Modeling and Error Compensation for Concentric Grinding of Spherical Surfaces

To improve the form accuracy of spherical surfaces generated by cup-wheel grinding, this paper presents a geometric modeling and error compensation method for concentric grinding of spherical surfaces. A cup-shaped arc grinding wheel, hereafter referred to as a cup wheel, is used as the grinding tool. The relative motion between the cup wheel and the workpiece is formulated so that the contact arc center of the wheel follows a trajectory that is concentric with the target spherical surface. Based on this principle, trajectory models for both convex and concave spherical surfaces are established, and the geometric constraints for cup-wheel dimension selection are analyzed. To compensate for tool-setting errors and wheel-wear-induced deviations, a central-peak-based error compensation model is further developed. Grinding experiments on a convex spherical sample were conducted to verify the proposed trajectory and compensation models. The results show that the form error PV value was reduced from 57.7 μm to 0.3 μm after compensation, demonstrating the effectiveness of the proposed model in improving spherical form accuracy.