 12/10 slot/pole combination, where two types of permanent, NdFeB and ferrite, are parallelly arranged in the rotor. Fig 1(b) shows the parametric rotor model, where the corresponding design variables are marked out. It is noted that there are two kinds of uncertainty factors in the PM material. The first one is the ferrite width, which might lead to a gap between steel and PM. The second one is the material characteristic of ferrite and NdFeB, including remeance and magnetization direction.Fig.2 describes the proposed robust optimization design process, where PM material uncertainty factors are treated as disturbance parameters. In the implement, the NdFeB and ferrite dimensions are set as design parameters, and the ferrite width, the width of the gap between ferrite and steel, the NdFeB and ferrite remeance, and magnetization direction are regarded as disturbance parameters. Based on multi-objective optimization and uncertainty analysis, the proposed approach conducts the optimization of the design parameters for machine performance enhancement.III. ResultsAfter optimization, the design scheme of the DPMBL machine is obtained. Fig 3 gives a comparison of output torque between before and after optimization. It can be seen that in the case of PM without any uncertainty factor, the average torque obtains an improvement from 35.87Nm to 38.21Nm and the torque ripple decreases from 11.26% to 8.78%. As the same PM uncertainty factor is applied to these two machines, the torque quality of the initial machine suffers an obvious decline while the optimized machine can maintain stability. To better validate the effectiveness of the optimization method, Fig 3(b) and Fig.3(c) give the torque and torque ripple distribution of a batch of machines with random PM uncertainty factors. It can be observed that the optimized machine possesses more concentrated performance. In conclusion, the proposed optimization method can resist the PM uncertainty factor and benefit the manufacturing of good quality PMBL machines.More detailed design process descriptions and experimental validation will be presented in the full paper. **