Multi-objective optimization design of novel differential permanent magnet spring based on analytical modeling

This paper proposes a novel structure of annular differential permanent magnet spring with an octagonal moving ring and its multi-objective optimization design procedure based on analytical modeling. Compared with the typical annular differential permanent magnet spring with rectangular cross-section, this novel configuration has larger stiffness, smaller volume, and can effectively save permanent magnet materials. Based on the analytical modeling of the rectangular cross-section magnetic ring, the theory of attraction-repulsion boundary line is proposed, which is used to determine the key dimensions and optimal cross-section shape of the octagonal moving ring and is verified by the FEM simulation afterward. The octagonal moving ring is further decomposed into several types of basic permanent magnet elements to obtain their respective analytical expressions, which are then re-superimposed into the whole octagon to obtain the analytical force-displacement equation of the whole spring. Based on the analytical modeling, a multi-objective optimization procedure is performed to optimize the design parameters in order to balance the different performance requirements. The Pareto front of the desired objectives are obtained and three weighed solutions in Pareto front are selected by analytic hierarchy process. Finally, three prototypes based on the final optimization results are manufactured and tested. The experimental results verify the correctness of the design theory and optimization process.