Brake Squeal Analysis In Time Domain Using ABAQUS
Brake Squeal Analysis in Time Domain Using ABAQUSFinite Element Simulation of Brake Squeal for Passenger CarsMaster’s Thesis in Automotive Engineering ProgrammeMir Arash KeshavarzDepartment of Applied MechanicsCHALMERS UNIVERSITY OF TECHNOLOGYGothenburg, Sweden 2017
MASTER’S THESIS IN AUTOMOTIVE ENGINEERINGBrake Squeal Analysis in Time Domain UsingABAQUSFinite Element Simulation of Brake Squeal for Passenger CarsMir Arash KeshavarzDepartment of Applied MechanicsDivision of DynamicsCHALMERS UNIVERSITY OF TECHNOLOGYGöteborg, Sweden 2017
Brake Squeal Analysis in Time Domain Using ABAQUSFinite Element Simulation of Brake Squeal for Passenger CarsMir Arash Keshavarz Mir Arash Keshavarz, 2017-01-01Master’s Thesis 2017:24ISSN 1652-8557Department of Applied MechanicsDivision of DynamicsChalmers University of TechnologySE-412 96 GöteborgSwedenTelephone: 46 (0)31-772 1000Cover:The Complete Finite Element Model of Brake System for Brake Squeal Analysis.Name of the printers- Department of Applied MechanicsGöteborg, Sweden
Brake Squeal Analysis in Time Domain Using ABAQUSFinite Element Simulation of Brake Squeal for Passenger CarsMaster’s Thesis in Automotive Engineering ProgrammeMir Arash KeshavarzDepartment of Applied MechanicsDivision of DynamicsChalmers University of TechnologyABSTRACTOne of the main quality concerns of car manufacturers is brake squeal. There are twoCAE (Complex Aided Engineering) method for prediction of brake squeal, CEA(Complex Eigenvalue Analysis) and TDA (Transient Dynamic Analysis). However,CEA method is a quite usual tool to evaluate brake squeal propensity despite itsintrinsic overestimation of any system instabilities. In contrast, TDA provides areduced number of predicted instabilities, but it is too time consuming for completeFE models. The purpose of this thesis is the comparison of TDA with CEA to identifybrake squeal frequencies. The finite element model of studied brake system consistsof a brake disc, and pair of brake pads (friction material and backplate). Using theCEA method, brake squeal frequencies are identified by coalescence modes andcalculation of Negative Damping Ratio (NDR) for various pressure and frictioncoefficient. As a comparison with CEA, TDA is performed by use of dynamic explicitsolver to extract the variation of amplitude at a node on the brake disc friction surfaceover time. The frequency response function of a node on brake disc can be calculatedby Discrete Fourier Transform (DFT), the frequencies correspond to the peaks offrequency response function can be considered as a representative of brake squealfrequency.The comparison of TDA and CEA reveals that even though five modes are introducedby NDR criteria for brake squeal onset, merely two of them are detected by TDA.Taking account of CEA overestimation about unstable modes, it can be concludedthat the frequency response derived from the transient response can be a reliablemethod to represent the system instability. In addition, regarding TDA results brakesqueal might happen in an unstable mode even with low value of real part as well asNDR.Key words: Brake, squeal, complex eigenvalue analysis, transient Dynamic analysis,stabilityI
CONTENTSABSTRACT .ICONTENTS .IIPreface .IIINotation IVAbbreviation . .IV1Introduction 11.1 Brake squeal in automotive industry .11.2 Numerical methods to predict brake squeal.11.3 Brake systems-functions and types .21.4 Disc brake components in brake squeal .31.5 Brake noises and vibrations .41.6 Brake squeal: roots and causes .51.7 State-of-the-art . .62Mathematical formulation of brake vibration . .142.1 Complex Eigenvalue Analysis (CEA) and Stability Condition . .142.2 Negative Damping Ratio (NDR) . 152.3 Transient Dynamic Analysis (TDA) .152.4 Discrete Fourier Transform (DFT) .172.5 Advantages and disadvantages of CEA and TDA .183Finite element modeling 193.1 FE mesh, material property and boundary conditions .193.2 Simplified FE model for CEA .203.3 Complete FE model of brake assembly for CEA .223.4 Simplified FE model for TDA .233.5 Limitationof TDA 244Results .264.1 CEA results for “simplified model” 264.1.1Eigenfrequencies .264.1.2Negative Damping Ratio (NDR) for simplified FE model .264.2 NDR of complete FE model 314.3 Results of TDA for simplified model .325Concluding and remarks 356Future work .367References 377II
