Self-interrupted regenerative metal cutting in turning

International Journal of Non-Linear Mechanics

Volumn 43, Issue 2, 2008, Pages 111-123

  Wahi, Pankaj ^a   Chatterjee, Anindya ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

^b INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Bifurcation diagram; Global dynamics; Regenerative chatter; Self interruption; Turning

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; DYNAMICS; GALERKIN METHODS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PHASE DIAGRAMS; TURNING;

BIFURCATION DIAGRAMS; GLOBAL DYNAMICS; REGENERATIVE CHATTER; SELF INTERRUPTION;

METAL CUTTING;

EID: 38549127248     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2007.10.010     Document Type: Article

References (41)

1. Tobias S.A. Machine-Tool Vibration (1965), Blackie and Sons Ltd., London
2. Tlusty J. Analysis of the state of research in cutting dynamics. Ann. CIRP 27 (1978) 583-589
3. Stépán G., and Kalmár-Nagy T. Nonlinear regenerative machine tool vibrations. Proceedings of the DETC'97, ASME Design Engineering Technical Conference. Sacramento, CA, USA (1997)
4. Kalmár-Nagy T., Stépán G., and Moon F.C. Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations. Nonlinear Dyn. 26 (2001) 121-142
5. Stépán G. Modelling non-linear regenerative effects in metal cutting. Proc. R. Soc. London A 359 (2001) 739-757
6. Stépán G., Szalai R., and Insperger T. Nonlinear dynamics of high-speed milling subjected to regenerative effect. In: Radons G. (Ed). Nonlinear Dynamics of Production Systems (2003), Wiley-VCH, New York 111-128
7. Kalmár-Nagy T., Pratt J.R., Davies M.A., and Kennedy M.D. Experimental and analytical investigation of the subcritical instability in metal cutting. Proceedings of the DETC'99 17th ASME Biennial Conference on Mechanical Vibration and Noise. Las Vegas, Nevada, USA (1999)
8. Moon F.C., and Kalmár-Nagy T. Nonlinear models for complex dynamics in cutting materials. Proc. R. Soc. London A 359 (2001) 695-711
9. Stépán G. Retarded Dynamical Systems (1989), Longman Group, UK
10. Stépán G. Delay differential equation models for machine tool chatter. In: Moon F.C. (Ed). Dynamics and Chaos in Manufacturing Processes (1997), Wiley, New York 165-191
11. Nayfeh A.H., Chin C.M., and Pratt J.R. Applications of perturbation methods to tool chatter dynamics. In: Moon F.C. (Ed). Dynamics and Chaos in Manufacturing Processes (1997), Wiley, New York 193-213
12. Pratt J.R., and Nayfeh A.H. Design and modelling for chatter control. Nonlinear Dyn. 19 (1999) 49-69
13. Pratt J.R., and Nayfeh A.H. Chatter control and stability analysis of a cantilever boring bar under regenerative cutting conditions. Proc. R. Soc. London A 359 (2001) 759-792
14. Wahi P., and Chatterjee A. Regenerative tool chatter near a codimension 2 Hopf point using multiple scales. Nonlinear Dyn. 40 (2005) 323-338
15. Hanna N.H., and Tobias S.A. A theory of non-linear regenerative chatter. ASME J. Eng. Ind. 96 (1974) 247-255
16. Shi M., and Tobias S.A. Theory of finite amplitude machine tool instability. Int. J. Mach. Tool Des. Res. 24 (1984) 45-69
17. Balachandran B. Nonlinear dynamics of milling process. Proc. R. Soc. London A 359 (2001) 793-819
18. Altintas Y., and Budak E. Analytical prediction of stability lobes in milling. Ann. CIRP 44 1 (1995) 357-362
