Bifurcation analysis on a turning system with large and state-dependent time delay

Journal of Sound and Vibration

Volumn 331, Issue 25, 2012, Pages 5562-5580

  Kim, Pilkee ^a   Bae, Sanghyun ^a   Seok, Jongwon ^a  

^a Chung Ang University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC FORMULATION; ASYMPTOTIC SOLUTIONS; BIFURCATION ANALYSIS; BIFURCATION DIAGRAM; CHATTER VIBRATIONS; CUTTING FORCES; GLOBAL BEHAVIORS; HARMONIC BALANCE; HOPF BIFURCATION POINT; LARGE DELAYS; LARGE TIME DELAY; LIMIT CYCLE; LINEAR STABILITY; METHOD OF MULTIPLE SCALE; NON-LINEAR STIFFNESS; NUMERICAL INTEGRATIONS; ORDERING PROCESS; PERIODIC SOLUTION; ROTATING SPEED; STABILITY AND BIFURCATION ANALYSIS; STATE-DEPENDENT; TURNING PROCESS; TURNING SYSTEMS; TWO DEGREES OF FREEDOM; WORK PIECES;

CUTTING; HOPF BIFURCATION; STIFFNESS; TURNING;

TIME DELAY;

EID: 84865684809     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2012.07.028     Document Type: Article

References (51)

