Multi-objective free-form shape optimization of a synchronous reluctance machine

TL;DR

This paper presents a gradient-based free-form shape optimization method for designing a synchronous reluctance machine, significantly reducing computational time compared to stochastic methods.

Contribution

It introduces a shape derivative-based optimization approach that avoids geometric parametrization and extends to multi-objective optimization with Pareto front approximation.

Findings

Gradient-based optimization takes minutes, stochastic methods take hours.

Results produce similar shapes to parametric optimization.

Multi-objective extension approximates Pareto fronts effectively.

Abstract

This paper deals with the design optimization of a synchronous reluctance machine to be used in an X-ray tube, where the goal is to maximize the torque, by means of gradient-based free-form shape optimization. The presented approach is based on the mathematical concept of shape derivatives and allows to obtain new motor designs without the need to introduce a geometric parametrization. We validate our results by comparing them to a parametric geometry optimization in JMAG by means of a stochastic optimization algorithm. While the obtained designs are of similar shape, the computational time used by the gradient-based algorithm is in the order of minutes, compared to several hours taken by the stochastic optimization algorithm. Finally, we show an extension of the free-form shape optimization algorithm to the case of multiple objective functions and illustrate a way to obtain an approximate Pareto front.