Experimental Investigation of Evolution Process of Nonlinear Characteristics from Chatter Free to Chatter
Fansen Kong, Peng Liu, Xiaoming Wang
DOI: 10.4236/jmp.2011.29126   PDF    HTML     5,335 Downloads   9,038 Views   Citations


The vibration acceleration time history of the cutter holder was separated into three parts; namely, chatter free, transition and chatter processes. The reconstructed attractor and probability distribution of vibration acceleration time series were studied in order to observe the system’s behavior. The Lyapunov exponent andKolmogorov entropy were used to help judge the cutting state. Meanwhile, the relation curves of the Lyapunov exponent and entropy versus machining parameters were plotted and discussed. The research shows that Lyapunov exponent and Kolmogorov entropy are toned up when vibration acceleration time his- tory goes from chatter free, transition to chatter. When cutting state transited from chatter free to chatter, the Lyapunov exponent and Kolmogorov entropy increase with increasing amplitude. In addition, the relation curves looks like stability lobes. The experimental study allow us to select optimal machining parameters for decreasing the uncertainty of cutting vibration.

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F. Kong, P. Liu and X. Wang, "Experimental Investigation of Evolution Process of Nonlinear Characteristics from Chatter Free to Chatter," Journal of Modern Physics, Vol. 2 No. 9, 2011, pp. 1041-1050. doi: 10.4236/jmp.2011.29126.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] S. A. Tobias, “Machine Tool Vibration,” Blackie, London, 1965.
[2] I. Koenigsberger and J. Tlusty, “Structures of Machine Tools,” Pergamon Press, Oxford, 1971.
[3] H. E. Merritt, “Theory of Self-Excited Machine Tools Chatter,” Journal of Engineering for Industry-Trans- actions of the ASME, Vol. 87, 1965, pp. 447-454.
[4] N. H. Hanna and S. A. Tobias, “A Theory of Nonlinear Regenerative Chatter,” ASME Journal of Engineering for Industry-Transactions, Vol. 96, 1974, pp. 247-255. doi:10.1115/1.3438305
[5] H. M. Shi, S. A. Tobias, “Theory of Finite Amplitude Machine Tool Instability,” International Journal of Ma-chine Tool Design and Research, Vol. 1, No. 24, 1984, pp. 45-60. doi:10.1016/0020-7357(84)90045-3
[6] J. Tlusty and F. Ismal, “Basic Nonlinearity in Machining Chatter,” Annals of the CIRP, Vol. 30, No. 1, 1981, p. 299. doi:10.1016/S0007-8506(07)60946-9
[7] I. Grabec, “Chaos Generated by the Cutting Process,” Physics Letters, Vol. 117, No. 8, 1986, pp. 384-386. doi:10.1016/0375-9601(86)90003-4
[8] I. Grabec, “Chaotic Dynamics of the Cutting Process,” International Journal of Machine Tools Manufacturing, Vol. 28, 1988, pp. 19-32. doi:10.1016/0890-6955(88)90004-1
[9] I. Grabec, “Explanation of Random Vibrations in Cutting on Grounds of Deterministic Chaos,” Robotics and Computer& Integrated Manufacturing, Vol. 4, 1988, pp. 129-134. doi:10.1016/0736-5845(88)90067-1
[10] R. F. Gans, “When Is Cutting Chaotic?” Journal of Sound and Vibration, Vol. 1, No. 188, 1995, pp. 75-83. doi:10.1006/jsvi.1995.0579
[11] J. Gradisek, E. Govekar and I. Grabec, “A Chaotic Cutting Process and Determining Optimal Cutting Parameter Values Using Neural Networks,” International Journal of Machine Tools and Manufacture, Vol. 10, No. 36, 1996, pp. 1161-1172. doi:10.1016/0890-6955(96)00007-7
[12] J. Gradisek, E. Govekar and I. Grabec, “Time Series Analysis in Metal Cutting: Chatter Versus Chatter-Free Cutting,” Mechanical Systems and Signal Processing, Vol. 6, No. 12, 1998, pp. 839-854. doi:10.1006/mssp.1998.0174
[13] S. T. S. Bukkapatnam, A. Lakhtakia and S. R. T. Kumara, “Analysys of Sensor Signals Shows Turning on a Lathe Exhibits Low-Dimensional Chaos,” Physical Review E, Vol. 3, No. 52, 1995, pp. 2375-2378. doi:10.1103/PhysRevE.52.2375
[14] T. Insperger, D. A. W. Barton and G. Stepan, “Criticality of Hopf Bifurcation in State-Dependent Delay Model of Turning Process,” International Journal of Nonlinear Mechanics, Vol. 43, No. 2, 2008, pp. 140-149. doi:10.1016/j.ijnonlinmec.2007.11.002
[15] A. Wolf, J. B. Swift, H. L. Swinney and J. A. Vastano, “Determining Lyapunov Exponents from a Time Serie,” Physica D, Vol. 16, 1985, pp. 285-317. doi:10.1016/0167-2789(85)90011-9
[16] P. Grassberger and T. Procaccia, “Estimation of the Kolmogorov Entropy from a Chaotic Signal,” Physical Review A, Vol. 28, No. 4, 1983, pp. 2591-2593. doi:10.1103/PhysRevA.28.2591
[17] M. T. Rosensteiin, J. J. Collins, et al., “A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets,” Journal of Physics D, Vol. 65, No. 1-2, 1993, pp. 117-134
[18] H. Kantz and T. Schreiber, “Nonlinear Time Series Analysis,” Cambridge University Press, Cambridge, 1997.
[19] C. S. Hsu, “Probabilistic Theory of Nonlinear Dynamical Systems Based on the Cell State Space Concept,” Journal of Applied Mechanics, Transactions ASME, Vol. 4, No. 49, 1982, pp. 895-902. doi:10.1115/1.3162633
[20] F. C. Mooon, “Chaotic Vibrations—An Introduction for Applied Scientist and Engineers,” John Wiley& Sons, Hoboken, 1987.
[21] H. Kantz, “A Robust Method to Estimate the Maximal Lyapunov Exponent of a Time Series,” Physics Letters A, Vol. 185, No. 1, 1994, pp. 77-87. doi:10.1016/0375-9601(94)90991-1
[22] L. M. Hively and V. A. Protopopescu, “Machine Failure Forewarning via Phase-Space Dissimilarity Measures,” Chaos, Vol. 2, No. 14, 2004, pp. 408-420.

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