Email this article 
Analysis of Bifurcations, Rattle and Chaos in a Gear Transmission System
(*) Corresponding author
DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)
Abstract
This paper is concerned with the analysis of systems with gears. An experimental set-up is presented to study the complex behavior exhibited by this class of dynamical systems, focusing in particular on all those phenomena associated to noisy operation. Specifically, using an appropriate model of the experimental rig, the coexistence of several periodic orbits characterized by different numbers of impacts per period is shown to be a fundamental mechanism in organizing the system dynamics. The system of interest is characterized by helical involute tooth pairs. The presence of damping due to squeeze oil effects is taken explicitly into account. The aim is to uncover the effects of such damping on the complex behavior exhibited by the system. Preliminary two-parameter bifurcation diagrams will be presented together with phase space trajectories to support the analysis.
Copyright © 2013 Praise Worthy Prize - All rights reserved.
Keywords
References
R. J. Comparin, R. Singh, H. Xie, "Analysis of automotive neutral gear rattle.", Journal of sound and vibration, Vol. 131, pages 177-196, 1989.
Grasso C., Forcelli A., Pappalardo T. "A new approach for objective measurements of transmission gear rattle noise." JSAE Annual Congress, pages 19-21, 2004.
M. Martorelli, P. Liccardo, L. Tosato, M. Uberti, M. Malusardi, F.Sbarbati ,C.Grasso, " Gear rattle optimisation." FISITA 2004, World Automotive Congress, pages 23-27, 2004.
B. Bertsche, S. N. Dogan, J. Ryborz., "Design of low-noise manual automotive transmissions.", Proceedings of IMechE, Part K, Journal of Multi-body Dynamics, pages 79-95, 2006.
R.Brancati, E.Rocca, R.Russo, "Experimental investigations about the influence of oil lubricant between teeth on the gear rattle phenomenon", Journal of Sound and Vibration, vol. 321, pages 647-661, 2009.
E. Rocca, R. Russo, “Theoretical and experimental investigation into the influence of the periodic backlash fluctuations on the gear rattle”, Journal of Sound and Vibration, vol. 330, pages 4738-4752, 2011.
R. Russo, R. Brancati, E. Rocca, "A gear rattle model accounting for oil squeeze between the meshing gear teeth." Proceedings of IMechE, part D, Journal of Automobile Engineering, Vol. 219 pages 1075-1083, 2005.
R. Russo, R. Brancati, E. Rocca. "An analysis of the automotive driveline dynamic behaviour focusing on the influence of the oil squeeze effect on the idle rattle phenomenon. Journal of Sound and Vibration, vol. 303, pages 858–872, 2007.
R. Brancati, F. Farroni, E. Rocca. S. Savino. "Analysis of gear rattle by means of a wavelet-based signal processing procedure”. Meccanica, (DOI) 10.1007/s11012-012-9674-7, 2013.
R. Alzate, M. di Bernardo, U. Montanaro, S. Santini, "Experimental and numerical verification of bifurcations and chaos in cam-follower impacting systems", Nonlinear Dynamics, 50(3), pages 409-429, 2007.
G. Osorio, M. di Bernardo, S. Santini, "Corner-Impact Bifurcations: A Novel Class of Discontinuity-Induced Bifurcations in Cam-Follower Systems", SIAM Journal on Applied Dynamical Systems, 7(1), pages. 18–38, 2008.
R. Alzate, M. di Bernardo, U. Montanaro, S. Santini, "Experimental analysis of chattering, Bifurcation and chaos in an hybrid impacting dynamical system", The 10th Experimental Chaos Conference, Catania (Italy), 2008.
R. Alzate, M. di Bernardo, G. Giordano, G. Rea, S. Santini. "Experimental and Numerical Investigation of Coexistence, Novel Bifurcations, and Chaos in a Cam-Follower System.", SIAM Journal on Applied Dynamical Systems, pages 592-623, 2009.
M. di Bernardo, U. Montanaro and S. Santini, Hybrid Model Reference Adaptive Control of Piecewise Affine Systems, IEEE Transactions on Automatic Control, vol. 58, Issue 2, pages 304-316.
M. di Bernardo, U. Montanaro, J. M. Olm and S. Santini, Model reference adaptive control of discrete-time piecewise linear systems, International Journal of Robust and Nonlinear Control, Volume 23, Issue 7, pages 709 – 730,
M. di Bernardo, U. Montanaro and S. Santini, Canonical Forms of Generic Piecewise Linear Continuous Systems, IEEE Transactions on Automatic Control. vol. 56, no. 8, pages 1911 – 1915.
M. di Bernardo, U. Montanaro and S. Santini, Minimal Control Synthesis Adaptive Control of Continuous Bimodal Piecewise Affine Systems, SIAM Journal on Control and Optimization, volume. 48, Issue 7, pages. 4242-4261.
J. A. Taborda, M. di Bernardo, F. Angulo, S. Santini (2009). Active Chaos Control of a Cam-Follower Impacting System using FPIC Technique. Chaos09 Second IFAC meeting related to analysis and control of chaotic systems. London, 2009, p. 327-332, ISBN: 9783902661654, doi: 10.3182/20090622-3-UK-3004.00061
Y. Ca, "Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon (a new stiffness function of helical involute tooth pair)". Transactions of ASME, Journal of Mechanical Design,vol. 177, pages 460-469, 1995.
V. Kumar, J. C. Gerdes., "An impact model of mechanical backlash for control system analysis.", Proceeding of the American Control Conference, June 1995.
M. T. Mata-Jimknez, T. B. Brogliato, A. Goswami, "On the control of mechanical systems with dynamic backlash.", Proceedings of the 36th Conference on Decision and Control San Diego, Dicember 1997.
M. di Bernardo M.E. Homer C.K. Halse, R.E. Wilson. "Coexing solutions and bifurcations in mechanical oscillators with backlash." Journal of Sound and Vibration, vol.305, pages 854-885, 2007.
A. R. Champneys, P. Kowalczyk, M. Di Bernardo, C. J. Budd., Piecewise smooth dynamical systems: Theory and Applications. Springer Verlag, 2007.
Refbacks
- There are currently no refbacks.
Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize
