Optimization method of tool axis vector based on kinematical characteristics of rotary feed axis for curved surface machining

  • Jian-wei MaEmail author
  • Guo-qing Hu
  • Feng-ze Qin
  • Wei-wei Su
  • Zhen-yuan Jia


Complex surface parts are widely used in the industrial applications, and 5-axis NC machining with ball-end cutter is the commonly adopted method for curved surface parts. Due to the additional rotary feed axis comparing with 3-axis NC machining, the tool orientation control is complex for curved surface machining. With the more complexity of curved surface parts, it is a known problem that the large incoherent movement of the rotary feed axis will easily appear in curved surface machining, which may even be beyond the kinematical performances of the rotary feed axis in machine tool, so as to affect the machining quality of curved surface parts. In order to overcome this issue, an optimization method of tool axis vector based on the kinematical characteristics of the rotary feed axis for curved surface machining is proposed. Firstly, the optimizing interval of the toolpath for tool axis vector is selected based on the relationship between the rotation angle of rotary feed axis and the accumulation arc length of toolpath. Then, the equalization method of tool axis vector based on the quaternion method is used to optimize the tool axis vector with the kinematical characteristics of rotary feed axis. Finally, the angular change curve of rotary feed axis with the optimized angular value and cumulative arc length is adjusted by the principle of least-squares fitting after the local optimization of tool axis vector. Simulation and experiment on test parts are carried out to verify the validity of the proposed method, and the achievements are significant to improve the processing quality of complex curved surface parts.


Curved surface Tool axis vector Kinematical characteristics Rotary feed axis Angular velocity Angular acceleration 


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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 Science Challenge Project of China (No. TZ2018006-0101-02), National Natural Science Foundation of China (No. 51575087 and No. 51675081), National Science and Technology Major Project of China (No. 2016ZX04001-002), 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 2018

Authors and Affiliations

  • Jian-wei Ma
    • 1
    Email author
  • Guo-qing Hu
    • 1
  • Feng-ze Qin
    • 1
  • Wei-wei Su
    • 1
  • Zhen-yuan Jia
    • 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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