Skip to main content
SpringerLink
Log in

Nonlinear error compensation based on the optimization of swing cutter trajectory for five-axis machining

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

A Correction to this article was published on 27 June 2022

This article has been updated

Abstract

In order to solve the problem of deviation between actual and theoretical machining paths due to the presence of rotation axis in five-axis machining, an interpolation algorithm based on the optimization of swing cutter trajectory and the method of corresponding nonlinear error compensation are proposed. Taking A-C dual rotary table five-axis machine tool as an example, the forward and reverse kinematic model of the machine tool is established according to the kinematic chain of the machine tool. Based on the linear interpolation of rotary axis, the generation mechanism of nonlinear error is analyzed, the modeling methods of cutter center point, and cutter axis vector trajectory are proposed respectively, and the parameterized model of swing cutter trajectory is formed. The formula for the nonlinear error is obtained from the two-dimensional cutter center point trajectory. According to the established model of swing cutter trajectory, the synchronous optimization method of cutter center point trajectory and cutter axis vector trajectory is proposed, and the nonlinear error compensation mechanism is established. First, pre-interpolation is performed on the given cutter location data to obtain a model of the swing cutter trajectory for each interpolated segment. Then, the magnitude of the nonlinear error is calculated based on the parameters of the actual interpolation points during formal interpolation, and the nonlinear error is compensated for the interpolation points where the error exceeds \([\varepsilon ]\). In the VERICUT simulation, the maximum machining error was reduced from 50 to 5 μm by this paper method. In actual machining, the surface roughness of the free-form surface was reduced from 10.5 μm before compensation to 1.8 μm. The experimental results show that the proposed method can effectively reduce the impact of nonlinear errors on processing, and is of high practical value for improving the accuracy of cutter position and the quality of complex free-form machining in five-axis machining.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Availability of data and material

The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.

Code availability

The codes used or analyzed during the current study are available from the corresponding author on reasonable request.

Change history

References

  1. Cheng Q, Wu C, Gu PH, Chang WF, Xuan DS, Li SH (2013) An analysis methodology for stochastic characteristic of volumetric error in multiaxis CNC machine tool. Math Probl Eng 2013:863283

    Article  Google Scholar 

  2. Liu W, Fan LY, Zhu QX, Zhu SM, Wang TL, Tang F (2022) Five-axis iso-error numerical control path generation for flat-end tool machining sculptured surface. Int J Adv Manuf Technol 119(11–12):7503–7516

    Article  Google Scholar 

  3. Hu Q, Chen YP, Jin XL, Yang JX (2020) A Real-Time C-3 continuous tool path smoothing and interpolation algorithm for five-axis machine tools. J Manuf Sci Eng 142(4):041002

    Article  Google Scholar 

  4. Geng C, Wu YH, Qiu J (2018) Analysis of nonlinear error caused by motions of rotation axes for five-axis machine tools with orthogonal configuration. Math Probl Eng 2018:6123596

    Article  Google Scholar 

  5. Lv XH, Guo QJ, Yuan W, Wang WH, Zhu YQ, Wang HT (2022) Error identification method of five-axis machine tool based on sample test method. Int J Adv Manuf Technol 119(11–12):8069–8075

    Article  Google Scholar 

  6. Wu S, Liu TR, Liu XL, Fan ZD, Li YP (2022) Nonlinear analysis of axial of vibration of five-axis machine tool worktable with double turntable. Int J Adv Manuf Technol 120(5–6):4097–4112

    Article  Google Scholar 

  7. Sang YC, Yao CL, Lv YQ, He GY (2020) An improved feedrate scheduling method for NURBS interpolation in five-axis machining. Precis Eng 64:70–90

    Article  Google Scholar 

  8. Ma JW, Chen SY, Li GL, Qu ZW, Lu X (2020) Study on tool orientation feasible region with constraint of non-linear error for high-precision five-axis machining. Int J Adv Manuf Technol 106(9–10):4169–4181

    Article  Google Scholar 

  9. Liang H, Hong H, Svoboda J (2003) A cutter orientation modification method for the reduction of non-linearity errors in five-axis CNC machining. Mach Sci Technol 7(1):1–18

    Article  Google Scholar 

  10. Liu HJ, Zhang AG, Zhao JB, Shang J, Liu J (2014) Analysis and compensation strategy of non-linear error in five-axis CNC machining. Appl Mech Mater 644:4967–4970

    Article  Google Scholar 

  11. Tutunea Fatan OR, Feng HY (2005) Determination of geometry-based errors for interpolated tool paths in five-axis surface machining. J Manuf Sci Eng 127(1):60–67

