Friction-induced vibration considering multiple types of nonlinearities
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ORIGINAL PAPER
Friction-induced vibration considering multiple types of nonlinearities Ningyu Liu . Huajiang Ouyang
Received: 14 June 2020 / Accepted: 24 October 2020 Ó The Author(s) 2020
Abstract The friction-induced vibration of a novel 5-DoF (degree-of-freedom) mass-on-oscillating-belt model considering multiple types of nonlinearities is studied. The first type of nonlinearity in the system is the nonlinear contact stiffness, the second is the nonsmooth behaviour including stick, slip and separation, and the third is the geometrical nonlinearity brought about by the moving-load feature of the mass slider on the rigid belt. Both the linear stability of the system and the nonlinear steady-state responses are investigated, and rich dynamic behaviours of the system are revealed. The results of numerical study indicate the necessity of the transient dynamic analysis in the study of friction-induced-vibration problems as the linear stability analysis fails to detect the occurrence of selfexcited vibration when two stable solutions coexist in the system. The bifurcation behaviour of the steadystate responses of the system versus some parameters is determined. Additionally, the significant effects of each type of nonlinearity on the linear stability and nonlinear steady-state responses of the system are discovered, which underlie the necessity to take multiple types of nonlinearities into account in the research of friction-induced vibration and noise.
N. Liu H. Ouyang (&) School of Engineering, University of Liverpool, The Quadrangle, Liverpool L69 3GH, UK e-mail: [email protected]
Keywords Friction-induced vibration Multiple nonlinearities Non-smooth Linear stability analysis Transient dynamic analysis Nonlinear steady-state response
1 Introduction Friction-induced vibration is widespread in mechanical systems as well as in everyday life, e.g. the sound of bowed instruments, the squeaking windscreen wiper, the chattering machine tools, the stick–slip oscillations of drill strings and the automobile brake noise [1–3]. Among them, the automobile brake noise attracts great attention of engineers and researchers due to its noise impact and scientific intricacy of this problem [3]. There have been a number of published studies which revealed rich dynamic behaviours in the friction-excited systems. Popp et al. [4, 5] studied discrete and continuous models exhibiting a stick–slip phenomenon, and rich bifurcation and chaotic behaviours were observed. Elmaian et al. [6] investigated the friction-induced vibration of a 3-DoF model that displayed three distinct dynamic states, i.e. stick, slip and separation, and the variations of time ratios of the three states in the whole process with the system parameters which can be linked to the appearance of different categories of noises. Zhang et al. [7] used a
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N. Liu, H. Ouyang
flexible pin-on-disc system to simulate how squeal noise could be generated in frictional contact and the features of time-varyin
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