Experimental and numerical verification of bifurcations and chaos in cam-follower impacting systems

Abstract

In this paper we present the design, modelling and experimental validation of a novel experimental cam-follower rig for the analysis of bifurcations and chaos in piecewise-smooth dynamical systems with impacts. Experimental results are presented for a cam-follower system characterized by a radial cam and a flat-faced follower. Under variation of the cam rotational speed, the follower is observed to detach from the cam and then show the emergence of periodic impacting behaviour characterized by many impacts and chattering. Further variations of the cam speed cause the sudden transition to seemingly aperiodic behaviour. These results are compared with the numerical simulation of a mathematical model of the system which shows the same qualitative behaviour. Excellent quantitative agreement is found between the numerical and experimental results

Discontinuity-induced bifurcations of piecewise smooth dynamical systems

“…sawtooth signal). Corner collisions have recently been detected also in impacting systems and, most notably, can be used to explain the bifurcation phenomena often detected in cam-follower mechanical systems, as detailed in Alzate et al (2007), Osorio et al (2005Osorio et al ( , 2008 and Budd & Piiroinen (2006).…”

Dynamics of an impact oscillator near a degenerate graze

“…For generic choice of the functions f and g in (1) and for an open dense set of choices of the clearance c the function a c (τ ) will have isolated zeros each with a c (τ ) = 0. In particular this is the case for the linear system (6), since here a c (τ ) = −c + cos ωτ .…”

“…However, there are many engineering contexts in which oscillations are a highly undesirable feature of performance, especially when these lead to impacts between moving parts or against rigid supports, generating noise and wear and ultimately leading to mechanical breakdown: for some examples see Alzate et al [1], Mason et al [31], Stewart [40], Pavlovskaia et al [35] as well as those described in books such as Babitsky et al [5], Brogliato [8] and di Bernardo et al [7].…”

Experimental analysis of maximum valve lift effects in cam-follower system for internal combustion engines

“…The presence of unavoidable camshaft fluctuations can affect the accuracy of the follower motion at high-speed [4,5]. The fluctuation phenomenon is known as cam jump or bounce, which cause undesired vibration.…”

“…Therefore engine volumetric efficiency and performance reduce at high operating speed [7]. So, the decreasing of valve jump must be a primary goal when the cam profile design for quiet and smooth operation of the camfollower system at high speeds [4]. Determination of safe run zones and conditions are important for the stable operation of the cam-follower system.…”