Measurement and Evaluation Methods of Highly Steep Free-form Surfaces Based on Coordinate Measurement

doi:10.3901/JME.2025.11.336

Abstract

Abstract: High-steepness characteristic optical elements are widely used in precision physics experiments, and their high steepness and sudden curvature change nature constrain the requirement of high-precision measurement. Aiming at the problem that the detection of such elements exceeds the dynamic range and reachable space limit of the measuring instrument, the optimized measurement method of subfaces segmentation and splicing is proposed. First, the subfaces are segmented based on the actual face shape of the high steepness free-form surfaces; second, the measurement steepness is reduced by changing the spatial position of the high steepness workpiece; and finally, the common areas of the subfaces are spliced and optimized to obtain the actual face shape. Otherwise, in view of the unknown attitude transformation problem of subfaces under different geometrical positional shapes, the evaluation model and algorithm for the contour error of complex surfaces based on point-triangular slice distance approximation and isometric surface matching are proposed, and the surface shape evaluation model based on the radius compensation is established, which realizes the high-precision measurement of high-steepness complex surfaces. The high steepness comparison experiments show that the slice measurement method is more accurate than the full-caliber direct measurement method, and the measurement accuracy of the surface shape error evaluation method is better than 1 μm, and the repeatability of multiple measurements is better than 0.5 μm.

Key words: highly steep surface, curvature mutation, freeform surface, slicing measurement, stitching optimization

CLC Number:

TH741

WANG Pengxiang, PENG Xiaoqiang, LAI Tao, LIU Junfeng, CHEN Shanyong, LI Zelong. Measurement and Evaluation Methods of Highly Steep Free-form Surfaces Based on Coordinate Measurement[J]. Journal of Mechanical Engineering, 2025, 61(11): 336-347.

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