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Design Optimization of a Tubular Permanent Magnet Machine for Cryocoolers

A tubular permanent magnet brushless linear motor with Halbach magnet array is developed as an actuator for cryocoolers. The design method and simplified equations for the harmonic vibration actuator are proposed. A lumped circuit model is established first to predict the magnetic fields from which some dimensionless parameters can be identified. Including these dimensionless parameters, seven variables are selected to develop a parametric machine model for the 2-D finite-element analysis and design optimization. To determine the optimal variables, design of experiments and response surface methodology are applied to develop these mathematical relationships between the input design parameters and the output performance parameters of a motor of 100 W, 50 Hz, and 10 mm (stroke). Three performance parameters of the efficiency, the specific power, and the cost are optimized. Both single-objective and multiobjective optimization solution are obtained. Based on these optimizations, two candidate motors are further studied and compared.