Skip to main content
SpringerLink
Log in

An improved cutting force model in micro-milling considering the comprehensive effect of tool runout, size effect, and tool wear

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

Abstract

Tool runout, cutting edge radius-size effect, and tool wear have significant impacts on the cutting force of micro-milling. In order to predict the micro-milling force and the related cutting performance, it is necessary to establish a cutting force model including tool runout, cutting edge radius, and tool wear. In this study, an instantaneous uncut chip thickness (IUCT) model considering tool runout, a nonlinear shear/ploughing coefficient model including cutting-edge radius, and a friction force coefficient model embedded with flank wear width are respectively constructed. By integrating the IUCT, the nonlinear shear/ploughing coefficient and the friction force coefficient, a comprehensive micro-milling force model including tool runout, cutting edge radius, and tool wear is derived. Experiment results show that the proposed comprehensive model is efficient to predict the nonlinear cutting force of micro-milling with variable tool runout, cutting edge radius, and tool wear.

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

Similar content being viewed by others

Abbreviations

f z :

Feed per tooth (μm)

h :

Instantaneous uncut chip thickness (μm)

h m :

Minimum uncut chip thickness (μm)

θ s :

Stagnant angle (rad)

β s :

Friction angle (rad)

σ m :

Ploughing coefficient (N/μm2)

τ m :

Friction stress in ploughing region (N/μm2)

τ s :

Shear stress (N/μm2)

r e :

Cutting edge radius (μm)

r o :

Length of tool runout (μm)

γ o :

Angle of tool runout (rad)

τ v :

Tangential friction stress (N/μm2)

σ v :

Radial friction stress (N/μm2)

VB :

Flank wear width (μm)

VB * :

Width of elastic contact region (μm)

K c,vb :

Tangential friction force coefficient (N/μm)

K r,vb :

Radial friction force coefficient (N/μm)

K c,sp :

Shear-ploughing coefficient in tangential direction (N/μm2)

K r,sp :

Shear-ploughing coefficient in radial direction (N/μm2)

\(\triangle\theta_{m,k}^z\) :

The angle between the equivalent radii (rad)

References

  1. Mian AJ, Driver N, Mativenga PT (2009) Micromachining of coarse-grained multi-phase material. Pi Mech Eng Bj Eng 223(4):377–385

    Google Scholar 

  2. Chen N, Li HN, Wu J, Li Z, Li L, Liu G, He N (2020) Advances in micro milling: from tool fabrication to process outcomes. Int J Mach Tools Manuf 103670

  3. Mustapha KB, Zhong ZW (2013) A hybrid analytical model for the transverse vibration response of a micro-end mill. Mech Syst Signal Process 34(1–2):321–339

    Article  Google Scholar 

  4. Jia Z, Lu X, Gu H, Ruan F, Liang SY (2021) Deflection prediction of micro-milling Inconel 718 thin-walled parts. J Mater Process Tech 291:117003

  5. Singh KK, Kartik V, Singh R (2018) Stability modeling with dynamic run-out in high speed micromilling ofTi6Al4V. Int J Mech Sci 150:677–690

    Article  Google Scholar 

  6. Zhang X, Yu T, Dai Y, Qu S, Zhao J (2020) Energy consumption considering tool wear and optimization of cutting parameters in micro milling process. Int J Mech Sci 178:105628

  7. Ray D, Puri AB, Naga H, Saurav H (2020) Analysis on specific cutting energy in micro milling of bulk metallic glass. Int J Adv Manuf 108(1–2):245–261

    Article  Google Scholar 

  8. Bao WY, Tansel IN (2000) Modeling micro-end-milling operations, Part II: tool run-out. Int J Mach Tools Manuf 40(15):2175–2192

    Article  Google Scholar 

  9. 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 176:105540

  10. Lu XH, Wang FR, Jia ZY, Si LK, Zhang C, Liang SY (2017) A modified analytical cutting force prediction model under the tool flank wear effect in micro-milling nickel-based superalloy. Int J Adv Manuf 91:3709–3716

    Article  Google Scholar 

  11. Wan M, Wen DY, Ma YC, Zhang WH (2019) On material separation and cutting force prediction in micro milling through involving the effect of dead metal zone. Int J Mach Tools Manuf 146:103452

  12. Lai XM, Li HT, Li CF, Lin ZQ, Ni J (2008) Modelling and analysis of micro scale milling considering size effect, micro cutter edge radius and minimum chip thickness. Int J Mach Tools Manuf 48:1–14

    Article  Google Scholar 

  13. Wojciechowski S, Matuszak M, Powałka B, Madajewski M, Maruda RW, Krolczyk GM (2019) Prediction of cutting forces during micro end milling considering chip thickness accumulation. Int J Mach Tools Manuf 147:103466

