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Cutting force prediction considering force–deflection coupling in five-axis milling with fillet-end cutter

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Abstract

With the increasing demand for higher quality and performance of equipment and assembly in aerospace, shipbuilding, medical and other fields, the machining accuracy of parts is facing higher requirements. It is particularly important to predict the cutting force accurately, which is the main physical quantity in the machining process and basis of process inspection and quality control. In this paper, the cutting force model in five-axis milling with fillet-end cutter is proposed, which reveals the law of force–deflection coupling. Firstly, the initial cutter deflection model induced by the ideal cutting force ignoring the effect of deflection is built based on analysis of the geometric characteristics of fillet-end cutter. Then, the undeformed chip thickness model is educed considering the cutter posture and cutter deflection. Further, the iterative method is utilized to resolve the coupling relationship between cutter deflection and cutting force. Finally, the cutting force model under force–deflection coupling is established for achieving more accurate prediction. To verify the effectiveness of the proposed cutting force model, the milling experiment is carried out on a five-axis milling center. The measured cutting force values are utilized to inspect the accuracy of prediction models considering and not considering force–deflection coupling, respectively. The results show that the proposed method could improve the prediction accuracy of cutting force, which show the effectiveness of taking force–deflection coupling law into consideration clearly. The influence of cutter posture on cutting force is analyzed using the proposed cutting force model. The cutting force decreases with the increase in lead angle or tilt angle, and the influence of tilt angle is greater than that of lead angle under experimental conditions of five-axis milling using the set process parameters.

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Availability of data and material

The measuring data in our paper are available from the corresponding author by request, and other related materials can also be obtained from the corresponding author.

Code availability

The code for cutting force model during the study is available from the corresponding author by request.

Abbreviations

P :

Element of cutting edge

r :

Fillet radius of the arc edge

R r :

Radius of the center circle of the sweep surface of the fillet-end cutter edge

z :

Axial position

κ :

Axial contact angle

ψj(z):

Radial position angle

j :

Cutting edge number

N :

Number of cutting edges of the cutter

θ :

Rotation angle of the spindle

φ(z):

Radial lag angle

β t :

Nominal helix angle

δ :

Deflection angle

τ :

Deviation angle

ρ :

Deflection of cutter

m :

Projection of reduction of the cutter length along Z-axis direction

L :

Length of the overhanging part of the cutter

df a :

Axial force

df r :

Radial force

df t :

Tangential force

O W X W Y W Z W :

Workpiece coordinate system

O L X L Y L Z L :

Cutter coordinate system

n(z):

Normal vector

h :

Undeformed chip thickness

db :

Undeformed chip width

k r ,k t ,k a :

Radial, tangential and axial cutting force coefficients

References

  1. Martellotti ME (1941) An analysis of the milling process. Tans ASME 63(2):677–700

  2. Malekian M, Mostofa MG, Park SS, Jun MBG (2012) Modeling of minimum uncut chip thickness in micro machining of aluminum. J Mater Process Technol 212(3):553–559. https://doi.org/10.1016/j.jmatprotec.2011.05.022

  3. Tuysuz O, Altintas Y, Feng HY (2013) Prediction of cutting forces in three and five-axis ball-end milling with tool indentation effect. Int J Mach Tools Manuf 66:66–81. https://doi.org/10.1016/j.ijmachtools.2012.12.002

  4. Wojciechowski S, Matuszak M, Powałka B, Madajewski M, Maruda RW, Królczyk GM (2019) Prediction of cutting forces during micro end milling considering chip thickness accumulation. Int J Mach Tools Manuf 147:1–51. https://doi.org/10.1016/j.ijmachtools.2019.103466

  5. Zhang X, Yu T, Zhao J (2020) An analytical approach on stochastic model for cutting force prediction in milling ceramic matrix composites. Int J Mech Sci 168:1–14. https://doi.org/10.1016/j.ijmecsci.2019.105314

