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The Method of Geometric Error Measurement of NC Machine Tool Based on the Principle of Space Vector’s Direction Measurement

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International Journal of Precision Engineering and Manufacturing Aims and scope Submit manuscript

Abstract

To achieve the quick and accurate calibration of the geometric errors of NC machine tool, a new method with laser tracker on the basis of space vector’s direction measurement principle is proposed in the paper. A series of measuring points are mounted on the moving part of the machine tool, and then adjacent measuring points are connected to form a space vector respectively. Due to the motion error of the machine tool, the direction of the vectors composed will be changed. Meanwhile, the deviation of vector’s direction only relates to angular displacement error rather than linear displacement error. Based on the characteristic, the change of vectors’ direction is measured by laser tracker based on the multi-station and time-sharing measurement during the motion of machine tool, and then the angular displacement errors and linear displacement errors of each axis can be accurately identified successively, which reduces the complexity of error identification. By establishing the mathematical model of geometric error measurement of machine tool based on the principle of space vector’s direction measurement, the base station calibration algorithm by measuring the motion of the designed precise turntable, the measuring point determination algorithm and geometric error separation algorithm are derived respectively, and the accuracy of these algorithms are verified by simulations. In addition, the results of the experiments show the feasibility of the proposed method.

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Abbreviations

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

X-axis position error

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

X-axis horizontal straightness error

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

X-axis vertical straightness error

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

X-axis roll error

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

X-axis pitch error

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

X-axis yaw error

\(A\) :

Measuring point

\(\overrightarrow {AB}\) :

Vector composed of measuring points \(A\) and \(B\)

\(T\) :

Theoretical homogeneous transformation matrix

\(U\) :

Error homogeneous transformation matrix

\(P_{1}\) :

First base station

\(x_{p1}\) :

\(x\) coordinate of base station \(P_{1}\)

\(R\) :

Distance between the center of cat eye and turntable

\(l_{1i}\) :

Corresponding ranging data of laser tracker

\(x_{p1}^{0}\) :

Approximations of \(x_{p1}^{{}}\)

\(R^{0}\) :

Approximations of \(R\)

\(\Delta R\) :

Deviation between \(R^{0}\) and \(R\)

\(f_{i}\) :

Residuals

\(H\) :

Objective function

\(W\) :

Coordinate system transformation matrix

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Acknowledgement

This research was supported by National Natural Science Foundation of China (Grant No. 51305370), China Postdoctoral Science Foundation (Grant No. 2015M572491), and Fundamental Research Funds for the Central Universities (Grant No. 2682017CX025).

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Authors and Affiliations

  1. School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Jin-Dong Wang & Qing-Jie Wang

  2. College of Mechanical and Electrical Engineering, Shaanxi University of Science and Technology, Xi’an, 710021, China

    Hai-Tao Li

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  1. Jin-Dong Wang
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Correspondence to Hai-Tao Li.

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Wang, JD., Wang, QJ. & Li, HT. The Method of Geometric Error Measurement of NC Machine Tool Based on the Principle of Space Vector’s Direction Measurement. Int. J. Precis. Eng. Manuf. 20, 511–524 (2019). https://doi.org/10.1007/s12541-019-00062-8

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  • DOI: https://doi.org/10.1007/s12541-019-00062-8

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