Abstract
Freeform optics are defined as nonrotational symmetric optical surfaces in the manufacturing industry. Freeform optics are extensively applied to many areas in order to improve system performance. Fast tool servo (FTS) assisting single-point diamond turning technology has high application prospects in freeform optics machining. This paper discusses the interpolation algorithm for tool path generation of FTS through the application of a radial basis function (RBF) algorithm. For this purpose, a positive definite RBF with compact support was employed as the interpolant. The existence is mathematically proven. Numerical simulations were performed to compare the performances of the RBF algorithm and commonly used algorithms for satisfying the requirements of existence, smoothness, and accuracy. Machining experiments were also conducted to validate the applicability of the algorithm. The simulation results showed that the RBF interpolation algorithm outperformed other algorithms in terms of smoothness. The RBF algorithm also provided the highest interpolation accuracy. Furthermore, the RBF interpolation algorithm exhibited the highest accuracy for error distribution, with large errors distributed mainly in transition areas. The machining results were also in general agreement with the simulation results although obvious practical errors were observed. Overall, RBF interpolation can provide higher accuracy and better smoothness in the tool path generation of FTS.
Highlights
Freeform optics are extensively applied in various areas, such as aerospace, energy, and life science, to improve system performance and reduce overall system complexity and system weight [1, 2]
Radial basis function (RBF) interpolation was applied as the interpolation algorithm in the tool path generation of fast tool servo (FTS) to process freeform optics
The existence requirement of FTS is satisfied by the radial basis function (RBF) interpolation algorithm. us, the RBF interpolation algorithm can be employed in the tool path generation of FTS to regenerate surfaces
Summary
Freeform optics are extensively applied in various areas, such as aerospace, energy, and life science, to improve system performance and reduce overall system complexity and system weight [1, 2]. FTS assisting single-point diamond turning has very good application prospects in freeform optics for improving machining accuracy, surface roughness, and machining speed. An interpolation algorithm with higher accuracy in the tool path generation technique was investigated to improve the machining profile accuracy of FTS. E interpolation algorithm in the tool path generation of FTS affects the machining accuracy of freeform optics. Different kinds of interpolation algorithms are applied to realize regeneration of the freeform surface in the tool path generation of FTS. Radial basis function (RBF) interpolation was applied as the interpolation algorithm in the tool path generation of FTS to process freeform optics. RBF interpolation was adopted because it can satisfy the three requirements of FTS It has the advantage of high accuracy, improving machining accuracy. It has the advantage of fast convergence, which facilitates the acquisition of a determinate solution at any point on the surface. irdly, most RBFs are second-order differentials, ensuring high smoothness of the surface approximated by RBF interpolation. e better smoothness further ensures better surface roughness
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