Road vehicle rely on the brake system to reduce the speed of the car and eventually to stop the moving car. In a brake system, when the pedal is pressed by the driver the brake pads will be pushed towards the rotating rotor and make contact and hence friction is generated. The kinetic energy of moving vehicle will be converted to heat energy due to the friction between the pad and the disc rotor.
When drivers are trying a new car, the performance of brake system will be one of the important characteristics which need to be considered by them as an important safety system. The maximum capability of brake system is not often used in daily life, but we want this system to work at all times and in particular in emergency situations to avoid accidents. The shorter brake distance may avoid an inevitable traffic accident in certain situation. (Thomas 1998)
The performance of brake system depends upon the friction characteristics between disc pads and disc rotor. The adhesion force between these two assemblies will be overcome by the two sliding surfaces together. This ratio can be described as the coefficient of friction. (T.P Newcomb 1983)
2.2 Fundamentals of Disc Brake
Before we start learning the generation of squeal noise, clear understanding for disc brake assembly is necessary. Generally, disc brake is a sort of braking assembly which is composed by a rotor connects with vehicle wheel and a calliper equipped with two brake pads. Braking effect is generated by high-pressure brake oil that promotes brake pad to clamp the interface of rotor, because disc brake assembly has no self-servo action. (Thomas 1998)
2.2-2 The Disc brake operation
The calliper contains two disc pads and a hydraulic piston and it is used for transfer brake torque from pads to wheel rotor. It is set close to each side of the rotary metal rotor and brake pads are the point of contact between the calliper and metal rotor. Figure (2.1) shows the structure of disc brake assembly.
Figure 2.1 disc brake component
After depressing the brake pedal, the high-pressure brake oil flows through the master cylinder then act on the piston which connects with caliper. Hence the piston presses against the disc pads to make frictional contact with rotary rotor to slow down the vehicle. (Thomas 1998)
2.3 Brake Squeal
2.3-1 Disadvantages of Brake Squeal Noise
If the assembly is designed inappropriately or the brake pad being wearing off the results could be excessive vibration during vehicle braking. The vibration could accompanied by loud noise which is the high frequency squeal noise. This can mount to a 100 dB sound pressure level as shown in Figure(2.2). Driver could be disrupted by this high-level of noise and has negative effect on comfort. Not only the comfort of driver is being compromised by the squeal noise but also the service life of assembly can be shorter.
Figure(2.2) Driver can not suffer the squeal.
2.3-2 Generation of Squeal Noise by Vibration
Generally speaking, most of noise is generated by frictional contact that one metal surface slide over another object surface. The main cause of brake squeal noise occurs in a high frequency when disc pads contact with rotating rotor.(Chen2002)
Figure(2.3) shows the surface of brake pad:
Figure(2.3) The surface of disc pad
When vibration take place, the brake pads will bounce as they contact with the rotor. The vibration goes up and the callipers and calliper piston will create a squeal sound. The sound is going to be louder as the vibration becomes stronger.
2.3-3 Elements of Brake Squeal Noise
There are several decisive elements which effect brake squeal noise. Firstly, increasing damping on disc rotor cause squeal noise instability. Secondly, the friction coefficient effects the stability of a brake system and hence could create squeal noise. A certain test result shows when the coefficient of friction reaches more than 0.35, will result in louder squeal noise. The last control factor is stiffness which is quite vital for brake system instability. The increase of the contact stiffness between pad and rotor could generate higher vibration frequency and hence could result in higher squeal noise.(Frank Chen2006)
2.4 Study of some fundamental vibration models
2.4-1 One Degree of Freedom Model
The vibration of a full system can be simplified and analysed by considering the whole system as a One Degree of Freedom (1-DOF) system.(Thomson 1993) A system with 1-DOF is the simplest case to describe the motion of a full system. Figure(2.4) shows a simple vibration of 1-DOF:
Figure 2.4: 1-DOF model - translation vibration
And the general equation of this motion is:
m + c+ kx = F(t) (2.4-1)
Where c is the viscous damping force. If one assume the condition of undamped free vibration that is c=o, and assume that the load F(t)=0 as well.
