Identification of inherent position-independent geometric errors for three-axis machine tools using a double ballbar with an extension fixture

  • Seung-Han Yang
  • Hoon-Hee Lee
  • Kwang-Il LeeEmail author


This paper presents a double ballbar method with an extension fixture to identify the position-independent geometric errors of three-axis machine tools with respect to their entire workspace by conducting face- and body-diagonal length tests. To extend the length of the double ballbar to the required nominal length in the face- and body-diagonal directions, an extension fixture is designed and manufactured using a fused-deposition-modeling 3D printer to ensure that it is lightweight. Inherent position-independent geometric errors can be calculated from measured lengths by using homogeneous transformation matrices, which are multiplied under the assumption of small values, to determine the volumetric error produced by a machine tool. The relationships between the position-independent geometric errors, roll-pitch-yaw errors, and measured lengths can be derived according to the definition of the straightness errors, based on the end-point of the reference straight line. Finally, the position-independent geometric errors, with analysis of measurement uncertainties, can be identified by substituting the values of the roll-pitch-yaw errors, measured by a multi-axis calibrator, into the derived relations. The results can then be validated by re-measuring the face- and body-diagonal lengths with error compensation. The main advantage of the proposed approach is that it can be used to identify the inherent position-independent geometric errors of machine tool workspaces. This could contribute to reducing volumetric errors in machine-tool workspaces by allowing compensation for measurement errors, thus making machine tools more effective.


Position-independent geometric errors Position-dependent geometric errors Extension fixture Double ballbar Diagonal length tests Volumetric error Machine tools 


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Funding information

This work was supported by the National Research Foundation (NRF) of Korea funded by the Ministry of Education (2010-0020089), (2017R1D1A1B03028396).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringKyungpook National UniversityDaeguRepublic of Korea
  2. 2.School of Mechanical and Automotive EngineeringKyungil UniversityGyeongsan-siRepublic of Korea

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