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Milling Bifurcations from Structural Asymmetry and Nonlinear Regeneration

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Abstract

This paper investigates multiple modeling choices for analyzing the rich and complex dynamics of high-speed milling processes. Various models are introduced to capture the effects of asymmetric structural modes and the influence of nonlinear regeneration in a discontinuous cutting force model. Stability is determined from the development of a dynamic map for the resulting variational system. The general case of asymmetric structural elements is investigated with a fixed frame and rotating frame model to show differences in the predicted unstable regions due to parametric excitation. Analytical and numerical investigations are confirmed through a series of experimental cutting tests. The principal results are additional unstable regions, hysteresis in the bifurcation diagrams, and the presence of coexisting periodic and quasiperiodic attractors which is confirmed through experimentation.

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References

  1. Tlusty, J., Manufacturing Processes and Equipment., 1st edn., Prentice Hall, Upper Saddle River, NJ, 2000.

    Google Scholar 

  2. Altintas, Y., Manufacturing Automation., 1st edn., Cambridge University Press, New York, 2000.

    Google Scholar 

  3. Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations., Wiley, New York, 1979.

    MATH  Google Scholar 

  4. Davies, M. and Balachandran, B. ‘Impact dynamics in milling of thin-walled structures,’ Nonlinear Dynamics. 22., 2001, 375–392.

    Google Scholar 

  5. Mann, B. P., Bayly, P. V., Davies, M. A., and Halley, J. E., ‘Limit cycles, bifurcations, and accuracy of the milling process,’ Journal of Sound and Vibration. 277., 2004, 31–48.

    Article  Google Scholar 

  6. Doi, S. and Kato, S. ‘Chatter vibration of lathe tools,’ Transactions of the ASME. 78., 1956, 1127–1134.

    Google Scholar 

  7. Tlusty, J., Polacek, A., Danek, C., and Spacek, J., Selbsterregte Schwingungen an Werkzeugmaschinen., VEB Verlag Technik, Berlin, 1962.

    Google Scholar 

  8. Tobias, S. A., Machine Tool Vibration., Blackie, London, 1965.

    Google Scholar 

  9. Merritt, H., ‘Theory of self-excited machine tool chatter,’ Journal of Engineering for Industry. 87.(4), 1965, 447–454.

    Google Scholar 

  10. Smith, S. and Tlusty, J., ‘An overview of the modeling and simulation of the milling process,’ Journal of Engineering for Industry. 113., 1991, 169–175.

    Article  Google Scholar 

  11. Montgomery, D. and Altintas, Y., ‘Mechanism of cutting force and surface generation in dynamic milling,’ Journal of Engineering for Industry. 113., 1991, 160–168.

    Article  Google Scholar 

  12. Davies, M. A., Pratt, J. R., Dutterer, B., and Burns, T. J., ‘Stability prediction for low radial immersion milling,’ Journal of Manufacturing Science and Engineering. 124.(2), 2002, 217–225.

    Article  Google Scholar 

  13. Davies, M. A., Pratt, J. R., Dutterer, B., and Burns, T. J., ‘The stability of low immersion milling,’ Annals of the CIRP. 49., 2000, 37–40.

    Article  Google Scholar 

  14. Bayly, P. V., Halley, J. E., Mann, B. P., and Davies, M. A., ‘Stability of interrupted cutting by temporal finite element analysis,’ in Proceedings of the 18th Biennial Conference on Mechanical Vibration and Noise, Pittsburg, PA., 2001.

  15. Insperger, T. and Stépán, G., ‘Stability of high-speed milling,’ in Proceedings of Symposium on Nonlinear Dynamics and Stochastic Mechanics., Orlando, FL, AMD-241, 2000, pp. 119–123.

  16. Corpus, W. T. and Endres, W. J., ‘A high order solution for the added stability lobes in intermittent machining,’ in Proceedings of the Symposium on Machining Processes., Orlando, FL, (MED-11), 2000, pp. 871–878.

  17. Zao, M. X. and Balachandran, B., ‘Dynamics and stability of milling process,’ International Journal of Solids and Structures. 38., 2001, 2233–2248.

    Google Scholar 

  18. Bayly, P. V., Mann, B. P., Schmitz, T. L., Peters, D. A., Stépán, G., and Insperger, T., ‘Effects of radial immersion and cutting direction on chatter instability in end-milling,’ in Proceedings of ASME Engineering Congress and Exposition, New Orleans, LA., 2002.

  19. Mann, B. P., Insperger, T., Bayly, P. V., and Stépán, G., ‘Stability of up-milling and down-milling, Part 2: Experimental verification,’ International Journal of Machine Tools and Manufacture. 43., 2003, 35–40.

