Multi-Objective Optimization Design of a Modular Linear Permanent-Magnet Vernier Machine by Combined Approximation Models and Differential Evolution

Abstract

In this article, 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 article 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. And, the design principle of modular mover structure is introduced in detail in this article. 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 nonsensitive 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.