Skip to main content
SpringerLink
Log in

Constant load toolpath planning and stiffness matching optimization in robotic surface milling

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

Abstract

Freeform surfaces are widely present in the core components of advanced equipment such as aerospace and shipbuilding, and their high-level manufacturing is a key indicator of the national manufacturing industry. Industrial robots offer a promising solution for freeform surface milling due to their high flexibility and large workspace advantages. However, maintaining stability in milling force and ensuring robot stiffness are crucial factors affecting the quality of surface machining. In this work, we propose a method for constant load toolpath planning and stiffness-based robot posture optimization in freeform surface milling. Firstly, we combine the conformal mapping algorithm and variable radius trochoidal trajectory to develop a toolpath planning method with constant cutting load, based on the material removal rate simulation according to the Dexel model. Moreover, we introduce an evaluation index for robot stiffness matching, considering the prediction of MRR. To optimize the sequence of posture changes under robot motion constraints, we employ the dynamic A* algorithm. This ensures that the robot maintains optimal stiffness performance throughout the machining process. Simulations and experimental studies validate the effectiveness and practicality of our proposed approach. These studies demonstrate that our method successfully maintains milling force stability and enhances robot stiffness, enabling more efficient freeform surface 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

Similar content being viewed by others

References

  1. Tao B, Zhao X, Ding H (2019) Mobile-robotic machining for large complex components: a review study. Sci China Technol Sci 62:1388–1400

    Article  Google Scholar 

  2. Zhu Z, Tang X, Chen C, Peng F, Yang R, Zhou L, Li Z, Wu J (2022) High precision and efficiency robotic milling of complex parts: challenges, approaches and trends. Chin J Aeronaut 35(2):22–46

    Article  Google Scholar 

  3. Kim SH, Nam E, Ha TI, Hwang S-H, Lee JH, Park S-H, Min B-K (2019) Robotic machining: a review of recent progress. Int J Precis Eng Manuf 20:1629–1642

    Article  Google Scholar 

  4. Wang W, Guo Q, Yang Z, Jiang Y, Xu J (2023) A state-of-the-art review on robotic milling of complex parts with high efficiency and precision. Robot Comput Integr Manuf 79:102436

    Article  Google Scholar 

  5. Lin J, Ye C, Yang J, Zhao H, Ding H, Luo M (2022) Contour error-based optimization of the end-effector pose of a 6 degree-of-freedom serial robot in milling operation. Robot Comput Integr Manuf 73:102257

    Article  Google Scholar 

  6. Yue C, Gao H, Liu X, Liang SY, Wang L (2019) A review of chatter vibration research in milling. Chin J Aeronaut 32(2):215–242

    Article  Google Scholar 

  7. Sun Y, Jia J, Xu J, Chen M, Niu J (2022) Path, feedrate and trajectory planning for free-form surface machining: a state-of-the-art review. Chin J Aeronaut 35(8):12–29

    Article  Google Scholar 

  8. Erkorkmaz K, Layegh SE, Lazoglu I, Erdim H (2013) Feedrate optimization for freeform milling considering constraints from the feed drive system and process mechanics. CIRP Annals 62(1):395–398

    Article  Google Scholar 

  9. Wang Q, Wang W, Zheng L, Yun C (2021) Force control-based vibration suppression in robotic grinding of large thin-wall shells. Robot Comput Integr Manuf 67:102031

    Article  Google Scholar 

  10. Erdim H, Lazoglu I, Ozturk B (2006) Feedrate scheduling strategies for free-form surfaces. Int J Mach Tools Manuf 46(7–8):747–757

    Article  Google Scholar 

  11. Huang S, Li X, Zhao Y, Sun Q, Huang H (2021) A novel lapping process for single-crystal sapphire using hybrid nanoparticle suspensions. Int J Mech Sci 191:106099

    Article  Google Scholar 

  12. Ridwan F, Xu X, Ho FCL (2012) Adaptive execution of an NC program with feed rate optimization. Int J Adv Manuf Technol 63:1117–1130

