Friction Induced Vibrations in Moving Continua and Their Application to Brake Squeal

Abstract

Considerable effort is spent in the design and testing of disk brake systems installed in modern passenger cars. This effort can be reduced if appropriate mathematical–mechanical models are used for studying the dynamics of these brakes. In this context, the mechanism generating brake squeal in particular deserves closer attention. The present paper is devoted to the modeling of self-excited vibrations of moving continua generated by frictional forces. Special regard is given to an accurate formulation of the kinematics of the frictional contact in two and three dimensions. On the basis of a travelling Euler–Bernoulli beam and a rotating annular Kirchhoff plate with frictional point contact the essential properties of the contact kinematics leading to self-excited vibrations are worked out. A Ritz discretization is applied and the obtained approximate solution is compared to the exact one of the traveling beam. A minimal disk brake model consisting of the discretized rotating Kirchhoff plate and idealized brake pads is analyzed with respect to its stability behavior resulting in traceable design proposals for a disk brake.

Nonlinear Vibrations of Axially Moving Beams

“…Such simplified coupled governing equations were used in analytical investigations on axially moving elastic beams (Thurman & Mote, 1969), (Riedel & Tan, 2002), and (Sze et al, 2005). It should be remarked that there are different types of governing equations for axially moving beams (Tabarrok et al, 1974), (Wang & Mote, 1986, 1987, (Wang, 1991), (Hwang & Perkins, 1992a,b, 1994, (Vu-Quoc & Li 1995), (Behdinan, et al, 1997), (Hochlenert et al, 2007), (Pratiher & Dwivedy 2008), (Spelsbrg-Korspeter et al, 2008), and (Humer & Irschik, 2009). Actually, there are various beam theories such as Euler-Bernoulli theory, sheardeformable theories, and three-dimensional theories, and geometric nonlinearities may take different forms.…”

Minimal models for squealing of railway block brakes

“…An overview can be found in the survey papers [9,11,17]. Especially in recent papers, the focus has turned towards the excitation mechanism of the self-excited vibrations [7,15,16,18,20,23] using discrete and continuous models. It is evident that the friction forces between disk and pad are the origin of the self-excited vibrations.…”

Effects of equilibrium point displacement in limit cycle oscillation amplitude, critical frequency and prediction of critical input angular velocity in minimal brake system

“…In most cases, the modeling work is carried out assuming that deformations were small; thus, equilibrium point is set zero and linearization is performed at this point. [16][17][18][19][22][23][24][25] In this study, nonlinear equations of motion and friction models are considered and the behavior of that system for COF's model was analyzed by studying amplitude and frequency of limited cycle oscillation. However, the equilibrium point in large motion domains is not zero and linearization results in huge errors about 30 percent.…”