The results in the free vibration equation:
m ± kx = 0 (2.4-2)
The natural frequency of this single degree of freedom system can be written as :
ωn = rad/s (2.4-3)
or Fn =ωn /2π Hz (2.4-4)
The general solution for equation(2.4-2) can be obtained:
x = Asinωnt + Bcosωnt (2.4-5)
The Value of A and B are depended on initial conditions x(0) and (0) . Hence, the resulting solution can be written as :
x = ωn sinωn t + x(0) cosωn t
List of Abbreviations:
k= stiffness of spring
c= constant of proportionality
2.4-2 Two Degrees of Freedom Model
The major components of a modern disc brake include: the rotor, caliper, brake pad assemblies and a hydraulic actuation system. Although there is a considerable range of designs for these components, an attempt will be considered to give a brief overview of their function and composition.
Consider the schematic model shown in Figure (2.5). That represents the pad and disc that are connected together through a sliding friction interface. The system with subscript 1 denotes the pad, the system with subscript 2 denotes the disc, and m, k and c denote mass, stiffness and damping respectively. The motion of the first mass (m1)may represent the tangential motion of the pad, and the second mass (m2)may represent the in-plane motion of disc. The normal force acting on the interface is N=PS where P is the pressure applied and S is the surface area of the interface. The resulting frictional force Ff is dependent upon the normal force and the dynamic coefficient of friction between the two sliding surfaces. The disc motion is the superposition of a constant imposed velocity vo and velocity , and the pad motion has velocity .(Ibrahim 1994)
Figure 2.5 Two degree of freedom model
Stick-slip motion is usually described as a limit cycle in phase space, and requires non-linear analysis to determine the detailed behaviour of the system. However, since the existence or non-existence of a limit cycle depends on the stability of equilibrium points, then linear analysis can be used to determine the stability of these points. To conduct this investigation a linear friction model for the interface is used, and this is shown as a function of the relative velocity υr, between the pad and the disc in Figure (2.6),where μs is the static coefficient of friction and μ(υr) is the dynamic coefficient of friction. The function μ(υr), which has a negative gradient, has been specifically chosen for its simplicity, although it is recognized that more complicated functions might give a more detailed description of the interface properties.(Shin 2002)
Figure 2.6 Dynamic friction coefficient
Provided that the relative velocity is always positive, the frictional force is related to the normal force by
The equations of motion can be written as:
It can be seen in equations (2.4-7) and (2.4-8) that the terms Nα act as negative damping, and is the only term connecting the pad and disc. For stability analysis, where the forcing terms on the right side of equations are not considered, the characteristic equation for this system can be derived using:
The result in the following characteristic equation in a polynomial form:
Hence the conditions for instability are (Shin 2002):
a1<0, or a2
This chapter presented a brief review of the literature on braking mechanics. The components of a brake system were described. The theory of vibration of brake components were described and the equation of a simple mechanism related to a braking condition is presented.
Thomas W. Birch (1998) ''Automotive Braking Systems 3rd Edition''. Delemar Publishers, an International Thomson Publishing Company.
T P Newcomb & R T Spurr (1983) "Automobile Brakes & Braking 2nd Edition". Newnes Technical Books, Borough Green, Sevenoaks, Kent TN15 8PH.
Chen Guangxiong& Zhou zhongrong& Philippe kapsa& Leo Vincent(2002) "Effect of Surface Topography on Formation of Squeal Under Reciprocating Sliding" Tribology Research Institute, Southwest Jiaotong University, Chengdu, China.
Frank Chen& Chin An Tan& Ronald L& Quaglia (2006) "Disc Brake Squeal Mechanism, Analysis, Evaluation, and Reduction/Prevention" Copyright SAE International. Warrendale, Pennsylvania USA. ISBN 0-7680-1248-1.
William T. Thomson (1993) ''Theory of vibration with applications'' Prentice-Hall, Inc, Englewood Cliffs, New Jersey.
Shin K.& M,J Brennan.& Oh,J -E &Harris C.J. (2002) "Analysis of disk brake noise using a two-degree-of-freedom model". Journal of Sound and Vibration, vol. 254
Ibrahim, R.A.,1994, "Friction-induced vibration, chatter, squeal and chaos" part II: dynamics and modeling, ASME Applied Mechanics Reviews, vol. 47
S.M Hashemi-Dehkordi & M.Mailah (1991)"Suppressing Friction-Induced Vibration Due To Negative Damping and Mode Coupling Effects Using Active Force Control" Australian Journal of Basic and Applied Science. ISSN 1991-8178.