Numerical Analysis Of Automotive Disc Brake Squeal: A Review

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Int. J. Vehicle Noise and Vibration, Vol. 1, Nos. 3/4, 2005207Numerical analysis of automotive disc brake squeal:a reviewHuajiang Ouyang*Department of Engineering, University of Liverpool,Brownlow Street, Liverpool L69 3GH, UKFax: 0044 151 79 44848 E-mail: h.ouyang@liverpool.ac.uk*Corresponding authorWayne NackTechnical Center, General Motor Corporation,Warren, Michigan, USAYongbin YuanTechnical Center, TRW Automotive,Livonia, Michigan, USAFrank ChenAdvanced Engineering Center, Ford Motor Company,Dearborn, Michigan, USAAbstract: This paper reviews numerical methods and analysis procedures usedin the study of automotive disc brake squeal. It covers two major approachesused in the automotive industry, the complex eigenvalue analysis and thetransient analysis. The advantages and limitations of each approach areexamined. This review can help analysts to choose right methods and makedecisions on new areas of method development. It points out some outstandingissues in modelling and analysis of disc brake squeal and proposes newresearch topics. It is found that the complex eigenvalue analysis is still theapproach favoured by the automotive industry and the transient analysis isgaining increasing popularity.Keywords: automotive disc brake; friction; contact; vibration; noise; squeal;modelling; numerical methods; the finite element method; complex eigenvalueanalysis; transient analysis.Reference to this paper should be made as follows: Ouyang, H., Nack, W.,Yuan, Y. and Chen, F. (2005) ‘Numerical analysis of automotive disc brakesqueal: a review’, Int. J. Vehicle Noise and Vibration, Vol. 1, Nos. 3/4,pp.207–231.Biographical notes: Huajiang Ouyang is a Senior Lecturer at the Departmentof Engineering, University of Liverpool, UK. He was awarded a BE inEngineering Mechanics in 1982, an ME in Solid Mechanics in 1985, and a PhDin Structural Engineering in 1989, from Dalian University of Technology. Hehas published over 70 conference and journal papers. His major researchinterests are structural dynamics and computational mechanics.Copyright 2005 Inderscience Enterprises Ltd.

208H. Ouyang, W. Nack, Y. Yuan and F. ChenWayne V. Nack has published papers in brake squeal and moan as well as invehicle structural dynamics and optimisation. He received his BS inEngineering at Rose Hulman Institute, and his PhD in Theoretical and AppliedMechanics at the University of Illinois in Computational Mechanics. Waynehas 30 years of experience in developing new methods for the automotiveindustry and has published papers in the above areas.Yongbin Yuan is Chief Engineer of TRW Automotive, Shanghai. He was aSenior Manager and Fellow of TRW Automotive at Livonia, MI, before hispresent post. He has a PhD in Material Science. He has published a number ofpapers on disc brake noise and friction.Frank Chen is a Technical Specialist at the Ford Motor Company. He has beenworking in noise and vibration area for more than ten years. He has a PhD inMechanical System Engineering and has published a number of technicalpapers on disc brake noise.1IntroductionAutomotive disc brake squeal has been a challenging issue for many engineers andresearchers due to its immense complexity. Much progress and insight have been gainedin recent years and brakes have become quieter. However, squeal still occurs frequentlyand therefore much still needs to be understood and done. CAE simulation and analysismethods play an important role in understanding brake squeal mechanisms. It can also beused to interpret test results, prepare for upfront DoE (design of experiment), simulatestructural modifications and explore innovative ideas. The methodology is still underdevelopment. Some methods have matured and others are being refined. It is thought thatthe time has come to review the established methods to date.There is a wealth of literature on automotive disc brake squeal. Reviews(North, 1976; Crolla and Lang, 1991; Nishiwaki, 1990; Yang and Gibson, 1997;Kinkaid et al., 2003) conducted in the last 30 years provide a comprehensivesource of information. However, there has not been any paper that reviews the area ofnumerical analysis work on disc brake squeal. A recent comprehensive review paper(Kinkaid et al., 2003) has only lightly touched on finite element models of disc brakes.Therefore, this paper serves to fill this apparent gap and complement the existingliterature.According to the mechanism of generation, brake noise can be classified into threetypes. The first type is called creep-groan, which is caused by the stick-slip motionbetween the friction material and the rotor surface (Abdelhamid, 1995;Brecht et al., 1997). Creep-groan occurs at near-zero vehicle speed. The second type ofnoise is often called hot judder or rumble, which is caused by periodic features on therotor surface that result in cyclic brake torques (Abdelhamid, 1997; Swartzfager andSeingo, 1998; Kubota et al., 1998). The salient feature of this type of noise is that itsfrequency is a multiple of the rotor speed of rotation. The third type of noise ischaracterised by:

