Matching Measurement Strategy and Form Error Compensation for Freeform Surface Machining Based on STS Turning

Abstract

The freeform surface quality is limited by the measurement, and form error cannot be convergent via compensation machining. This paper proposed a surface matching measurement strategy based on the least squares principle and iterative precision adjustment to precisely obtain surface form error after manufacturing by single point diamond turning. Through the coordinate transformation of translation and rotation, the measured surface was aligned with theoretical surface at the same coordinate system. The corresponding simulation was carried out to verify the performance of the proposed method, and the simulation results indicated that this method can achieve accurate alignment in a sub-nanometer range. Finally, with XY polynomial freeform surface as the ideal surface, compensation experiments were undertaken. The form error of freeform converged continuously after compensation machining for three times, during which the form accuracy of PV and RMS were down to 335 nm and 34 nm respectively from 1.4 um and 173 nm. The results showed that capability of the proposed compensation method was verified and the form accuracy could be improved effectively.

Establishment and analysis of feasibility evaluation system and ultra-precision manufacturing technology for small aperture free-form surface optical element

“…Accurate matching requires translation and rotation of the measured surface morphology with six degrees of freedom to make it match the theoretical morphology best. It is theoretically based on that when the machined surface has no shape error, the surface morphology obtained by measurement should completely coincide with its theoretical morphology after being translated and rotated [25][26]. Thus, the principle of accurate matching is to translate and rotate the measured surface morphology with six degrees of freedom, so that the transformed morphology can best match the theoretical morphology in spatial position.…”

A New Method for Finding the Shape of the Main Cable in the Special Cable Plane

“…Secondly, this paper proposes a new form-finding method for space main cable-the hybrid quantum genetic algorithm. The algorithm first performs interval search by the modified quantum genetic algorithm [19] to obtain a high-precision iterative initial value, and then performs iterative calculation by the modified least squares method [20] until it meets the requirements. Finally, a suspension bridge with space special-shaped cable plane is taken as an example to study.…”