Huajiang Ouyang

Numerical analysis of automotive disc brake squeal: a review

This paper reviews numerical methods and analysis procedures used in the study of automotive disc brake squeal. It covers two major approaches used in the automotive industry, the complex eigenvalue analysis and the transient analysis. The advantages and limitations of each approach are examined. This review can help analysts to choose right methods and make decisions on new areas of method development. It points out some outstanding issues in modelling and analysis of disc brake squeal and proposes new research topics. It is found that the complex eigenvalue analysis is still the approach favoured by the automotive industry and the transient analysis is gaining increasing popularity.

Complex eigenvalue analysis and dynamic transient analysis in predicting disc brake squeal

There are typically two different methodologies that can be used to predict squeal in a disc brake, i.e., complex eigenvalue analysis and dynamic transient analysis. The positive real parts of complex eigenvalues indicate the degree of instability of the disc brake and are thought to associate with squeal occurrence or noise intensity. On the other hand, instability in the disc brake can be identified as an initially divergent vibration response using transient analysis. From the literature it appears that the two approaches were performed separately, and their correlation was not much investigated. In addition, there is more than one way of dealing the frictional contact in a disc brake. This paper explores a proper way of conducting both types of analyses and investigates the correlation between them for a large degree-of-freedom disc brake model. A detailed three-dimensional finite element model of a real disc brake is developed. Three different contact regimes are examined in order to assess the best correlation between the two methodologies.

A methodology for the determination of dynamic instabilities in a car disc brake

The dynamics of a car disc brake system is investigated by a combined analytical and numerical method. The disc is rotated past the stationary pads and calliper in sliding friction at constant speed. The modal data of the disc are obtained by means of modal testing whereby a dynamic model for the disc is derived based on the thin plate theory. Then the pads, calliper and mounting are analysed by means of the finite element method. Finally the equations of motion for the whole disc brake system are established through the interfaces between the pads and the disc. The stability of the vibrating system is studied by the method of state space.

Friction-induced vibration of an elastic slider on a vibrating disc

The in-plane vibration of a slider-mass which is driven around the surface of a flexible disc, and the transverse vibration of the disc, are investigated. The disc is taken to be an elastic annular plate and the slider has flexibility and damping in the circumferential (in-plane) and transverse directions. The static friction coefficient is assumed to be higher than the dynamic friction. As a result of the friction force acting between the disc and the slider system, the slider will oscillate in the stick-slip mode in the plane of the disc. The transverse vibration induced by the slider will change the normal force on the disc, which in turn will change the in-plane oscillation of the slider. A numerical method is used to solve the two coupled equations of the motion. Results indicate that normal pressure and rotating speed can drive the system into instability. The rigidity and damping of the disc and transverse stiffness and damping of the slider tend to suppress the vibrations. The in-plane stiffness and damping of the slider do not always have a stabilizing effect. The motivation of this work is the understanding of instability and squeal in physical systems such as car brake discs where there are vibrations induced by non-smooth dry-friction forces.

Vibration and squeal of a disc brake: Modelling and experimental results:

Abstract This paper presents a method for analysing the unstable vibration of a car disc brake, and numerical results are compared with squeal frequencies from an experimental test. The stationary components of the disc brake are modelled using many thousands of solid and special finite elements, and the contacts between the stationary components and between the pads and the disc are considered. The disc is modelled as a thin plate and its modes are obtained analytically. These two parts (stationary and rotating) of the disc brake are brought together with the contact conditions at the disc/pads interface in such a way that the friction-induced vibration of the disc brake is treated as a moving load problem. Predicted unstable frequencies are seen to be close to experimental squeal frequencies. The numerical simulation indicates that the stability can be improved by shifting the centre of the piston line pressure towards the trailing side of the pad.

Assignment of natural frequencies by an added mass and one or more springs

The problem of assigning natural frequencies to a multi-degree-of-freedom undamped system by an added mass connected by one or more springs is addressed. The added mass and stiffnesses are determined using receptances from the original system. The modifications required to assign a single natural frequency may be obtained by the non-unique solution of a polynomial equation. If more than one frequency is to be assigned, then a system of non-linear multivariate polynomial equations must be solved. Such a modification involves not only an added mass and one or more stiffness terms, but also an added coordinate. The paper presents a methodology, using Groebner bases for the solution of the multivariate polynomials, together with examples of natural frequency assignment. Realistic modifications are found to be bounded within certain frequency ranges. The effect of the modification on the natural frequencies not assigned and the antiresonances is explained.

A Moving-Load Model for Disc-Brake Stability Analysis

There are many elasto-mechanical systems that involve two components in moving contact where large-amplitude vibration and noise can be excited. This paper models the vibration and dynamic instability of a car disc brake as a moving load problem in which one component (the disc) is amenable to analytical treatment while the other component (the pads, calliper and mounting) has to be dealt with by the finite element method. A method is presented for solving the dynamic instability of the car disc brake as a nonlinear eigenvalue problem. The same approach can tackle other moving load problems.

Dynamic Instability of an Elastic Disk Under the Action of a Rotating Friction Couple

This paper investigates the instability of the transverse vibration of a disk excited by two corotating sliders on either side of the disk. Each slider is a mass-spring-damper system traveling at the same constant speed around the disk. There are friction forces acting in the plane of the disk at the contact interfaces between the disk and each of the two sliders. The equation of motion of the disk is established by taking into account the bending couple acting in the circumferential direction produced by the different friction forces on the two sides of the disk. The normal forces and the friction couples produced by the rotating sliders are moving loads and are seen to bring about dynamic instability. Regions of instability for parameters of interest are obtained by the method of state space. It is found that the moving loads produced by the sliders are a mechanism for generating unstable parametric resonances in the subcritical speed range. The existence of stable regions in the parameter space of the simulated example suggests that the disk vibration can be suppressed by suitable assignment of the parameter values of the sliders.

Parametric resonances in an annular disc, with a rotating system of distributed mass and elasticity; and the effects of friction and damping

The parametric resonances that occur in a stationary annular disc under the action of a distributed mass–spring–damper system which rotates, with friction, around the disc at subcritical speeds is the main focus of this paper. The distributed system occupies an annular sector and the stiffness, mass, damping and friction are each expanded in a Fourier series. When the distributed system is rotated then a set of stiffness, mass, damping and friction terms are obtained that vary both spatially and temporally. Finite element discretization is applied to the disc and the distributed system and the parametric resonances are determined by a multiple time–scales analysis of the finite element equations. The equations that define the transition curves are generally complex, although they are strictly real when damping and friction are omitted. Numerical results show that friction has a destabilizing effect over the entire subcritical speed range. Disc damping and damping in the rotating system both tend to suppress the vibrations of the disc when the speeds are subcritical. The effects of the distributed mass and stiffness are found to be almost neutral at subcritical speeds, but active in the supercritical range where the findings of other researchers are available for comparison and found to be in agreement.

On Automotive Disc Brake Squeal Part II: Simulation and Analysis

This paper reviews the state of the art of CAE simulation and analysis methods on disc brake squeal. It covers complex modes analysis, transient analysis, parametrical analysis, and operational simulation. The advantages and limitations of each analysis method are discussed. This review can help analysts to choose right methods and decide new lines of method development. For completeness, analytic methods dealing with continuum models are also briefly covered. This review was made from those papers that the authors are familiar with. It is not meant to be all-inclusive even though the best possible effort has been attempted.