PrefaceThis thesis is the final essay of my Master of Science in Automotive Engineering atChalmers University of Technology, Gothenburg, Sweden. The work was performedat Volvo Cars Corporation, Gothenburg, Sweden, at Driving Dynamics Centre at thedepartment of Braking Analysis and Verification during autumn 2016. It was a greatopportunity to learn and update my knowledge in nonlinear vibrations, CAE methodslinked to Noise, Vibration and Harshness (NVH) and transient analyses. In addition, itwas really interesting to get familiar with Volvo Cars Corporation environment.I want to appreciate my supervisors Dr. Gaël le Gigan and Dr. Patrick Sabiniaz whomalways have been helpful and willing to support me. I appreciate my family membersespecially my mother to support and encourage me in all stages of my life.Mir Arash Keshavarz,Gothenburg, May 2017III
Notations𝜇𝑠 . . .static coefficient of friction𝜇𝑑 . .dynamic coefficient of friction𝑣𝑠 . . the speed between sliding pad and disc𝐹𝑓 . . . friction forceL . . .normal force on surface𝜃 .the slope of line connecting the pivot to the mid-point of a pad’s contact area𝜆 . . . .complex eigenvalueα . .real part of complex eigenvalueβ . .imaginary part of complex eigenvalue𝐾 . .stiffness matrix𝑢𝑒𝑞 . . .equilibrium point𝐹𝑒𝑥𝑡 . .external force𝐹𝑛𝑙 . .force originated from nonlinearity𝑢 . . .displacement vector𝑢̅ . .displacement relative to equilibrium pointM . .mass matrixu̅̈ . .acceleration vectorC . .damping matrixu̅̇ . . velocity vector𝐴 . .eigenvector𝑡 . .time𝑢0 . . .initial displacement𝑣0 . .initial velocity𝜁 . .negative damping ratioℎ . . .time stepL . . .lower triangular matrixU .upper triangular matrixAbbreviationCAE . Computer Aided EngineeringCEA . Complex Eigenvalue AnalysisTDA Transient Dynamic AnalysisFRF .Frequency Response FunctionDFT . . Discrete Fourier TransformNVH . . Noise, Vibration and HarshnessNDR . Negative Damping RatioFE .Finite ElementFEA . Finite Element AnalysisFEM . .Finite Element MethodGEA . . GEnetic AlgorithmMAC Modal Assurance CriteriaMAI . .Modal Absorption IndexPSD . . .Power Spectral DensitySCLM . .Spectral Criterion based on Linearization MethodIV
1 Introduction1.1 Brake squeal in automotive industryNowadays, the refinement of vehicle Noise, Vibration and Harshness (NVH) hasconsiderably increased the contribution of brake noise in vehicle design anddevelopment process. As a general practice, brake noise is an irritating sound forconsumers who may believe that it is symptomatic of a defective brake system and filla warranty claim, even though the brake is functioning properly [1]. Thus,understanding, prediction and prevention of brake noise and vibration has become animportant aspect in brake design and development related to quality processes. Akaynoted that, for example, as early as 1930, brake noise appeared in the top-ten noiseproblems surveys performed by New York City [2].A wide variety of brake noise and vibration phenomena are described by variousterminologies such as brake squeal, creep groan, chatter, brake judder, brake moan,muh, squeak, etc. [1]. Among them, one general term, squeal, is probably the mostprevalent, disturbing to both vehicle passengers and environment, and expensive forbrake and automotive manufacturers in terms of warranty costs [1]. However, there isno precise definition of brake squeal that has gained complete acceptance, but it isgenerally agreed that squeal is a sustained, high frequency vibration (above 1 kHz andbelow 10 kHz) of brake system components during a braking action leads to audiblenoise to vehicle occupants or passengers [1].1.2 Numerical methods to predict brake squealThere exist two different methodologies available to predict brake squeal using FiniteElement Method (FEM), namely, Complex Eigenvalue Analysis (CEA) and TransientDynamic Analysis (TDA) [3]. Both methodologies have pros and cons that arediscussed in the following chapters. FEM is a