CHAPTER 1 INTRODUCTION, BACKGROUND AND LITERATURE REVIEW

1 CHAPTER 1 INTRODUCTION, BACKGROUND AND LITERATURE REVIEW 1.1 INTRODUCTION Squeal noise generation during braking is an important economic and technical issue in the automotive industry. A re-evaluation of customers' requirements puts comfort high on the list of vehicle's major design considerations, in order to provide a competitive and attractive product to the public. Akay (2002) stated that the warranty claims due to the noise, vibration and harshness (NVH) issues including brake squeal in North America alone were up to one billion US dollars a year. Disc brake squeal noise is mainly due to friction-induced vibration caused by the dynamic instability of the brake system, which usually radiates noise in the audible frequency 1 khz to 16 khz. Various theories and methods have been proposed to explain and predict the brake squeal phenomenon. However, it seems quite obvious that none of them can explain all events related to the squeal noise. The theories related to squeal have presented challenging problems for researchers and engineers because of their complex nature, which involves multiple disciplines such as non-linear dynamics, contact mechanics, and tribology. In the last few decades, a considerable amount of research has been done by many researchers on the possibility of eliminating brake squeal to improve vehicle users comfort and reducing the overall environmental noise

2 level. A good deal of progress has been made and a number of solutions have been suggested, for example, reducing the impulsive excitation, adding damping shims and shifting modal coupling. Despite these efforts, squeal still occurs frequently within the audible frequency range. Therefore, it is one of the most important issues that require a detailed and in-depth study for prediction as well as eliminating brake squeal. 1.2 BACKGROUND ON AUTOMOTIVE DISC BRAKE SYSTEMS The most significant safety aspect of an automobile is its brake system, which must slow the vehicle quickly and reliably under varying conditions. There are many types of brake systems that have been used since the inception of the motor car, but in principle they are all similar. The main function of brake system is to retard the vehicle by transforming the kinetic energy of the vehicle into heat by friction, and this heat must be effectively and efficiently dissipating to the surroundings by the brake components. The principle of the disc brake was first patented by Frederick Lanchester in his Birmingham factory in 1902, but was not popular until the spectacular win by the Jaguar racing cars in 1957 that their advantages were visibly demonstrated to the motoring public. Since the early 1960s, disc brake systems have become more common form in the most passenger vehicles, although some of the passenger vehicles use drum brakes on the rear wheels to keep costs and weight down as well as to simplify the provisions for a parking brake. Since the front brakes perform most of the braking effort, this can be a sensible compromise. The present investigation is attempted to study squeal noise of the passenger cars, therefore disc brakes will be the focus of this work. There are two types of disc brakes, fixed caliper and floating caliper. The fixed caliper usually contains two or more pistons that act

3 directly on both the inner and outer pads. In order to increase the braking power two pistons or more can be used. The pistons attempt to stop the rotating disc by exerting an equal amount of pressure against each side of the rotor as the each piston moves with equal pressure. The main limitation of the fixed caliper is requiring a rotor position which is not compatible with the geometric needs of the most modern front suspensions. Nowadays, the floating caliper is commonly used on the majority of automotive brake systems. Typical disc brake components are shown in Figure 1.1. It consists of a rotor that is rigidly mounted on the axle hub and therefore rotates with the automobile s wheel through drive axles, a floating caliper piston assembly where the piston slides inside the caliper, which is attached to an anchor bracket on the vehicle suspension system, and a pair of brake pads. The caliper is free to float laterally on its mounting pins. When hydraulic line pressure is applied, the piston is pushed forward to press the inner pad against the disc and simultaneously the outer pad is pressed by the caliper against the disc. The hydraulic pressure is converting into an applied force that presses the pad against the rotor. This generates the friction forces needed for the braking. Figure 1.1 Floating disc brake components

4 1.3 LITERATURE REVIEW Over the last decades, a large and varied amount of research has been dedicated to develop techniques which predict disc brake squeal and reduce its occurrence. This literature review aims to cover an overview on the published research into disc brake noise. The structure of the literature review is shown in Figure 1.2. Literature review Introduction to brake squeal noise Classifications of brake noise Low frequency brake noise Low frequency brake squeal High frequency brake squeal Mechanisms of brake squeal Stick-slip Sprag-slip Mode-coupling Investigations into brake squeal Numerical approaches Analytical approaches Experimental approaches Squeal reduction methods Major observations from literature Concluding remarks Figure 1.2 Structure of the literature review

