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Numerical analysis of automotive disc brake squeal: a review
Ouyang H, Nack W, Yuan Y, et al. Numerical analysis of automotive disc brake squeal: A review[J]. International Journal of Vehicle Noise amp; Vibration, 2005, 1(3-4):207-230.
Abstract: This paper reviews numerical methods and analysis procedures used in the study of automotive disc brake squeal. It covers two major approaches used in the automotive industry, the complex eigenvalue analysis and the transient analysis. The advantages and limitations of each approach are examined. This review can help analysts to choose right methods and make decisions on new areas of method development. It points out some outstanding issues in modelling and analysis of disc brake squeal and proposes new research topics. It is found that the complex eigenvalue analysis is still the approach favoured by the automotive industry and the transient analysis is gaining increasing popularity.
摘要：本文回顾了汽车盘式制动器尖叫的研究中使用的数值方法和分析程序。 它涵盖了汽车工业中使用的两种主要方法，复杂特征值分析法和瞬态分析法。 检查每种方法的优点和局限性。这项审查可以帮助分析师选择正确的方法，并在新的方法开发领域做出决定。它指出了盘式制动器尖叫的建模和分析中的一些突出问题，并提出了新的研究课题。发现复杂特征值分析法仍然是汽车行业青睐的方法，并且瞬态分析法越来越受欢迎。
1 Introduction
Automotive disc brake squeal has been a challenging issue for many engineers and researchers due to its immense complexity. Much progress and insight have been gained in recent years and brakes have become quieter. However, squeal still occurs frequently and therefore much still needs to be understood and done. CAE simulation and analysis methods play an important role in understanding brake squeal mechanisms. It can also be used to interpret test results, prepare for upfront DoE (design of experiment), simulate structural modifications and explore innovative ideas. The methodology is still under development. Some methods have matured and others are being refined. It is thought that the time has come to review the established methods to date.
汽车盘式制动器尖叫问题的巨大复杂性，它是许多工程师和研究人员的一个具有挑战性的问题。近年来人们对此取得了很大的进步和理解，制动器已经变得更安静了。然而，尖叫仍经常发生，因此仍需要理解和完成。CAE模拟和分析方法在理解制动尖叫机制中起着重要作用。它还可以用于解释测试结果，准备前期DoE（实验设计），模拟结构修改和探索创新的想法。该方法仍在开发中。一些方法已经成熟，另一些方法正在改进。所以现在是审查迄今为止已确立的方法的时候了。
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 comprehensive source of information. However, there has not been any paper that reviews the area of numerical 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 existing literature.
有大量关于汽车盘式制动器尖叫的文献。在过去30年中进行的评价（North，1976; Crolla和Lang，1991; Nishiwaki，1990; Yang和Gibson，1997; Kinkaid等，2003）提供了全面的信息来源。然而，还没有任何论文回顾了关于盘式制动器尖叫的数值分析工作的领域。最近的一份全面的综述报告（Kinkaid等人，2003）只是轻轻地谈到了盘式制动器的有限元模型。因此，本文用于填补这种明显的差距并补充现有的文献。
According to the mechanism of generation, brake noise can be classified into three types. The first type is called creep-groan, which is caused by the stick-slip motion between the friction material and the rotor surface (Abdelhamid, 1995; Brecht et al., 1997). Creep-groan occurs at near-zero vehicle speed. The second type of noise is often called hot judder or rumble, which is caused by periodic features on the rotor surface that result in cyclic brake torques (Abdelhamid, 1997; Swartzfager and Seingo, 1998; Kubota et al., 1998). The salient feature of this type of noise is that its frequency is a multiple of the rotor speed of rotation. The third type of noise is characterised by:
bull; the absence of apparent sticking at the rotor/pad sliding interface
bull; in general, one dominant high frequency fairly independent of the rotor speed
bull; occurrence of in-plane and/or out-of-plane flexible rotor modes.
根据发电机制，制动噪声可分为三种类型。第一种类型被称为蠕变-呻吟，这是由摩擦材料和转子表面之间的粘滑运动造成的（Abdelhamid，1995; Brecht et al。，1997）。蠕变嘎吱发生在接近零的车速。第二种类型的噪声通常被称为热颤抖或隆隆声，这是由转子表面上导致周期性制动扭矩的周期性特征引起的（Abdelhamid，1997; Swartzfager和Seingo，1998; Kubota等人，1998）。这种类型的噪声的显着特征是其频率是转子旋转速度的倍数。第三类噪声的特征在于：
bull;在转子/衬垫滑动界面处没有明显粘附
bull;一般来说，一个主导高频相当独立于转子速度
bull;出现面内和/或面外柔性转子模式
This 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. These are meant as a description of disc brake squeal rather than a definition, for there is no generally accepted precise definition (Kinkaid et al., 2003).
Squeal has been the primary subject of past studies on brake noise and is the focus of this review.
Investigation into brake squeal has been conducted by various experimental and analytic methods. Experimental methods, for all their advantages, are expensive mainly due to hardware cost and long turnaround time for design iterations. Frequently discoveries made on a particular type of brakes or on a particular type of vehicles are not transferable to other types of brakes or vehicles. Product development is frequently carried out on a trial-and-error basis. There is also a limitation on the feasibility of the hardware implementation of ideas. A stability margin is usually not found experimentally. Unfortunately, this produces designs that could be only marginally stable.
这种类型的噪声通常被称为尖叫声。主频率超过1kHz（或高于第一平面外转子频率）的噪声通常属于这一类别。这些意思是作为盘式制动器尖叫的描述而不是定义，因为没有普遍接受的精确定义（Kinkaid等人，2003）。
尖叫一直是过去研究制动噪声的主要议题，是本次审查的重点。
通过各种实验和分析方法进行制动尖叫的调查。实验方法的所有优点都是昂贵的，主要是由于硬件成本和设计迭代的周转时间长。在特定类型的制动器上或在特定类型的车辆上进行的经常发现不能转移到其他类型的制动器或车辆。产品开发经常在反复试验的基础上进行。对硬件实现思想的可行性也有限制。稳定性裕度通常不是通过实验发现的。不幸的是，这产生的设计可能只是边缘稳定。
Analytical or numerical modelling, on the other hand, can simulate different structures, material compositions and operating conditions of a disc brake or of different brakes or of even different vehicles, when used rightly. With these methods, noise improvement measures can be examined conc
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