Electromagnetic modeling and structure optimization of a spherical force sensing system

Force sensing system (FSS) is widely used to simulate the control force of aircrafts for pilots. Conventional FSS employs multiple single-axis motors and complex transmission mechanisms to achieve multiple degree-of-freedom (DOF) force output of joystick, which may cause mismatched inertia and affect the output performance of FSS significantly. Therefore, one novel FSS with multiple DOF direct-drive spherical actuator is proposed in this paper to reduce the simulator’s extra inertia. To analyze its output performance systematically, a hybrid modeling method is proposed to formulate both Ampere torque and cogging torque mathematically. Equivalent current method along with Ampere force law is used to obtain the Ampere torque due to irregular structure of magnet and coil poles. The cogging torque is then obtained from airgap flux density via Maxwell stress method. From the derived analytical model, an adaptive particle swarm optimization (PSO) algorithm based on expectation (the average value of minimum errors) is proposed for multiple-parameter structure optimization. It can avoid local optimization effectively. The study shows that the optimized value greatly helps to improve the torque generation. Then, one research prototype and one testbed is developed. The comparison between experimental result and analytical model shows that the two sets of data fit with each other well. Therefore, the analytical model could be employed for motion control of the system at the next stage.