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Impulsive Control of a Cam-Follower Oblique-Impact System

Published online by Cambridge University Press:  25 May 2017

N. Lu ,
X. M. Ren ,
T. D. Jiang  and
Y. F. Yang
N. Lu
Affiliation:
Institute of Vibration EngineeringNorthwestern Polytechnical UniversityXi'an, China
X. M. Ren
Affiliation:
Institute of Vibration EngineeringNorthwestern Polytechnical UniversityXi'an, China
T. D. Jiang
Affiliation:
Institute of Vibration EngineeringNorthwestern Polytechnical UniversityXi'an, China Guizhou Aero-Engine Research InstituteGuiyang, China
Y. F. Yang*
Affiliation:
Institute of Vibration EngineeringNorthwestern Polytechnical UniversityXi'an, China
*
*Corresponding author ([email protected])
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Abstract

The transient impact hypothesis was extended, and the oblique collision model was established by considering the tangential slip. In order to solve this problem, the oblique-impact equations for cam-follower were transformed into a linear complementarity problem. Impulsive control method was employed to control or anti-control the nonlinear responses. The simulation results show that the cam-follower system performs very complex nonlinear characteristics, such as period, quasi-period and chaos responses. Using the impulsive control method, the nonlinear responses of the cam-follower system can be controlled to P(n, n) and P(∞, n) or anti-controlled to chaos.

Keywords

Cam-followerOblique-impactImpulsive control methodChaos control
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 4 , August 2018 , pp. 475 - 482
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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References

1. Flores, P., Leine, R. and Glocker, C., “Modeling and Analysis of Planar Rigid Multibody Systems with Translational Clearance Joints Based on the Non-Smooth Dynamics Approach,” Multibody System Dynamics, 23, pp. 165–190 (2010).Google Scholar
2. Zhao, X. R., Xu, W., Yang, Y. G. and Wang, X. Y., “Stochastic Responses of a Viscoelastic-Impact System under Additive and Multiplicative Random Excitations,” Communications in Nonlinear Science and Numerical Simulation, 35, pp. 166–176 (2016).Google Scholar
3. Mankame, N. D. and Ananthasuresh, G. K., “Synthesis of Contact-Aided Compliant Mechanisms for Non-Smooth Path Generation,” International Journal for Numerical Methods in Engineering, 69, pp. 2564–2605 (2007).Google Scholar
4. Lima, R. and Sampaio, R., “Stick-Mode Duration of a Dry-Friction Oscillator with an Uncertain Model,” Journal of Sound and Vibration, 353, pp. 259–271 (2015).Google Scholar
5. Osorio, G., di Bernardo, M. and Santini, S., “Cornerimpact Bifurcations: A Novel Class of Discontinuity-Induced Bifurcations in Cam-Follower Systems,” SIAM Journal on Applied Dynamical Systems, 8, pp. 18–38 (2008).Google Scholar
6. Alzate, R., di Bernardo, M. and Montanaro, U., “Experimental and Numerical Verification of Bifurcations and Chaos in Cam-Follower Impacting System,” Nonlinear Dynamics, 50, pp. 409–429 (2007).Google Scholar
7. Shen, Y. and Stronge, W. J., “Painleve Paradox during Oblique Impact with Friction,” European Journal of Mechanics A/Solids, 30, pp. 457–467 (2011).Google Scholar
8. Yan, H. S., Tsai, M. and Hsu, M. H., “An Experimental Study of the Effect of the Cam Speed on Cam-Follower Systems,” Mechanism and Machine Theory, 31, pp. 397–412 (1996).Google Scholar
9. Zang, W. and Ye, M., “Local and Global Bifurcations of Valve Mechanism,” Nonlinear Dynamics, 6, pp. 301–316 (1996).Google Scholar
10. Alzate, R., Piiroinen, P. T. and di Bernardo, M., “From Complete to Incomplete Chattering: A Novel Route to Chaos in Impacting Cam-Follower Systems,” International Journal of Bifurcation and Chaos, 22, Article ID 1250102 (2012).Google Scholar
11. Alzate, R., di Bernardo, M., Giordano, G., Rea, G. and Santini, S., “Experimental and Numerical Investigation of Coexistence, Novel Bifurcations and Chaos in a Cam-Follower System,” SIAM Journal on Applied Dynamical Systems, 8, pp. 592–623 (2009).Google Scholar
12. Sundar, S., Dreyer, J. T. and Singh, R., “Rotational Sliding Contact Dynamics in a Non-Linear Cam-Follower System as Excited by a Periodic Motion,” Journal of Sound and Vibration, 332, pp. 4280–4295 (2013).Google Scholar
13. Ding, H., Chen, L. Q. and Yang, S. P., “Convergence of Galerkin Truncation for Dynamic Response of Finite Beams on Nonlinear Foundations under a Moving Load,” Journal of Sound and Vibration, 331, pp. 2426–2442 (2012).Google Scholar
14. Ding, H. and Chen, L. Q., “Galerkin Methods for Natural Frequencies of High-Speed Axially Moving Beams,” Journal of Sound and Vibration, 329, pp. 3484–3494 (2010).Google Scholar
15. Zhang, T., Li, H. G., Zhong, Z. Y. and G. P., “Hysteresis Model and Adaptive Vibration Suppression for a Smart Beam with Time Delay,” Journal of Sound and Vibration, 358, pp. 35–47 (2015).Google Scholar
16. Meingast, M. B., Legrand, M. and Pierre, C. A., “Linear Complementarity Problem Formulation for Periodic Solutions to Unilateral Contact Problems,” International Journal of Non-Linear Mechanics, 66, pp. 18–27 (2014).Google Scholar
17. Leine, R. I. and Glocker, C., “A Set-Valued Force Law for Spatial Coulomb-Contensou Friction,” European Journal of Mechanics - A/Solids, 22, pp. 193–216 (2003).Google Scholar
18. Flores, P., Leine, R. and Glocker, C., “Application of the Nonsmooth Dynamics Approach to Model and Analysis of the Contact-Impact Events in Cam-Follower Systems,” Nonlinear Dynamics, 69, pp. 2117–2133 (2012).Google Scholar
19. Glocker, C., “On Frictionless Impact Models in Rigid-Body Systems,” Philosophical Transactions of the Royal Society B Biological Sciences, 359, pp. 2385–2404 (2001).Google Scholar