5 1.3.1 Problem Definition Disc brake noise and vibration generation during braking has been one of the most important issues and definitely worrying problem to automotive manufacturers. Despite brake noise is not a safety issue and has little impact on braking performance, it gives customers the impression of underlying quality problems of the vehicle. In addition, the customers view that the noise emitted from the brake system is indicator of malfunctioning condition and consequently lose confidence on the quality of the vehicles. In order to solve problem of the brake noise and vibration, the influencing parameters must be known for improving the quiet and comfortable performance of vehicles. Most importantly, squeal noise which usually occurs in the frequency range between 1 khz and 16 khz. It is predominantly generated at low vehicle speeds (below 30 km/h) and at low brake pressures (brake line pressure below 2 MPa). The squeal noise in a disc brake is initiated by instability due to the friction forces leading to self-excited vibrations that result in audible noise. During the earlier years, researches were oriented towards understanding, identifying critical factors and possibly in reducing the effect of squeal. Increasing the knowledge of the mechanisms generating squeal is one important contribution to the extensive research and development work being performed in order to solve this problem. Much progress has been made in gaining physical insight into brake squeal mechanisms and causes in recent years and present brakes have become quieter. However, squeal still occurs frequently and therefore much work still needs to carry out. This is due to the fact that disc brake squeal has been a challenging problem due to its immense complexity which is very sensitive to variables including corner component design, component interaction, usage history and many operating and environmental condition.

6 1.3.2 Classifications of Brake Noise Generally, brake noise can be classified into many categories based on either the occurring frequencies or excitation sources (Papinniemi et al 2002, Kinkaid et al 2003, Chen et al 2005), as shown in Figure 1.3. In order to simplify the discussion presented in this work, brake noise is classified as a function of frequency and there are three groups introduced by (Dunlap et al 1999) namely; low frequency noise, low-frequency squeal and high-frequency squeal. Figure 1.3 Classifications of brake noise (Dai and Lim 2008) Low-frequency disc brake noise typically occurs in the frequency range between 100 and 1000 Hz and has different types namely; groan, moan and howl. This type of noise is caused by friction material excitation at the rotor and lining interface. The energy is transmitted as a vibratory response through the brake corner and couples with other chassis components. Low-frequency squeal is generally classified as a noise having a narrow frequency bandwidth in the frequency range above 1000 Hz. The mode of noise generation can be associated with frictional excitation coupled

7 with a phenomenon known as modal locking. The coupling of two or more modes of brake components producing optimum conditions for the occurrence of brake squeal. High-frequency brake squeal is defined as a noise which is produced by friction induced excitation causing by coupled resonances of the rotor itself as well as other brake components. It is typically classified as squeal noise occurring at frequencies above 3 khz (Dai and Lim 2008, Cantoni et al 2009). Among the different types of brake noise, squeal noise, because of its higher frequency contents, is the most troublesome and irritant one to car passengers and the environment, and is expensive to the brakes and car manufacturers in terms of warranty costs. 1.3.3 Mechanisms of Brake Squeal Understanding mechanisms of squeal generation is essential in designing silent brakes and for dealing with noisy brakes. A number of mechanisms of brake squeal have been presented in the research articles namely; stick-slip, sprag-slip, modal coupling, splitting the doublet modes and hammering excitation. In this literature review, the main mechanisms will be introduced to explain the brake squeal phenomenon as described later: 1.3.3.1 Stick-slip mechanism The first theory states that brake squeal is a result of a stick slip mechanism. The mechanism was believed to cause friction-induced vibrations in the brake at low speeds. These audible oscillations are produced as a result of the negative slope characteristics of dynamic friction coefficient against the

8 sliding velocity in the contact interface. Consequently, energy is fed into the system, which drives the brake instability. As cited by Kinkaid et al (2003), in his review paper that, Mills (1938), hypothesised that brake squeal originated because the dynamic friction coefficient is decreasing with increasing slipping velocity. Due to this negative slope, the steady state sliding becomes unstable and caused frictioninduced vibrations. To give a basic picture on the stick slip mechanism, a SDOF system consists of the brake pad as a mass (m) that rests on a rotating disc with a constant speed (v) and connects to a linear spring at a fixed end, as shown in Figure 1.4 (a). Initially, the spring force is smaller than the static friction force so that the mass moves together with the disc. As the deformation of the spring increases, the spring force increases to a value that equals or is larger than the static friction force, and the mass starts to slide relatively to the disc. As the mass slides, the motion is now governed by the dynamic friction force (which is smaller than the static friction force), and the deformation of the spring and spring force decrease. This causes the mass to gradually stop sliding, and the above cycle repeats to generate the stick slip. Mathematically, if the coefficient of friction µ between the pad and the disc in Figure 1.4 (b) is assumed to decrease linearly with the sliding velocity, i.e., µ= µ s - v, the equation of motion of the pad will be: or mx cx kx F F v x (1.1) s mx c F x kx F s v (1.2)

