{"title":"Accurate and Effective Geometric Error Compensation for Ultrahigh-Precision Coordinate Measuring Machine Using Laser Tracking Interferometer","authors":"Jian Liang;Zefeng Sun;Jiehu Kang;Shanzhai Feng;Shuyang Wang;Zongyang Zhao;Luyuan Feng;Shangyong Li;Bin Wu","doi":"10.1109/TIM.2025.3582324","DOIUrl":null,"url":null,"abstract":"Geometric errors in coordinate measuring machines (CMMs) significantly degrade measurement accuracy. While laser tracking interferometer (LTI)-based compensation methods are widely used due to their high efficiency, the limited precision of the existing positioning techniques restricts their application in ultrahigh-precision CMMs. To address these challenges, this study introduces an accurate and efficient geometric error compensation method that utilizes LTI positioning for ultrahigh-precision CMMs. The method begins with the development of a geometric error model that employs homogeneous transformation matrices (HTMs) to map end-position deviations to error parameters. A highly accurate and robust positioning algorithm for LTI is then designed, incorporating a two-step process: initial positioning through semidefinite programming (SDP) and fine-tuning using enhanced particle swarm optimization (EPSO). After parameter identification, geometric error compensation is applied based on the established model. The test experiments were conducted on a CMM with the nominal accuracy of <inline-formula> <tex-math>$2\\:\\pm \\: L$ </tex-math></inline-formula> [mm]/<inline-formula> <tex-math>$400 \\: \\:\\mu $ </tex-math></inline-formula>m. The positioning results show that the proposed method achieves a distance mean absolute error of 0.10871, demonstrating superior precision over conventional methods. Additionally, the method exhibits excellent robustness and stability under noise interference. After compensation, precision validation results showed that the maximum detection error was reduced to <inline-formula> <tex-math>$ 0.26\\:\\mu $ </tex-math></inline-formula>m, with length measurement errors within <inline-formula> <tex-math>$0.5\\:\\pm \\: L$ </tex-math></inline-formula> [mm]/<inline-formula> <tex-math>$400 \\:\\: \\mu $ </tex-math></inline-formula>m. These results highlight substantial improvements in both measurement precision and operational performance. This research presents an effective solution for geometric error compensation in CMMs, offering enhanced performance for industrial measurement applications.","PeriodicalId":13341,"journal":{"name":"IEEE Transactions on Instrumentation and Measurement","volume":"74 ","pages":"1-11"},"PeriodicalIF":5.6000,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Instrumentation and Measurement","FirstCategoryId":"5","ListUrlMain":"https://ieeexplore.ieee.org/document/11048723/","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
Geometric errors in coordinate measuring machines (CMMs) significantly degrade measurement accuracy. While laser tracking interferometer (LTI)-based compensation methods are widely used due to their high efficiency, the limited precision of the existing positioning techniques restricts their application in ultrahigh-precision CMMs. To address these challenges, this study introduces an accurate and efficient geometric error compensation method that utilizes LTI positioning for ultrahigh-precision CMMs. The method begins with the development of a geometric error model that employs homogeneous transformation matrices (HTMs) to map end-position deviations to error parameters. A highly accurate and robust positioning algorithm for LTI is then designed, incorporating a two-step process: initial positioning through semidefinite programming (SDP) and fine-tuning using enhanced particle swarm optimization (EPSO). After parameter identification, geometric error compensation is applied based on the established model. The test experiments were conducted on a CMM with the nominal accuracy of $2\:\pm \: L$ [mm]/$400 \: \:\mu $ m. The positioning results show that the proposed method achieves a distance mean absolute error of 0.10871, demonstrating superior precision over conventional methods. Additionally, the method exhibits excellent robustness and stability under noise interference. After compensation, precision validation results showed that the maximum detection error was reduced to $ 0.26\:\mu $ m, with length measurement errors within $0.5\:\pm \: L$ [mm]/$400 \:\: \mu $ m. These results highlight substantial improvements in both measurement precision and operational performance. This research presents an effective solution for geometric error compensation in CMMs, offering enhanced performance for industrial measurement applications.
期刊介绍:
Papers are sought that address innovative solutions to the development and use of electrical and electronic instruments and equipment to measure, monitor and/or record physical phenomena for the purpose of advancing measurement science, methods, functionality and applications. The scope of these papers may encompass: (1) theory, methodology, and practice of measurement; (2) design, development and evaluation of instrumentation and measurement systems and components used in generating, acquiring, conditioning and processing signals; (3) analysis, representation, display, and preservation of the information obtained from a set of measurements; and (4) scientific and technical support to establishment and maintenance of technical standards in the field of Instrumentation and Measurement.