1. T. Insperger, G. Stepan, and J. Turi State-dependent delay in regenerative turning processes Nonlinear Dynamics 47 13 2007 275 283
2. F. Hartung, T. Krisztin, H.-O. Walther, and J. Wu Functional differential equations with state-dependent delays: theory and applications A. Canada, P. Drabek, A. Fonda, Handbook of Differential Equations: Ordinary Differential Equations, Vol. 3 2006 Elsevier/North-Holland, 435 545
3. F. Hartung, J. Turi, Linearized stability in functional differential equations with state-dependent delays, Proceedings of the Conference Dynamical Systems and Differential Equations, added volume of Discrete and Continuous Dynamical Systems, 2001, pp. 416425.
4. T. Insperger, D.A.W. Barton, and G. Stepan Criticality of Hopf bifurcation in state-dependent delay model of turning processes International Journal of Non-Linear Mechanics 43 2 2008 140 149
5. P. Kim, and J. Seok Bifurcation analyses on the chatter vibrations of a turning process with state-dependent delay Nonlinear Dynamics 69 2012 891 912
6. P. Wahi, Supercritical bifurcation in the state-dependent delay model of turning, 22nd International Congress of Theoretical and Applied Mechanics, Adelaide, Australia, 2008, pp. 2529.
7. R.N. Arnold The mechanism of tool vibration in the cutting of steel Proceedings of the Institution of Mechanical Engineers 154 1946 261 284
8. S.A. Tobias, and W. Fishwick Theory of regenerative machine tool chatter The Engineer 205 1958 199 203 238239
9. J. Tlusty, M. Polacek, The stability of machine tools against self-excited vibrations in machining, Proceedings of International Research in Production Engineering, ASME, New York, 1963, pp. 465474.
10. H.E. Merrit Theory of self-excited machine-tool chatter Transactions of the ASME-Journal of Engineering for Industry 87 4 1965 447 454
11. D.W. Wu, and C.R. Liu An analytical model of cutting dynamics. Part 1: Model building Transactions of the ASME-Journal of Engineering for Industry 107 1985 107 111
12. D.W. Wu, and C.R. Liu An analytical model of cutting dynamics. Part 2: Verification Transactions of the ASME-Journal of Engineering for Industry 107 1985 112 118
13. N.H. Hanna, and S.A. Tobias A theory of nonlinear regenerative chatter Transactions of the ASME-Journal of Engineering for Industry 96 1974 247 255
14. M. Shi, and S.A. Tobias Theory of finite amplitude machine tool instability International Journal of Machine Tool Design and Research 24 1 1984 45 69
15. G. Stepan, T. Kalmar-Nagy, Nonlinear regenerative machine tool vibrations, Proceedings of the 17th Biennial Conference on Mechanical Vibration and Noise, ASME Design Engineering Technical Conferences, Sacramento, 1997, DETC 97/VIB-4021.
16. A. Nayfeh, C. Chin, and J. Pratt Perturbation methods in nonlinear dynamicsapplications to machining dynamics Transactions of the ASME-Journal of Manufacturing Science and Engineering 119 4A 1997 485 493
17. N. Deshpande, and M.S. Fofana Nonlinear regenerative chatter in turning Robotics and Computer-Integrated Manufacturing 17 2001 107 112
18. G. Stepan, T. Insperger, and R. Szalai Delay, parametric excitation, and the nonlinear dynamics of cutting process International Journal of Bifurcation and Chaos 15 9 2005 2783 2798
19. S. Doi, and S. Kato Chatter vibration of lathe tools Transactions of the ASME-Journal of Engineering for Industry 78 1956 1127 1134
20. M. Hamdan, and M.E. Bayoumi An approach to study the effects of tool geometry on the primary chatter vibration in orthogonal cutting Journal of Sound and Vibration 128 3 1989 451 469
21. E.P. Nosyreva, and A. Molinari Analysis of nonlinear vibrations in metal cutting International Journal of Mechanical Science 40 8 1998 735 748
22. R.J. Szakovits, and A.F. D'Souza Metal cutting dynamics with reference to primary chatter Transactions of the ASME-Journal of Engineering for Industry 98 1976 258 264
23. F.C. Moon, and T. Kalmar-Nagy Nonlinear models for complex dynamics in cutting materials Philosophical Transactions of the Royal Society of London Series A 359 1781 2001 695 711
24. M. Vogler, R. Devor, and S. Kapoor Nonlinear influence of effective lead angle in turning process stability Journal of Manufacturing Engineering and Science 124 2 2002 473 475
25. H. Moradi, F. Bakhtiari-Nejad, M.R. Movahhedy, and M.T. Ahmadian Nonlinear behaviour of the regenerative chatter in turning process with a worn tool: forced oscillation and stability analysis Mechanism and Machine Theory 45 2010 1050 1066
26. M. Wiercigroch, and E. Budak Sources of nonlinearities, chatter generation and suppression in metal cutting Philosophical Transactions of the Royal Society of London Series A 359 1781 2001 663 693
27. R. Sridar, R.E. Hohn, and G.W. Long A stability algorithm for the general milling process Transactions of the ASME-Journal of Engineering for Industry 90 1968 330 334
28. R.P.H. Faassen, N. van de Wouw, H. Nijmeijer, and J.A.J. Oosterling An improved tool path model including periodic delay for chatter prediction in milling ASME Journal of Computational and Nonlinear Dynamics 2 2 2007 167 179
29. X.-H. Long, B. Balachandran, and B.P. Mann Dynamics of milling process with variable time delays Nonlinear Dynamics 47 2007 49 63
30. X.-H. Long, and B. Balachandran Stability analysis for milling process Nonlinear Dynamics 49 2007 349 359
31. T. Kalmar-Nagy, G. Stepan, and F.C. Moon Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations Nonlinear Dynamics 26 2001 121 142
32. M.S. Fofana Delay dynamical systems and applications to nonlinear machine-tool chatter Chaos, Solitons and Fractals 17 2003 731 747
33. D.E. Gilsinn Estimating critical Hopf bifurcation parameters for a second-order delay differential equation with application to machine tool chatter Nonlinear Dynamics 30 2002 103 154
34. S.T. Ariaratnam, and M.S. Fofana The effects of nonlinearity in turning operation Journal of Engineering Mathematics 42 2002 143 156
35. S.F. Brandt, A. Pelster, and R. Wessel Variational calculation of the limit cycle and its frequency in a two-neuron model with delay Physical Review E 74 2006 036201
36. R. Rand, and A. Verdugo Hopf bifurcation in a DDE model of gene expression Communications in Nonlinear Science and Numerical Simulation 13 2008 235 242
37. P. Wahi, and A. Chatterjee Regenerative tool chatter near a codimension 2 Hopf point using multiple scales Nonlinear Dynamics 40 2005 323 338
38. A.H. Nayfeh Order reduction of retarded nonlinear systemsthe method of multiple scales versus centermanifold reduction Nonlinear Dynamics 51 2008 483 500
39. S.L. Das, and A. Chatterjee Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations Nonlinear Dynamics 30 2002 323 335
40. A.H. Nayfeh, and N.A. Nayfeh Analysis of the cutting tool on a lathe Nonlinear Dynamics 63 2011 395 416
41. G. Stepan Modelling nonlinear regenerative effects in metal cutting Philosophical Transactions of the Royal Society AMathematical, Physical and Engineering Sciences 359 2001 739 757
42. R. Szalai, G. Stepan, and S.J. Hogan Global dynamics of low immersion high-speed milling Chaos 14 2004 1069 1077
43. Z. Dombovari, D.A.W. Barton, R.E. Wilson, and G. Stepan On the global dynamics of chatter in the orthogonal cutting model International Journal of Non-Linear Mechanics 46 2011 330 338
44. D. Pieroux, T. Erneux, A. Gavrielides, and V. Kovanis Hopf bifurcation subject to a large delay in a laser system SIAM Journal on Applied Mathematics 61 3 2000 966 982
45. T. Erneux, Multiple time scale analysis of delay differential equations modeling mechanical systems, ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA, September 2005, pp. 883889.
46. S.L. Das, and A. Chatterjee Second order multiple scales for oscillators with large delay Nonlinear Dynamics 39 4 2005 375 394
47. K. Nandakumar, P. Wahi, and A. Chatterjee Infinite dimensional slow modulations in a well known delayed model for cutting tool vibrations Nonlinear Dynamics 62 2010 705 716
48. P. Wahi, and A. Chatterjee Self-interrupted regenerative metal cutting in turning International Journal of Non-Linear Mechanics 43 2008 111 123
49. J. Tlusty Manufacturing Processes and Equipment 2000 Prentice-Hall New Jersey
50. R. Bellman, and K.L. Cooke Differential-Difference Equations 1963 Academic Press New York
51. P. Kim, and J. Seok Bifurcation analysis on the hunting behavior of a dual-bogie railway vehicle using the method of multiple scales Journal of Sound and Vibration 329 2010 4017 4039