    Article  Google Scholar 

  12. Srijuntongsiri G, Makhanov SS (2015) Optimisation of five-axis machining G-codes in the angular space. Int J Prod Res 53(11):3207–3227

    Article  Google Scholar 

  13. Tajima S, Sencer B (2019) Accurate real-time interpolation of 5-axis tool-paths with local corner smoothing. Int J Mach Tools Manuf 142:1–15

    Article  Google Scholar 

  14. Wang H, Liu C, Wu JH, Xiong ZH (2019) Research of the real-time interpolation based on piecewise power basis functions. Proc Inst Mech Eng 233(3):889–899

    Article  Google Scholar 

  15. Zhu SW, Ding GF, Qin SF, Lei J, Zhuang L, Yan KY (2011) Integrated geometric error modeling, identification and compensation of CNC machine tools. Int J Mach Tools Manuf 52(1):24–29

    Article  Google Scholar 

  16. Fu GQ, Fu JZ, Shen HY, Yao XH, Chen ZC (2015) NC codes optimization for geometric error compensation of five-axis machine tools with one novel mathematical model. Int J Adv Manuf Technol 80(9–12):1879–1894

    Article  Google Scholar 

  17. Zhong GY, Wang CQ, Yang SF, Zheng EL, Ge YY (2015) Position geometric error modeling, identification and compensation for large 5-axis machining center prototype. Int J Mach Tools Manuf 89:142–150

    Article  Google Scholar 

  18. Makhanov SS, Munlin M (2007) Optimal sequencing of rotation angles for five-axis machining. Int J Adv Manuf Technol 35(1–2):41–54

    Article  Google Scholar 

  19. Wu JC, Zhou HC, Tang XQ, Chen JH (2015) Implementation of CL points preprocessing methodology with NURBS curve fitting technique for high-speed machining. Comput Ind Eng 81:58–64

    Article  Google Scholar 

  20. Fan LQ, Qi DG, Shen B (2011) Plane interpolation of tool orientation algorithm for 5-axis circumference milling. J Mech Eng 47(19):158–162

    Article  Google Scholar 

  21. Yang XJ, Zhou YS, Chen ZZ (2012) Analysis and control of tool path interpolation error in rotary axes montions of five-axis CNC milling. J Mech Eng 48(03):140–146

    Article  Google Scholar 

  22. She CH, Chang CC (2007) Design of a generic five-axis postprocessor based on generalized kinematics model of machine tool. Int J Mach Tools Manuf 47(3–4):537–545

    Article  Google Scholar 

  23. Kudabalage AE, Dang LV, Makhanov S (2020) Postprocessor for five-axis machining of STL surfaces based on Nagata interpolation and optimization of rotation angles. Int J Comput Integr Manuf 33(8):792–809

    Article  Google Scholar 

  24. Zhang K, Zhang LQ, Yan YC (2016) Single spherical angle linear interpolation for the control of non-linearity errors in five-axis flank milling. Int J Adv Manuf Technol 87(9–12):3289–3299

    Article  Google Scholar 

  25. Lin ZW, Fu JZ, Yao XH, Sun YF (2021) Improving machined surface textures in avoiding five-axis singularities considering tool orientation angle changes. Int J Mach Tools Manuf 98:41–49

    Article  Google Scholar 

Download references

Acknowledgements

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

Funding

This research was supported by Guangxi Natural Science Foundation under Grant No. 2021GXNSFAA220019 (grant recipient: Professor Liangji Chen).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Tiangong University, Tianjin, 300387, China

    Liangji Chen, Jinmeng Tang, Wenyi Wu & Zisen Wei

  2. College of Mechanical and Control Engineering, Guilin University of Technology, Guilin, China

    Liangji Chen

Authors
  1. Liangji Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jinmeng Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wenyi Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zisen Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The overarching research goals were developed by Liangji Chen and Jinmeng Tang. Liangji Chen and Jinmeng Tang established the models and calculated the predicted consequence. Liangji Chen, Jinmeng Tang, and Wenyi Wu analyzed the calculated results. The initial draft of the manuscript was written by Liangji Chen, Jinmeng Tang, Wenyi Wu, and Zisen Wei.

Corresponding author

Correspondence to Jinmeng Tang.

Ethics declarations

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The original online version of this article was revised: In Funding section, the grant recipient should be Professor Liangji Chen instead of Kaihong Zhou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, L., Tang, J., Wu, W. et al. Nonlinear error compensation based on the optimization of swing cutter trajectory for five-axis machining. Int J Adv Manuf Technol 124, 4193–4208 (2023). https://doi.org/10.1007/s00170-022-09534-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-022-09534-0

Keywords

Search

Navigation