9 where; k is the spring stiffness, m mass and F the friction force. The coordinate x is a measure of the displacement of the mass from the equilibrium position. The damping coefficient (c- F) may thus be negative if ( F > c) results in oscillation of the pad with increasing amplitude and could lead to squeal, rather than decreasing oscillations associated with positive damping. (a) (b) Figure 1.4 Schematic diagram of a stick-slip mechanism 1.3.3.2 Sprag-slip mechanism It was later realized that the stick slip mechanism was not the only reason for a brake squeal, and that self-excited vibrations could be produced under constant friction coefficient. As reported by Papinniemi et al (2002), sprag-slip mechanism was first defined by Spurr in 1961. He explained the contact behavior of internal and external drum and disc brakes as the form of locking a body in contact with a sliding surface, followed by a slip due to a displacement of the fixed end of the body. This is known as geometricallyinduced or kinematic constraint instability, which occurs even though the coefficient of friction is constant. In describing this mechanism, Spurr presented a semi-rigid strut that was inclined at an angle to a rubbing surface and pushed horizontal to the surface as shown in Figure 1.5. Assume F f = F N and consider the equilibrium of the system; the following equation is derived:

10 F f L L, FN 1 tan 1 tan (1.3) where is the coefficient of friction and L is the load. It can be seen that the friction force (F f ) will approach infinity as approaches cot. When = cot the strut sprags or locks and the surface motion become impossible. Due to the flexibility within the assembly the strut releases itself from the spragging condition and returns to its first state to repeat the cycle which could lead to a sprag-slip limit cycle. O Rigid rod pivoted at O L V F f Moving plate F N Figure 1.5 Schematic diagram of a sprag-slip theory The sprag-slip mechanism has been extended by Earles and Soar (1971), in an attempt to model a brake system. A SDOF model is developed to present the importance of non-linear coupling within the combined system. An experimental investigation based on the pin-on-disc model was carried out. It was observed that within a certain range of angles of orientation of the pin, instability of the self-induced vibration motion existed. This was due to the non-linearity in the system. They also concluded that generation of squeal was dependent on the mean coefficient of friction, direction of disc rotation and the presence of a torsion vibration mode of the pin subsystem.

11 1.3.3.3 Mode coupling mechanism As reported by Balvedi et al (2002), brake squeal noise is the result of vibration created by coupling of two vibration modes of brake component such as pads, rotor, caliper, suspension links etc. In mode coupling mechanism, two modes of vibration geometrically matched (same wavelength) and close resonances can induce more energy into the system than it can dissipate (Triches et al 2004). Figure 1.6 show couple between the rotor and the pad at the same frequency. The mode coupling is often locked depending on operational conditions such as (speed, pressure and temperature) and interface characteristics such as contact stiffness, roughness, adhesive force, etc. There are other names used to define this mechanism namely; binary flutter, mode lock-in and non-conservative displacement dependent forces. Modal coupling of the structure involved sliding parts and the coupling results in changes of friction forces which is necessary for selfexcited vibration. Figure 1.6 Modal coupling between brake components (Triches et al 2004) North's (1972) presented a significant advance in the analysis of brake noise by proposing a binary flutter model for a disc brake. He published the first experimental work on a real brake apparatus and correlated his measurements with 8-DOFs model that included two brake pads, a disc and caliper. The distinctive features of this theory were the presence of the disc and the friction forces produced by pressure of brake pads, and the presence

12 of two independent disc modes. The contribution of this model was the friction forces between the disc and the layer of brake pad were incorporated as follower forces and a possible instability condition was met by using only a constant friction coefficient. Murakami et al (1984) performed a combination of stick-slip and sprag-slip in the FE models. They reported that the excitation of brake squeal was influenced by both mechanisms. The stick-slip was reasoned to add an energy source for the squeal, and the sparg-slip provides the pathway for squeal occurrence. In addition, Rhee et al (1989) found both the stick-slip and sprag-slip theories lacking in that they only described the conditions under which brake noise might occur, but they do not clearly define the physical phenomenon which causes brake noise. Later, Chen et al (2003) found that squeal can occur in regions with both negative and positive friction velocity slopes. Hence, there is no correlation between negative friction velocity slope and the generation of squeal. As more experimental evidence and simulation results become available, it was found that none of the above mechanisms alone can explain all events related to the squeal noise. In spite of all of this, mode coupling is generally recognized to be one of the most significant mechanisms leading to self-excited vibration in relative sliding systems with friction (Hoffman et al 2003). 1.3.4 Investigations into Brake Squeal Problem Research on brake squeal noise has been conducted using theoretical, experimental and numerical approaches. In theoretical investigations, the complicated brake system has to be considerably simplified using lumped models to help in understanding the mechanism of brake squeal. Experimental approaches have been used to measure the brake frequencies and mode shapes for the system in squeal and to verify possible solutions that can eliminate or significantly reduce squeal. Finite element method (FEM), on

