Numerical and experimental analysis of the bi-stable state for frictional continuous system
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ORIGINAL PAPER
Numerical and experimental analysis of the bi-stable state for frictional continuous system D. Tonazzi
. M. Passafiume . A. Papangelo . N. Hoffmann . F. Massi
Received: 19 April 2020 / Accepted: 23 September 2020 The Author(s) 2020
Abstract Unstable friction-induced vibrations are considered an annoying problem in several fields of engineering. Although several theoretical analyses have suggested that friction-excited dynamical systems may experience sub-critical bifurcations, and show multiple coexisting stable solutions, these phenomena need to be proved experimentally and on continuous systems. The present work aims to partially fill this gap. The dynamical response of a continuous system subjected to frictional excitation is investigated. The frictional system is constituted of a 3D printed oscillator, obtained by additive manufacturing that slides against a disc rotating at a prescribed velocity. Both a finite element model and an D. Tonazzi (&) M. Passafiume F. Massi DIMA - Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Rome, Italy e-mail: [email protected] A. Papangelo Department of Mechanics, Mathematics and Management, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy A. Papangelo N. Hoffmann Department of Mechanical Engineering, Hamburg University of Technology, Am Schwarzenberg-Campus 1, 21073 Hamburg, Germany N. Hoffmann Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
experimental setup has been developed. It is shown both numerically and experimentally that in a certain range of the imposed sliding velocity the oscillator has two stable states, i.e. steady sliding and stick–slip oscillations. Furthermore, it is possible to jump from one state to the other by introducing an external perturbation. A parametric analysis is also presented, with respect to the main parameters influencing the nonlinear dynamic rcecsponse, to determine the interval of sliding velocity where the oscillator presents the two stable solutions, i.e. steady sliding and stick–slip limit cycle. Keywords Nonlinear behaviour Bi-stable state Frictional system Finite element model Experiments
1 Introduction Friction-induced vibrations (FIV) [1] are ubiquitous in mechanics and unstable FIV are considered a common problem in several fields of engineering, ranging from automotive [2], railways industry [3], aerospace [4–7] and bioengineering [8, 9]. The problem is very widespread as in engineering applications almost all mechanical systems are assembled together and include contacting interfaces, e.g. joints [8, 10, 11], dampers and brake systems [12–14]. High amplitude
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FIV is commonly the consequences of friction instabilities that give rise to tedious noise [15–18] usually classified in squeal, groan or chatter depending on the frequency band in which it occurs [19]. One of the phenomena at the origins of such noises are stick
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