Stiffness-optimized precession motion control for compliant bonnet polishing of high-gradient curved surfaces

Conventional motion control algorithms in bonnet polishing of high-gradient curved surfaces face challenges such as unreachable tool trajectories and insufficient dynamic response at large tilt angles, significantly limiting the adaptability and machining accuracy of bonnet polishing for complex surface geometries. To address these issues, this paper proposes a what we believe to be novel precession motion control method for high-gradient surface bonnet polishing based on stiffness-optimal solutions. Using multi-body system theory, a mapping relationship among the workpiece normal vector at the machining point, the spindle vector, and the rotary axis angles of the machine tool is established. By minimizing the B-axis tilt angle as the stiffness-optimal condition, a constrained spindle vector model for the bonnet tool is developed, and the corresponding A/B-axis angles are derived through inverse kinematic solutions. Furthermore, a spindle vector homogenization distribution algorithm based on axis velocity constraints is proposed to achieve synchronized dynamic response between the A and B rotary axes. By integrating stiffness optimization and axis dynamic response as joint constraints, this study develops an optimized precession motion control algorithm for high-gradient surface bonnet polishing. The achievable machining gradient is increased from 20° to over 35°, enabling high-precision conformal polishing of large-aperture high-gradient optical surfaces with a form preservation rate of 91.5%. This advancement significantly enhances the engineering applicability of the polishing technology.