13 the other hand, is able to include more detailed brake component models along with the presence of friction. Moreover, FEM can potentially simulate any changes made on the disc brake components much faster and easier than experimental methods. In this section, three approaches will be reviewed to show the progress in squeal research. 1.3.4.1 Experimental approaches Over the years, experimental approaches using brake dynamometers or on-road tests have been widely used to examine the brake squeal, to investigate the effects of different parameters and operating conditions, to understand the characteristics of the brake system during a squeal event and to verify possible solutions that can eliminate or reduce the squeal occurrence. The brake noise dynamometer has become the main testing platform for identifying propensity to generate noise during braking. There are two designs for the brake dynamometer. The first design is an inertia-type brake dynamometer that has flywheel attached to it and can be used to measure squeal at negative velocity slope (Triches et al 2004, Chen 2005). The second design is a drag-type brake dynamometer that can only test brake squeal at a constant speed (Dunlap et al 1999, Bergman et al 1999, Cunefare and Graf 2002, James 2003, Fieldhouse et al 2004). Accelerometer and double-pulsed laser holographic interferometry are two effective tools for determining the natural frequencies, vibration mode shapes and forced response. However, the experiments are mostly expensive and time consuming. Furthermore, the remedies found from experimental study on one specific brake system may not be applicable to another type of brake systems.

14 Experimental modal analysis is suitable to determine the dynamic properties of brake system. Traditional accelerometers have been used for conducting modal analysis at individual component and assembly levels and measuring the unstable frequencies during squeal occurrence. Tarter (1983) measured vibration characteristics and sound intensity during squeal generation using an accelerometer and a microphone. He performed several tests on noise with friction material, modified disc and pad contact geometry. It was observed that properties of friction material and pad contact geometry have a significant effect in reducing squeal occurrence. Matsui et al (1992) measured frequency responses of the brake assembly. Vibration modes of the pad, disc and caliper during squeal were identified through modal analysis. In their experiments, the caliper, rotor and outer pad vibrated in a coupled manner at a resonant frequency identical to the squealing frequency. It was found that friction vibration is amplified when the system's coupled resonance mode is unstable, therefore leading to squeal generation. They suggested that increasing the stiffness of the caliper and optimising the geometry of the pad pressure surface were potential noise cures. Ishihara et al (1996) used brake dynamometer to examine squeal generation of the disc brake assembly. After determining the squeal region, random oscillation waves were applied to the caliper by an electromagnetic shaker in the normal and circumferential direction of the rotor. Accelerometers are fixed on the caliper to measure the response while the rotor was rotating on a brake dynamometer and pressure was applied. It was found that as the friction increased the caliper had coupled vibrations between the normal and in-plate direction of the rotor. They also conducted theoretical analysis based on the experimental results. It was reported that the caliper s diagonal deformation and the linear stiffness of the lining material had a great

15 effect on the generation of squeal (lining material was assumed to be linear isotropic in nature even though the friction material itself is a composite material). Chen et al (2002) examined several rotor designs to establish the frequency relationship between the in-plane and bending modes of a rotor. They concluded that coupling of rotor tangential in-plane modes and rotor bending modes were the primary cause of high frequency brake squeal. The squeal frequency would occur at the rotor in-plane frequency, but the mode shape would correspond to the coupled out-of-plane mode. Chen et al (2004) studied the relationship between in-plane and outof-plane modes. A key influence other than the rotor design was the brake pad. They found that friction forces tend to excite the in-plane modes, and pad bending can excite out-of-plane modes. Changing pad resonant frequencies through chamfering can reduce high frequency in-plane related noise. They reported that high frequency squeal highlights the importance of the brake rotor modes while low frequency squeal has been found to depend more strongly on the caliper components in addition to the rotor. Steel et al (2004) utilized double-pulsed laser holography to investigate both in-plane and out-of-plane vibration of twin caliper disc brake at frequency of 2.2 khz. They separated dynamic images of the in-plane and out-of-plane vibration by particular technique. It was shown that the disc modes are extremely complex and further indication is the in-plane amplitudes are significantly larger than out-of-plane vibration amplitudes. Jaber et al (2006) showed the operational deflection shape (ODS) contains both rotor in-plane and out-of-plane modes. Modal participation analysis with modal assurance criterion (MAC) calculation between mode components in free condition and system real modes showed there is also a

16 major contribution from caliper mode in the complex mode, besides rotor tangential mode. However, there is also evidence that when the rotor is modified to shift its in-plane mode frequency, the squeal frequency is shifted accordingly with the in-plane mode frequency. Giannini et al (2006) used real lining material with reduced dimensions to investigate of tribological/dynamic aspects due to contact conditions using a laboratory brake set-up. They developed a modal model which is able to predict the squeal frequencies that occur during experiments. The proposed model accounts for the out-of-plane dynamics of the disc. The small brake pad was modeled and its eigenfrequency proved to be crucial for squeal. They reported that when the eigenfrequency of the pad was nearly equal to that of a doublet mode, the frequency of the doublet split, and instability occurred. 1.3.4.2 Theoretical approaches The first attempt in understanding the causes of brake noise has been made through the study of simple lumped-models. Though these simplified models can provide some good insight into understanding the mechanism of brake squeal, a key issue concerns the information that can be extrapolated from these models and reliability of the results. A 3-DOF mathematical model is presented by Watany et al (1999), which consists of a disc, a pad and caliper. Individual experimental analysis of the brake parts was performed to determine the modal stiffness and consequently to calculate the effective coupling stiffness between the brake pad and disc incorporated in simple mathematical model. They pointed that the natural frequencies of the brake components have great influence on squeal propensity. It was shown through the theoretical eigenvalue analysis

