基于坐标测量的高陡度自由曲面测量与评价方法

doi:10.3901/JME.2025.11.336

机械工程学报 ›› 2025, Vol. 61 ›› Issue (11): 336-347.doi: 10.3901/JME.2025.11.336

• 数字化设计与制造 • 上一篇

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基于坐标测量的高陡度自由曲面测量与评价方法

王鹏翔^1,2, 彭小强^1,2, 赖涛^1,2, 刘俊峰^1,2, 陈善勇^1,2, 黎泽龙^1,2

1. 国防科技大学装备综合保障技术重点实验室长沙 410073;
2. 国防科技大学超精密加工技术湖南省重点实验室长沙 410073

收稿日期:2024-06-14 修回日期:2024-10-09 发布日期:2025-07-12
作者简介:王鹏翔，男，1997年出生，博士研究生。主要研究方向为精密工程。E-mail：554367403@qq.com;彭小强，男，1977年出生，博士，研究员，博士研究生导师。主要研究方向为光学零件先进制造装备和工艺、超精密切削加工工艺及装备、超精密机电系统测控、纳米精度形面测量评价和高性能成像系统技术等。E-mail：pxq2000@vip.sina.com;赖涛(通信作者)，男，1991年出生，博士，讲师。主要研究方向为精密工程。E-mail：laitao_nudt@163.com;刘俊峰，男，1987年出生，博士，副研究员，博士研究生导师。主要研究方向为机械系统动力学、超精密加工、典型惯性器件超精密检测与动态分析等。E-mail：ljf20090702122@163.com
基金资助:
国家自然科学基金(52205505，51991371，52293494，52375473)、国家重点研发计划(2019YF0708903)和基础科研计划(JCKY2023529A001)资助项目。

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

WANG Pengxiang^1,2, PENG Xiaoqiang^1,2, LAI Tao^1,2, LIU Junfeng^1,2, CHEN Shanyong^1,2, LI Zelong^1,2

1. Laboratory of Science and Technology on Integrated Logistics Support, National University of Defense Technology, Changsha 410073;
2. Hunan Key Laboratory of Ultra-Precision Machining Technology, National University of Defense Technology, Changsha 410073

Received:2024-06-14 Revised:2024-10-09 Published:2025-07-12

摘要/Abstract

摘要： 高陡度特征光学元件广泛应用于精密物理实验，其高陡度、曲率突变的性质制约了高精度的测量要求。针对该类元件检测时超出了测量仪器的动态范围和可达空间极限的问题，提出了子面片分割与拼接优化测量方法。首先，基于高陡度自由曲面的实际面形进行面片分割；其次，通过改变高陡度工件的空间位姿降低测量陡度；最后，将子面片的公共区域进行拼接优化，得到实际面形。此外，针对不同几何位形下子面片存在未知的位姿变换问题，提出了基于点-三角片距离近似和等距面匹配的复杂曲面轮廓误差评价模型与算法，建立了基于半径补偿的面形评价模型，实现了高陡度复杂曲面的高精度测量。高陡度对比实验可知：分片测量方法比全口径直接测量方法精度更高，面形误差评价方法的测量精度优于1 μm，多次测量重复性优于0.5μm。

关键词: 高陡曲面, 曲率突变, 自由曲面, 切片测量, 缝合优化

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

中图分类号:

TH741

王鹏翔, 彭小强, 赖涛, 刘俊峰, 陈善勇, 黎泽龙. 基于坐标测量的高陡度自由曲面测量与评价方法[J]. 机械工程学报, 2025, 61(11): 336-347.

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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基于坐标测量的高陡度自由曲面测量与评价方法

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

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