    Article  Google Scholar 

  13. Wang L, Yuan X, Si H, Duan F (2020) Feedrate scheduling method for constant peak cutting force in five-axis flank milling process. Chin J Aeronaut 33(7):2055–2069

    Article  Google Scholar 

  14. Wu S, Zhao Z, Wang CY, Xie Y, Ma W (2016) Optimization of toolpath with circular cycle transition for sharp corners in pocket milling. Int J Adv Manuf Technol 86:2861–2871

    Article  Google Scholar 

  15. Kim H-C (2007) Tool path modification for optimized pocket milling. Int J Prod Rese 45(24):5715–5729

    Article  Google Scholar 

  16. Rahman AA, Feng H-Y (2013) Effective corner machining via a constant feed rate looping tool path. Int J Prod Res 51(6):1836–1851

    Article  Google Scholar 

  17. Ma J, Song D, Jia Z, Hu G, Su W, Si L (2018) Tool-path planning with constraint of cutting force fluctuation for curved surface machining. Precis Eng 51:614–624

    Article  Google Scholar 

  18. Wang Q-H, Wang S, Jiang F, Li J-R (2016) Adaptive trochoidal toolpath for complex pockets machining. Int J Prod Res 54(20):5976–5989

    Article  Google Scholar 

  19. Luo M, Han C, Hafeez HM (2019) Fouraxis trochoidal toolpath planning for rough milling of aero-engine blisks. Chin J Aeronaut 32(8):2009–2016

    Article  Google Scholar 

  20. Ye C, Yang J, Zhao H, Ding H (2021) Task-dependent workpiece placement optimization for minimizing contour errors induced by the low posture-dependent stiffness of robotic milling. Int J Mech Sci 205

  21. Xu P, Yao X, Liu S, Wang H, Liu K, Kumar AS, Lu WF, Bi G (2021) Stiffness modeling of an industrial robot with a gravity compensator considering link weights. Mech Mach Theory 161:104331

    Article  Google Scholar 

  22. Liao Z-Y, Wang Q-H, Xie H-L, Li J-R, Zhou X-F, Pan T-H (2021) Optimization of robot posture and workpiece setup in robotic milling with stiffness threshold. IEEE/ASME Transactions on Mechatronics 27(1):582–593

    Article  Google Scholar 

  23. Liao Z-Y, Li J-R, Xie H-L, Wang Q-H, Zhou X-F (2020) Region-based toolpath generation for robotic milling of freeform surfaces with stiffness optimization. Robot Comput Integr Manuf 64:101953

    Article  Google Scholar 

  24. Xiong G, Ding Y, Zhu L (2019) Stiffness-based pose optimization of an industrial robot for five-axis milling. Robot Comput Integr Manuf 55:19–28

    Article  Google Scholar 

  25. Bu Y, Liao W, Tian W, Zhang J, Zhang L (2017) Stiffness analysis and optimization in robotic drilling application. Precis Eng 49:388–400

    Article  Google Scholar 

  26. Chen C, Peng F, Yan R, Li Y, Wei D, Fan Z, Tang X, Zhu Z (2019) Stiffness performance index based posture and feed orientation optimization in robotic milling process. Robot Comput Integr Manuf 55:29–40

    Article  Google Scholar 

  27. Lin Y, Zhao H, Ding H (2017) Posture optimization methodology of 6r industrial robots for machining using performance evaluation indexes. Robot Comput Integr Manuf 48:59–72

    Article  Google Scholar 

  28. Lin Y, Zhao H, Ding H (2018) Spindle configuration analysis and optimization considering the deformation in robotic machining applications. Robot Comput Integr Manuf 54:83–95

    Article  Google Scholar 

  29. Park HS, Qi B, Dang DV, Park DY (2018) Development of smart machining system for optimizing feedrates to minimize machining time. J Comput Des Eng 5(3):299–304

