基于“误差流”理论的精密线性平台微行程定位精度表征方法

doi:10.3901/JME.2023.13.049

机械工程学报 ›› 2023, Vol. 59 ›› Issue (13): 49-58.doi: 10.3901/JME.2023.13.049

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基于“误差流”理论的精密线性平台微行程定位精度表征方法

唐皓¹, 张栋¹, 张贺¹, 高贵兵¹, 郑煜²

1. 湖南科技大学机电工程学院湘潭 411201;
2. 中南大学机电工程学院长沙 410083

收稿日期:2022-07-11 修回日期:2022-12-18 出版日期:2023-07-05 发布日期:2023-08-15
作者简介:唐皓,男,1988年出生,副教授。主要研究方向为复杂精密系统误差分析。E-mail:tanghao@hnust.edu.cn
基金资助:
国家自然科学基金(51705149)和湖南省教育厅优秀青年(20B212)资助项目。

Positioning Accuracy Characterization Approach in Micro-scale Displacement for Precise Linear Stage Based on Stream of Variation Theory

TANG Hao¹, ZHANG Dong¹, ZHANG He¹, GAO Guibing¹, ZHENG Yu²

1. College of Mechanical Engineering, Hunan University of Science and Technology, Xiangtan 411201;
2. College of Mechanical and Electronical Engineering, Central South University, Changsha 410083

Received:2022-07-11 Revised:2022-12-18 Online:2023-07-05 Published:2023-08-15

摘要/Abstract

摘要： 定位精度是衡量精密线性平台运动准确度的关键指标，传统方法无法准确揭示定位误差传递过程，其数学意义与对应分布规律难以准确映射，无法满足微行程尺度的需求。提出一种基于“误差流”理论的概率密度函数传递方法，通过建立微行程尺度下的定位误差数学模型，揭示定位误差传递规律，获取可用于表征定位精度分布规律的行程-定位误差函数，为后续误差预测与补偿提供理论基础与技术支撑。首先，剖析精密线性平台的机械结构，分析误差源，比较宏、微行程尺度下影响定位精度各因素及其权重，获取敏感误差项与相应的分布信息；其次，构建精密线性平台拓扑构型图，揭示定位误差传递规律；第三，基于“误差流”理论，建立“组件加工工艺—加工误差—装配误差—微动特性—微行程定位误差”的数学模型，逐阶段推导微行程尺度下定位精度的函数表达式，建立微行程尺度下定位误差与分布规律的数学映射关系。实验结果表明，影响定位精度各因素权重随行程变化的趋势与基于“误差流”理论的数学模型一致，新方法分布曲线在微行程(0.01～1 mm)下与实验结果更接近。

关键词: 精密线性平台, 微行程, 定位精度, 误差流理论, 概率密度函数

Abstract: Positioning accuracy is an essential index for judging the moving accuracy of precise linear stage, and conventional approach cannot reveal the positioning error transmission process precisely. This issue results in that the mathematical meaning is difficult to map the distribution law, and the requirements for micro displacement scale cannot be meet. A propagation approach of probability density function based on stream-of-variation theory is proposed. Through establishing the positioning error model in micro-scale displacement, the positioning error propagation law is revealed, and the function expression for characterizing the distribution pattern of positioning accuracy is derived, which is beneficial for following error prediction and compensation. Firstly, the mechanical structure of precise linear stage is analyzed. By comparing the error terms weight for positioning accuracy between micro and normal scale, the sensitive error terms and corresponding information is developed. Secondly, through adopting Homogeneous Transformation Matrix, the topology schematic of precise linear stage is established, and the positioning error propagation law is revealed. Thirdly, based on the stream-of-variation theory, the error model that from "part processes-mechanical error-assembly error-micro dynamic characteristic-micro displacement positioning accuracy" is established, and the mathematical relationship between positioning error and distribution law in micro displacement scale can be developed. The experimental results indicate that the trend that the error term weight for positioning accuracy changing with the displacement is in coincidence with the error model based on stream-of-variation theory, and the new approach is more accurate and closer to experimental results in micro-scale (0.01-1 mm).

Key words: precise linear stage, micro-scale displacement, positioning accuracy, stream-of-variation theory, probability density function

中图分类号:

TH115

唐皓, 张栋, 张贺, 高贵兵, 郑煜. 基于“误差流”理论的精密线性平台微行程定位精度表征方法[J]. 机械工程学报, 2023, 59(13): 49-58.

TANG Hao, ZHANG Dong, ZHANG He, GAO Guibing, ZHENG Yu. Positioning Accuracy Characterization Approach in Micro-scale Displacement for Precise Linear Stage Based on Stream of Variation Theory[J]. Journal of Mechanical Engineering, 2023, 59(13): 49-58.

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基于“误差流”理论的精密线性平台微行程定位精度表征方法

Positioning Accuracy Characterization Approach in Micro-scale Displacement for Precise Linear Stage Based on Stream of Variation Theory

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