Squeal analysis of gyroscopic disc brake system based on finite element method

In this paper, the dynamic instability of a car brake system with a rotating disc in contact with two stationary pads is studied. For actual geometric approximation, the disc is modeled as a hat-disc shape structure by the finite element method. From a coordinate transformation between the reference and moving coordinate systems, the contact kinematics between the disc and pads is described. The corresponding gyroscopic matrix of the disc is constructed by introducing the uniform planar-mesh method. The dynamic instability of a gyroscopic non-conservative brake system is numerically predicted with respect to system parameters. The results show that the squeal propensity for rotation speed depends on the vibration modes participating in squeal modes. Moreover, it is highlighted that the negative slope of friction coefficient takes an important role in generating squeal in the in-plane torsion mode of the disc.     

Brake squeal: Linear and nonlinear numerical approaches

“Brake squeal” groups a large set of high-frequency sound emissions from brake systems. They are generated during the braking phase and are characterized by a harmonic spectrum. The onset of squeal is due to an unstable behaviour occurring in linear conditions during the braking phase, and a general approach used by several authors to determine the system instabilities is the complex eigenvalues analysis. When the brake begins to squeal, the response of the system reaches a new limit cycle where the linear models cannot be used anymore. This paper presents the integration of two different numerical procedures to identify the mechanism bringing to squeal instability and to analyse its dynamics. The first approach is a finite element modal analysis of the brake system and is used to identify its eigenvalues and to relate them to the squeal occurrence. The second one is a specific finite element programme, Plast3, appropriate for nonlinear dynamic analyses in the time domain and is particularly addressed to study contact problems with friction between deformable bodies. This programme computes the contact stresses and permits to determine the dynamics of the system along the contact surface, both in the linear and nonlinear fields. The two models are compared and the onset of squeal is predicted both in the frequency domain by the linear model and in the time domain by the nonlinear one. The instability predictions, obtained by the two models, are discussed. To simplify the dynamics of its components, the study is carried out on a simple model, made of a disc, a small friction pad and a beam supporting the pad. The geometry of the model is related to an experimental set-up used to validate the models and to compare the numerical results with the experiments.     

约束对盘形制动摩擦噪声影响的有限元研究

建立了铁路车辆盘形制动装置的三维实体有限元模型，分别为该模型中的制动盘、闸片和夹钳等部件设置了不同的材料特性。利用线性弹簧力模拟制动摩擦面间的法向力，摩擦力取为线性弹簧力与摩擦因数的乘积。通过对系统有限元运动方程进行复特征值分析，根据复特征根实部为正值判断系统发生失稳的模态，这也是可能产生摩擦噪声的模态。仿真结果显示，系统的约束条件对摩擦噪声的形成有显著的影响。改变模型的约束条件，可以抑制制动系统的摩擦噪声发生趋势，说明通过优化设置约束条件来提高摩擦系统的运动稳定性从而抑制摩擦噪声的发生是可行的。     

基于盘／销装置的摩擦尖叫噪声研究

为了研究摩擦尖叫的产生机理,利用汽车制动盘、摩擦材料及铝合金圆销设计了一种长度可调的盘／销摩擦试验装置,进行了不同销长的摩擦尖叫试验。基于盘／销零件的约束模态试验结果,建立了装置的有限元模型。利用复特征值分析方法研究了销长、摩擦因数、载荷、速度和材料特性等因素对摩擦尖叫噪声的影响。结果表明：当圆销和制动盘间弯曲模态频率相近时会形成模态耦合,系统不稳定,产生摩擦尖叫噪声;通过改进系统结构、适当降低摩擦因数和调整材料特性可以减轻或消除摩擦尖叫。     

Brake squeal analysis by coupling spectral linearization and modal identification methods

Brake squeal is induced by self-excited vibrations, consequences of local nonlinearities at the contact interface. This paper deals with a new way to analyze the brake squeal behavior. The proposed method is based on a spectral linearization of the brake nonlinear dynamic response with unilateral contact and friction conditions. The approach enables to identify modal parameters of an equivalent linear system by a combination of the random decrement technique and the Ibrahim time domain method. It is applied to the analysis of a pad/beam squealing contact. The obtained results are compared to the classical complex eigenvalues analysis and nonlinear temporal dynamic finite element analysis ones.     