17 and the experimental testing that the geometric characteristics of the pad was found to have a major effect on squeal propensity. A 7-DOF theoretical model of a disc brake assembly was developed by El-Butch and Ibrahim (1999), in order to study the influence of the geometrical characteristics and the contact parameters on brake squeal generation. The model includes the disc, pad, caliper and piston, where the first three components have both translational and rotational DOF, whereas the latter only translational DOF. The Langragian technique was used to derive the governing set of differential equations and the state space formulation to create the first order equivalents. Time domain response was used to exhibit vibrations behaviour in the system. It was found that location of the piston towards the trailing edge of the pad has significant effect on the system stability. It was also shown that the contact stiffness of the caliper was another parameter that could be used to control the stability of the system. Chowdhary et al (2001) used a mathematical model using Rayleigh-Ritz approach in which the disc was represented by a thin plate and the backing plates were modeled as thin annular sector plates. The results showed that disc brake squeal was a result of flutter-type instability caused by the modes coupling between the components with very close natural frequencies. They found that squeal was highly sensitive to the lining material stiffness, where even very small value of friction coefficient (µ = 0.05) could lead to squeal for some particular values of lining stiffness. A multi-degree of freedom model with 14-DOFs was presented and verified by the experimental data by Rudolph and Popp (2001). The model consists of a disc, two pads, a caliper and a carrier, contact together by 18 coupling elements. An important feature of this model is that the coefficient of friction is assumed to depend on the brake line pressure at the initial temperature of the disc. They calculated the changes in real parts of

18 eigenvalues due to a parameter variation to evaluate how parameter modifications affect stability for a fixed coefficient of friction. They found that a high friction coefficient increases the likelihood of squeal occurrence, and therefore the critical value of friction coefficient (µ cr ) can be used as a measure of the degree of instability. Shin et al (2002) suggested two simple 2-DOFs models to describe the dynamical interaction between the pad and the rotor of a disc brake system. They have shown that the friction mechanism acts as a negative damping in the in-plane vibration and both damping parameters of the pad and the disc must be sufficiently large to suppress the effect of negative damping. However, the model only accounts for the in-plane dynamics, and hence it may not be directly related to a general noise problem. Joe et al (2008) developed a theoretical model using complex eigenvalues analysis to investigate the dynamic stability. They performed an experimental modal test and a dynamometer test to verify the theoretical model. The experimental and theoretical results showed a good agreement and the analysis indicated that modal coupling due to friction forces is responsible for disc brake squeal. The parametric analysis showed that increasing the friction coefficient, lining stiffness, length of the pads and thickness of the lining increased the instability. Recently, the SDOF oscillator was used by Kang et al (2009), to study the stick slip oscillations of discrete systems interacting with translating energy source through a non-linear smooth friction curve. The stick slip limit cycle oscillations were examined by means of divergence and numerical time-integration methods. From the numerical and analytical investigations, it was found that the steady-state response of the coupled oscillator can be divided into two different forms of oscillations (modemerged and mode-separated) according to the frequency separation of two

19 modes. The oscillation pattern of the steady-state response was found to depend on the system parameters such as energy source speed and normal contact load. 1.3.4.3 Finite element approaches Simplistic mathematical representations of a physical disc brake system have proved to be inadequate in providing a design tool that could predict and eliminate noise, due to the limited number of degrees of freedom involved in the associated theoretical models. Computational advances in the 1990's and the consequent development of advanced finite element analysis software allowed the generation of models with a vast number of degrees of freedom. The integrated analytical techniques developed thereafter have minimised costs related to trial and error experimental techniques and provided a better understanding of the brake systems' physical behaviour and subsequently noise generation. The success of this method is evident by the number of proposed finite element noise-predictive tools that have been developed by the automotive industry. This section reviews the contributions that appeared in the literature based on the FEM approach. There are two main approaches to simulate and analyze disc brake squeal using FEM methods: one is linear or nonlinear instability analysis using complex eigenvalue analysis (CEA) and the other is dynamic transient analysis (DTA). Table 1.1 summaries the main advantages and disadvantages of these two methods.

20 Table 1.1 Advantages and disadvantages of CEA and DTA Advantages Disadvantages CEA (frequency domain) -Predicts all unstable vibration modes of the brake system. -Predicts all unstable eigenvalues in one run -Design modifications can be easily examined -Low computational time with respect to transient analysis -Non-stationary features, such as material properties (timedependent) cannot be included -Is over-predictions and sometimes missing unstable frequencies -Uses a linear model, despite the strong nonlinearities associated with the contact problems DTA (time domain) -Provides more insight into the transient nonlinear character. -Predicts amplitude of a limit-cycle motion -Time-varying properties can be considered -Enables a vibration solution in the time-domain to be found -One run of transient analysis takes much longer than a complex eigenvalue analysis -Does not provide any information on unstable modes -Requires a lot of memory storage -Design iterations are hard to perform i) Complex Eigenvalue Analysis Currently the complex eigenvalue analysis is commonly used in investigating the squeal propensity of the brake system. One of the earliest researchers who attempted to incorporate the complex eigenvalue analysis with a large FE model and used modal analysis to validate each of disc brake components was Liles (1989). The complex eigenvalue analysis was

21 successfully used in brake squeal problems and became the preferred method. However, the shortcomings of this method were over-predictions and sometimes missing unstable modes in the squeal frequency range. To overcome on the limitations of CEA and increase the prediction accuracy, Chen (2009) in the recent review, stated that considering positive system damping leads to avoid the probability of over prediction while introducing negative damping tends to minimize under prediction. Yuan (1995) used complex eigenvalue analysis using finite element method to study the effect of the negative µ-v slope on brake squeal generation. The FE model was developed by considering the disc and the pads as beam elements and the caliper as a rigid body with 2-DOFs. It was found that brake squeal could occur due to coupled vibration of the brake assembly even at constant friction coefficient. However, with the presence of negative friction-velocity slope, it would increase squeal propensity. The results suggested that increasing back plate thickness, friction material thickness and the pad compressibility reduced the squeal. Guan and Jiang (1998) developed the finite element model consisting of a disc, two pads, a caliper and an anchor bracket to study disc brake squeal. Based on the FE model and mode synthesis methods, components contribution to disc brake squeal is examined. A closed-loop coupling model with a few degrees of freedom was established. Spring elements with appropriate stiffness were used to represent contact interactions between the components. They reported that higher friction coefficient always brought instability in the brake system. It was also found that some modes of the bracket dominate the squeal occurrence and change of frequency of those modes could reduce or eliminate the brake squeal. Kung et al (2000) utilized the complex eigenvalue analysis to study a low frequency squeal. Experimental component and vehicles tests were

22 performed to provide structural dynamic characteristics and squeal frequency information used for modeling correlation. The results showed that changing the rotor material may decouple the modal interaction and eliminate dynamic instability. Bae and Wickert (2000) developed a finite element model of a disc brake which combines both the top hat and circular disc to examine the influence of the geometry on the modes of vibration of the brake rotor. The results showed how the natural frequencies were related to the circular disc thickness and hat structure. Bajer et al (2003) used the complex eigenvalue analysis and derived contact pressure distribution between the disc and pads using surfaceto-surface contact elements through the FEA software (ABAQUS). They used the contact surface-to-surface scheme replacing by linear "imaginary" springs which was used traditionally to define contact surfaces between disc and pad. In this approach, the surfaces in contact do not need to have matching meshes and it can reduce data-preparation time. Lee et al (2003) used the complex eigenvalue analysis technique to predict the unstable frequencies. They performed a nonlinear contact analysis prior to complex eigenvalue extraction to predict the contact force distribution. The result from the contact analysis was used to locate the linear gap elements between disc and pad. Mode shape pattern analysis permitted the study of motion linked to each mode shape by constructing real and imaginary plots of each brake component. The results showed that the brake squeal was found to be influenced by the coefficient of friction as the level of interface friction increases. Bajer et al (2004) used CEA to study friction-induced instability of brake systems including the effect of lining wear, negative damping, positive

23 damping, and geometric nonlinearities. The results showed that the inclusions of lining wear increased accuracy of complex eigenvalue results, the negative damping increase the instability of squeal mode that has large tangential motion, the positive damping reduced over-predictions and makes actual squeal modes more prominent, and the geometric nonlinearities in frequency extraction analysis of brake systems may affect the results significantly. Cao (2004) presented a method for modelling car disc brakes and predicting squeal frequencies. The disc brake is treated as a moving load problem consisting of two parts: the rotating disc and the stationary components, which are dealt with respectively by a classical analysis and the finite element method. A plausible squeal mechanism for inducing dynamic instability is incorporated into the model. The unstable frequencies of the disc brake are obtained from a linear, complex valued, asymmetric eigenvalue formulation. The predicted unstable frequencies showed a good agreement with the experimentally established squeal frequencies. Kim et al (2005) investigated the effect of piston and finger offset on the contact pressure distribution at the pad interface. The effect of offset piston centerline and caliper finger was estimated. It was found that relative sliding between the rotor and pads led to an interface centre of pressure offset to the leading edge. Comparison between contact area and contact force was presented using a bar graph, which shows that uniform pressure distribution when offset was adopted. Liu et al (2007) studied disc brake squeal using a simplified FE brake model through a complex eigenvalue extraction. The prediction results showed that significant pad bending vibration may be responsible for the disc brake squeal. It was also shown that squeal can be reduced by decreasing the friction coefficient, increasing the stiffness of the disc, using damping

