A New Adaptive Analytical Model for the Spherical Reluctance Motor Based on Hybrid Trigonometric Function–Power Function

To realize the multiple-degree-of-freedom motion, in this article, we propose a new spherical reluctance motor (SPRM). For the nonlinear characteristics of flux linkage and excessively complex torque calculation, this article proposes a new adaptive analytical model for SPRM based on hybrid trigonometric function–power function. A sixth-degree polynomial is used to represent the five coefficients of this model, and these coefficients are calculated from flux-linkage–rotor angle–phase current data using numerical curve fitting with nonlinear least square. Based on the criterion of minimizing the sum of squared error between the flux linkage obtained by finite-element analysis and the flux linkage calculated by analytical model, the optimal trigonometric function angular frequency coefficient and the optimal power function exponent are adaptively obtained by iterative algorithm. The feasibility and accuracy of this model are validated by comparing with the existing models. Furthermore, the experimental results show that the calculated torque has good agreement with the measured torque, which further verifies the validity of the proposed analytical model. The versatility of the proposed model for SPRMs with different structure parameters is discussed as well.