【摘要】
本文對(duì)一輛車的制動(dòng)系統(tǒng)中旋轉(zhuǎn)閥瓣接觸兩個(gè)固定墊的動(dòng)力失穩(wěn)性進(jìn)行了研究。在現(xiàn)行的近似幾何中，盤被有限元分析法以帽盤型結(jié)構(gòu)為模型。從參考坐標(biāo)系和移動(dòng)坐標(biāo)系見的坐標(biāo)變換，對(duì)盤和墊之間的接觸運(yùn)動(dòng)學(xué)進(jìn)行了闡述。通過(guò)引入統(tǒng)一的二維網(wǎng)的方法來(lái)構(gòu)造閥瓣相應(yīng)的陀螺矩陣。陀螺儀的非保守性制動(dòng)系統(tǒng)的動(dòng)力不穩(wěn)定性是對(duì)系統(tǒng)參數(shù)的數(shù)值預(yù)測(cè)。結(jié)果表明, 尖叫聲傾向于轉(zhuǎn)速，轉(zhuǎn)速取決于參與尖叫聲模式下的振動(dòng)模式。而且,它強(qiáng)調(diào)摩擦系數(shù)的負(fù)斜率對(duì)在盤的面內(nèi)扭轉(zhuǎn)模式下產(chǎn)生尖叫聲起著至關(guān)重要的作用。

【關(guān)鍵詞】
陀螺儀；盤型制動(dòng)；制動(dòng)尖叫；耦合模式

1. 介紹
盤式制動(dòng)尖叫已經(jīng)被許多學(xué)者研究了數(shù)十年。通過(guò)對(duì)尖叫機(jī)械的研究積累了許多有價(jià)值的信息。Kinkaid等[1]提供了關(guān)于各種盤型制動(dòng)尖叫研究的概述。Ouyang 等[2]發(fā)行了以汽車盤型制動(dòng)尖叫的數(shù)值分析為集中研究的評(píng)論性文章。他們顯示一個(gè)主要研究制動(dòng)尖叫的方法，是線性穩(wěn)定分析。從線性化的運(yùn)動(dòng)微分方程來(lái)看,真正的部分特征值被計(jì)算出來(lái)，用于決定均衡的穩(wěn)定性。在文獻(xiàn)中，有兩個(gè)關(guān)于線性尖叫分析的主要方向：靜態(tài)平穩(wěn)的復(fù)雜特征值分析——滑動(dòng)平穩(wěn)[3–8]和旋轉(zhuǎn)制動(dòng)系統(tǒng)的穩(wěn)定性分析 [9–12,14]。
固定盤和墊的靜態(tài)的滑動(dòng)穩(wěn)定的穩(wěn)定性分析提供尖叫原理作為頻繁摩擦領(lǐng)域里的合并模式的特性。Huang等[6]使用本征值攝動(dòng)法發(fā)展必要的條件沒(méi)有直接的本征結(jié)果。Kang等[7]推導(dǎo)了盤對(duì)之間的合并模式的封閉解。由于固定盤假設(shè),有限元(FE)方法被容易地應(yīng)用于上面提到的評(píng)論性文章[2]. 同樣的，Cao 等[13]從一個(gè)有移動(dòng)墊和固定盤的FE盤型制動(dòng)模型模型研究了移動(dòng)荷載效應(yīng)，因此,陀螺儀的影響被忽視了。Giannini等[15,16]驗(yàn)證其合并模式行為,通過(guò)使用實(shí)驗(yàn)尖叫頻率作為尖叫開始。
另一方面，旋轉(zhuǎn)盤型制動(dòng)的穩(wěn)定性已經(jīng)調(diào)查了分析的方法。旋轉(zhuǎn)盤型制動(dòng)系統(tǒng)已經(jīng)模擬了一個(gè)環(huán)形物[10]和一個(gè)環(huán)形板[12]恰當(dāng)?shù)呐c兩個(gè)墊的接觸，并且環(huán)形板受制于分布式摩擦牽引力[9]?？紤]陀螺儀的影響，真正的部分特征值對(duì)系統(tǒng)參數(shù)的影響已經(jīng)被解決了。盡管由于復(fù)雜的旋轉(zhuǎn)盤建模，旋轉(zhuǎn)（FE）盤型制動(dòng)建模仍舊沒(méi)有被發(fā)展。
最近，Kang等[14] 用綜合法開發(fā)了一種理論盤型制動(dòng)模型。盤型制動(dòng)模型由一個(gè)旋轉(zhuǎn)的環(huán)形板接觸兩個(gè)固定環(huán)的扇形板組成。綜合分析法解釋了被耦合模式和


Abstract
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.

Keywords Gyroscopic; Disc brake; Brake squeal; Mode-coupling

1. Introduction
Disc brake squeal has been investigated by many researchers for several decades. Much valuable information on squeal mechanisms has been accumulated throughout the research. Kinkaid et al. [1] presented the overview on the various disc brake squeal studies. Ouyang et al. [2] published the review article focused on the numerical analysis of automotive disc brake squeal. They have shown that one major approach on brake squeal study is the linear stability analysis. From the linearized equations of motion, the real parts of eigenvalues have been calculated for determining the equilibrium stability. In the literature, there are two major directions on the linear squeal analysis: the complex eigenvalue analysis of the static steady- sliding equilibrium [3–8] and the stability analysis of rotating brake system [9–12,14]. The stability analysis at the static steady-sliding equilibrium of the stationary disc and pads provides the squeal mechanism as mode-merging character in the friction–frequency domain. Parti- cularly, Huang et al. [6] used the eigenvalue perturbation method to develop the necessary condition for mode-merging without the direct eigensolutions. Kang et al. [7] derived the closed-form solution for mode-merging