Numerical analysis of automotive disc brake squeal: a review the absence of apparent sticking at the rotor/pad sliding interface in general, one dominant high frequency fairly independent of the rotor speed occurrence of in-plane and/or out-of-plane flexible rotor modes.209This type of noise is usually called squeal. Noise with a dominant frequency over 1 kHz(or above the first out-of-plane rotor frequency) generally belongs to this category. Theseare meant as a description of disc brake squeal rather than a definition, for there is nogenerally accepted precise definition (Kinkaid et al., 2003).Squeal has been the primary subject of past studies on brake noise and is the focus ofthis review.Investigation into brake squeal has been conducted by various experimental andanalytic methods. Experimental methods, for all their advantages, are expensive mainlydue to hardware cost and long turnaround time for design iterations. Frequentlydiscoveries made on a particular type of brakes or on a particular type of vehicles are nottransferable to other types of brakes or vehicles. Product development is frequentlycarried out on a trial-and-error basis. There is also a limitation on the feasibility of thehardware implementation of ideas. A stability margin is usually not foundexperimentally. Unfortunately, this produces designs that could be only marginallystable.Analytical or numerical modelling, on the other hand, can simulate differentstructures, material compositions and operating conditions of a disc brake or of differentbrakes or of even different vehicles, when used rightly. With these methods, noiseimprovement measures can be examined conceptually before a prototype is made andtested. Theoretical results can also provide guidance to an experimental set-up andhelp interpret experimental findings. The authors’ intention is to offer a review of thestate-of-art of CAE simulation and analysis for disc brake squeal. The authors believethat theoretical methods and experimental methods are equally important. Both areneeded to capture the underlying physics so that eventually a commercial code would bedeveloped to complement and partly replace expensive and time-consuming experimentalstudy. These methods will remain an indispensable tool for understanding brake squealand for achieving improvements on noise performance in the foreseeable future.Simulation and analysis methods may be divided into two big categories: complexeigenvalue analysis in the frequency domain and transient analysis in the time domain.The transient results can be converted to the frequency domain by an FFT. Brake modelswith a large number of degrees-of-freedom (DoFs) or with infinite number of DoFs(continuous media) are of interest to the authors. Models composed of a small number ofdegrees-of-freedom (lumped-parameter models) will not be covered in this review.The papers being reviewed here have all been published in the public domain (exceptYuan, 1997). These exclude internal reports and private communications. This reviewcould not be all-inclusive even though the best possible effort has been attempted.Brake squeal is the result of friction-induced vibration, which was reviewedcomprehensively by Oden and Martins (1985), and also by Ibrahim (1994).Friction-generated sound and noise in general was reviewed recently by Akay (2002).This review paper consists of five major sections: Introduction, Complex EigenvalueAnalysis, Transient Analysis, Outstanding Issues and Conclusions. There is also anappendix for notations used in the paper after references.