    Google Scholar 

  30. Wang Q-H, Liao Z-Y, Zheng Y-X, Li J-R, Zhou X-F (2018) Removal of critical regions by radius-varying trochoidal milling with constant cutting forces. Int J Adv Manuf Technol 98:671–685

  31. Xu C-Y, Li J-R, Wang Q-H, Hu G-H (2019) Contour parallel tool path planning based on conformal parameterisation utilising mapping stretch factors. Int J Prod Res 57(1):1–15

    Article  Google Scholar 

  32. Fan S, Fan S (2019) Approximate stiffness modelling and stiffness defect identification for a heavy-load parallel manipulator. Robotica 37(6):1120–1142

    Article  Google Scholar 

  33. Alici G, Shirinzadeh B (2005) Enhanced stiffness modeling, identification and characterization for robot manipulators. IEEE Trans Robot 21(4):554–564

    Article  Google Scholar 

  34. Salisbury JK (1980) Active stiffness control of a manipulator in cartesian coordinates 95–100. IEEE

  35. Guo Y, Dong H, Ke Y (2015) Stiffness-oriented posture optimization in robotic machining applications. Robot Comput Integr Manuf 35:69–76

    Article  Google Scholar 

  36. Cardou P, Bouchard S, Gosselin C (2010) Kinematic-sensitivity indices for dimensionally nonhomogeneous Jacobian matrices. IEEE Trans Robot 26(1):166–173

    Article  Google Scholar 

  37. Yao J, Lin C, Xie X, Wang AJ, Hung C-C (2010) Path planning for virtual human motion using improved A* star algorithm. In: 2010 Seventh International Conference on Information Technology: New Generations, pp. 1154–1158. IEEE

  38. Ju C, Luo Q, Yan X (2020) Path planning using an improved A-star algorithm. In: 2020 11th International Conference on Prognostics and System Health Management (PHM-2020 Jinan), pp. 23–26. IEEE

  39. Chen G, Wang H, Lin Z (2014) Determination of the identifiable parameters in robot calibration based on the POE formula. IEEE Trans Robot 30(5):1066–1077

    Article  Google Scholar 

Download references

Acknowledgements

This work was co-supported by the Key R &D Program of Guangzhou City [Grant NO. 202103020004], and the National Natural Science Foundation of China [Grant No. U22A20176], and the Guang-dong Basic and Applied Basic Research Foundation [Grant No.2021A1515110898], the GDAS’ Project of Science and Technology Development [2022GDASZH-2022010108], and the Guangdong HUST Industrial Technology Research Institute, Guangdong Provincial Key Laboratory of Manufacturing Equipment Digitization [Grant No. 2020B1212060014], and Key Areas R &D Program of Dongguan City [Grant NO. 20201200300062].

Author information

Authors and Affiliations

  1. Institute of Intelligent Manufacturing, Guangdong Academy of Sciences, Guangdong Key Laboratory of Modern Control Technology, Guangzhou, 510070, China

    Zhao-Yang Liao & Xue-Feng Zhou

  2. School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, 510641, China

    Zhen-Zhong Qin, Hai-Long Xie & Qing-Hui Wang

Authors
  1. Zhao-Yang Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhen-Zhong Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hai-Long Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qing-Hui Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xue-Feng Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Zhao-Yang Liao: Writing-original draft, Investigation, Methodology, Formal analysis, Validation. Zhen-Zhong Qin: Investigation, Writing-review & editing, Validation. Hai-Long Xie: Investigation, Validation. Qing-Hui Wang: Investigation, Supervision, Project administration. Xue-Feng Zhou:Investigation, Methodology.

Corresponding author

Correspondence to Qing-Hui Wang.

Ethics declarations

Competing of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liao, ZY., Qin, ZZ., Xie, HL. et al. Constant load toolpath planning and stiffness matching optimization in robotic surface milling. Int J Adv Manuf Technol 130, 353–368 (2024). https://doi.org/10.1007/s00170-023-12639-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-023-12639-9

Keywords

Search

Navigation