INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH .

INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 2, ISSUE 4, APRIL 2013contribute in brake squeal noise. The researchers showed thatwhen the system has higher vibration amplitude, it will have ahigher tendency to be operated in an unstable region. If thetransverse mode of the rotor has the same resonant frequencyof radial mode the squeal noise will amplify. René et al [15]used camera beside the ESPI to capture the disc mode shapeas René et al [16] used the same apparatus on drum brake.1.4 LASER DOPPLER VIBROMETER (LDV)McDaniel et al [17] applied a LDV to scan the disc at thenormal velocity of a shaker-excited stationary brake systemand they found that the resonant behaviour was associatedwith squeal mechanism. The LDV is an instrument that wasused with a non-contact to measure the vibration of the discsurface. The laser beam from the LDV was directed to thesurface of disc, and due to the motion of the disc surface thelaser doppler frequency changed, however the vibrationamplitude and frequency were extracted from this alter. Theyunderstand from the findings that the rotor was responsible forthe most noise and primary radiator to the sound since therotor area is much larger than other component. Thesemethods have two advantages, it does not require difficult taskin the laboratory and it allows measuring the frequency on astationary rotor. Svend et al. [18] applied LDV on the brakeand they found additional benefit of this method that thefrequency range of measure can be quite high. This includeshigh spatial resolution in the measurement and faster thanESPI. Chen et al. [19] used LDV to measure the rotordiametral. Their result indicated that the coupling of the inplane rotor modes and diametral mode of the rotor wasresponsible for the generation of high frequency squeal. ClausThomas [20] carried out vibration analysis of squealing brakesystem under running condition. These experimentalapproaches used accelerometer, laser-interferometry andacoustic camera. The diametral mode shape with zero padpressure was investigated for entire brake systems at differentfrequencies.1.5 REDUCE BRAKE SQUEAL METHODJoin Flint [21] analysed the effect of a rubber coated steelplate- a shim- on the backing plate of a brake pad during thebrake squeal. The results illustrate that the thick constrainedshims layer gives high damping at low frequencies, while thinlayer give high damping at high frequencies. Kung, S. - W. etal [22] made many modifications on disc brake system toreduce the brake squeal by focusing on solution to reduce thestiffness of the rotor. This is accomplished by a reduction inthe young’s modulus of the rotor material. The simplemodification was done by changing the amount of the graphitein the cast iron to shift the natural frequency of the rotor, sothe young’s modulus of the rotor is 96GPa as opposed to 120GPA. The result showed that changing the rotor material maydecouple the modal interaction and eliminate dynamicinstability. Fieldhouse and Beveridge [23] studied the effect ofnon-chamfered and chamfered pads on the frequency. Theelastic fix shims was proven as useful at higher frequenciesover 6000 Hz but it was not so effective at the lowerfrequencies of around 2000Hz. They investigated the effectsof the calliper angel, pressures and temperatures on the brakesqueal for two types of friction material. From the result it isseen that the brake squeal become quite at angle 166 degreeand above. Gouya and Nishiwaki [24] found that in everydoublet mode there is a critical contact span angle. HomffmanISSN 2277-8616CT [25] studied the reduce of brake squeal by using aviscoelastic material (damping material) on the back of theback plate of the pads and found it can effect in reducingsqueal when the pad in bending vibration.2 ANALYSIS OF SQUEAL BY USING FINITE ELEMENTMETHODThe finite element is the tool for modelling disc brake systemand providing a new insight into the problem of brake squeal.FEM allows accurate representation of complex geometriesand boundary condition. The finite element method has beenemployed by the researchers in the brake squeal study. Oneof the uses of finite element method is to investigate themodes and the natural frequency of the brake rotor withcomplex eigenvalue then they used modal participationmethod in order to analyse the contribution of each part of thebrake system in generating the squeal. The third section isanalysing the squeal by using beam-disc system. Then studythe two direction response due to the self-excited vibration.2.1 PREDICTING SQUEAL WITH COMPLEX EIGENVALUELiles [26] used solid elements to build his finite element modelfor each brake component and carried out modal testing onthese components. Friction was added into the model as ageometric coupling. A complex eigenvalue formulation wasderived for the system. The complex eigenvalue wasconstructed by solving the equation of the motion and consistof two parts. The first is real indicating to the stability while thesecond was imaginary indicating to the damped frequency. Heconstructed the friction stiffness matrix using relativedisplacements between mating surfaces. Kido et al. [27]studied the relation between the squeal propensity and theratio of the eigenvalues. They showed in the finite elementresults that higher ratio of eigenvalue increased the tendencyto squeal. Blashchke et al [28] used the complex eigenvalueanalysis to detect the unstable mode of the system. Theymodelled the rotor and pad interface to create the matrix of thecontact and used it inside the equation of motion. The contactmatrix made both the mass matrix and the stiffness matrix tobe a non-symmetric, so that the eigensolution becamecomplex. A cure (one of the brake parts) was proposed joiningthe system in order to add some lumped masses to the drum.The benefit of that method was to add the effect of the brakingpressure, rotation velocity and temperature to this analysis.Nack [29] used complex eigenvalue in his study on brakesqueal. The aim of complex eigenvalue was to shift thosecomplex eigenvalues that appear in the right-hand side of theplane (root locus diagram) to the left-hand side of the sameplane. He also presented a method to add the friction stiffnessto his vehicle modal inside FE software and use eigenvalueanalysis to determine the necessary condition for the systemto become unstable and grow into a state of limit cycles. Kunget al. [30] used complex eigenvalue to investigate the effect ofcontact friction on the squeal. The results showed that majornoise frequencies are higher than 5 kHz. The cause wasmostly due to the involvement of tangential modes. The shearmode would contribute to squeal problem at frequency 12.5kHz (that mode is outside the audible mode). If the diametralmode be coincided with the longitudinal mode, the noisewould line up. Zhang et al. [31] found by using complexeigenvalue that not all the unstable mode squeal but anunstable mode was just one necessary condition for squeal.Their result also showed that if damping included in the model,62IJSTR 2013www.ijstr.org

INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 2, ISSUE 4, APRIL 2013some unstable modes became stable while some modesappear at very low friction coefficient. Chung et al. [32]presented a new process to analyses brake squeal byapplying modal domain analysis using FEM to provide a newmethod instead of complex eigenvalue called virtual designprocess. Kung et al. [33] used complex eigenvalue to analysedisc brake squeal. The brake pressure was iterated form0.69MPa to 2.76MPa (brake pressure range) and the resultwas plotted in complex plane. Material damping and frictiondamping between the lining material and the rotor was addedto the system. Complex eigenvalue was found in the sameprevious iteration pressure and it was found that the numberof unstable mode was decreased. The researchers showedthat the major noise frequency appeared at a frequency higherthan 5KHz due to involve tangential mode and shear mode.Lou [34] used complex eigenvalue to study disc brake squeal.He was applied coulomb’s friction at the contact interface andproduced unsymmetrical contact matrix which yield complexeigenvalue. His analysis showed that any complex eigenvaluewith a positive real part indicated an unstable mode, whichmay results in squeal. In his work Lou searched for the moderesponsible about the squeal and the percentage of thepropensity (eigenvalue with positive real part). He found thatthe bigger propensity appeared with higher unstable mode.Cao et al. [35] modeled the disc brake component using FE.The disc was modelled as a thin plate. The pads mate withdifferent spatial area as the disc rotates and vibrates. The discbrake and the stationary component are studied as a movingload problem. Due to the asymmetry of the real brake thereare no double frequencies in the finite element model of thereal disc. A linear complex value was derived for the frictioninduced vibration of the disc brake in order to present theunstable frequency. Joe et al. [36] used complex eigenvalue toinvestigate the dynamic instability of the brake system. If thereal part of an eigenvalue is positive, the correspondingimaginary part was thought to be possible squeal frequency.The analysis indicates that modal coupling is responsible fordisc brake squeal due to the friction force. The friction isintroduced by altering the system stiffness matrix to beunsymmetrical. Higher friction coefficients always tend tomake two modes merging and form unstable complex mode.Increasing the stiffness of the lining material causes thesystem to become more unstable. Increasing the length of thepad causes the system to become more unstable, as increasethe thickness of the lining material. Increasing the discthickness, the unstable mode above 10000Hz becomeunstable. The squeal at 5000Hz and below is due to the modalcoupling while above 10000Hz is due to the modal splitting.Fritz et al. [37] used FEM to compute complex eigenvaluetechnique. They found that by adding damping to the systemthe real parts of eigenvalue

measure the disc brake system vibration. The beam-on-disc consists of a cantilever beam which represents the pad while the rotation disc represents the disc brake rotor. The beam and the disc are pressed against each other by a weight. They classified the friction noise to rubbing and squeal. They found that the noise was caused by the lateral .