title: Non-smooth Dynamic Behaviour of Friction-induced Self-excited Vibration
Creators: name: Li, Z
Publisher: name: University of Liverpool Repository
Year: 2018

description: Friction is everywhere and important in our daily life as well as in industry. In general, dry friction acts as a resistance to the relative motion and dissipates energy of a system; however, under certain conditions, it can cause self-excited vibration of a system, which is known as friction-induced vibration. Friction-induced vibration can potentially cause problems like wear, fatigue failure, and noise, among which brake squeal is a typical engineering problem. As a comprehensive understanding of friction-induced vibration has not been achieved, friction-induced vibration is still a challenging research topic. The aim of this research is to carry out a theoretical study of the dynamic behaviour of nonlinear/non-smooth friction-induced vibration of phenomenological mechanical models. Discrete and continuous mechanical models with dry friction that involve nonlinear contact stiffness, stick-slip motion, or separation and reattachment at the contact interface are proposed, and numerical simulations of the transient dynamic behaviour of the non-smooth frictional systems are implemented. Their complex dynamic behaviour and the influences by various system parameters are predicted. In addition, a reduction strategy for the complicated frictional systems is presented and validated via theoretical and experimental results, which is a preliminary step in analysing complicated systems (real structures) with nonlinear/non-smooth friction behaviour in future research. The main objectives of the research work reported in this thesis are: 1. To carry out the transient dynamic analysis of non-smooth friction-induced vibration. A varying time-step numerical algorithm, which combines Runge-Kutta method that is specifically for the second-order differential equation of motion and the bisection method, is proposed (Chapter 3). This algorithm ensures the accuracy of the results of the non-smooth vibration in which the motion states keep switching among distinct motion states of separation and reattachment, or stick and slip, which is testified by providing the same results of a classic non-smooth stick-slip vibration of a single-degree-of-freedom model. 2. In consideration of improving previous research on theoretical mechanical models with the assumptions that the contact stiffness is linear or separation is ignored, a nonlinear 2-degree-of-freedom slider-on-moving-belt model developed from Hoffmann’s model and the theoretical formulations are proposed (Chapter 4), in which a cubic contact spring is included; loss of contact (separation) at the slider-belt interface is allowed and importantly reattachment of the slider to the belt after separation is also considered. The stability and dynamic behaviour of the system are investigated. Complex eigenvalue analysis (CEA) indicates that the roles of the preload and the nonlinear stiffness on the stability of the nonlinear system are not monotonous. Transient dynamic analysis (TDA) shows that separation and reattachment could happen. Ignoring separation between bodies in sliding frictional contact in vibration is unsafe as this may underestimate the vibration amplitude, and predicts incorrect effects of the key parameters on the vibration, thus considering separation is very important. Moreover, frequency domain results show the necessity of implementing both CEA and TDA in the study of nonlinear friction-induced vibration and the importance of considering separation from the frequency domain point of view. Finally, non-smooth Coulomb’s law of friction is introduced in the nonlinear 2-degree-of-freedom (2-DoF) slider-belt model. Numerical results show that diverse dynamic behaviour of this 2-DoF system with nonlinearity/non-smoothness can be generated when both of the stick-slip and mode-coupling instability are involved. 3. Separation, reattachment and impact are considered in the study of friction-induced vibration of a system having an elastic disc, excited by the in-plane stick–slip vibration of a moving mass-damper-spring slider attached to a rigid wall that is dragged around on the disc surface at a constant rotating speed (Chapter 5). Theoretical formulations and the numerical procedure for the current non-smooth system are developed. Numerical results show that separation and reattachment could occur in a low speed range well below the critical disc speed in the context of a constant rotating load. Poincare maps of the system of the two distinct cases (considering separation and ignoring separation) are plotted which exhibit the diversity of nonlinear dynamic behaviour of the system and the importance of considering separation. Furthermore, the roles of the key system parameters on the vibration are investigated. Time-frequency analysis reveals the time-varying properties of this system and the contributions of separation and in-plane stick-slip vibration to the system frequencies. One major finding is that ignoring separation, as is usually done, often leads to very different dynamic behaviour and possibly misleading results. 4. Based on the idea of mode synthesis method, a reduction strategy for complicated frictional systems is put forward, in which the natural contact interfaces and the tangential friction force are involved, and its applications and experimental validation are presented (Chapter 6). Firstly, its application to a theoretical multi-degree-of-freedom model with linear contact verifies the accuracy and feasibility of the strategy. The influence of the system parameter, and the mode number that is used in the reduced model on the stability of the reduced model are investigated. The reduced model is capable of preserving the key features (bifurcation of the eigenvalue and unstable frequencies) of the original model. Furthermore, a specific reduction strategy, for a real pad-on-disc test rig and its corresponding finite element model which involve direct contact of the interface, is proposed. The results of the reduced model with a small number of modes of the substructures correlate fairly well with theoretical results of the full model and the test results in terms of predicting mode-coupling instability and unstable frequencies, which validates this promising method for future work on friction-induced vibration of complicated frictional systems or real structures.