TY - JOUR
T1 - Development of positioning error measurement system based on geometric optics for long linear stage
AU - Liu, Chien Sheng
AU - Zeng, Jie Yu
AU - Chen, Yu Ta
N1 - Funding Information:
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.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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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U2 - 10.1007/s00170-021-07332-8
DO - 10.1007/s00170-021-07332-8
M3 - Article
AN - SCOPUS:85106670284
SN - 0268-3768
VL - 115
SP - 2595
EP - 2606
JO - International Journal of Advanced Manufacturing Technology
JF - International Journal of Advanced Manufacturing Technology
IS - 7-8
ER -