某中級(jí)轎車前輪制動(dòng)器設(shè)計(jì)[別克君威GS2.0T前輪盤式]【三維SW】【10張CAD圖紙+PDF圖】

喜歡這套資料就充值下載吧。資源目錄里展示的都可在線預(yù)覽哦。下載后都有，請(qǐng)放心下載，文件全都包含在內(nèi)，【有疑問咨詢QQ:414951605 或 1304139763】=喜歡這套資料就充值下載吧。資源目錄里展示的都可在線預(yù)覽哦。下載后都有，請(qǐng)放心下載，文件全都包含在內(nèi)，【有疑問咨詢QQ:414951605 或 1304139763】= 畢業(yè)設(shè)計(jì)（論文）中期報(bào)告題目：某中級(jí)轎車前輪制動(dòng)器設(shè)計(jì)系 別 機(jī)電信息系 專 業(yè) 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 班 級(jí) 姓 名 學(xué) 號(hào) 導(dǎo) 師 2013年 03 月28日1. 設(shè)計(jì)（論文）進(jìn)展?fàn)顩r1).收集和整理資料，參閱部分收集到的資料，對(duì)論文命題有了初步的認(rèn)識(shí)。 2).完成開題報(bào)告，并通過指導(dǎo)老師和論文開題答辯小組審查。 3).查找與閱讀論文相關(guān)的合適的英文文獻(xiàn)，對(duì)其進(jìn)行翻譯并完成。 4).通過文獻(xiàn)研究和實(shí)踐研究，對(duì)論文命題有了較為全面的理解后，結(jié)合前人的研究成果，完成論文中需要計(jì)算的部分并完成。主要計(jì)算過程如下：制動(dòng)器的設(shè)計(jì)：制動(dòng)盤直徑D制動(dòng)盤直徑D希望盡量大些，這時(shí)制動(dòng)盤的有效半徑得以增大，就可以降低制動(dòng)鉗的夾緊力，降低摩擦襯塊的單位壓力和工作溫度。但制動(dòng)盤直徑D受輪毅直徑的限制通常，制動(dòng)盤的直徑D選擇為輪毅直徑的70%79%，總質(zhì)量大于2t的車輛應(yīng)取其上限。通常，制造商在保持有效的制動(dòng)性能的情況下，盡可能將零件做的小些，輕些。輪輞直徑為17英寸，又因?yàn)镸=2025kg。在本設(shè)計(jì)中,輪轂為： D=70%79%Dr=0.79*17*25.4=301341.122mm取D=340mm 制動(dòng)盤厚度h制動(dòng)盤厚度h直接影響著制動(dòng)盤質(zhì)量和工作時(shí)的溫升。為使質(zhì)量不致太大，制動(dòng)盤厚度應(yīng)取得適當(dāng)小些;為了降低制動(dòng)工作時(shí)的溫升，制動(dòng)盤厚度又不宜過小。制動(dòng)盤可以制成實(shí)心的，而為了通風(fēng)散熱，可以在制動(dòng)盤的兩工作面之間鑄出通風(fēng)孔道。通風(fēng)的制動(dòng)盤在兩個(gè)制動(dòng)表面之間鑄有冷卻葉片。這種結(jié)構(gòu)使制動(dòng)盤鑄件顯著的增加了冷卻面積。車輪轉(zhuǎn)動(dòng)時(shí)，盤內(nèi)扇形葉片的選擇了空氣循環(huán)，有效的冷卻制動(dòng)。通常，實(shí)心制動(dòng)盤厚度為l0mm20mm，具有通風(fēng)孔道的制動(dòng)盤厚度取為20mm 50mm，但多采用20mm30mm。在本設(shè)計(jì)中選用通風(fēng)制動(dòng)盤式制動(dòng)盤，h取22mm。摩擦襯塊外半徑R2與內(nèi)半徑R1推薦摩擦襯塊外半徑R2與內(nèi)半徑R1的比值不大于1.5。若比值偏大，工作時(shí)襯塊的外緣與內(nèi)側(cè)圓周速度相差較多，磨損不均勻，接觸面積減少，最終將導(dǎo)致制動(dòng)力矩變化大。在本設(shè)計(jì)中取外半徑為R2=165mm，,則內(nèi)半徑R1=110mm。內(nèi)通軸直徑初選為65mm 摩擦襯塊工作面積A摩擦襯塊單位面積占有的車輛質(zhì)量在1.6kg/3.5kg/范圍內(nèi)選取，為72.32A158.2。在本設(shè)計(jì)中取襯塊的夾角為70。