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A novel error equivalence model on the kinematic error of the linear axis of high-end machine tool

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Abstract

The kinematic errors of the linear axis play a key role in machining precision of high-end CNC (computer numerical control) machine tool. The quantification of error relationship is still an urgent problem to be solved in the assembly process of the linear axis, especially considering the effect of the elastic deformation of rollers. In order to obtain the kinematic errors of the linear axis of machine tool, a systematic error equivalence model of slider is proposed. The linear axis contains the base, the linear guide rail, and carriage. Firstly, the geometric errors of assembly surface of linear guide rail are represented by small displacement torsor. Then, according to the theory of different motion of robots, the error equivalence model of a single slider is established, namely the geometric errors of assembly surface of linear guide rail and the pose error of slider are equivalent to the elastic deformation of roller. Based on the principle of vector summation, the kinematic error of a single slider is mapped to the carriage, and the kinematic error of the linear axis is obtained. At the same time, experiments validation of kinematic error model of the linear axis is carried out. It is indicated that the proposed model is accurate and feasible. The analysis of key design parameters shows that the proposed model can provide an accurate guidance for the manufacturing and operation performance of the linear axis in quantification, and a more effective reference for the engineers at the design and assembly stage.

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Funding

This work is provided the financial support by the National Science and Technology major project (No. 2017ZX04016001) and the National Natural Science Foundation of China (NSFC No. 51775346).

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Authors and Affiliations

  1. State Key Laboratory of Mechanical System and Vibration & Shanghai Key Laboratory of Digital Manufacture for Thin-Walled Structures, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Xinxin LI, Sun JIN, Jichang ZHANG & Zhihua NIU

  2. State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Zhimin LI

  3. Shanghai SmartState Technology Co., Ltd, Pudong New Area, 201306, Shanghai, People’s Republic of China

    Jichang ZHANG

  4. Institute of Intelligent Manufacturing, School of Mechanical Engineering, Dong Hua University, Shanghai, 201600, People’s Republic of China

    Siyi DING

Authors
  1. Xinxin LI
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  2. Zhimin LI
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  3. Sun JIN
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  4. Jichang ZHANG
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  5. Siyi DING
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Contributions

Xinxin LI: Conceptualization, Methodology, Software, Validation, Visualization, Writing—original draft, Writing—review and editing

Zhimin LI: Conceptualization, Methodology, Validation, Visualization, Supervision, Writing—review and editing

Sun JIN: Conceptualization, Supervision

Jichang ZHANG: Conceptualization, Supervision

Siyi DING: Conceptualization, Software

Zhihua NIU: Conceptualization, Visualization

Corresponding author

Correspondence to Zhimin LI.

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LI, ., LI, Z., JIN, S. et al. A novel error equivalence model on the kinematic error of the linear axis of high-end machine tool. Int J Adv Manuf Technol 118, 2759–2785 (2022). https://doi.org/10.1007/s00170-021-07941-3

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