Improving the computational efficiency and accuracy of the semi-discretization method for periodic delay-differential equations

European Journal of Mechanics, A/Solids

Volumn 27, Issue 6, 2008, Pages 975-985

  Henninger, Christoph ^a   Eberhard, Peter ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Computational efficiency; Cutting process; Delay differential equations; Machine tool chatter; Semi discretization method

Indexed keywords

COMPUTATIONAL EFFICIENCY; CONTROL SYSTEMS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); MILLING (MACHINING); SWITCHING CIRCUITS; VOLUME MEASUREMENT;

APPROXIMATED SYSTEM; COMPUTATIONAL COSTS; CUTTING PROCESS; DELAY-DIFFERENTIAL EQUATIONS; DISCRETIZATION SCHEME; INTERRUPTED CUTTING; MACHINE-TOOL CHATTER; MILLING PROCESSES; SEMI-DISCRETIZATION METHOD; SEMI-DISCRETIZATION METHODS; TRANSITION MATRICES;

COMPUTATIONAL METHODS;

EID: 50549101224     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechsol.2008.01.006     Document Type: Article

References (26)

1. Altintas Y., and Budak E. Analytical prediction of stability lobes in milling. Annals of the CIRP 44 1 (1995) 357-362
2. Bayly P.V., Halley J.E., Mann B.P., and Davies M.A. Stability of interrupted cutting by temporal finite element analysis. ASME Journal of Manufacturing Sciences and Engineering 125 2 (2003) 220-225
3. Budak E., and Altintas Y. Analytical prediction of chatter stability in milling - Part I: General formulation. ASME Journal of Dynamic Systems, Measurement, and Control 120 (1998) 22-30
4. Budak E., and Altintas Y. Analytical prediction of chatter stability in milling - Part II: Application of the general formulation to common milling systems. ASME Journal of Dynamic Systems, Measurement, and Control 120 (1998) 31-36
5. Cahlon B., and Schmidt D. Asymptotic stability of a mechanical robotics model with damping and delay. Journal of Mathematical Analysis and Applications 303 1 (2005) 36-53
6. Davies M.A., Pratt J.R., Dutterer B.S., and Burns T.J. The stability of low radial immersion milling. Annals of the CIRP 49 1 (2000) 37-40
7. Gradišek J., Kalveram M., Insperger T., Weinert K., Stépán G., Govekar E., and Grabec I. On stability prediction for milling. International Journal of Machine Tools and Manufacture 45 (2005) 769-781
8. Hemami H., and Özbay H. Modeling and control of biological systems with multiple afferent and efferent transmission delays. Journal of Robotic Systems 17 11 (2001) 609-622
9. Henninger, C., Eberhard, P., 2005. Avoiding chatter by tuning the dynamics of the machine structure with a damped vibration absorber. In: Proceedings of the 5th Euromech Nonlinear Dynamics Conference. Eindhoven
10. Henninger C., and Eberhard P. A new curve tracking algorithm for efficient computation of stability boundaries of cutting processes. ASME Journal of Computational and Nonlinear Dynamics 2 4 (2007) 360-365
11. Henninger, C., Eberhard, P., 2007b. An investigation of pose-dependent regenerative chatter for a parallel kinematic milling machine. In: Proceedings of the 12th World Congress in Mechanism and Machine Science IFToMM. Besançon, France
12. Insperger T., Mann B., Stépán G., and Bayly P. Stability of up-milling and down-milling, Part 1: Alternative analytical methods. International Journal of Machine Tools and Manufacture 43 (2003) 25-34
13. Insperger T., and Stépán G. Semi-discretization method for delayed systems. International Journal for Numerical Methods in Engineering 55 (2002) 503-518
14. Insperger T., and Stépán G. Updated semi-discretization method for periodic delay-differential equations with discrete delay. International Journal for Numerical Methods in Engineering 61 (2004) 117-141
15. Kataria A., Özbay H., and Hemami H. Controller design for natural and robotic systems with transmission delays. Journal of Robotic Systems 19 5 (2002) 231-244
16. Minis I., Yanushevsky R., and Tembo A. Analysis of linear and nonlinear chatter in milling. Annals of the CIRP 39 1 (1990) 459-462
17. Mukhopadhyay B., and Bhattacharyya R. Dynamics of a delayed epidemiological model with nonlinear incidence: The role of infected incidence fraction. Journal of Biological Systems 13 4 (2005) 341-361
18. Olgac N., and Hosek M. Active vibration absorption using delayed resonator with relative position measurement. Journal of Vibrations and Acoustics 119 (1997) 131-136
19. Sipahi R., and Olgac N. Active vibration suppression with time delayed feedback. ASME Journal of Vibration and Acoustics 125 3 (2003) 284-288
20. Stépán G. Retarded Dynamical Systems: Stability and Characteristic Functions (1989), Longman, London
21. Tang Z., White J., Chiasson J., and Birdwell J. Modeling and closed loop control for resource-constrained load balancing with time delays in parallel computations. In: Chiasson J., and Loisseau J. (Eds). Applications of Time Delay Systems. Lecture Notes in Control and Information Sciences vol. 352 (2007), Springer, Berlin 57-76
22. Tlustý J. Machine Dynamics. In: King R. (Ed). Handbook of High-Speed Machining Technology (1985), Chapman and Hall, New York, London 48-154
23. Tlustý J., Poláček M., Daněk O., and Špaček L. Selbsterregte Schwingungen an Werkzeugmaschinen (1962), VEB Verlag Technik, Berlin (in German)
24. Tobias S. Machine-Tool Vibration (1965), Blackie and Sons, London
25. Vareille J., Le Parc P., and Marcé L. Web remote control of mechanical systems: Delay problems and experimental measurements of round trip time. In: Chiasson J., and Loisseau J. (Eds). Applications of Time Delay Systems. Lecture Notes in Control and Information Sciences vol. 352 (2007), Springer, Berlin 117-132
26. Weck M., and Teipel K. Dynamisches Verhalten spanender Werkzeugmaschinen (1977), Springer, Berlin (in German)