  6. Wang H, Hu Y, Cong W, Hu Z (2019) A mechanistic model on feeding-directional cutting force in surface grinding of CFRP composites using rotary ultrasonic machining with horizontal ultrasonic vibration. Int J Mech Sci 155:1–36. https://doi.org/10.1016/j.ijmecsci.2019.03.009

    Article  Google Scholar 

  7. Wang L, He Y, Wang Y, Li Y, Liu C (2020) Analytical modeling of material removal mechanism in dry whirling milling process considering geometry, kinematics and mechanics. Int J Mech Sci 172:1–41. https://doi.org/10.1016/j.ijmecsci.2020.105419

  8. Zhang X, Zhang J, Zheng X W, Pang B, Zhao W (2017) Tool orientation optimization of 5-axis ball-end milling based on an accurate cutter/workpiece engagement model. CIRP J Manuf Sci Technol 426:106–116. https://doi.org/10.1016/j.cirpj.2017.06.003

  9. Li Z, Zhu L (2018) An accurate method for determining cutter-workpiece engagements in five-axis milling with a general tool considering cutter runout. ASME J Manuf Sci Eng 140(2):1–28. https://doi.org/10.1115/1.4036783

  10. Guo D, Ren F, Sun Y (2010) An approach to modeling cutting forces in five-axis ball-end milling of curved geometries based on tool motion analysis. J Manuf Sci Eng 132(4), 041004:1–8. https://doi.org/10.1115/1.4001420

  11. Jing X, Lv R, Chen Y, Tian Y, Li H (2020) Modelling and experimental analysis of the effects of run out, minimum chip thickness and elastic recovery on the cutting force in micro-end-milling. Int J Mech Sci 176:1–16. https://doi.org/10.1016/j.ijmecsci.2020.105540

  12. Zhou L, Deng B, Peng F, Yang M, Yan R (2020) Semi-analytic modelling of cutting forces in micro ball-end milling of NAK80 steel with wear-varying cutting edge and associated nonlinear process characteristics. Int J Mech Sci 169:1–40. https://doi.org/10.1016/j.ijmecsci.2019.105343

    Article  Google Scholar 

  13. Salehi M, Schmitz TL, Copenhaver R, Haas R, Ovtcharova J (2018) Probabilistic sequential prediction of cutting force using Kienzle model in orthogonal turning process. ASME J Manuf Sci Eng 141(1), 011009:1–12. https://doi.org/10.1115/1.4041710

  14. Song Q, Liu Z, Ju G, Wan Y (2019) A generalized cutting force model for five-axis milling processes. J Eng Manuf 233(1):1–15. https://doi.org/10.1177/0954405417711970

  15. Zhu K, Zhang Y (2017) Modeling of the instantaneous milling force per tooth with tool run-out effect in high speed ball-end milling. Int J Mach Tools Manuf 118–119:37–48. https://doi.org/10.1016/j.ijmachtools.2017.04.001

  16. Li Z, Zhu L (2016) Mechanistic modeling of five-axis machining with a flat end mill considering bottom edge cutting effect. J Manuf Sci Eng: Trans ASME 138(11), 111012:1–11. https://doi.org/10.1115/1.4033663

  17. Ozturk E, Tunc L T, Budak E (2009) Investigation of lead and tilt angle effects in 5-axis ball-end milling processes. Int J Mach Tools Manuf 49(14):1053–1062. https://doi.org/10.1016/j.ijmachtools.2009.07.013

  18. Wang J, Zhuang K, Hu C, Ding H (2020) A PSO-based semi-analytical force prediction model for chamfered carbide tools considering different material flow state caused by edge geometry. Int J Mech Sci 169(105329):1–10. https://doi.org/10.1016/j.ijmecsci.2019.105329

  19. Wang M, Gao L, Zheng Y (2014) An examination of the fundamental mechanics of cutting force coefficients. Int J Mach Tools Manuf 78:1–7. https://doi.org/10.1016/j.ijmachtools.2013.10.008

