Movement modeling and control of precession mechanism for bonnet polishing based on static highest-stiffness strategy

Abstract

Movement modeling and control of a ‘bonnet tool’ polishing machine, based on a strategy of static highest-stiffness, are presented. The aim is to achieve polishing controllability as the bonnet tool executes a precessive motion trajectory. Taking an aspheric optical surface, e.g. lens or mirror, as the workpiece, the precessive polishing tool trajectory is designed as if the moving parts were rigid bodies connected by ideal articulations. Then by establishing the Jacobian stiffness matrix of the bonnet tool machine, the static stiffness of the machine is derived taking into account tool loading along its path. To minimize deformation, the control algorithm that achieves a maximum static stiffness strategy is superposed on the rigid body system tool trajectory model. This combined bonnet tool trajectory is produced by numerical simulation. Finally suitability of the rigid body movement model, compensated for desired static, but not inertial, load deflection, is assessed by simulating the trajectory of the tool’s rotational axis to determine how much angular deviation it sustains from the local surface normal. It was found that this bonnet polishing tool compensation method, based on a greatest static stiffness strategy, will produce satisfactory results.