Instabilities generated by friction in a pad–disc system during the braking process

This paper presents a numerical and experimental study of a pad–disc tribometer. The explicit dynamic finite element software PLAST 3 in 3-D is used to simulate the behaviour of the two bodies involved. Coulomb's friction law is used at the contact surface with a constant coefficient. For this application, temporal simulations show that separation occurs between surfaces, proof of instabilities. This unstable state is characterized by a stick–slip–separation wave. We show that instabilities describe a periodic shock phenomenon at the contact interface. Consequently, the acceleration spectrum recorded on the surface of the pad reveals periodicity in the frequency domain. It shows also that, in this case, the vibrations responsible for the instability are localized in the pad. The mode responsible for squealing can be obtained by a modal analysis of the pad–disc system by assuming that the interface is stuck. We highlight the importance of the pad Poisson's ratio in the occurrence of this unstable state. A numerical/experimental comparison has been performed and the fundamental frequency of squeal obtained experimentally and its magnitude agree with those calculated numerically with PLAST 3.     

闸片沟槽织构对盘式制动尖叫的影响

为研究制动闸片沟槽织构对盘式制动系统制动尖叫的影响,基于摩擦自激振动理论,建立盘式制动系统普通闸片和沟槽闸片有限元模型,采用复特征值分析法研究该盘式制动系统的摩擦自激振动特性。利用该有限元模型开展沟槽的宽度和深度的参数化分析,获得其对制动尖叫的影响规律。结果表明：制动闸片与制动盘间的摩擦自激振动是导致制动尖叫发生的主要原因,沟槽型闸片对抑制制动尖叫具有明显效果;当闸片沟槽深度在5~20 mm区间内,盘式制动系统的稳定性随沟槽深度的增大而呈现逐渐降低的趋势,表明沟槽深度越小,发生摩擦自激振动的可能性越小;在沟槽宽度5~20 mm范围内,随沟槽宽度的增大,盘式制动系统的稳定性先增大后降低,在沟槽宽度为10 mm时,系统发生制动噪声的可能达到最大。     

Evaluation of Disc Brake Materials for Squeal Reduction

A nontraditional evaluation tool is introduced to examine the effects of different materials, in practical applications, that are used in fabricating disc brake components for commonly used or special requirements such as heavy-duty performance and racing cars. As an extension to earlier finite element (FE) disc brake models, a detailed FE model of the whole disc brake corner that incorporates the wheel hub and steering knuckle is developed and validated using experimental modal analysis. Stability analysis of the disc brake corner using the finite element software ABAQUS is carried out to predict squeal occurrence also taking into account the negative and positive damping effects and friction material real surface to increase the accuracy of prediction. A Taguchi method–based design of experiment is used to better assess the contributions of different materials and its interaction effects for effective reduction of brake squeal. The results showed that the pad friction material contributes 56% to the total system instability (squeal generation). The rotor material contributes 22% of the system instability. Caliper and bracket materials participate 11 and 11%, respectively.     

