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

机译:基于界限约束最小二乘在确定性光学精加工的机床动态性能约束下基于有界约束最小二乘的停留时间算法

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摘要

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.
机译:停留时间算法是确定性光学表面技术中最重要的技术之一。现有停留时间算法通常基于非负最小二乘(NNL),而不考虑机床的动态性能约束。这是一种导致收敛准确性差的情况。在本文中,已经开发出基于机床动态性能约束的基于限制约束最小二乘(BCLS)的停留时间算法。停留时间模型的上下约束可以通过CNC(计算机数控)机床的加速和减速机制来导出。用于解决大规模停留时间模型的双度量投影牛顿迭代算法大大提高了计算效率。实验和仿真的结果表明,该算法将为具有不同动态性能的机床提供非常高的收敛精度。当机器加速度设定为低至0.1g时,表面图PV(峰 - 谷)和RMS(均方根)的精度分别在使用时分别提高40.8%和55.2%。 BCLS算法。还研究了对停留时间解决方案的不同动态性能对停留时间解决方案的影响,这将在确定性抛光机床的设计中提供良好的指导。

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