widely used numerical method topredict squeal in car brakes because it offers much faster and more cost-efficientsolutions than experimental methods, and it can predict squeal noise at early stages ofdevelopment process before prototyping [3].The CEA determines the complex eigenvalues by linearization of the equation ofmotion around equilibrium point. According to the basic stability theory, the positivereal parts of the complex eigenvalues indicate the degree of instability of the linearmodel of a disc brake and are thought to show the likelihood of squeal occurrence [3].Even though, CEA allows identification of all unstable frequencies in one run at agiven operating conditions whereas not all unstable frequencies can be observed inexperiments as instability. Thus, it can be understand that CEA overestimates theinstabilities. The cause and reason of this over estimation are discussed in the nextchapters. On the other hand, TDA is able to predict real unstable frequencies that canbe verified by experiments. The drawback of TDA is that it is very time consuming aswell as it does not provide any information on unstable mode shapes [3]. The purposeof this project is transient analysis of brake system in commercial FE software as wellas the comparison of TDA with CEA.1
1.3 Brake systems-functions and typesThe fundamental functions of a brake system can be summarized as follow [4] Reducing the speed of vehicle and if necessary to a requested stationaryposition (normal braking) Prevent unwanted acceleration while travelling downhill Maintain the vehicle at stationary condition by parking brake Conduct the vehicle to full stop with high deceleration braking (emergencybraking) Ensure vehicle stability (under and over-steering and maintain tire friction)The principal type of brake used to generate braking force at the wheels is calledfriction brake. Friction braking converts the potential and kinetic energy into heat.Friction brakes can be categorized into two types: disc brakes and drum brakes [4].Figure 1 depicts a disc brake assembly with suspension and part of the subframe. Thebrake assembly consists mainly of a brake disc, a calliper and a pair of pads withshims and under layer designed to generate a brake torque. During braking, thecalliper pushes the pads onto disc by hydraulic piston. The friction force generated atthe frictional surfaces between the brake pads and rotating brake disc generates therequired braking torque transferred to the wheel/tire to stop the vehicle. Disc brakesare used in all front axle of passenger cars and in some cases can also be found in therear axle. Despite their higher cost as compared to drum brakes, disc brakes are morerobust and have better cooling performance.Figure 1.Suspension assembly with brake system [5].Drum brakes, see Figure 2, are radial brakes combining a brake shoe mounted on thestub axle and a rotating brake drum mounted on the axle. Drum brakes are composedof two brake shoes (seldom one only) that are pressed outward against the frictionsurface of the drum by the action of hydraulic piston during braking. When thebraking operation is done, a spring pulls back the brake shoes to ensure a clearancebetween the surface of drum and brake pad. Drum brakes are less sensitive to external2
dust and rain as it is a closed component and is cheaper than disc brakes. However,drum brakes suffer from poor cooling characteristics and early cracking.Figure 2. The drum brake components. [6]1.4 Disc brake components in brake squealThe “simplified FE model” of a brake system, see Figure 3, is composed of brakedisc, a pair of brake pads. Here, the brake pads include the backplate but no shimneither friction material under layer is modelled. The backplates is made of steel, seeFigure 4, to push the pad onto the brake disc and generate the requested frictiontorque. The normal force and frictional torque, i e tangential friction force, betweenthe brake pads and brake disc may excite the brake disc to vibrate. The friction forcemakes the problem as nonlinear vibration so that the linear vibration theory is not ableto model the squeal problem properly. The equation of motion and mathematicalmodeling of nonlinear vibration of simplified brake system will be discussed in thefollowing chapters.Figure 3. A simplified model of disc brake system. [7]Figure 4, shows the multi-layer pad and backplate structure in detail. The shimfunction is damping of vibration propensity that is modeled in complete FE model.3