CRH2盘形制动系统制动尖叫噪声研究

为了研究高速动车组的制动尖叫噪声,建立CRH2拖车盘形制动系统的摩擦耦合有限元模型,对其进行运动稳定性和制动自激振动的瞬态动力学分析,研究了摩擦因数、闸片以及制动盘弹性模量对制动系统尖叫噪声的影响。结果表明：随着摩擦因数μ的增大,盘形制动系统发生制动尖叫噪声的趋势增加;随着闸片弹性模量的增大,制动系统发生制动尖叫噪声的趋势增加,并且激发的噪声频率也明显变大;随着制动盘弹性模量增大,制动系统发生制动尖叫噪声的趋势先降低后增大。     

叶根尺寸误差对叶片固有频率的影响

采用三维有限元模型,考虑叶片变形的几何非线性和叶根接触非线性,研究常用的枞树型叶根尺寸误差对叶片固有频率的影响。分析结果表明叶根误差发生的位置对叶片弯曲振型的固有频率影响较大,对扭转振型影响较小;误差的大小对叶片的各阶固有频率影响均较小,但对叶根接触状态或者说对叶根应力分布有影响;比较发现,在计算固有频率时,将叶片在叶根处简单地处理成固支位移边界是不合理的。     

基于有限元的摩托车振动分析与控制

振动是影响汽车、摩托车等车辆乘坐舒适性和可靠性的重要因素,运用有限元分析和实验模态分析方法对车辆的 振动进行分析,可以将振动问题在设计阶段解决,以缩短产品开发周期,节约开发成本。以摩托车为对象,建立了摩托车 的有限元模型,对模型进行理论模态分析和谐响应分析,并用实验分析对比验证理论模型,通过分析找到摩托车振动的 原因和控制振动的有效方法。     

采用全联热-机械有限元模型计算盘式制动器尖叫声的预测工具(二)

本文提出一个制动器尖叫模拟的新的综合方法,它集中开发采用全考虑制动器结构响应热负荷的影响的正确的热-机械有限元模型.该综合研究包括实现与时间有关的非线性接触和全联瞬态热分析,在进行不稳定研究前,采用复杂固有值技术,提供在制动器内的接触和温度分布.其结果依次通过制动全部系统固有值证实制动尖叫性质的变化.     

Analysis of Friction-Induced Vibration Leading to Brake Squeal Using a Three Degree-of-Freedom Model

Friction-induced vibration is a common phenomenon in nature and thus has attracted many researchers’ attention. Many of the mathematical models that have been proposed on the basis of mode coupling principle, however, cannot be utilized directly to analyse the generation of friction-induced vibration that occurs between two bodies because of a difficulty relating model parameters to definite physical meaning for real friction pairs. In this paper, a brake squeal experiment is firstly carried out by using a simple beam-on-disc laboratory apparatus. Experimental results show that brake squeal correlates with the bending mode of the beam and the nodal diameter out-of-plane mode of the disc as well as the cantilever length of the beam. Then, a specific three degree-of-freedom dynamic model is developed of the beam-on-disc system and the vibration behaviour is simulated by using the complex eigenvalue analysis method and a transient response analysis. Numerical simulation shows that the bending mode frequency of the beam a little greater than the frequency of the nodal diameter out-of-plane mode and a specific incline angle of the leading area to the normal line of the disc as well as a certain friction coefficient, are necessary conditions for the mode coupling of a frictional system. Results also show that when the frictional system is transited from a steady state to an unstable state for the variation of parameters, its kinetic and potential energy increase with time due to continuous feed-in energy from the friction force while the dynamic responses of the system change from the beating oscillation to the divergent, which leads to the friction-induced vibration and squeal noise.     

Analytical formulation of mode-coupling instability in disc-pad coupled system

This paper describes the mode-coupling-type squeal mechanism in a disc brake system. The mode shapes of a disc and a brake pad (an annular sector plate) are obtained using the component eigenvalue analysis and the Rayleigh-Ritz method, respectively. The disc-pad coupled system subject to friction-couple is discretized by the truncated set of system component modes. Mode-coupling instability is determined in closed form resulting from a reduced-order friction-coupling model, which subsequently defines the modal stability index. The proposed index parameter determines the necessary condition for flutter instability without solving system complex eigenvalues. The numerical investigation shows that the disc-pad modal interaction has a strong squeal tendency when two pads are not identical.     

