Dynamic stability analysis and parametric investigation of nonlinear friction-induced vibrations on a mass-sliding belt experiment

Abstract

Physical mechanical systems exhibit different nonlinear behavior, which arise due to elastic, friction, kinematic, and clearance nonlinearities. Hence, the dynamic investigation of these systems with analytical approaches becomes either more complicated or impossible. Though, as opposed to linear systems, inherent nonlinearities in mechanical systems lead to several interesting dynamic responses, such as dynamic instability, limit cycle oscilations, bifurcations, etc. Hence, this dissertation aims to investigate the dynamic response behavior of a mechanical system, which is inspired by the problem known as brake squeal phenomenon. This problem is implemented on a simplified yet controlled mass-sliding belt experiment, which exhibits friction, clearance and kinematic nonlinearities. Brake squeal as a dynamic instability phenomenon is a major comfort problem observed in automotive disc brake systems. The brake squeal problem is studied through experimental, numerical, analytical and meta-model approaches. In this context, the dissertation is divided into three main parts in order to investigate the source mechanism of brake squeal and to predict the brake squeal noise generation. First study is aimed to investigate the effects of certain operational parameters on squeal initiation. The problem is investigated both experimentally and mathematically from the perspective of system stability. Hence, a mass-sliding belt experiment is designed and built, with a focus on three key operational parameters (preload, motor angular speed and angular configuration). Experiments are conducted at a wide range of these operational parameters, and the data is investigated in both time and frequency domains. The contact stiffness, which is a required parameter for the mathematical model, is determined with modal tests performed on the experiment. Corresponding data collected from the experiment is also used to obtain the characteristics of the friction coefficient at the mass and sliding belt contact interface. Next, a nonlinear mathematical model of the experiment is developed, though it is then linearized through certain assumptions for the investigation of the system stability. Data reveal local dynamic amplifications in time histories of certain operational parameters, which lead to the emergence of super-harmonics in frequency domain. The effects of key operational parameters on system stability are observed. It is concluded that there is a good correlation between the model predictions and experiments, and an extensive understanding about the effects of key operational parameters on system stability is obtained. Finally, stability analysis based on linearized model is validated with the experimental data, and the critical values of dynamic friction coefficient and motor angular speed are obtained. The main objective of second study is to investigate the effect of pad stiffness on the dynamic behavior of brake squeal problem. Hence, a two degree of freedom masssliding belt model is developed where the friction model at the mass and sliding belt interface derived through experiments. It is observed that the experimentally obtained friction model resambles Stribeck type friction model characteristics. This model consists of a mass (brake pad), which is attached to the common ground via four linear springs, and a sliding belt (brake disc) under the mass. Furthermore, two of the linear springs are attached to the mass with arbitrary angles. The nonlinear model is linearized again with some assumptions to check the system stability through complex eigenvalue analysis. The linear stability analysis reveals that the system exhibit mode coupling behavior as a physical mechanism that initiates the squeal noise. Furthermore, it is observed that the value of the critical pad stiffness (value of stiffness at which instability begins) decreases with the preload applied through the springs on the mass. On the contrary, the value of critical pad stiffness is found to be increased as the belt velocity increases. The results of the linear stability analyses are compared to the numerical solution of the nonlinear governing equations, and it is observed that the results of linear stability analyses are in accordance with the numerical solutions. Third study aims to investigate the predictability of a friction-induced nonlinear dynamic behavior on a simplified yet controlled laboratory experiment through the fuzzy logic approach. Experiments are carried out on the mass-sliding belt experiment to observe the effects of several operating parameters on the occurrence of nonlinear dynamic behavior. Experiments are performed at various levels of these operating parameter, and the data are collected. Then, fuzzy logic model architectures with different membership functions are built, where these operating parameters are assumed as the input parameters. The output of the fuzzy logic model architecture is defined as a new parameter, which is called as squeal index. Finally, a fuzzy logic model with a 96.97% prediction accuracy is obtained. Hence, it is shown that the proposed model can provide insight about the dynamic behavior of the system of interest without solving the nonlinear governing equations. Furthermore, the proposed model allows the prediction of the system state at operating conditions where experimentation is not possible, and it can be used for the determination of the critical operating parameters at which the system behavior switches from one state to another.