Impact of Flux Barriers Type and Parameterization in Reluctance Machine Torque Optimization

This paper analyzes the impact of the flux barriers (FB) type and their parameterization on the torque optimization of synchronous reluctance machines. Four different types are considered: rectangular FB, round FB, hyperbolic FB, and finally Joukowski FB, which follow the natural flux lines in a solid rotor. A parameterization that simplifies the non-overlapping constraints is introduced, and, for each of these types, the num- ber of parameters is discussed. A multi-objective optimization algorithm is run to maximize the mean torque while minimizing the torque ripple. Evaluations are performed by a 2D nonlinear finite element magnetic model. The obtained Pareto fronts show that the optimization is able to reduce the torque ripple down to about 4% for all the types, with little impact on the mean torque. The round FB have the highest mean torque and a better convergence speed than rectangular and hyperbolic FB, whereas the Joukowski FB, with half as many parameters, reaches 98% of the round FB torque. Also, the proposed parameterization reaches the optimization convergence up to 3.5 times faster than a conventional parameterization, for all the FB type