Skip to main content
SpringerLink
Log in

Improved Full-Discretization Method for Milling Chatter Stability Prediction with Multiple Delays

  • Conference paper
Intelligent Robotics and Applications (ICIRA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6425))

Included in the following conference series:

Abstract

This paper presents an analytical stability prediction method in milling chatter analysis with multiple delays. The improved full-discretization method is used to determine the critical boundary of chatter stability. The proposed method can take many practical factors into consideration, such as helix angle, non-constant pitch, and cutter runout, etc. The influence of the multiple delays is explored in detail and the simulation results show that the cutter runout has the great influence on the elevation of the stability boundary. The finding proves the validity of the proposed method by experiment verification.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Stépán, G.: Retarded dynamical systems: stability and characteristic functions. Longman Scientific & Technical New York, New York (1989)

    Google Scholar 

  2. Budak, E., Altintas, Y.: Analytical Prediction of Chatter Stability in Milling—Part I: General Formulation. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME 120(1), 22–30 (1998)

    Article  Google Scholar 

  3. Merdol, S.D., Altintas, Y.: Multi Frequency Solution of Chatter Stability for Low Immersion Milling. Journal of Manufacturing Science and Engineering, Transactions of the ASME 126(3), 459–466 (2004)

    Article  Google Scholar 

  4. Insperger, T., Stépán, G.: Semi-discretization method for delayed systems. International Journal for Numerical Methods in Engineering 55(5), 503–518 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Insperger, T., Stépán, G.: Updated semi-discretization method for periodic delay-differential equations with discrete delay. International Journal for Numerical Methods in Engineering 61(1), 117–141 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bayly, P.V., Halley, J.E., Mann, B.P., Davies, M.A.: Stability of Interrupted Cutting by Temporal Finite Element Analysis. Journal of Manufacturing Science and Engineering, Transactions of the ASME 125(2), 220–225 (2003)

    Article  Google Scholar 

  7. Faassen, R., Van de Wouw, N., Oosterling, J., Nijmeijer, H.: Prediction of regenerative chatter by modelling and analysis of high-speed milling. International Journal of Machine Tools and Manufacture 43(14), 1437–1446 (2003)

    Article  Google Scholar 

  8. Smith, S., Tlusty, J.: An overview of modeling and simulation of the milling process. Journal of Engineering for Industry (Transactions of the ASME) 113(2), 169–175 (1991)

    Article  Google Scholar 

  9. Balachandran, B.: Nonlinear dynamics of milling processes. Philosophical Transactions: Mathematical. Physical and Engineering Sciences, 793–819 (2001)

    Google Scholar 

  10. Zhao, M., Balachandran, B.: Dynamics and stability of milling process. International Journal of Solids and Structures 38(10-13), 2233–2248 (2001)

    Article  MATH  Google Scholar 

  11. Schmitz, T., Davies, M., Medicus, K., Snyder, J.: Improving high-speed machining material removal rates by rapid dynamic analysis. CIRP Annals-Manufacturing Technology 50(1), 263–268 (2001)

    Article  Google Scholar 

  12. Zatarain, M., Munoa, J., Peigne, G., Insperger, T.: Analysis of the influence of mill helix angle on chatter stability. CIRP Annals - Manufacturing Technology 55(1), 365–368 (2006)

    Article  Google Scholar 

  13. Insperger, T., Munoa, J., Zatarain, M., Peigne, G.: Unstable islands in the stability chart of milling processes due to the helix angle. In: CIRP 2nd Int. Conference High Performance Cutting, Vancouver, British Columbia, Canada (2006)

    Google Scholar 

  14. Szalai, R., Stépán, G.: Stability boundaries of high-speed milling corresponding to period doubling are essentially closed curves. In: Proceedings of IMECE 2003 ASME International Mechanical Engineering Congress and R&D Expo, Washington D.C, pp. 63–68 (2003)

    Google Scholar 

  15. Szalai, R., Stépán, G.: Lobes and lenses in the stability chart of interrupted turning. Journal of Computational and Nonlinear Dynamics 1(3), 205–211 (2006)

