Analysis of the cutting tool on a lathe

Nonlinear Dynamics

Volumn 63, Issue 3, 2011, Pages 395-416

  Nayfeh, Ali H ^a   Nayfeh, Nader A ^b  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b Northrup Grumman   (United States)

Author keywords

Bifurcation control; Floquet theory; Harmonic balance; Hopf bifurcation; Machine tool chatter; Method of multiple scales; Normal form

Indexed keywords

BIFURCATION CONTROL; FLOQUET THEORY; HARMONIC BALANCE; MACHINE-TOOL CHATTER; METHOD OF MULTIPLE SCALES; NORMAL FORM;

COMPUTER SIMULATION; CUTTING TOOLS; DIFFERENTIAL EQUATIONS; HARMONIC ANALYSIS; LATHES; MACHINE TOOLS; METAL WORKING TOOLS; NUMERICAL METHODS;

HOPF BIFURCATION;

EID: 79751538835     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-010-9811-6     Document Type: Article

References (23)

1. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley-Interscience, New York (1979)
2. N.H. Hanna S.A. Tobias 1974 A theory of nonlinear regenerative chatter ASME J. Eng. Ind. 96 247 255 10.1115/1.3438305
3. H.M. Shi S.A. Tobias 1984 Theory of finite amplitude machine tool instability Int. J. Mach. Tool Des. Res. 24 45 69 10.1016/0020-7357(84)90045-3 (Pubitemid 14584083)
4. A.H. Nayfeh C.M. Chin J.R. Pratt 1997 Perturbation methods in nonlinear dynamics: applications to machining dynamics J. Manuf. Sci. Eng. 119 485 493 10.1115/1.2831178 (Pubitemid 127825755)
5. Nayfeh, A.H.: Perturbation Methods. Wiley-Interscience, New York (1973)
6. Nayfeh, A.H.: Introduction to Perturbation Techniques. Wiley-Interscience, New York (1981)
7. J.R. Pratt A.H. Nayfeh 1999 Design and modeling for chatter control Nonlinear Dyn. 19 49 69 0953.70524 10.1023/A:1008322520352
8. J.R. Pratt A.H. Nayfeh 2001 Chatter control and stability analysis of a cantilever boring bar under regenerative cutting conditions Philos. Trans. R. Soc., Math. Phys. Eng. Sci. 359 759 792 1169.74437 10.1098/rsta.2000.0754 (Pubitemid 33255325)
9. F.C. Moon T. Kalmár-Nagy 2001 Nonlinear models for complex dynamics in cutting materials Philos. Trans. R. Soc. Lond. 359 695 711 0998.74038 10.1098/rsta.2000.0751
10. T. Kalmár-Nagy G. Stépán F.C. Moon 2001 Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations Nonlinear Dyn. 26 121 142 1005.70019 10.1023/A:1012990608060 (Pubitemid 34058435)
11. D. Gilsinn 2002 Estimating critical Hopf bifurcation parameters for a second-order delay differential equation with application to machine tool Nonlinear Dyn. 30 103 154 1039.70015 10.1023/A:1020455821894 1934163 (Pubitemid 35298656)
12. A.H. Nayfeh 2008 Order reduction of retarded nonlinear systems: The method of multiple scales versus center-manifold reduction Nonlinear Dyn. 51 483 500 1170.70355 10.1007/s11071-007-9237-y 2380338
13. G. Stépán 2001 Modeling nonlinear regenerative effects in metal cutting Proc. R. Soc. Lond. A 359 739 757 1169.74431
14. P. Wahi A. Chatterjee 2005 Regenerative tool chatter near a codimension 2 Hopf point using multiple scales Nonlinear Dyn. 40 323 338 1172.70309 10.1007/s11071-005-7292-9 2144752 (Pubitemid 40666316)
15. N.K. Chandiramani T. Pothala 2006 Dynamics of 2-dof regenerative chatter during turning J. Sound Vib. 290 448 464 10.1016/j.jsv.2005.04.012 (Pubitemid 41802257)
16. R.P.H. Faassen N. van de Wouw H. Nijmeijer J.A.J. Oosterling 2007 An improved tool path model including periodic delay for chatter prediction in milling J. Comput. Nonlinear Dyn. 2 167 179 10.1115/1.2447465 (Pubitemid 46736213)
17. X.-H. Long B. Balachandran B.P. Mann 2007 Dynamics of milling processes with variable time delay Nonlinear Dyn. 47 49 63 1180.70030 10.1007/s11071-006- 9058-4 (Pubitemid 46064023)
18. X.-H. Long B. Balachandran 2007 Stability analysis for milling process Nonlinear Dyn. 49 349 359 1177.70024 10.1007/s11071-006-9127-8 (Pubitemid 46976737)
19. T. Insperger G. Stépán J. Turi 2007 State-dependent delay in regenerative turning processes Nonlinear Dyn. 47 1-3 275 283 1177.74197 (Pubitemid 46064037)
20. T. Insperger D.A.W. Barton G. Stépán 2008 Criticality of Hopf bifurcation in state-dependent delay model of turning processes Int. J. Non-Linear Mech. 43 140 149 10.1016/j.ijnonlinmec.2007.11.002
21. F.W. Taylor 1907 On the art of cutting metals ASME 28 31 350
22. Kalmár-Nagy, T., Pratt, J.R., Davies, M.A., Kennedy, M.D.: Experimental and analytical investigation of the subcritical instability in metal cutting. In: Balachandran, B., Kurdila, A., Pratt, J.R., Murphy, K. (eds.) Proceedings of DETC'99, 17th ASME Biennial Conference on Mechanical Vibration and Noise, Las Vegas, NV, September 12-15, pp. 1-9. ASME, New York (1999)
23. Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics. Wiley-Interscience, New York (1995)