Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold

SAMSUNG Electronics Co.Opto-Mechatronics LabDigital Media R&D Center416 Maetan-3Dong, Paldal-GuSuwon City, Kyungki-DoKorea 442-742E-mail: hocheol@samsung.comMinyang YangKorea Advanced Institute of Science andTechnologyDepartment of Mechanical Engineering373-1 Kusong-dong, Yusong-guTaejonKorea 305-701E-mail: myyang@kaist.ac.krAbstract. We describe a dwell time algorithm for the polishing of smallaxis-symmetrical aspherical surfaces. The dwell time distribution of thescanning polishing tool on the rotating workpiece is calculated to reducethe residual surface error. The dwell time at each discrete grid is calcu-lated as an integer multiple of the workpiece rotation period, which isalso useful for the spatially varying case in the local polishing area. Aspherical polyurethane tool with abrasives is adopted for a computer-controlled polishing process. A linear algebraic equation of removaldepth, removal matrix, and dwell time is derived by convolution of theremoval depth at the dwell positions. The nonnegative least-squaresmethod gives a solution to minimize residual error. Parametric effectssuch as the dwell grid interval are simulated. Finally, an experiment fortool mark removal is performed and the dwell time algorithm is evaluatedto be valid.