Study on tool orientation feasible region with constraint of non-linear error for high-precision five-axis machining

  • Jian-wei MaEmail author
  • Si-yu Chen
  • Guan-lin Li
  • Zi-wen Qu
  • Xiao Lu


Five-axis machine is one of the most versatile machine tools in complex surface machining while the machining interference occurs easily. To avoid the adverse consequences caused by interference, interference detection, and feasible region, solution are proposed. However, with the required processing accuracy of the complex surface parts increasing, the common feasible region solution is generally difficult to achieve. The error caused by the tool orientation variation along the tool path, just the non-linear error, may exceed the specified tolerance. Considering that both the interference problem and the non-linear problem could be solved by modifying the tool orientation, this study proposes a feasible region solution for tool orientation with the constraint of non-linear error, which can avoid tool interference and achieve high geometric accuracy for tool path planning in the extreme high-precision machining. The detection region that corresponds to the tool orientation at cutter contact (CC) point is calculated to avoid the collision firstly, and the feasible region of tool orientation for a certain CC point is established. After building the tool path equations between two adjacent CC points, the relationship between the movement angles of rotation axis and the machining error is built. By considering the non-linear error of the different rotatory axes respectively, the calculation formula for the movement angle variation of the rotation axis is deduced. Finally, according to the single point non-interference feasible region of the tool angle, the non-interference feasible region for the extreme high-precision processing is constructed with the constraint of non-linear error. A comparative experiment is carried out to verify the proposed feasible region construction method. The experimental results show that with the proposed method, the profile arithmetic average error and the maximum of profile deviation are 53 μm and 71 μm, respectively, which decrease by 30.13% and 32.31% compared with the conventional non-interference feasible region. The achievements have good applicability and are significant for the improvement of processing quality, which provide guidance for the extreme high-precision machining of complex surface parts.


Feasible region Interference detection Non-linear error High-precision machining Five-axis machining 



The authors wish to thank the anonymous reviewers for their comments which led to improvements of this paper.

Funding information

The project is supported by National Key Research and Development Program of China (No. 2018YFA0703304), Science Challenge Project of China (No. TZ2018006-0101-02), National Natural Science Foundation of China (No. 51675081 and No. 51575087), Science and Technology Innovation Fund of Dalian (No. 2018J12GX038), Innovation Project for Supporting High-level Talent in Dalian (No. 2016RQ012), Science Fund for Creative Research Groups (No. 51621064), and the Fundamental Research Funds for the Central Universities.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  • Jian-wei Ma
    • 1
    Email author
  • Si-yu Chen
    • 1
  • Guan-lin Li
    • 1
  • Zi-wen Qu
    • 1
  • Xiao Lu
    • 1
  1. 1.Key Laboratory for Precision and Non-traditional Machining Technology of the Ministry of Education, School of Mechanical EngineeringDalian University of TechnologyDalianChina

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