The slot and chamfer are introduced to control the brake squeal propensity. For thisproject, the pad material is considered as anisotropic in FE model.Figure 4. Brake pad composition. [8]1.5 Brake noises and vibrationsThere are various kinds of brake noises and vibrations with numerous terminologiesto nominate the phenomena in the literature that are probably inconsistent. One of theterminologies is shown in Figure 5. It can be seen that noises and vibrations can beclassified into groups that are based on frequency range. Some types of brake noiseand vibration can be summarized as follow:NVH-Events (Noise)Drum BrakesWire BrushMoanHot JudderCold JudderSqueal NoiseWhistle NoiseHot JudderDisc BrakesMuhWire BrushCreep & GroanNVH-Events (Noise)1020[Hz]50500Frequency10015[kHz]Figure 5. Classification of brake noise and vibrations during braking.41015
Squeal [9] is a high frequency noise (1-15 kHz) in which the sound is emittedfrom vibrating brake disc. Squeal will happen at vehicle speed less than 50km/h in rare few cases but mainly under 10 km/h.Wire Brush [9] is a kind of high frequency noise. The excitation mechanism isthe same as squeal but with the modulations of sound wave.Judder [9] is a high speed vibration problem, and can usually be felt in thebrake pedal. It is the result of friction variation due to either Disc ThicknessVariation (DTV caused by uneven wear) or by variations of coefficient offriction at disc surface.Muh [9] is another high speed phenomenon with frequency below 500 Hz. Avibration in the brake parts transferred to some larger surface such as doorpanel or window.Groan [9] is a low frequency noise (less than 100 Hz) originated from stickslip behaviour in the brake and make resonance in drive shaft and suspension.1.6 Brake squeal: roots and causesAs mentioned above, brake squeal is a type of friction induced vibration. The brakesystem may not lead to squeal until at least one of the following phenomenon excitedby friction force. The phenomenon that generate brake squeal are as follows: Stick-slipDisc-brake squeal has the characteristic of a frictional vibration which can beinduced by a frictional pair having either a static coefficient of friction 𝜇𝑠higher than the dynamic coefficient (𝜇𝑑 ), or the negative slope of dynamic𝑑𝜇coefficient with respect to speed ( 𝑑 0, 𝑣𝑠 is the speed between sliding𝑑𝑣𝑠brake pads and brake disc) [1]. Indeed,𝑑𝜇𝑑𝑑𝑣𝑠 0 theory has not received muchattention in recent years [1]. Sprag-slipBrake squeal occur in such a position in which the frictional force is increasedmuch above the value it would have in a perfectly rigid system. In otherwords, the Sprag-slip can be illustrated as in Figure 6. The friction force can𝜇𝑑 𝐿in which L, 𝜇𝑑 and angle 𝜃 are respectively,be derived as 𝐹𝑓 1 𝜇𝑑 .tan (𝜃)normal force, dynamic friction coefficient and the slope of the line connectingthe pivot point P to the mid-point of a pad’s contact area. According to Sprag1slip theory, if 𝜃 𝑡𝑎𝑛 1 (𝜇 ), then 𝐹𝑓 will be a large value that represent thesqueal condition.𝑑Figure 6. Schematic model of disc and pad in Sprag-Slip theory [1].5
Dynamic instability (flutter type)The premise of this theory is that the squeal happens when the complexeigenvalue correspond to a pair of modes, has conjugate real part and equalimaginary part (two modes happen at the same frequency). This phenomenonis called coalescence, in which two eigenfrequencies - one eigenfrequencywith positive real part cause the instability and the other eigenfrequency withnegative real part is stable - has coincidence with each other and excite thesystem to unstable condition. For this thesis, this theory is applied to detectbrake squeal frequencies for CEA method. HammeringThis mechanism corresponds to imperfection and uneven surface of padmaterial during the