Torque modeling of reluctance spherical motors using the virtual work method

Compared to traditional single-axis motors, reluctance spherical motors (RSMs) can generate rotational torque in three spatial latitudes on a single motor, thus enabling three degrees-of-freedom (DOF) motion. Due to the complexity of their structure, the finite element method (FEM) is usually used to calculate the torque, but this method has the problem of consuming huge computational resources and long computation time. To address the problem that the FEM for calculating the torque of RSM consumes a lot of computation time, the torque model of RSM is developed by using the virtual work method considering the nonlinear cases of the magnetic circuit in this paper. Firstly, the inductance simulation of a single stator coil of a RSMs is carried out using finite element simulation software to obtain its inductance model. When the magnetic circuit is linear, the torque is obtained by partial differential calculation of the inductance surface. When the magnetic circuit is nonlinear, the distribution of flux linkage is first solved. Then, the electromagnetic torque is obtained by partial differential calculation of the magnetic co-energy. The calculated results are then projected to the global coordinate system to convert the two-DOF torque to the three-DOF torque. Finally, the experimental torque measurement platform is built, and the torque is measured and compared with the analytical calculation results. The results show that this method greatly reduces the amount of computing and simulation work with accurate modeling and provides a theoretical basis for the study of energization strategies and real-time control of the reluctance spherical motors.