Trigonometric-spline dwell time scheduling and real-time interpolator under dynamic constraints for deterministic polishing.

Dwell time scheduling is a critical stage of deterministic polishing for ultra-precision fabrication of optics. Recently the dwell time algorithms for deterministic polishing have been widely studied. Nevertheless, there exist some shortcomings when those methods were applied in the industry, including low computational efficiency, large memory consumption, insufficiently-considered dynamic constraints, poor smoothness of the feedrate profile, and reliance on non-open CNC interpolator. To overcome those deficiencies, this work proposes a highly-efficient dwell time algorithm under the dynamic constraints of machine tools. The method calculates the initial dwell time density (DTD) sequence through non-blind deconvolution algorithm, and provides the feasible set of DTD profiles based on trigonometric-spline model. And the DTD repairing tactics are developed based on a self-adaptive offset algorithm under confined feedrate and acceleration. Finally, a C-continuous DTD profile satisfying dynamic constraints is generated. A real-time interpolator based on trigonometric-spline DTD profile is developed. The simulation results show that the proposed method generates a C-continuous feedrate profile rigidly respecting dynamic constraints, and preserves the ideal dwell time gradient distribution, achieving a more ideal residual error with high computational efficiency compared with the previous methods. The comparative experiments demonstrate that the proposed method performs better in suppressing the multi-frequency errors compared with the previous methods, and achieves high computational efficiency. The algorithm is applicable to highly-precise and highly-efficient fabrication of large-aperture optical components.