Numerical integration method for prediction of milling stability

Journal of Manufacturing Science and Engineering

Volumn 133, Issue 3, 2011, Pages

  Ding, Ye ^a   Zhu, Limin ^a   Zhang, Xiaojian ^b   Ding, Han ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Floquet theory; integral equation; milling; numerical integration; stability prediction

Indexed keywords

DIFFERENTIAL EQUATIONS; FORECASTING; INTEGRATION; MILLING (MACHINING); NUMERICAL METHODS; STABILITY; VIBRATION ANALYSIS;

APPROXIMATE SOLUTION; FLOQUET THEORY; NUMERICAL INTEGRATION FORMULAE; NUMERICAL INTEGRATION METHODS; NUMERICAL INTEGRATIONS; REGENERATIVE EFFECTS; STABILITY PREDICTION; STATE TRANSITION MATRIX;

INTEGRAL EQUATIONS;

EID: 79959308719     PISSN: 10871357     EISSN: 15288935     Source Type: Journal    
DOI: 10.1115/1.4004136     Document Type: Article

References (48)

1. Altintas, Y., 2000, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design, Cambridge University Press, Cambridge.
2. Altintas, Y., and Weck, M., 2004, "Chatter Stability of Metal Cutting and Grinding," CIRP Ann. - Manuf. Technol., 53(2), pp. 619-642. (Pubitemid 40108523)
3. Balachandran, B., 2001, "Nonlinear Dynamics of Milling Processes," Philos. Trans. R. Soc. London, Ser. A, 359, pp. 793-819.
4. Wiercigroch, M., and Budak, E., 2001, "Sources of Nonlinearities, Chatter Generation and Suppression in Metal Cutting," Philos. Trans. R. Soc. London, Ser. A 359(1781), pp. 663-693.
5. Schmitz, T. L., 2000, "Predicting High-Speed Machining Dynamics by Substructure Analysis," CIRP Ann. - Manuf. Technol., 49(1), pp. 303-308.
6. Schmitz, T. L., Davies, M. A., and Kennedy, M. D., 2001, "Tool Point Frequency Response Prediction for High-Speed Machining by RCSA," ASME J. Manuf. Sci. Eng., 123(4), pp. 700-707. (Pubitemid 33715871)
7. Budak, E., Altintas, Y., and Armarego, E. J. A., 1996, "Prediction of Milling Force Coefficients from Orthogonal Cutting Data," ASME J. Manuf. Sci. Eng., 118(2), pp. 216-224.
8. Altintas, Y., Stépán, G., Merdol, D., and Dombovari, Z., 2008, "Chatter Stability of Milling in Frequency and Discrete Time Domain," CIRP J. Manuf. Sci. Technol., 1(1), pp. 35-44.
9. Minis, I., and Yanushevsky, R., 1993, "A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling," J. Eng. Ind., 115(1), pp. 1-8. (Pubitemid 23631743)
10. Altintas, Y., and Budak, E., 1995, "Analytical Prediction of Stability Lobes in Milling," CIRP Ann.-Manuf. Technol., 44(1), pp. 357-362.
11. Budak, E., and Altintas, Y., 1998, "Analytical Prediction of Chatter Stability in Milling-Part I: General Formulation," ASME J. Dyn. Syst,. Meas., Control, 120(1), pp. 22-30. (Pubitemid 128651911)
12. Budak, E., and Altintas, Y., 1998, "Analytical Prediction of Chatter Stability in Milling-Part II: Application of the General Formulation to Common Milling Systems," ASME J. Dyn. Syst., Meas., Control, 120(1), pp. 31-36. (Pubitemid 128651912)
13. Merdol, S. D., and Altintas, Y., 2004, "Multi Frequency Solution of Chatter Stability for Low Immersion Milling," ASME J. Manuf. Sci. Eng., 126(3), pp. 459-466. (Pubitemid 40122758)
14. Davies, M. A., Pratt, J. R., Dutterer, B., and Burns, T. J., 2002, "Stability Prediction for Low Radial Immersion Milling," ASME J. Manuf. Sci. Eng., 124(2), pp. 217-225. (Pubitemid 35202609)
15. Insperger, T., and Stépán, G., 2002, "Semi- Discretization Method for Delayed Systems," Int. J. Numer. Methods Eng., 55(5), pp. 503-518.
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. (Pubitemid 39115803)
17. Insperger, T., Stépán, G., and Turi, J., 2008, "On the Higher-Order Semi-Discretizations for Periodic Delayed Systems," J. Sound Vib., 313(1-2), pp. 334-341.
18. Seguy, S., Insperger, T., Arnaud, L., Dessein, G., and Peigné, G., 2010, "On the Stability of High-Speed Milling with Spindle Speed Variation," Int. J. Adv. Manuf. Technol., 48(9-12), pp. 883-895.
19. Seguy, S., Dessein, G., Arnaud, L., and Insperger, T., 2010, "Control of Chatter by Spindle Speed Variation in High-Speed Milling," Adv. Mater. Res., 112(1), pp. 179-186.
20. Sims, N. D., Mann, B., and Huyanan, S., 2008, "Analytical Prediction of Chatter Stability for Variable Pitch and Variable Helix Milling Tools," J. Sound Vib., 317(3-5), pp. 664-686.
21. Dombovari, Z., Altintas, Y., and Stepan, G., 2010, "The Effect of Serration on Mechanics and Stability of Milling Cutters," Int. J. Mach. Tools Manuf., 50(6), pp. 511-520.
22. Bayly, P. V., Halley, J. E., Mann, B. P., and Davies, M. A., 2001, "Stability of Interrupted Cutting by Temporal Finite Element Analysis," Proceedings of the ASME Design Engineering Technical Conference, Vol. 6C, pp. 2361-2370.
