Analytical investigation of stick-slip motions in coupled brake-driveline systems

Abstract

In this paper, we investigate the brake creepgroan problem by formulating the issues in terms of two dynamic sub-systems that are coupled at the friction interface, and thus, experience stick-slip motions. Thorough examination of the nature of discontinuous solutions using numerical methods is a useful prelude to analytical studies. We examine such dynamics through parametric studies for magnitude and rate of brake release, where the vehicle is initially at rest and under low constant drive torque. Dependency on the initial conditions and solution flow before reaching the orbit will thus be illustrated. Four types of motions (one steady sliding and three stick-slip) are found based on extensive studies. Our formulation and analysis should lead to a better understanding of the brake groan phenomenon and systems coupled by interfacial friction.

Analytical study of brake groan through a coupled 2DOF brake model

“…Secondly, the model is solved numerically and perturbation study is carried on various driving conditions. New types of stick-slip motion are identified except the four types proposed by Crowther and Singh [5,6]. Finally, analytical analysis is performed based on Laplace transform theory and the results from numerical and analytical study verify each other.…”

“…A 4DOF drive train model including a drive J d , brake and rotor, J r and J b , and tire J t inertias was proposed in [5], as shown in Fig. 1.…”

“…However, most of these mathematical models are based on linear modal analysis by oversimplifying the actual mechanism of the brake vibration and its nonlinear characteristics. The very recently, Crowther and Singh [5,6] proposed a method to describe the friction-induced groan in brake system by adopting the model coupling method and applying a piecewise function friction force. They examined the forced response under a negatively varying brake load and they typed different stick-slip motions by mapping phase trajectory.…”

A Transient Dynamic Model of Brake Corner and Subsystems for Brake Creep Groan Analysis

“…(1) Therefore, nodes 1 and 5 in leading area tend to move in direction and nodes 2 and 4 in trailing area tend to move opposite to direction from 0.1 s to 0.6 s. In this case, there are two resistance 13 and 23 from disc and piston, and a pair of action and reaction forces 14 and 24 between the parts of leading and trailing. These forces are subject to the following inequality:…”

“…Considering the components of brake and driveline, and even tire and vehicle mass, a three DOFs translational model [11], a two DOFs torsional model [12], and a four DOFs torsional model [13,14] were proposed. By taking into account the front and rear suspensions [15], a five DOFs lumped-parameters model was built.…”