Structural Design Optimization of Electric Motors to Improve Torque Performance.

Abstract

The goal of this research is to investigate an approach to find the optimal geometry of electric motors for the enhancement of force/torque performance. To predict the magnetic force/torque of electric motors having complex structure, the finite element method for magnetostatic analysis is extensively investigated. The finite element formulations for two/three dimensional problems using nodal/edge elements and for non-linear problems with Newton-Raphson iteration, are described in detail. From the obtained magnetic field, the magnetic force/torque can be calculated using various methods: Maxwell stress tensor method, virtual work method, equivalent source method, body force calculation method using the virtual air-gap scheme. Their formulations are briefly derived for both linear and non-linear problems. The observation of force calculation results confirms that total magnetic force is consistent regardless of calculation methods, but local force distribution depends on calculation methods. The structural topology optimization approach is applied to find optimal geometries in magnetic field problems. As a basic study, two optimization examples are presented. The first example aims to examine the properties of a magnetic circuit with respect to the force/torque performance. In the second example, the structural topology optimization is employed in a coupled magneto-structural problem. The mechanical compliance caused by the distributed local magnetic force is minimized when maximizing the global magnetic force. The design results reveal that different force distributions, depending on calculation method, result in the completely different optimal geometry in the magneto-structural problem. As a practical application, switched reluctance motors are designed using structural topology optimization. The design goal is to minimize torque ripple under the constrained current. To represent motor performance in a steady-state operation explicitly, the mathematical analysis model is newly developed. Magnetic characteristics are modeled using the finite element method and interpolation functions. Then, the current curve is calculated by solving the circuit equation, and the torque profile is obtained from the global virtual work method. Using the sequential linear programming method, the rotor/stator shape and voltage on-off angles are designed to improve torque performance. Two/three dimensional designs in the linear B-H relation and the design considering the nonlinearity due to magnetic saturation are presented.