Electric Motor Design Framework Based on Topology Optimization Applicable to Surface Permanent Magnet Synchronous Motors

Abstract

This dissertation presents a topology optimization based structural design framework for improving performances of electric motors. Topology optimization is an attractive methodology that can find the optimal design by mathematically determining the layout of materials without the designer’s intuition or an initial structure. In order to apply the topology optimization to the motor design, the multi-material topology optimization scheme for electromechanical devices and the motor performance analysis are described in this dissertation. Afterward, this dissertation takes into account three topics in order to apply topology optimization to the practical design framework of electric motors. The first topic is to develop a structural design framework based on topology optimization for electric motor design. Since topology optimization is a method to find an optimal material layout in a fixed design domain, the motor dimension (i.e., diameters of the rotor and stator, stack length) cannot be determined. The dimension of electric motors occupies a large part in the determination of performances such as torque, efficiency, weight, etc. Thus, it is necessary to consider the dimension of electric motors. In this dissertation, a three-stage sequential structural design framework is presented in which the response surface method and size optimization are placed before topology optimization. Therefore, in the first stage, the response surface is constructed based on the design of experiments. Then, the diameters of the rotor and stator, the stacking length, and the size of the stator teeth are determined through the size optimization. In the second stage, the layout of permanent magnet and iron materials is designed using the multi-material topology optimization in the design domain determined in the first stage. Finally, in stage 3, the stator tooth topology is designed to obtain the final design result. The torque density of a surface permanent magnet synchronous motor (SPMSM) is maximized through the proposed structural design framework. The second topic is to improve the convergence speed of topology optimization in SPMSM design. Since the design variables of the topology optimization exist for each finite element within the design domain, the optimization algorithm needs to handle a large number of design variables. In addition, since the magnetic field analysis of an electric motor is a highly nonlinear problem, a high computational cost occurs to calculate the performances. Especially, the elapsed time of torque analysis accounts for a large portion of total elapsed time in topology optimization of SPMSM. To reduce computational cost of the torque calculation, the torque analysis approach which uses the relationship between flux linkages and input currents in a rotational coordinate system is applied to the torque calculation. This torque analysis approach requires fewer finite element analyzes than the torque profile based torque analysis approach. Thus, the computational cost of the design process can be reduced. Since torque ripple, another important performance of electric motors, cannot be computed in this torque calculation approach, a function of sinusoidal air gap magnetic flux density distribution is introduced. Through this function, the torque ripple can be considered indirectly in the design result. In this dissertation, the effectiveness of the proposed approach is verified through the rotor design of an SPMSM. The third topic is the fabrication and experimental verification of topology optimization results. A topology optimization result is a form of material distribution expressed as a number between 0 and 1 within the design domain. Therefore, when the design result of topology optimization is fabricated, the motor may not drive with expected performance. It may even be impossible to manufacture due to highly complicated geometry. In this dissertation, one of the design results is post-processed with a computer-aided design (CAD) program, and the result is fabricated through a wire-cutting process. In addition, the measured back-EMF by a no-load test is compared with the predicted back-EMF by FEA for validation of the result.