Geometric parameter identification for spherical actuator calibration based on torque formula

This paper presents a geometric calibration approach of a permanent magnet (PM) spherical actuator to improve its positioning accuracy. The proposed actuator consists of a ball-shaped rotor with multiple PM poles and a spherical-shell-shaped stator with circumferential air-core coils. Due to manufacturing and assembly restrictions, the actual geometric parameters of the spherical actuator differ from their nominal values. Hence, the identification of such errors is significant for high accuracy motion control. The calibration model is formulated based on the differential form of torque equation. To identify the position vector errors in the magnetization axes of PM poles and coils axes, an iterative least-squares algorithm is employed. The proposed calibration method can also be applied to other PM spherical actuators. To verify the robustness and effectiveness of the proposed calibration algorithm, simulations are conducted on the spherical actuator. The results have shown that the positioning accuracy of the spherical actuator is greatly improved after calibration.