19. Szalai R., Stépán G., and Hogan S.J. Continuation of bifurcations in periodic delay-differential equations using characteristic matrices. SIAM J. Sci. Comput. 28 (2006) 1301-1317
20. Szalai R., Mann B.P., and Stépán G. Period-two and quasi-periodic vibrations of high-speed milling. 9th CIRP International Workshop on Modelling of Machining Operations. Bled, Slovenia (2006)
21. Stépán G., Szalai R., Mann B.P., Bayly P.V., Insperger T., Gradisek J., and Govekar E. Nonlinear dynamics of high-speed milling-analysis numerics and experiments. ASME J. Vib. Acous. 127 (2005) 197-203
22. Tlusty J., and Ismail F. Basic non-linearity in machining chatter. Ann. CIRP 30 (1981) 299-304
23. Kondo Y., Kawano O., and Sato H. Behavior of chatter due to multiple regenerative effect. ASME J. Eng. Ind. 103 (1981) 324-329
24. Batzer S.A., Gouskov A.M., and Voronov S.A. Modelling vibratory drilling dynamics. ASME J. Vib. Acoust. 123 (2001) 435-443
25. Z. Dombóvári, Bifurcation analysis of a cutting process. Master's Thesis Budapest University of Technology and Economics, Budapest, Hungary, 2006, 〈http://www.mm.bme.hu/∼dombo/Downloads〉.
26. D.A.W. Barton, Personal communication.
27. Taylor F.W. On the art of cutting metal. Trans. ASME 28 (1907) 31-350
28. Wiercigroch M., and Budak E. Sources of non-linearities, chatter generation and suppression in metal cutting. Proc. R. Soc. London A 359 (2001) 663-693
29. Grabec I. Chaotic dynamics of the cutting process. Int. J. Mach. Tools Manuf. 28 (1988) 19-32
30. Wiercigroch M. Chaotic vibration of a simple model of the machine tool cutting process system. ASME J. Vib. Acoust. 119 (1997) 468-475
31. Wiercigroch M., and Krivtsov A.M. Frictional chatter in orthogonal metal cutting. Proc. R. Soc. London A 359 (2001) 713-738
32. Davies M.A., and Burns T.J. The dynamics of chip formation in machining. In: Moon F.C. (Ed). New applications of Nonlinear and Chaotic Dynamics in Mechanics (1999), Kluwer Academics Publishers, Dordrecht 183-192
33. Davies M.A., and Burns T.J. Thermomechanical oscillations in material flow during high speed machining. Proc. R. Soc. London A 359 (2001) 821-846
34. Wahi P., and Chatterjee A. Galerkin projections for delay differential equations. ASME J. Dyn. Syst. Meas. Control 127 1 (2005) 80-87
35. P. Wahi, A study of delay differential equations with applications to machine tool vibrations. Ph.D. Dissertation, Indian Institute of Science, Bangalore, India, 2005.
36. di Bernardo M., Feigen M.I., Hogan S.J., and Homer M.E. Local analysis of C-bifurcations in n-dimensional piecewise-smooth dynamical systems. Chaos Solitons Fractals 10 11 (1999) 1881-1908
37. Dankowicz H., and Nordmark A.B. On the origins and bifurcations of stick-slip oscillations. Physica D 136 (2000) 280-302
38. di Bernardo M., Budd C.J., and Champneys A.R. Grazing and border-collision in piecewise-smooth systems: a unified analytical approach. Phy. Rev. Lett. 86 12 (2001) 2553-2556
39. Leine R.I., and Nijmeijer H. Dynamics and Bifurcations of Non-Smooth Mechanical Systems (2004), Springer, New York, USA
40. Kowalczyk P., di Bernardo M., Champneys A.R., Hogan S.J., Piiroinen P.T., Kuznetsov Yu.A., and Nordmark A.B. Two-parameter discontinuity-induced bifurcations of limit cycles: classification and open problems. Int. J. Bifurcation Chaos 16 3 (2006) 601-629
41. T. Kalmár-Nagy, Delay-differential models of cutting tool dynamics with non-linear and mode-coupling effects, Ph.D. Dissertation, Cornell University, Ithaca, USA, 2002.