24 material on the back plates of the pads, and modifying the shape of the brake pads. Zhu et al (2008) examined the squeal propensity using the complex eigenvalue method. The use of a coupled model led to the extraction of imaginary and real parts to represent the instability and frequency spectra. As the problem was investigated under heating and cooling test sequences, the results showed that temperature, which previously had been neglected in FEA, plays an important role in the squeal predictions. Triches et al (2008) used FE model for disc brake and brake dynamometer to study the effect of some operational parameters on the stability characteristics of a disc brake system. They observed that higher friction coefficient increased the degree of system instability, wear has a strong effect on the stability characteristics, and brake temperature had the effect of reducing the brake pad stiffness, altering the coupling mechanisms between the rotor and pad. Additionally, increasing temperature led to increase in the damping loss factor of the brake pads. Dai and Lim (2008) developed FE model with friction coupling to evaluate brake pad structure design modifications for squeal noise reduction. The corresponding friction coupling formulation that gives rise to a set of asymmetric stiffness matrix is first developed for a low order lumped parameter model and then later used in the proposed FE model. The lumped theory is utilized to assess initial pad prototypes, while the FE representation is applied to tune and refine the pad design. They concluded that shorter lining reduces the likelihood of squeal, higher coefficient of friction increase squeal occurrences, and higher damping in the out-of-plane direction tends to decrease squeal.

25 ii) Transient Analysis Method Although the complex eigenvalue analysis has been used to predict the onset of brake squeal and there is a good agreement with experimental results, a nonlinear dynamic transient method can provide more insight into the transient nonlinear character of brake squeal. As brake squeal is a transient phenomenon, it would be useful to apply time domain analysis for simulating brake squeal. Nagy et al (1994) pioneered the nonlinear transient analysis of disc brakes using the finite element method. MSC/PATRAN was used to develop the models of the disc brake components and MSC/DYNA to conduct the analysis. Nonlinearity of the friction at the disc/pad interface was also considered. They pointed out that stability characteristics of the disc brake model was mainly affected by frictional coupling between the pads and the rotor but was not sensitive to relative speeds. Hu and Nagy (1997) improved the method of Nagy et al (1994) and applied it to a large FE model of a disc brake. They performed a non-linear transient analysis using LS/DYNA and achieved good correlation of measured noise performance. The key benefits of the analysis as compared to complex eigenvalue analysis that they identified were: the ability to implement more sophisticated friction behaviour, it was not necessary to determine system static state prior to analysis, and finally the variation in component contact during vibration is captured. Chargin et al (1997) conducted non-liner transient analysis to obtain disc brake squeal. They developed a simple finite element model of the brake and used high order implicit integration algorithm with tangent matrices of the steady-state solution. The matrices could be transferred to the complex eigenvalue analysis to identify the critical modes and damping factors. Lagrange multipliers were defined to impose the contact constraints. The gap elements were used to calculate the contact and friction forces whilst the

26 friction coefficient could be defined as a function of sliding speed, normal force and temperature. Chern et al (2002) have also performed non-linear transient analysis using LS-DYNA. The model includes rotor, pads, two pistons, sliding pins, and anchor bracket. Squeal frequency is identified using frequency domain analysis of the numerical time-domain output. The main drawback of the technique is the demand on computer resources. The size of time increments, which is a function of element mesh size and propagation velocity of vibration waves, requires an enormous number of solutions to be performed. Massi et al (2007) developed a simple FE model made of a disc, a small friction pad and a beam supporting the pad. They used the complex eigenvalues analysis to predict the squeal onset in a wide range of driving parameters and the nonlinear dynamic analyses to reproduce the squeal phenomena in the time domain. They demonstrated that the nonlinear model agree with the squeal characteristics obtained during experiments and concluded that the real part of the unstable eigenvalues is not a sufficient parameter to give a reliable instability index. 1.3.5 Squeal Reduction Methods The elimination of brake squeal noise is important as it causes discomfort of the vehicle occupants as well as any pedestrians. Generally, there are a number of techniques and methods that can be followed in order to reduce squeal noise for the improvement of passengers comfort, including adding damping shims; changing structural modifications and reducing modal coupling between rotor and other brake components. In practice, damping seems to be the most popular solutions to squeal noise. It can be easily fixed to the back plate by glued or riveted in addition to their lower cost. Many researchers investigated the role of damping through analytical, numerical and