    Article  Google Scholar 

  20. Insperger, T., Mann, B. P., Stépán, G., and Bayly, P. V., ‘Stability of up-milling and down-milling, Part 1: Alternative analytical methods,’ International Journal of Machine Tools and Manufacture. 43., 2003, 25–34.

    Article  Google Scholar 

  21. Insperger, T., Stépán, G., Bayly, P. V., and Mann, B. P., ‘Multiple chatter frequencies in milling processes,’ Journal of Sound and Vibration. 262., 2003, 333–345.

    Article  Google Scholar 

  22. Balachandran, B., ‘Non-linear dynamics of milling process,’ Philosophical Transactions of the Royal Society of London A. 359., 2001, 793–819.

    MATH  Google Scholar 

  23. Bayly, P. V., Halley, J. E., Davies, M. A., and Pratt, J. R., ‘Stability analysis of interrupted cutting with finite time in the cut,’ in Proceedings of ASME Design Engineering Technical Conference, Manufacturing in Engineering Division., Orlando, FL, 2001.

  24. Bayly, P., Halley, J., Mann, B., and Davies, M., ‘Stability of interrupted cutting by temporal finite element analysis,’ Journal of Manufacturing Science and Engineering. 125., 2003, 220–225.

    Article  Google Scholar 

  25. Stépán G., ‘Modelling nonlinear regenerative effects in metal cutting,’ Philosophical Transactions of the Royal Society of London A. 359., 2001, 739–757.

    MATH  Google Scholar 

  26. Davies M. and Burns, T., ‘Thermomechanical oscillations in material flow during high-speed machining,’ Philosophical Transactions of the Royal Society of London A. 359., 2001, 821–846.

    MATH  Google Scholar 

  27. Grabec, I., ‘Chaotic dynamics of the cutting process,’ International Journal of Machine Tools and Manufacture. 28., 1988, 19–32.

    Article  Google Scholar 

  28. Altintas, Y. and Budak, E., ‘Analytical prediction of stability lobes in milling,’ CIRP Annals. 44.(1), 1995, 357–362.

    Article  Google Scholar 

  29. Hanna, N. H. and Tobias, S. A., ‘A theory of nonlinear regenerative chatter,’ Journal of Engineering for Industry. 96., 1974, 247–255.

    Google Scholar 

  30. Nayfeh, A. H., Chin, C. M., and Pratt, J., ‘Applications of Perturbation Methods to Tool Chatter Dynamics.,’ in Dynamics and Chaos in Manufacturing Processes., Wiley, New York, 1997.

  31. Stephenson, D. A. and Agapio, J. S., Metal Cutting Theory and Practice., 1st edn., Marcel Dekker, New York, 1997,

    Google Scholar 

  32. Jaluria, Y., Computational Heat Transfer., 1st edn., Hemisphere Publishing Corporation, Washington, 1986.

    Google Scholar 

  33. Peters, D. A. and Idzapanah, A. P., ‘HP-version finite elements for the space-time domain,’ Computational Mechanics. 3., 1988, 73–78.

    Article  MATH  Google Scholar 

  34. Virgin, L. N., Introduction to Experimental Nonlinear Dynamics., Cambridge University Press, Cambridge, UK, 2000.

    MATH  Google Scholar 

  35. Yamamoto, T. and Ishidam, Y., Linear and Nonlinear Rotordynamics., Wiley Series in Nonlinear Science, Wiley, New York, 2001.

  36. Xie, A. and Dai, H., ‘On the sensitivity of multiple eigenvalues of nonsymmetric matrix pencils,’ Linear Algebra and Its Applications. 374., 2003, 143–158.

    Article  MathSciNet  MATH  Google Scholar 

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Author notes

  1. B. P. Mann

    Present address: Department of Mechanical & Aerospace Engineering, University of Missouri – Columbia, Engineering Bldg East, Columbia, MO, 65203, U.S.A.

Authors and Affiliations

  1. Nonlinear Dynamics Laboratory, Department of Mechanical and Aerospace Engineering, University of Florida-Gainesville, P.O. Box 116300, FL, 32611, U.S.A.

    B. P. Mann & N. K. Garg

  2. Advanced Manufacturing Research and Development, The Boeing Company, St. Louis, MO, 63166, U.S.A.

    K. A. Young & A. M. Helvey

Authors
  1. B. P. Mann
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  2. N. K. Garg
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  3. K. A. Young
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  4. A. M. Helvey
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Correspondence to B. P. Mann.

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Mann, B.P., Garg, N.K., Young, K.A. et al. Milling Bifurcations from Structural Asymmetry and Nonlinear Regeneration. Nonlinear Dyn 42, 319–337 (2005). https://doi.org/10.1007/s11071-005-5719-y

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  • DOI: https://doi.org/10.1007/s11071-005-5719-y

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