Nonlinear analysis of chatter vibration in a cylindrical transverse grinding process with two time delays using a nonlinear time transformation method

Nonlinear Dynamics

Volumn 66, Issue 4, 2011, Pages 441-456

  Chung, Kwok Wai ^a   Liu, Zhaoheng ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b ÉCOLE DE TECHNOLOGIE SUPÉRIEURE   (Canada)

Author keywords

Chatter vibration; Differential equations; Grinding system; Limit cycles; Nonlinear time transformation; Two time delays

Indexed keywords

ANALYTICAL SOLUTIONS; APPROXIMATE SOLUTION; BIFURCATION POINTS; CHATTER VIBRATIONS; COMPLEX PLANES; DELAYED DIFFERENTIAL EQUATIONS; EIGENVALUES; GRINDING PROCESS; GRINDING SYSTEM; HARMONIC BALANCE APPROACH; LIMIT CYCLE; NON-LINEAR DYNAMIC SYSTEMS; NONLINEAR NORMAL FORCES; NONLINEAR TIME TRANSFORMATIONS; NUMERICAL ALGORITHMS; PARAMETER VALUES; PERIODIC SOLUTION; RECTANGULAR REGIONS; REGENERATIVE EFFECTS; RETARDED SYSTEM; SPRING-DAMPER ELEMENT; STABLE LIMIT CYCLE; SUPERCRITICAL BIFURCATION; THIRD HARMONIC; WORK PIECES;

ALGORITHMS; BIFURCATION (MATHEMATICS); DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); DYNAMICAL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; FOURIER SERIES; GRINDING (MACHINING); GRINDING WHEELS; NONLINEAR ANALYSIS; NONLINEAR DYNAMICAL SYSTEMS; NONLINEAR EQUATIONS; TIME DELAY; VIBRATION ANALYSIS;

MATHEMATICAL TRANSFORMATIONS;

EID: 82255184190     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-010-9924-y     Document Type: Article

References (17)

1. Tobias, S.A.: Machine-Tool Vibration. Wiley, New York (1965)
2. Inasaki, I.; Yonetsu, S.: Regenerative chatter in grinding. In: International Machine Tool Design and Research Conference, London, England, September 14-16, pp. 423-429 (1977)
3. Y. Altinas M. Weck 2004 Chatter stability of metal cutting and grinding CIRP Ann. Manuf. Technol. 53 2 619 642 10.1016/S0007-8506(07)60032-8 (Pubitemid 40108523)
4. Z. Liu G. Payre 2007 Stability analysis of doubly regenerative cylindrical grinding process J. Sound Vib. 301 950 962 10.1016/j.jsv.2006.10.041 (Pubitemid 46149847)
5. Davies, M.A.: Dynamic problems in hard-turning, milling, and grinding. In: Dynamics and Chaos in Manufacturing Processes, pp. 57-91. Wiley, New York (1998)
6. Nayfeh, A.H.; Chin, C.-M.; Pratt, J.: Application of perturbation methods to tool chatter dynamics. In: Moon, F.C. (ed.) Dynamics and Chaos in Manufacturing Processes, pp. 193-213 (1998)
7. M.S. Fofana 2002 Effect of regenerative process on the sample stability of a multiple delay differential equation Chaos Solitons Fractals 14 301 309 1898252 1006.34075 10.1016/S0960-0779(01)00234-X (Pubitemid 34154210)
8. T. Kalmar-Nagy G. Stepan F.C. Moon 2001 Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations Nonlinear Dyn. 26 121 142 1881432 1005.70019 10.1023/A:1012990608060 (Pubitemid 34058435)
9. G. Werner 1978 Influence of work material on grinding forces CIRP Ann. 27 1 243 248 (Pubitemid 9392661)
10. H.S.Y. Chan K.W. Chung Z. Xu 1996 A perturbation-incremental method for strongly non-linear oscillators Int. J. Non-Linear Mech. 31 59 72 1385138 0864.70015 10.1016/0020-7462(95)00043-7 (Pubitemid 126349085)
11. W.Q. Zhu Z.L. Huang Y. Suzuki 2001 Response and stability of strongly non-linear oscillators under wide-band random excitation Int. J. Non-Linear Mech. 36 1235 1250 1849693 05137993 10.1016/S0020-7462(00)00093-7 (Pubitemid 32705122)
12. L.C. Chen W.Q. Zhu 2009 Stochastic averaging of strongly nonlinear oscillators with small fractional derivative damping under combined harmonic and white noise excitations Nonlinear Dyn. 56 231 241 2495951 1170.70372 10.1007/s11071-008-9395-6
13. K.W. Chung C.L. Chan Z. Xu G.M. Mahmoud 2002 A perturbation-incremental method for strongly nonlinear autonomous oscillators with many degrees of freedom Nonlinear Dyn. 28 243 259 1911877 1015.70017 10.1023/A:1015620928121 (Pubitemid 34691529)
14. K.W. Chung C.L. Chan J. Xu 2003 An efficient method for switching branches of period-doubling bifurcations of strongly non-linear autonomous oscillators with many degrees of freedom J. Sound Vib. 267 787 808 2012796 10.1016/S0022-460X(02)01437-2
15. K.W. Chung C.L. Chan J. Xu 2006 A perturbation-incremental method for delay differential equations Int. J. Bifurc. Chaos 16 9 2529 2544 2273467 1142.34388 10.1142/S0218127406016239 (Pubitemid 44826578)
16. J. Xu K.W. Chung C.L. Chan 2007 An efficient method for studying weak resonant double Hopf bifurcation in nonlinear systems with delayed feedbacks SIAM J. Appl. Dyn. Syst. 6 1 29 60 2299635 1210.34086 10.1137/040614207
17. J. Xu K.W. Chung 2009 A perturbation-incremental scheme for studying Hopf bifurcation in delayed differential systems Sci. China Ser. E 52 3 1 11 2486199