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Adaptive Identification of the Position-independent Geometric Errors for the Rotary Axis of Five-axis Machine Tools to Directly Improve Workpiece Geometric Errors

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Abstract

Identification of, and compensation for, geometric errors is a cost-effective way to reduce the volumetric errors of five-axis machine tools and thus reduce workpiece geometric errors. An adaptive identification method is introduced to directly reduce workpiece geometric errors. We determined the relation between the root-sum-square values of geometric error sensitivity coefficients and workpiece geometric errors. Then, an optimal measurement path minimizing those values was adaptively determined to identify position-independent geometric errors of the rotary axis. We applied our method to improve the radial deviation of the cone-shaped ISO 10791-7 testpiece, as an example. The radial deviations were 22.6 and 27.6 μm in the counterclockwise (CCW) and clockwise (CW) directions, respectively, after compensating for the position-independent geometric errors identified using a common measurement path. These values improved by 27% and 17% to 16.4 and 22.9 μm in the CCW and CW directions, respectively, after compensating for the position-independent geometric errors identified using the optimal measurement path, thus confirming the validity of our approach.

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Abbreviations

\(b\) :

Setting angle of a ball on the workpiece table, degrees

\(n_{A}\) :

Sample number of A-axis measurements, μm

\(n_{C}\) :

Sample number of C-axis measurements, μm

\(n_{W}\) :

Sample number along the workpiece toolpath, μm

\(o_{ij}\) :

Offset error of the j-axis relative to the i-direction \(\left( {i = x,y,z;\quad j = a,c} \right)\), μm

\(s_{ij}\) :

Squareness error of the j-axis around the i-direction \(\left( {i = x,y,z;\quad j = a,c} \right)\), μrad

\(R\) :

Nominal radius of a circular measurement path for the A-axis, mm

\(\Delta R_{i,j,k}\) :

k-Th deviation in the j-direction of the i-axis \(\left( {i = A,C;\quad j = radial,axial;\quad k = 1, \ldots ,n_{A} {\text{ for A - axis}};\quad k = 1, \ldots ,n_{C} {\text{ for C - axis}}} \right)\), μm

\(\left( {x_{M,i} ,y_{M,i} ,z_{M,i} } \right)\) :

Measured positional deviations \(\left( {i = 1, \ldots ,n_{A} {\text{ for A - axis}};\quad i = 1, \ldots ,n_{C} {\text{ for C - axis}}} \right)\), μm

\(\left( {x_{W,i} ,y_{W,i} ,z_{W,i} ,a_{W,i} ,c_{W,i} } \right)\) :

iTh workpiece coordinate \(\left( {i = 1, \ldots ,n_{W} } \right)\)

\(\left( {x_{TP,i} ,y_{TP,i} ,z_{TP,i} ,a_{TP,i} ,c_{TP,i} } \right)\) :

Toolpath command corresponding to the ith workpiece coordinate \(\left( {i = 1, \ldots ,n_{W} } \right)\)

\(\left( {\Delta x_{W} ,\Delta y_{W} ,\Delta z_{W} } \right)\) :

Set-up error of a ball on the workpiece table, μm

\(\left\{ {\mathbf{i}} \right\}\) :

Coordinate system of the i-axis \(\left\{ {i = X,Y,Z,A,C} \right\}\)

\(\left\{ {\mathbf{R}} \right\}\), \(\left\{ {\mathbf{W}} \right\}\), \(\left\{ {\mathbf{t}} \right\}\) :

Coordinate system of the reference, workpiece, and tool, respectively

\({\mathbf{VE}}_{i} \left( {x_{VE,i} ,y_{VE,i} ,z_{VE,i} } \right)\) :

Volumetric errors at the ith toolpath command \(\left( {i = 1, \ldots ,n_{W} } \right)\)

\({{\varvec{\uptau}}}_{i}^{j}\) :

4 × 4 Homogeneous transformation matrix from the j to i coordinate system

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Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.NRF-2023R1A2C2003189).

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Authors and Affiliations

  1. School of Mechanical Engineering, Kyungpook National University, 80, Daehak-ro, Buk-gu, Daegu, 41566, Republic of Korea

    Seung-Han Yang

  2. School of Mechanical and Automotive Engineering, Kyungil University, 50, Gamasil-gil, Hayang-eup, Gyeongsan-si, Gyeongbuk, 38428, Republic of Korea

    Kwang-Il Lee

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Yang, SH., Lee, KI. Adaptive Identification of the Position-independent Geometric Errors for the Rotary Axis of Five-axis Machine Tools to Directly Improve Workpiece Geometric Errors. Int. J. Precis. Eng. Manuf. 25, 995–1010 (2024). https://doi.org/10.1007/s12541-024-00966-0

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