27 experimental approaches. Ouyang et al (1999) studied damping analytically using elastic slider-on-disc model. It was found that damping of either the disc or slider in the out-of-plane direction capable of stabilizing the system but in-plane damping of the slider only reduces vibration magnitudes without stabilising any otherwise unstable motion. Flint and Hald (2003) investigated the effects of damping shims using acoustic holography. They found that shims can provide additional damping for the brake system, decouple the caliper- pad interface and alter the pressure distribution between components. Triches et al (2004) attempted to suppress squeal generation using damping shims which is made of a viscoelastic material that is sandwiched between two steel plates and is bonded to the back plate. Several types of shims were tested in the dynamometer. It was found that shims can be effectively suppressing squeal up to 20 db for frequencies between 1 khz to 7 khz. Liu et al (2007) used CEA through FEA. They stated that modifying the shape of the brake pads, adding damping material on the back of the pads and reducing the friction coefficient could reduce the propensity of squeal. Massi et al (2006) concluded that shims decouple the calliper assembly and rotor (low-frequency squeal) by increasing the former s tune-in range but fail to decouple the rotor and the pad (high-frequency squeal) from being in direct contact. Also, Massi and Giannini (2008) studied the influence of damping experimentally and numerically by means of a laboratory brake and a CEA. They point out that increasing the damping of brake parts does not always lead to systems having a lower propensity at generating squeal. More specifically, conventional damping has two effects: one is positive that reduces the value of the positive real part of an unstable eigenvalue; while the other is negative that increases the range of the instability. Moreover, many researchers attempted to eliminate brake squeal by modifying the parameters which influence the squeal generation. Liles (1989)

28 reported that increase in stiffness of back plate, reduction in the area of pads and usage softer disc could reduce squeal. Liu and Pfeifer (2000) examined several chamfer and slot configurations in order to obtain the optimal pad shape for reduction the squeal noise. They found that pad shape modification is effective in reducing noise at some frequencies, but may worsen the noise performance at other frequencies. They also found that combination of chamfer and slot could reduce the squeal generation. Lee et al (2003) reported that reducing back plate thickness lead to non-uniform contact pressure distributions and consequently increasing the squeal. Furthermore, Dessouki et al (2003) discussed the prevention method of the disc brake squeal. They differentiated three classes of disc brake squeal as (i) caliper bracket induced squeal (ii) pad induced squeal and (iii) disc induced squeal. They proposed that the common countermeasure for caliper bracket induced squeal was to introduce mass loading to the caliper bracket or alternatively to stiffen the bracket. For pad-induced squeal, they proposed chamfers, shorter length pads and insulators. For disc-induced squeal, use of slice cuts in the radial direction, increase in cheek thickness and disc damping could prevent in-plane squeal. Recently, Dai and Lim (2008) pointed out that the pads with a radial chamfer possess lesser tendency towards squeal occurrence. Joe et al (2008) proposed a lumped and distributed parameter model to represent the disc brake system. They have reported that increasing friction coefficient, length of the pads, lining thickness and stiffness of lining increasing system instability. In addition, increasing mass and Young s modulus of both the disc and pad reduce system instability. More recently, Chen et al (2009) provides guidelines to suppress and eliminate squeal occurrence. The methods are altering the excitation characteristics between pad and rotor, considering structural modifications

29 and reducing system coupling. In addition, pad friction material under-layer damping, caliper smooth motion (pressure centre shift) and caliper finger position/shape may also have influence on squeal elimination. 1.4 MAJOR OBSERVATIONS FROM LITERATURE REVIEW From the literature review, it is observed that extensive research has been carried out in the area of disc brake squeal. In spite of extensive research carried out in this domain, some areas are identified where there is scope for further contribution by researchers. These areas identified in five categories are discussed in the following section. 1. Most of the published works on the study of brake squeal indicated that many researchers varied the geometric details of the brake FE models, as shown in Figure 1.7. FE models from 1 to 4 are previous models, which have been considered by some researchers using different brake components. To further study, some researchers recommended considering effects of the wheel hub and steering knuckle as a future work which have a significant influence on the squeal generation. 2. Literature review revealed that through extensive work has been carried out to estimate the brake squeal using FEA, limited research has been done considering the effects of damping. For example; friction damping, friction-velocity slope damping and adding damping through shim. 3. Many researchers had validated their models at the components stage without considering assembly. Some of them have used FE models that have been validated at the components and assembly level based on modal testing data without considering steering assembly. A few of researchers

30 validated at the components level, assembly level and experimental squeal test. In addition, a few researchers modeled a real pad surface roughness. 4. In the FE assembly model, usually, disc brake components are interacted by friction springs through a number of imaginary linear spring elements. A requirement for linear spring connection is coincident node meshing between components which need long time for fitting. In addition to selecting spring stiffness values takes a lot of time and requires engineering intuition to identify more influential springs and pick up appropriate spring constants. In recent years, an alternative method associated with the direct connection of brake components have been suggested to eliminate the "imaginary springs". It can reduce data-preparation time. A few of researchers considered direct contact between disc and pad and it was not applied for full brake model. 5. Substantial research has been conducted through several approaches to evaluate effects of structural modifications on brake squeal. These methods are changing one factor at a time where as squeal is influencing by a large numbers of factors. Hence, a new approach is required to determine effects of several factors on squeal and its interaction. Figure 1.7 FE models with variation in geometric details