Non-linear oscillations of milling

Mathematical and Computer Modelling of Dynamical Systems

Volumn 11, Issue 3, 2005, Pages 273-290

  Balachandran, B ^a,b   Gilsinn, D ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

Chatter; Loss of contact; Milling; Variable time delay

Indexed keywords

CHATTER; DELAY DIFFERENTIAL SYSTEMS; MILLING OPERATION; NONLINEAR OSCILLATION; REGENERATIVE EFFECTS; STABILITY ANALYSIS; TIME-DELAY EFFECT; VARIABLE TIME DELAY;

MATHEMATICAL MODELS; OSCILLATORS (MECHANICAL); TIME DELAY;

MILLING (MACHINING);

EID: 27844592273     PISSN: 13873954     EISSN: None     Source Type: Journal    
DOI: 10.1080/13873950500076479     Document Type: Article

References (25)

1. Kahles, J. F., Field, M. and Harvey, S. M., 1978, High speed machining possibilities and needs. Annals of the CIRP, 27, 551-558.
2. King, R. I., 1985, Handbook of High-Speed Machining Technology (New York: Chapman and Hall).
3. Schulz, H., 1993. High-speed machining. Annals of the CIRP, 42, 637-645.
4. Komanduri, R., McGee, J., Thompson, R. A., Covy, J. P., Truncale, F. J., Tipnis, V. A., Stach, R. M. and King, R. I., 1985, On a methodology for establishing the machine tool system requirements for high-speed/high-throughput machining. ASME Journal of Engineering for Industry, 107, 316-324.
5. Tlusty, J. and Polacek, M., 1963, The stability of the machine tool against self-excited vibration in machining. Proceedings of the Conference on International Research in Production Engineering, Pittsburgh, PA, pp. 465-474 (ASME).
6. Tobias, S. A., 1965, Machine-Tool Vibration (New York: Wiley).
7. Opitz, H., Dregger, E.U. and Roese, H., 1966, Improvement of the dynamic stability of the milling process by irregular tooth pitch. Proceedings of the 7th International MTDR Conference (New York: Pergamon Press).
8. Sridhar, R., Hohn, R. E. and Long, G. W., 1968, A stability algorithm for the general milling process. ASME Journal of Engineering for Industry, 90, 330-334.
9. Hanna, N. H. and Tobias, S. A., 1974, A theory of nonlinear regenerative chatter. ASME Journal of Engineering for Industry, 96, 247-255.
10. Minis, I. and Yanushevsky, R., 1993, A new theoretical approach for the prediction of machine tool chatter in milling. ASME Journal of Engineering for Industry, 115, 1-8.
11. Altintas, Y. and Budak, E., 1995, Analytical prediction of stability lobes in milling. Annals of CIRP, 44, 357-362.
12. Balachandran, B., 2001, Nonlinear dynamics of milling processes. Philosophical Transactions of the Royal Society, London, A, 359, 793-819.
13. Balachandran, B. and Zhao, M. X., 2000, A mechanics based model for study of dynamics of milling operations. Meccanica, 35, 89-109.
14. Zhao, M. X. and Balachandran, B., 2001, Dynamics and stability of milling process. International Journal of Solids and Structures, 38, 2233-2248.
15. Hahn, W., 1961, On difference-differential equations with periodic coefficients. Journal of Mathematical Analysis and Applications, 3, 70-101.
16. Nayfeh, A. H. and Mook, D. T., 1979, Nonlinear Oscillations (New York: Wiley).
17. Insperger, T. and Stépán, G., 2002, Semi-discretization method for delayed systems. International Journal of Numerical Methods in Engineering, 55, 503-518.
18. Insperger, T. and Stépán, G., 2003, Stability of the damped Mathieu equation with time delay. ASME Journal of Dynamic Systems, Measurement, and Control, 166, 166-171.
19. Gilsinn, D., 2004, Approximating limit cycles of a van der Pol equation with delay. Proceedings of Dynamic Systems and Applications 4 (Altanta).
20. Long, X.-H. and Balachandran, B., Stability analysis of milling process. Nonlinear Dynamics, accepted for publication, 2002.
21. Long, X. -H. and Balachandran, B., Milling dynamics with a variable time delay. Proceedings of ASME IMECE 2004, Anaheim, CA, November 13-19, Paper No. IMECE 2004-59207.
22. Farkas, M.: Periodic Motions Springer-Verlag, New York, 1994.
23. Nayfeh, A. H. and Balachandran, B., 1995, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods (New York: Wiley).
24. Halanay, S., 1966, Differential Equations, Oscillations, Time Lags (New York, Academic Press).
25. Shampine, L. F. and Thompson, S., 2001, Solving DDE's in MATLAB. Applied Numerical Mathematics, 37, 441-458.