Dwell Time Algorithm Based on Bounded Constrained Least Squares Under Dynamic Performance Constraints of Machine Tool in Deterministic Optical Finishing

Abstract

The dwell time algorithm is one of the most important techniques within the deterministic optical surfacing technologies. The existing dwell time algorithms are generally based on non-negative least squares (NNLS) without considering the dynamic performance constraints of machine tools. This is a circumstance that leads to poor convergence accuracy. In this paper, a dwell time algorithm, based on bounded constrained least-squares (BCLS) under dynamic performance constraints of the machine tool, has been developed. The upper and lower constraints of the dwell time model could be derived through the acceleration and deceleration mechanism of the CNC (Computer Numerical Control) machine tools. A two-metric projection Newton iteration algorithm was used to solve the large-scale dwell time model, which greatly improved the computation efficiency. The results of the experiments and simulations showed that the proposed algorithm will give a very high convergence accuracy for optical finishing with machine tools with different dynamic performances. When the machine acceleration was set to a value as low as 0.1 g, the accuracies of the surface figures PV (Peak-to-Valley) and RMS (Root Mean Square) till improved by 40.8% and 55.2%, respectively, when using the BCLS algorithm. The influences of different dynamic performances of the machine tools on the dwell time solutions have also been investigated, which will provide a good guidance in the design of deterministic polishing machine tools.