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A Novel Approach to Separate Geometric Error of the Rotary Axis of Multi-axis Machine Tool Using Laser Tracker

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Abstract

It is highly desirable to enhance machining accuracy for multi-axis machine tool, in which the geometric accuracy of rotary axis is a main contributing factor. Thus, how to achieve the fast and accurate identification of each geometric error of rotary axis, as well as its correction and compensation has become a key issue. This paper presents a novel method of geometric error separation of the rotary axis by means of laser tracker. For this method, the direction variation of the vectors composed by some adjacent measuring points during the rotation of turntable is measured, and rotary axis’s six geometric errors including three linear displacement and three angular displacement errors can be accurately identified on the basis of the mapping relationship between the vector’s direction variation and each geometric error. Meanwhile, the multi-station and time-sharing measurement is adopted based on GPS principle, aiming to overcome the effect of angle measurement error using laser tracker. Eventually, the geometric error separation mathematical model on rotary axis with this novel method is established, and the corresponding measurement algorithms containing the base station calibration and the measuring point determination based on the hybrid genetic algorithm, as well as each geometric error separation algorithm are deduced respectively. Furthermore, the numerical simulations are conducted to examine the validity of the derived algorithms. Results of the comparative experiment demonstrate that high-efficiency and high-precision measurement for the geometric error of the rotary axis can be accomplished by the proposed approach.

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Abbreviations

\(\delta_{x} (\theta )\) :

Linear displacement error of C-axis in X direction

\(\varepsilon_{x} (\theta )\) :

Angular displacement error of C-axis around X-axis

\(T_{1}\) :

Theoretical transformation matrix

\(T_{2}\) :

Error transformation matrix

\(A_{0}\) :

Initial measuring point

\(\overrightarrow {{A_{i} B_{i} }}\) :

Vector formed by measuring points \(A_{i}\) and \(B_{i}\)

\(P_{1}\) :

Position of the first base station

\(l_{1i}\) :

Distance from the base station \(P_{1}\) to measuring point \(A_{i}\)

\(\Delta l_{1i}\) :

Change of distance from the base station \(P_{1}\) to measuring point \(A_{i}\)

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Acknowledgements

This research was supported by State Key Laboratory of Precision Measuring Technology and Instruments (Tianjin University) (Grant No. pilab1904), Fundamental Research Funds for the Central Universities (Grant No. 2682017CX025).

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Correspondence to Jindong Wang.

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Wang, J., Cheng, C. & Li, H. A Novel Approach to Separate Geometric Error of the Rotary Axis of Multi-axis Machine Tool Using Laser Tracker. Int. J. Precis. Eng. Manuf. 21, 983–993 (2020). https://doi.org/10.1007/s12541-020-00329-5

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