2102H. Ouyang, W. Nack, Y. Yuan and F. ChenComplex eigenvalue analysisThe complex eigenvalue approach refers to what results are sought, not on how thestructural model is constructed. The model may be derived by analytical methods, theassumed-modes method and the finite element method. There must be a means (known asa squeal mechanism) of incorporating friction as a sort of nonconservative force in themodel. Squeal mechanisms were reviewed by North (1976), Crolla and Lang (1991),Nishiwaki (1990), Yang and Gibson (1997) and Kinkaid et al. (2003).2.1 Analytical methodsMost early works on instability analysis were performed with hand-derived equations formass-spring models that were used to represent real structures. Insight gained from suchsimple models in the early days of research greatly enhanced the understanding of themechanisms of friction-induced noise and vibration. The analyses for more complicatedmass-spring models by Jarvis and Mills (1963–1964), Earles and Lee (1976),North (1976), Millner (1978), and many others have revealed that even when the frictioncoefficient is constant, the model can be unstable if the friction force couples twodegrees-of-freedom together. A large-scale finite element analysis of the stability of thelinearised brake system also confirms that instability arises when two modes coalesceunder the influence of friction.2.2 The assumed-modes methodBrake components are continuous media of infinite number of DoFs. Because thesecomponents are of complicated geometrical shape, the finite element method is mostappropriate. Among the brake components, the rotor is the only component that hasrather regular geometry. A solid rotor has a number of cyclic symmetry that equals thenumber of mounting holes in the top-hat section. A vented rotor is also quite close tohaving many degrees of cyclic symmetry. Both solid rotors and vented rotors possesspairs of very close frequencies (an axially symmetric rotor possesses pairs of identicalfrequencies).Chan et al. (1994) considered a brake rotor as a thin, annular plate and thus expressedthe transverse vibration of the rotor as a linear sum of analytic component modes.This approach has been followed by Mottershead and coworkers (Mottersheadet al., 1997; Ouyang et al., 1998). Hulten and Flint (1999), and Flint (2000) used theassumed modes method for their beam model of the rotor. In the work of Chowdhary etal. (2001), individual brake components (disc and pads both modelled as thin plates) weremodelled and solved separately for their modal characteristics. Then, these were coupledtogether at the contact interface and the equations of motion were derived through theLagrangian approach. Chakraborty et al. (2002) also used thin plate model for the disc.They introduced (cubic) nonlinear spring for the pads. von Wagner et al. (2003) furtherdemonstrated that the frequency of the limit-cycle vibration of the disc was very close tothat of the linear unstable vibration obtained through a complex eigenvalue analysis.Wauver and Heilig (2003) considered both friction and heating at the contact pointsbetween the pads (lumped masses with springs) and the disc (a rotating ring).Like Chakraborty et al. (2002) and von Wagner et al. (2003), Galerkin’s approach wasused to discretise the equations of motion.

Numerical analysis of automotive disc brake squeal: a review211Recognising the importance of the in-plane modes of the disc, Tzou et al. (1998)derived the analytical solution of 3-D elastodynamics for a cylinder of arbitrary thicknessusing the Ritz method. They concluded “in-plane loading of the disc, with concomitantresonance of an in-plane mode, is expected to be one mechanism for the generation ofout-of-plane vibration”. Tseng and Wickert (1998) obtained the analytic solution of thein-plane stresses of a rotating disc and used it in the equation of motion of the disc. Thein-plane shear stresses due to the friction were considered as follower forces (distributedload acting on a sector of the disc), instead of friction itself being the follower force.Gyroscopic and centripetal effects were included so that the work can apply to discsrotating at higher speeds.Discs (rotors in the automotive industry) are basic mechanical elements that arewidely used in engineering industry, such as wood saws, computer disks, and turbinediscs and so on. Disc vibration was reviewed by Mottershead (1998).Since the assumed-modes method normally applies to a model where an analyticalsolution (closed-form or approximate) may be found, for example, a beam or a platemodel for the disc, it is not as widely used as the finite element method. It deservesa place when testing a squeal mechanism, such as in Hulten and Flint (1999),or when incorporating some special features, such as moving loads (Ouyang andMottershead, 2000), where a complicated system model should be avoided initially.2.3 The finite element methodThe complex eigenvalue approach linearises the brake squeal solution at static steadysliding states. It is a good approximation if it is linearised properly in the vicinity of anequilibrium point like the steady sliding position. This procedure is referred to as alinearised stability analysis and it is discussed by Nack (1995, 2000). Currently, mostproduction work in industry uses this method. Nonlinear transient soluti

Numerical analysis of automotive disc brake squeal: a review 211 Recognising the importance of the in-plane modes of the disc, Tzou et al. (1998) derived the analytical solution of 3-D .

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