rotation generate the periodic impacts on disc and excite itto instability.As mentioned above, there are various mechanisms that contribute to the brake squealonset. In addition, the identification of dominant mechanism might be a complexproblem. As more test evidence and analysis results become available, it seems quiteobvious that none of the above mechanisms alone can provide a complete explanationof the squeal phenomenon [10]. In some cases, Sprag-slip may seem more proper, butin others, dynamic instability may be a better explanation [10]. Consequently, asdiscussed in the following section, many studies tried to predict brake squeal bytransient and nonlinear methods. However, there are still some issues to work on.1.7 State-of-the-artVarious theories and methods have been formulated in order to simulate brake squealusing Finite Element Method (FEM). At first, it is beneficial to understand the mainparameters and mechanisms responsible for brake squeal such as pressure, frictioncoefficient and component stiffness. For example, Baillet et. al [11] studied the effectof simplified brake system parameters that could contribute to occurrence ofinstability. The simplified FE model consists of a sliding beam and stationary pad inlaboratory code, PLAST3 in explicit dynamic formulation, was implemented. Thevarious values for model parameters such as Young’s modulus of pad, beam speed,pad dimensions, pressure, and friction coefficient are investigated in time domain andfrequency domain. Other researchers such as Liu [12]
1.4 Disc brake components in brake squeal The “simplified FE model” of a brake system, see . Figure 3, is composed of brake disc, a pair of brake pads. Here, the brake pads include the backplate but no shim neither friction material under layer is modelled. The backplates is made of steel, see
(2) Install the front disc brake anti-squeal shim to each front disc brake pad. NOTICE Figure 3. 1 Front Disc Brake Anti-squeal Shim 3. Road test the vehicle to confirm proper brake pad installation. NOTICE When applying disc brake grease, use the grease enclosed with a front disc brake pad kit or supplied
Keywords: Squeal, brake pad, wear, EDX, Optical Microscope Abstract. Brake squeal has always been a major NVH problem to many car makers due to significant number of warranty claims. Brake squeal is a high frequency noise (above 1 kHz) emanating from car disc brakes that get excited due to one or more mechanisms such as mode
on the disc squeal. The simulations performed in this work present a guideline to reduce the squeal noise of the disc brake system. 2. Methodology and numerical model 2.1. Complex eigenvalue extraction For brake squeal analysis, the most important source of nonlinearity is the frictional sliding contact between the disc and the pads.
pads and the disc, the stiffness of the disc, and the stiffness of the back plates of the pads, on the disc squeal. G. Lou [6] Disk brake squeal noise is mainly due to unstable friction-induced vibration. A typical disk brake system includes two pads, a rotor, a caliper and a piston. In order to predict if a
The existence of brake squeal has been recognized as a problem for some time primarily because of its occurrence in highway vehicle drum and disc brake systems. Rail transit cars have also exhibited brake squeal from their tread and disc brakes. In the United States three transit systems use disc brakes:
Disc brake squeal is of major concern to the automotive industry as well as customers. It appears in the audible frequency range above kHz [1, 2]. Below 1kHz, structure-borne noises are dominant, as in brake moan and groan, but airborne noises such as brake judder [3] are also present. Low-frequency squeal is defined as noise which oc-
pad-disc separation is better understood with the proposed model. In conclusion, an improved insight for the brake squeal source mechanisms is obtained while overcoming the limitation of prior models. 1 INTRODUCTION Brake squeal is a friction-induced high frequency noise problem that is observed in many automotive brake systems1, 2. Minimal .
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