Skip to main content
SpringerLink
Log in

An effective time domain model for milling stability prediction simultaneously considering multiple modes and cross-frequency response function effect

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

Abstract

The dynamic properties of the machine tool structure usually contain multiple modes and significant cross-frequency response functions whose vibration in one direction is caused by a force in the orthogonal direction. To simplify the stability prediction model, the stability of a milling process has been traditionally predicted in the time domain by selecting only the most flexible mode and neglecting the cross-frequency response functions. This paper proposes an effective stability prediction model simultaneously considering multiple modes and the cross-frequency response functions in the time domain. When introducing the cross-frequency response functions, mechanical mobility and impedance transformation method dealing with measured frequency response functions is proposed to establish the dynamic matrix equation. In considering the multiple modes, the approaches of multiple modal parameter normalization on the tool tip and reducing the vibration variable number in modal space are described in detail. The comparisons of numerical simulation results between the proposed method and the frequency domain method demonstrate the effectiveness of the proposed model. A cutting experiment produces results in agreement with the theoretical prediction. The analysis of the numerical simulation and the experimental data indicates that the multiple modes have great effect on stability boundary. Additionally, it also shows that the cross-frequency response functions influence the stability boundary increasingly along with the increasing amplitude ratio of the cross-frequency response functions and direct frequency response functions.

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

Similar content being viewed by others

References

  1. Tlusty J, Polacek M (1963) The stability of machine tools against self excited vibrations in machining. Int Res Prod Eng 1:465–474

    Google Scholar 

  2. Smith S, Tlusty J (1991) An overview of modeling and simulation of the milling process. J Eng Ind 113:169–175

    Article  Google Scholar 

  3. Yang YQ, Liu Q, Zhang B (2014) Three-dimensional chatter stability prediction of milling based on the linear and exponential cutting force model. Int J Adv Manuf Technol 72:1175–1185

    Article  Google Scholar 

  4. Wang MH, Gao L, Zheng YH (2014) Prediction of regenerative chatter in the high-speed vertical milling of thin-walled workpiece made of titanium alloy. Int J Adv Manuf Technol 72:707–716

    Article  Google Scholar 

  5. Solis E, Peres CR, Jiménez JE, Alique JR, Monje JC (2004) A new analytical-experimental method for the identification of stability lobes in high-speed milling. Int J Mach Tools Manuf 44:1591–1597

    Article  Google Scholar 

  6. Mann BP, Young KA, Schmitz TL, Dilley DN (2005) Simultaneous stability and surface location error predictions in milling. J Manuf Sci Eng 127:446–453

    Article  Google Scholar 

  7. Tang WX, Song QH, Yu SQ, Sun SS, Li BB, Du B, Ai X (2009) Prediction of chatter stability in high-speed finishing end milling considering multi-mode dynamics. J Mater Process Technol 209:2585–2591

    Article  Google Scholar 

  8. Wan M, Ma YC, Zhang WH, Yang Y (2015) Study on the construction mechanism of stability lobes in milling process with multiple modes. Int J Adv Manuf Technol 79:589–603

    Article  Google Scholar 

  9. Berglind L, Ziegert J (2015) Analytical time-domain turning model with multiple modes. CIRP Ann Manuf Technol 64:137–140

    Article  Google Scholar 

  10. Cao H, Li B, He Z (2012) Chatter stability of milling with speed-varying dynamics of spindles. Int J Mach Tools Manuf 52:50–58

    Article  Google Scholar 

  11. Zhang XJ, Xiong CH, Ding Y, Feng MJ, Xiong YL (2012) Milling stability analysis with simultaneously considering the structural mode coupling effect and regenerative effect. Int J Mach Tools Manuf 53:127–140

    Article  Google Scholar 

  12. Altintas Y, Budak E (1995) Analytical prediction of stability lobes in milling. CIRP Ann Manuf Technol 44:357–362

    Article  Google Scholar 

  13. Merdol SD, Altintas Y (2004) Multi frequency solution of chatter stability for low immersion milling. J Manuf Sci Eng 126:459–466

    Article  Google Scholar 

  14. Bachrathy D, Stepan G (2013) Improved prediction of stability lobes with extended multi frequency solution. CIRP Ann Manuf Technol 62:411–414

    Article  Google Scholar 

  15. Bayly PV, Halley JE, Mann BP, Davies MA (2003) Stability of interrupted cutting by temporal finite element analysis. J Manuf Sci Eng 125:220–225

    Article  Google Scholar 

  16. Insperger T, Stépán G (2002) Semi-discretization method for delayed systems. Int J Numer Methods Eng 55:503–518

    Article  MathSciNet  MATH  Google Scholar 

  17. Insperger T, Stépán G (2004) Updated semi-discretization method for periodic delay-differential equations with discrete delay. Int J Numer Methods Eng 64:117–141

    Article  MathSciNet  MATH  Google Scholar 

  18. Ding Y, Zhu LM, Zhang XJ, Ding H (2010) A full-discretization method for prediction of milling stability. Int J Mach Tools Manuf 50:502–509

    Article  Google Scholar 

  19. Ding Y, Zhu LM, Zhang XJ, Ding H (2011) Numerical integration method for prediction of milling stability. J Manuf Sci Eng 133:031005

    Article  Google Scholar 

  20. Liang XG, Yao ZQ, Luo L, Hu J (2013) An improved numerical integration method for predicting milling stability with varying time delay. Int J Adv Manuf Technol 68:1967–1976

    Article  Google Scholar 

  21. Niu JB, Ding Y, Zhu LM, Ding H (2014) Runge–Kutta methods for a semi-analytical prediction of milling stability. Nonlinear Dyn 76:289–304

    Article  MathSciNet  MATH  Google Scholar 

  22. Gradišek J, Kalveram M, Insperger T, Weinert K, Stépán G, Govekar E, Grabec I (2005) On stability prediction for milling. Int J Mach Tools Manuf 45:769–781

    Article  Google Scholar 

  23. Mann BP, Edes BT, Easley SJ, Young KA, Ma K (2008) Chatter vibration and surface location error prediction for helical end mills. Int J Mach Tools Manuf 48:350–361

    Article  Google Scholar 

  24. Munoa Dombovari JZ, Mancisidor I, Yang YQ, Zatarain M (2013) Interaction between multiple modes in milling processes. Mach Sci Technol 17:165–180

    Article  Google Scholar 

  25. Altintas Y (2000) Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC design. Cambridge University Press, Cambridge

    Google Scholar 

  26. Budak E, Altintas Y, Armarego EJA (1996) Prediction of milling force coefficients from orthogonal cutting data. J Manuf Sci Eng 118:216–224

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Numerical Control System Engineering Research Centers, Huazhong University of Science and Technology, Wuhan, 430074, China

    Xiaowei Tang, Rong Yan, Yanhong Gong & Xin Li

  2. State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    Fangyu Peng

Authors
  1. Xiaowei Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fangyu Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rong Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yanhong Gong
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rong Yan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, X., Peng, F., Yan, R. et al. An effective time domain model for milling stability prediction simultaneously considering multiple modes and cross-frequency response function effect. Int J Adv Manuf Technol 86, 1037–1054 (2016). https://doi.org/10.1007/s00170-015-8129-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-015-8129-4

Keywords

Search

Navigation