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Development of positioning error measurement system based on geometric optics for long linear stage

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Abstract

The positioning error of the moving stage has a significant influence on the machining accuracy of a machine tool. Therefore, the positioning error must be measured accurately. Laser interferometer systems are widely used for positioning error calibration due to their accuracy, but these systems also have many shortcomings in standard procedure and measurement methods. In this study, a positioning error measurement system for a long linear stage by using geometric optics rather than interference principles is proposed. However, as the stage moves, geometric errors apart from the positioning error are produced. Accordingly, the proposed measurement system is designed to not only measure the positioning error but also simultaneously measure the multi-degree-of-freedom (MDOF) geometric errors of the linear stage. The proposed measurement system was characterized numerically by using the commercial software Zemax; the mathematical model of the errors was constructed by using a skew-ray tracing method, a homogeneous transformation matrix, and a first-order Taylor series expansion. The feasibility and effectiveness of the proposed measurement system were experimentally verified by using a laboratory-built prototype. The experimental results demonstrate that compared with conventional laser interferometers, the proposed measurement system has similar accuracy and can simultaneously measure the six-degree-of-freedom (6-DOF) geometric errors of a long linear stage.

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Funding

The authors gratefully acknowledge the financial support provided to this study by the Ministry of Science and Technology of Taiwan under grant nos. MOST 106-2628-E-006-010-MY3 and 108-2218-E-002-071.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Cheng Kung University, No. 1, University Road, Tainan City, 70101, Taiwan

    Chien-Sheng Liu & Jie-Yu Zeng

  2. Center for Measurement Standards, Industrial Technology Research Institute, No. 321, Sec. 2, Kuang Fu Rd., Hsinchu, 30011, Taiwan

    Yu-Ta Chen

  3. Department of Mechanical Engineering, Minghsin University of Science and Technology, No. 1, Xinxing Rd., Xinfeng Township, Hsinchu County, 30401, Taiwan

    Yu-Ta Chen

Authors
  1. Chien-Sheng Liu
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  2. Jie-Yu Zeng
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Contributions

Jie-Yu Zeng: writing (original draft preparation), conceptualization, methodology, software, validation. Chien-Sheng Liu: writing (reviewing and editing), supervision, project administration. Yu-Ta Chen: conceptualization.

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Correspondence to Chien-Sheng Liu.

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Liu, CS., Zeng, JY. & Chen, YT. Development of positioning error measurement system based on geometric optics for long linear stage. Int J Adv Manuf Technol 115, 2595–2606 (2021). https://doi.org/10.1007/s00170-021-07332-8

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  • DOI: https://doi.org/10.1007/s00170-021-07332-8

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