23. Bayly, P. V., Mann, B. P., Schmitz, T. L., Peters, D. A., Stepan, G., and Insperger, T., 2002, "Effects of Radial Immersion and Cutting Direction on Chatter Instability in End-Milling," American Society of Mechanical Engineers, Manufacturing Engineering Division, MED, Vol. 13, pp. 351-363.
24. Mann, B. P., Young, K. A., Schmitz, T. L., and Dilley, D. N., 2005, "Simultaneous Stability and Surface Location Error Predictions in Milling," ASME J. Manuf. Sci. Eng., 127(3), pp. 446-453. (Pubitemid 41283968)
25. Mann, B. P., Edes, B. T., Easley, S. J., Young, K. A., and Ma, K., 2008, "Chatter Vibration and Surface Location Error Prediction for Helical End Mills," Int. J. Mach. Tools Manuf., 48(3-4), pp. 350-361.
26. Butcher, E. A., Ma, H., Bueler, E., Averina, V., and Szabo, Z., 2004, "Stability of Linear Time-Periodic Delay-Differential Equations Via Chebyshev Polynomials," Int. J. Numer. Methods Eng., 59(7), pp. 895-922. (Pubitemid 38285936)
27. Maghami Asl, F., and Ulsoy, A. G., 2003, "Analysis of a System of Linear Delay Differential Equations," ASME J. Dyn. Syst., Meas., Control, 125(2), pp. 215-223.
28. Yi, S., Nelson, P. W., and Ulsoy, A. G., 2007, "Delay Differential Equations Via the Matrix Lambert W Function and Bifurcation Analysis: Application to Machine Tool Chatter," Math. Biosci. Eng., 4(2), pp. 355-368. (Pubitemid 47147354)
29. Olvera, D., Calva, V., Gonzalez, J. L., Pacheco, J., Elias-Zuniga, A., and De Lacalle, L. N. L., 2008, "Milling Stability Lobes Computation through the Lambert W Function," Transactions of the North American Manufacturing Research Institution of SME, Vol. 36, pp. 233-239.
30. Olgac, N., and Sipahi, R., 2005, "A Unique Methodology for Chatter Stability Mapping in Simultaneous Machining," ASME J. Manuf. Sci. Eng., 127(4), pp. 791-800. (Pubitemid 41680968)
31. Olgac, N., and Sipahi, R., 2007, "Dynamics and Stability of Variable-Pitch Milling," J. Vib. Control, 13(7), pp. 1031-1043. (Pubitemid 47114415)
32. Butcher, E. A., Bobrenkov, O. A., Bueler, E., and Nindujarla, P., 2009, "Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels," J. Comput. Nonlinear Dyn., 4(3), pp. 031003.
33. Ding, Y., Zhu, L., Zhang, X., and Ding, H., 2010, "A Full-Discretization Method for Prediction of Milling Stability," Int. J. Mach. Tools Manuf., 50(5), pp. 502-509.
34. Ding, Y., Zhu, L., Zhang, X., and Ding, H., 2011, "On a Numerical Method for Simultaneous Prediction of Stability and Surface Location Error in Low Radial Immersion Milling," ASME J. Dyn. Syst., Meas. Control, 133(2), p. 024503.
35. Insperger, T., 2010, "Full-Discretization and Semi-Discretization for Milling Stability Prediction: Some Comments," Int. J. Mach. Tools Manuf., 50(7), 658-662.
36. Feng, K., and Shi, Z.-C., 2001, Mathematical Theory of Elastic Structures, Springer, Berlin; New York.
37. Yang, D., and Zhao, Z., 2006, The Boundary Element Theory and Application, Beijing Institute of Technology Press, Beijing, in Chinese.
38. Delves, L. M., and Mohamed, J. L., 1985, Computational Methods for Integral Equations, Cambridge University Press, Cambridge.
39. Li, X., 2008, Integral Equations, Science Press, Beijing, in Chinese.
40. Gradisek, J., Kalveram, M., Insperger, T., Weinert, K., Stepan, G., Govekar, E., and Grabec, I., 2005, "On Stability Prediction for Milling," Int. J. Mach. Tools Manuf. 45(7-8), pp. 769-781. (Pubitemid 40259554)
41. Yang, W. Y., Cao, W., Chung, T.-S., and Morris, J., 2005, Applied Numerical Methods Using Matlab, Wiley-Interscience, Hoboken, NJ.
42. Farkas, M., 1994, Periodic Motions, Springer-Verlag, New York.
43. Serre, D., 2002, Matrices: Theory and Applications, Springer-Verlag, New York.
44. Altintas, Y., Engin, S., and Budak, E., 1999, "Analytical Stability Prediction and Design of Variable Pitch Cutters," ASME J. Manuf. Sci. Eng., 121(2), pp. 173-178.
45. Insperger, T., Mann, B. P., Stepan, G., and Bayly, P. V., 2003, "Stability of up-Milling and Down-Milling, Part 1: Alternative Analytical Methods," Int. J. Mach. Tools Manuf., 43(1), pp. 25-34. (Pubitemid 35385282)
46. Henninger, C., and Eberhard, P., 2008, "Improving the Computational Efficiency and Accuracy of the Semi-Discretization Method for Periodic Delay- Differential Equations," Eur. J. Mech. A=Solids, 27(6), pp. 975-985.
47. Budak, E., 2003, "An Analytical Design Method for Milling Cutters with Nonconstant Pitch to Increase Stability, Part I: Theory," ASME J. Manuf. Sci. Eng., 125(1), pp. 29-34.
48. Budak, E., 2003, "An Analytical Design Method for Milling Cutters with Nonconstant Pitch to Increase Stability, Part 2: Application," ASME J. Manuf. Sci. Eng., 125(1), pp. 35-38.