  20. Ozturk E, Ozkirimli O, Gibbons T, Saibi M, Turner S (2016) Prediction of effect of helix angle on cutting force coefficients for design of new tools. CIRP Ann Manuf Technol 65(1):125–128. https://doi.org/10.1016/j.cirp.2016.04.042

  21. Duan X, Peng F, Yan R, Zhu Z, Huang K, Li Bin (2016) Estimation of cutter deflection based on study of cutting force and static flexibility. J Manuf Sci Eng Trans ASME 138(4), 041001:1–15. https://doi.org/10.1115/1.4031678

  22. Kim GM, Kim BH, Chu CN (2003) Estimation of cutter deflection and form error in ball-end milling processes. Int J Mach Tools Manuf 43(9):917–924. https://doi.org/10.1016/s0890-6955(03)00056-7

  23. Huo D, Chen W, Teng X, Lin C, Yang K (2017) Modeling the influence of tool deflection on cutting force and surface generation in micro-milling. Micromachines 8(6),188:1–10. https://doi.org/10.3390/mi8060188

  24. Zhang X, Yu T, Wang W (2017) Prediction of cutting forces and instantaneous tool deflection in micro end milling by considering tool run-out. Int J Mech Sci 136:124–133. https://doi.org/10.1016/j.ijmecsci.2017.12.019

  25. Zeroudi N, Fontaine M (2015) Prediction of tool deflection and tool path compensation in ball-end milling. J Intell Manuf 26(3):425–445. https://doi.org/10.1007/s10845-013-0800-8

  26. Altintas Y, Tuysuz O, Habibi M, Li ZL (2018) Virtual compensation of deflection errors in ball end milling of flexible blades. CIRP Ann 1710:1–4. https://doi.org/10.1016/j.cirp.2018.03.001

  27. Soori M, Arezoo B, Habibi M (2016) Tool deflection error of three axis computer numerical control milling machines, monitoring and minimizing by a virtual machining system. J Manuf Sci Eng Trans ASME 138(8), 081005:1–11. https://doi.org/10.1115/1.4032393

  28. Duan X, Peng F, Yan R, Zhu Z, Li B (2015) Experimental study of the effect of tool orientation on cutter deflection in five-axis filleted end dry milling of ultrahigh-strength steel. Int J Adv Manuf Technol 81(1):653–666. https://doi.org/10.1007/s00170-015-7134-y

  29. Rodríguez P, Labarga JE (2015) Tool deflection model for micro milling processes. Int J Adv Manuf Technol 76(1–4):199–207. https://doi.org/10.1007/s00170-014-5890-8

  30. Duan X, Peng F, Zhu Z, Jiang G (2019) Cutting edge element modeling-based cutter-workpiece engagement determination and cutting force prediction in five-axis milling. Int J Adv Manuf Technol 3082(7):1–10. https://doi.org/10.1007/s00170-018-3082-7

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Acknowledgements

This work was supported by National Natural Science Foundation of China under Grant No. 52005201.

Funding

This work was supported by National Natural Science Foundation of China under Grant No. 52005201.

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Authors and Affiliations

  1. Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan, 430081, Hubei, China

    Xianyin Duan & Lantao Li

  2. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China

    Chen Chen, Zerun Zhu & Fangyu Peng

  3. Key Laboratory of Metallurgical Equipment and Control Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan, 430081, Hubei, China

    Sheng Yu

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  1. Xianyin Duan
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Contributions

Xianyin Duan, Lantao Li and Chen Chen proposed the article’s innovative thinking, derived the core formula of the article and completed the English writing of the article. Sheng Yu accomplished some parts of experimental validations. Zerun Zhu and Fangyu Peng putted forward many constructive suggestions for the experiments and the writing of the whole paper.

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Correspondence to Chen Chen.

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Duan, X., Li, L., Chen, C. et al. Cutting force prediction considering force–deflection coupling in five-axis milling with fillet-end cutter. Int J Adv Manuf Technol 119, 7353–7367 (2022). https://doi.org/10.1007/s00170-022-08654-x

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