An improved tool path model including periodic delay for chatter prediction in milling

Journal of Computational and Nonlinear Dynamics

Volumn 2, Issue 2, 2007, Pages 167-179

  Faassen, R P H ^a   van de Wouw, N ^a   Nijmeijer, H ^a   Oosterling, J A J ^b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b TNO   (Netherlands)

Author keywords

Finite difference method; High speed milling; Periodic delay differential equations; Stability; Tool path

Indexed keywords

CUTTING; DIFFERENTIAL EQUATIONS; ERRORS; FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; VIBRATIONS (MECHANICAL);

HIGH-SPEED MILLING; PERIODIC DELAY DIFFERENTIAL EQUATIONS; TOOL PATH;

MILLING (MACHINING);

EID: 34248400742     PISSN: 15551423     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2447465     Document Type: Article

References (24)

1. Tlusty, J., and Polacek, M., 1963, "The Stability of Machine Tools against Self-Excited Vibrations in Machining," Proceedings ASME International Research in Production Engineering, Pittsburgh, PA, pp. 465-474.
2. Tobias, S. A., and Fishwick, W., 1958, "The Chatter of Lathe Tools Under Orthogonal Cutting Conditions," Trans. ASME, 80, pp. 1079-1088.
3. Davies, M. A., Pratt, J. R., Dutterer, B., and Burns, T. J., 2002, "Stability Prediction for Low Radial Immersion Milling," J. Manuf. Sci. Eng., 124(2), pp. 217-225.
4. Insperger, T., and Stépán, G., 2004, "Vibration Frequencies in High-Speed Milling Process or a Positive Answer to Davies Pratt, Dutterer, and Burns," J. Manuf. Sci. Eng., 126(3), pp. 481-487.
5. Stépán, G., Insperger, T., and Szalai, R., 2005, "Delay Parametric Excitation, and the Nonlinear Dynamics of Cutting Processes," Int. J. Bifurcation Chaos Appl. Sci. Eng., 15(9), pp. 2783-2798.
6. Szalai, R., and Stépán, G., 2006, "Lobes and Lenses in the Stability Chart of Interrupted Turning," ASME J. Comput. Nonlinear Dyn. 1(3), pp. 205-211.
7. Szalai, R., Stépán, G., and Hogan, S. J., 2004, "Global Dynamics of Low Immersion High-Speed Milling," Chaos, 14(4), pp. 1069-1077.
8. Altintas, Y., 2000, Manufacturing Automation, Cambridge University Press, Cambridge, UK.
9. Insperger, T., Stépán, G., Bayly, P. V., and Mann, B. P., 2003, "Multiple Chatter Frequencies in Milling Processes," J. Sound Vib., 262(2), pp. 333-345.
10. Martellotti, M. E., 1941, "An Analysis of the Milling Process," Trans. ASME, 63, pp. 677-700.
11. Martellotti, M. E., 1945, "An Analysis of the Milling Process. Part 2. Down Milling," Trans. ASME, 67, pp. 233-251.
12. Li, H. Z., Liu, K., and Li, X. P., 2001, "A New Method for Determining the Undeformed Chip Thickness in Milling," J. Mater. Process. Technol., 113, pp. 378-384.
13. Spiewak, S., 1994, "Analytical Modeling of Cutting Point Trajectories in Milling," J. Eng. Ind., 116, pp. 440-448.
14. Spiewak, S., 1995, "An Improved Model of the Chip Thickness in Milling," CIRP Ann., 44(1), pp. 39-42.
15. Altintas, Y., and Budak, E., 1995, "Analytical Prediction of Stability Lobes in Milling," CIRP Ann., 44(1), pp. 357-362.
16. Insperger, T., and Stépán, G., 2004, "Updated Semi-Discretization Method for Periodic Delay-Differential Equations With Discrete Delay," Int. J. Numer. Methods Eng., 61(1), pp. 117-141.
17. Long, X. H., and Balachandran, B., 2004, "Milling Model With Variable Time Delay," Proceedings ASME International Mechanical Engineering Congress and Exposition, Anaheim, CA, November, Vol. 15, pp. 933-940.
18. Faassen, R. P. H., van de Wouw, N., Oosterling, J. A. J., and Nijmeijer, H., 2003, "Prediction of Regenerative Chatter by Modelling and Analysis of High-Speed Milling," Int. J. Mach. Tools Manuf., 43(14), pp. 1437-1446.
19. Insperger, T., and Stépán, G., 2004, "Stability Analysis of Turning With Periodic Spindle Speed Modulation via Semi-discretization," J. Vib. Control, 10, pp. 1835-1855.
20. Insperger, T., Stépán, G., Hartung, F., and Turi, J., 2005, "State Dependent Regenerative Delay in Milling Processes," Proceedings ASME International Design Engineering Technical Conferences, Long Beach, CA, September, Paper No. DETC2005-85282.
21. Balachandran, B., 2001, "Nonlinear Dynamics of Milling Processes," Philos. Trans. R. Soc. London, 359(1781), pp. 793-819.
22. Nayfeh, A. H., and Balachandran, B., 1995, Applied Nonlinear Dynamics, Analytical, Computational, and Experimental Methods, Wiley-International, Chichester, UK.
23. Parker, T., S., and Chua, L. O., 1989, Practical Numerical Algorithms for Chaotic Systems, Springer, Berlin, Germany.
24. Faassen, R. P. H., van de Wouw, N., Oosterling, J. A. J., and Nijmeijer, H., 2005, "Updated Tool Path Modelling With Periodic Delay for Chatter Prediction in Milling," Proceedings 5th Euromech Nonlinear Dynamics Conference (ENOC), Eindhoven, The Netherlands, August, Paper No. 08-109, pp. 1080-1089.