Failure characteristics of a thin metallic sandwich plate with metallic sheared dimple cores under low-velocity impact loading

The functionality and the performance of a lightweight sandwich plate with periodic cellular metal (PCM) cores are influenced by failure characteristics of the lightweight sandwich plate. The goal of this paper is to investigate the failure characteristics of a thin metallic sandwich plate with metallic sheared dimple cores under low-velocity impact loading through nonlinear finite element analysis. The influence of the imperfection mode of the cores on the impact response of a thin sandwich plate is examined to obtain a proper simulation model. Repeated finite element analyses are performed to examine the failure modes of the sandwich plate for different impact conditions. Normalized impact parameters are defined in order to generalize a dynamic failure map (DFM). DFMs of the thin metallic sandwich plate have been estimated via the regression analysis of critical impact conditions for each failure mode. In addition, the influence of the normalized impact parameters on the failure mode has been investigated using the DFM.     

摩擦噪声系统的振动特性研究

建立了一个往复滑动摩擦系统1∶1实体装配模型,采用有限元方法对该系统的振动特性进行研究,获得了系统的自然频率和振动模态。将得到的系统振动频率与系统的试验噪声的频率进行比较,发现它们的一些结果有很好的一致性。对系统的计算模态分析显示,发生噪声的模态同时具有切向和法向振动特征。     

Study on dynamic friction characteristics in reciprocating friction drive system

The dynamic friction characteristics of a reciprocating friction drive system are investigated under conditions of dry contact using 0·45% carbon steel pair. Three friction modes are found during the operation, i.e. stick-slip, sticking and a transition region. The critical operating conditions in classifying these three modes are examined under various driver speeds, normal loads and spring constants. The critical values of driver speed and normal load increase with increasing spring constant. Generally, in the friction drive system the disappearance of the stick-slip results in smooth rolling. It is also found that the slope at the first period of slip on the traction force–relative slip velocity curve would have a transition from negative to positive value when the friction mode of stick-slip changes into sticking. Moreover, results show that the sticking mode gives the best positioning accuracy with the least wear on the contact surfaces. In addition, a transition from severe wear to mild wear is found when the friction mode is transferred from stick-slip to sticking only.     

盘式制动器的结构场有限元分析

首先探讨盘式制动器在制动过程中的摩擦接触和非线性动力学问题.具体的分析方法包括:摩擦接触算法,非线性有限元方法.按照制动盘与摩擦片的实际几何尺寸,建立了具有速度可变效应的三维瞬态结构应力有限元模型,利用非线性有限元方法,较真实地模拟了制动器的制动过程.通过以上分析得出制动过程的一些结构上的性能变化.将同相同制动条件下的实心盘式制动器和通风盘式制动器对比,得出通风盘式制动器在制动过程中的接触应力,各向位移等.     

汽车盘制动器优化设计热和机械特性的研究(一)

由于热量集中于制动盘的表面造成热弹不稳定性(TEI)而引起热变形.这样可能发生大家知道的低频强烈振动.因为在盘和衬块的接触面间的摩擦系数变化,在摩擦衬决发生尖叫声.通过对热聚集和尖叫现象的联合分析,对高热和机械特性可设计一最佳的盘和摩擦衬块.本文同时考虑了热和机械不稳定性按照盘的厚度,卡钳的加压方式,衬片弧长进行了数值...     

双足反向型直线超声电机的优化设计及性能仿真

为实现成对微部件反向同步动作的精密定位,设计了一种双足反向型直线超声电机。该电机以矩形板面内一阶纵振和二阶弯振模态为工作模态,通过三角形结构将激励振动放大并在驱动足位置形成椭圆运动,从而驱动两滑条实现反向直线输出。基于工作频率一致性要求进行了电机结构优化,采用谐响应分析验证了设计的可行性。建立定子滑条刚柔接触有限元模型,实现了电机输出性能的仿真。仿真结果说明该电机具有较好的稳定性,空载速度和输出推力分别达到120mm/s和30N。