Int. J. of Applied Electromagnetics and Mechanics 9 (1998) 263–275 263 IOS Press Shape optimization of synchronous machine rotor O. Gizolme, F. Thollon ∗ , G. Clerc and G. Rojat CEGELY – UPRESA CNRS 5005, Ecole Centrale de Lyon, BP 163-69131 Ecully cedex, France Received 1 April 1997 Abstract. This paper describes a shape optimization of a synchronous machine rotor to reduce torque ripples. The procedure of optimization is based on coupling a finite element 2D software and a genetic algorithm. One of the most important criteria for minimizing the torque ripple is the distribution of the flux density in the airgap of the machine. Therefore, in the first investigations, we search to minimize the harmonics’ rate of the flux density. The field analysis is done through the finite element method. Simplifying assumptions, involving material characteristic and geometrical domains, are made in order to limit computational time. Different objective functions (taking into account flux density harmonics) used by the genetic algorithm for the optimization and different strategies of evolution are tested and some results are presented. One of these is used to calculate torque ripples by the finite element method. This result is compared with the initial torque and shows the improvement on the torque ripple. 1. Introduction The design of electromagnetic devices is usually based on solving Maxwell’s equations with finite element method (FEM) or boundary integrals method (BIM). Nevertheless, the large number of geo- metrical and electrical parameters implies many 2D or 3D calculations, and many results that cannot be easily used by the designer. The system is then difficult to optimize. Therefore, developing au- tomatic optimization procedures for the design of electromagnetic devices has become indispensable [3,4]. To improve automatic design optimization, a finite element software (FLUX2D, distributed by CEDRAT) is associated with a genetic algorithm (GA). The genetic algorithm, in comparison with the others algorithms, can supply the global optimum without being trapped in a local extremum. It needs neither a starting point nor the calculation of the gradient. The algorithm does not interact with the choice of resolution method. They act on a set of possible solutions, representing design configurations, associated with a value of objective function. It only uses this function for optimization. So, the resolution FEM package does not have to be modified when a genetic algorithm is used. However, the computed time is still important. For electrical machine design, especially for an electrical drive, one of the most important purposes is to obtain a torque as smooth as possible. In this paper, we present a study on the torque ripple optimization of a synchronous machine. The optimization is applied on the pole shape of the rotor. The general organization of the optimization procedure is described. The performances of this package are tested with different objective functions. Then, the obtained results for the initial geometry and for different optimized geometries are compared. * Corresponding author. Fax: +33 04 78 43 37 17; E-mail: thollon@trotek.ec-lyon.fr. 1383-5416/98/$8.00  1998 – IOS Press. All rights reserved