  14. Li K, Zhu K, Mei T (2016) A generic instantaneous undeformed chip thickness model for the cutting force modeling in micromilling. Int J Mach Tool Manu 105:23–31

    Article  Google Scholar 

  15. Zhu KP, 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 118:37–48

    Article  Google Scholar 

  16. Bissacco G, Hansen HN, Slunsky J (2008) Modelling the cutting edge radius size effect for force prediction in micro milling. CIRP Ann-Manuf Technol 57(1):113–116

    Article  Google Scholar 

  17. Liu Z, Shi Z, Wan Y (2013) Definition and determination of the minimum uncut chip thickness of microcutting. Int J Adv Manuf 69(5):1219–1232

    Google Scholar 

  18. Chen N, Li L, Wu J, Qian J, He N, Reynaerts D (2019) Research on the ploughing force in micro milling of soft-brittle crystals. Int J Mech Sci 155:315–322

    Article  Google Scholar 

  19. Liu X, DeVor RE, Kapoor SG (2006) An analytical model for the prediction of minimum chip thickness in micromachining. J Manuf Sci Et Asme 128(2):474–481

    Article  Google Scholar 

  20. Son SM, Lim HS, Ahn JH (2005) Effects of the friction coefficient on the minimum cutting thickness in micro cutting. Int J Mach Tools Manuf 45(4–5):529–535

    Article  Google Scholar 

  21. Altintas Y (2012) Manufacturing automation: metal cutting mechanics, machine tool variations, and cnc design, 2nd edn. Cambridge University Press, New York, USA

    Google Scholar 

  22. Malekian M, Mostofa MG, Park SS, Jun MBG (2012) Modeling of minimum uncut chip thickness in micro machining of aluminum. J Mater Process Tech 212(3):553–559

    Article  Google Scholar 

  23. Bao WY, Tansel IN (2000) Modeling micro-end-milling operations. Part III: influence of tool wear. Int J Mach Tools Manuf 40:2193–2211

    Article  Google Scholar 

  24. Hou YF, Zhang DH, Wu BH, Luo M (2015) Milling force modeling of worn tool and tool flank wear recognition in end milling. IEEE/ASME Trans Mechatron 20(3):1024–1035

    Article  Google Scholar 

  25. 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 169:105343

  26. Li GC, Li S, Zhu KP (2020) Micro-milling force modeling with tool wear and runout effect by spatial analytic geometry. Int J Adv Manuf 107(1):631–643

    Article  Google Scholar 

  27. Liu TS, Zhu KP, Wang G (2020) Micro-milling tool wear monitoring under variable cutting parameters and runout using fast cutting force coefficient identification method. Int J Adv Manuf Technol 111:3175–3188

    Article  Google Scholar 

  28. Oliveira FB, Rodrigues AR, Coelho RT, Souza AF (2015) Size effect and minimum chip thickness in micromilling. Int J Mach Tools Manuf 89:39–54

    Article  Google Scholar 

  29. Kang IS, Kim JS, Seo YW (2011) Investigation of cutting force behaviour considering the effect of cutting edge radius in the micro-scale milling of AISI 1045 steel. Proceedings of the institution of mechanical engineers, Part B: J Eng Manuf 225(2):163–171

    Article  Google Scholar 

  30. Zong WJ, Huang YH, Zhang YL, Sun T (2014) Conservation law of surface roughness in single point diamond turning. Int J Mach Tools Manuf 84:58–63

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Lab of Precision Manufacturing, Institute of Advanced Manufacturing Technology, Chinese Academy of Sciences, for providing the experimental data.

Funding

This work is supported by the National Natural Science Foundation of China (Grant No. 51905360) and the fellowship of China Postdoctoral Science Foundation (2020M681699).

Author information

Authors and Affiliations

  1. School of Mechanical and Electric Engineering, Soochow University, Suzhou 215021, Jiangsu, China

    Tongshun Liu, Yayun Liu & Kedong Zhang

Authors
  1. Tongshun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yayun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kedong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Tongshun Liu constructed the theoretical model and wrote the manuscript. Yayun Liu designed and directed the project. Kedong Zhang analyzed the data.

Corresponding author

Correspondence to Yayun Liu.

Ethics declarations

Ethics approval

This paper does not contain any studies with human participants or animals performed by any of the authors.

Consent to participate

All of the authors consent to participate.

Consent for publication

All of the authors consent for publication.

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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, T., Liu, Y. & Zhang, K. An improved cutting force model in micro-milling considering the comprehensive effect of tool runout, size effect, and tool wear. Int J Adv Manuf Technol 120, 659–668 (2022). https://doi.org/10.1007/s00170-022-08777-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-022-08777-1

Keywords

Search

Navigation