    Article  Google Scholar 

  16. Altintas, Y., Engin, S., Budak, E.: Analytical stability prediction and design of variable pitch cutters. Journal of Manufacturing Science and Engineering 121(2), 173–178 (1999)

    Article  Google Scholar 

  17. Budak, E.: An analytical design method for milling cutters with nonconstant pitch to increase stability, Part 2: Application. Journal of Manufacturing Science and Engineering, Transactions of the ASME 125(1), 35–38 (2003)

    Article  Google Scholar 

  18. Budak, E.: An analytical design method for milling cutters with nonconstant pitch to increase stability, Part I: Theory. Journal of Manufacturing Science and Engineering, Transactions of the ASME 125(1), 29–34 (2003)

    Article  MathSciNet  Google Scholar 

  19. Schmitz, T.L., Couey, J., Marsh, E., Mauntler, N., Hughes, D.: Runout effects in milling: Surface finish, surface location error, and stability. International Journal of Machine Tools and Manufacture. 47(5), 841–851 (2007) (SPEC. ISS.)

    Article  Google Scholar 

  20. Insperger, T., Mann, B.P., Surmann, T., Stépán, G.: On the chatter frequencies of milling processes with runout. International Journal of Machine Tools and Manufacture 48(10), 1081–1089 (2008)

    Article  Google Scholar 

  21. Ding, Y., Zhu, L., Zhang, X., Ding, H.: A full-discretization method for prediction of milling stability. International Journal of Machine Tools and Manufacture 50(5), 502–509 (2010)

    Article  Google Scholar 

  22. Wan, M., Zhang, W., Dang, J., Yang, Y.: A unified stability prediction method for milling process with multiple delays. International Journal of Machine Tools and Manufacture 50(1), 29–41 (2010)

    Article  Google Scholar 

  23. Kline, W., DeVor, R.: The effect of runout on cutting geometry and forces in end milling. International journal of machine tool design & research 23(2-3), 123–140 (1983)

    Article  Google Scholar 

  24. Gu, Y., Chen, B., Zhang, H., Guan, Z.: Precise time-integration method with dimensional expanding for structural dynamic equations. AIAA journal 39(12), 2394–2399 (2001)

    Article  Google Scholar 

  25. Altintas, Y., Engin, S., Budak, E.: Analytical stability prediction and design of variable pitch cutters. Journal of Manufacturing Science and Engineering 121(2), 173–178 (1999)

    Article  Google Scholar 

  26. Gouskov, A., Voronov, S., Paris, H., Batzer, S.: Nonlinear dynamics of a machining system with two interdependent delays. Communications in Nonlinear Science and Numerical Simulation 7(4), 207–221 (2002)

    Article  MATH  Google Scholar 

  27. Sims, N.D., Mann, B., Huyanan, S.: Analytical prediction of chatter stability for variable pitch and variable helix milling tools. Journal of Sound and Vibration 317(3-5), 664–686 (2008)

    Article  Google Scholar 

  28. Liang, S., Wang, J.: Milling force convolution modeling for identification of cutter axis offset. International Journal of Machine Tools and Manufacture 34(8), 1177–1190 (1994)

    Article  Google Scholar 

  29. Insperger, T.: Full-discretization and semi-discretization for milling stability prediction: Some comments. International Journal of Machine Tools and Manufacture 50(7), 658–662 (2010)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    XiaoJian Zhang & CaiHua Xiong

  2. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Ye Ding

Authors
  1. XiaoJian Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. CaiHua Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ye Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Creative Technologies, The University of Portsmouth, PO1 2DJ, Portsmouth, UK

    Honghai Liu

  2. Robotics Institute, Shanghai Jiao Tong University, 200240, Shanghai, China

    Han Ding , Zhenhua Xiong  & Xiangyang Zhu ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhang, X., Xiong, C., Ding, Y. (2010). Improved Full-Discretization Method for Milling Chatter Stability Prediction with Multiple Delays. In: Liu, H., Ding, H., Xiong, Z., Zhu, X. (eds) Intelligent Robotics and Applications. ICIRA 2010. Lecture Notes in Computer Science(), vol 6425. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16587-0_50

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16587-0_50

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16586-3

  • Online ISBN: 978-3-642-16587-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation