Control Method and Tool Path Interpolation of Aspherical Grinding-Polishing

An interpolation and curve partition method is proposed for the grinding and polishing of aspherical lenses. The aspherical tool path was typically partitioned using the lens coordinate, because the path cannot be written with the tool coordinate. The new partitioning method proposed in this study solved this problem using numerical analysis and made user-based partitioning possible. The interpolation algorithm was derived from the equation of asphericity. The idea for this came from the motion profile of commercial motion controllers. Each section in the separated path has ideal inputs, such as the acceleration and velocity, which are corrected afterwards by position feedback. A nano accuracy machine was constructed to test the proposed algorithm. The position error, the control accuracy, was monitored during the tracking of the tool path of the aspherical lens. The performance of the new partitioning method was compared with that of the conventional partitioning methods. We found that the proposed method was more effective at a higher feed rate, so that the processing time can be reduced simply by improving partitioning. The best accuracy in the test was under 100 nm.