摩擦襯塊的工作面積A：，A取369。同步附著系數(shù)的選取通過對(duì)汽車的受力分析可知，制動(dòng)時(shí)前后輪同時(shí)抱死，對(duì)附著條件的利用，制動(dòng)時(shí)汽車的方向穩(wěn)定性等均有利，此時(shí)的前后輪制動(dòng)器制動(dòng)力Fu1和Fu2的關(guān)系曲線，稱為理想的前后輪制動(dòng)器制動(dòng)力分配曲線。在任何附著系數(shù)的路面上，前后輪同時(shí)抱死的條件是：前后輪制動(dòng)器制動(dòng)力之和等于附著力；并且前后輪制動(dòng)器制動(dòng)力分別等于各自的附著力，即： (3.1) (3.2) (3.3)其中：重力前后制動(dòng)力地面對(duì)前后輪法向反作用力前后制動(dòng)器的理想制動(dòng)力的分配關(guān)系式為 (3.4)其中L軸距a汽車質(zhì)心距前軸距離b汽車質(zhì)心距后軸距離附著系數(shù) 現(xiàn)在不少汽車的前后制動(dòng)器制動(dòng)力之比為一固定值，常用前制動(dòng)力與總制動(dòng)力之比來表明分配比例，稱為制動(dòng)器動(dòng)力分配系數(shù)，用表示，即： (3.5)式中Fu汽車制動(dòng)器總制動(dòng)力所以 (3.6)若用為一直線通過坐標(biāo)原點(diǎn)，且其斜率為： (3.7)將(3-4)代入(3-6得)因?yàn)樗O(shè)計(jì)的轎車制動(dòng)器為輕型轎車的盤式制動(dòng)器，而現(xiàn)代轎車的行使?fàn)顩r較好，特別是高級(jí)公路的高速要求，同步附著系數(shù)可選大些，在此，選取=0.7，由于已經(jīng)確定同步附著系數(shù)代入數(shù)據(jù)得分配系數(shù) =0.691所以 (3.8) (3.9) N (3.10)由(3-6，8，9，10)得 Fu1=4486.3N Fu2=9405.2N2. 存在問題及解決措施到目前為止，在論文的寫作中主要有以下幾個(gè)問題：1).對(duì)論文所涉及的知識(shí)認(rèn)識(shí)得不夠深刻，所以對(duì)命題的探討不夠深入。2).研究中引入的數(shù)據(jù)不夠，對(duì)相關(guān)問題的支撐程度不足。4).論文的各部分之間的銜接不夠強(qiáng)，有的地方缺少邏輯。導(dǎo)致上述問題主要有兩個(gè)原因，一是研究不夠深入，二是撰寫不夠嚴(yán)密。針對(duì)這兩個(gè)原因，解決方法有：.對(duì)論文所涉及的知識(shí)以及前人的研究成果理解程度需要更加深刻，在這個(gè)基礎(chǔ)上才能得到有深度的結(jié)論。.需要對(duì)已完成的內(nèi)容進(jìn)行多次審閱，從內(nèi)容、結(jié)構(gòu)及用語等方面給予調(diào)整。.對(duì)于寫作過程中遇到的具體難題要多向指導(dǎo)老師請(qǐng)求援助。3. 后期工作安排在往后的論文寫作中主要研究任務(wù)是在已完成的基礎(chǔ)上給予完善以及二維圖紙的繪制和三維建模，具體的方法是參閱更多的相關(guān)研究文章，尤其是研究較為完整系統(tǒng)的書籍，深度提取其成果，結(jié)合本文的研究方向與思路來引用，另外，論文的進(jìn)度方面，在初稿基礎(chǔ)上進(jìn)行修改，圖紙的繪制以及三維建模也要抓緊時(shí)間爭取在五月初完成論文終稿。指導(dǎo)教師簽字： 年 月 日畢業(yè)設(shè)計(jì)(論文)外文資料翻譯系 別： 機(jī)電信息系 專 業(yè)： 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 班 級(jí)： 姓 名： 學(xué) 號(hào)： 外文出處：International Journal of Engineering, Science and Technology Vol. 1, No. 1, 2009, pp. 254-271附 件： 1. 原文； 2. 譯文 2013年03月一個(gè)復(fù)雜的特征值分析與設(shè)計(jì)相結(jié)合的方法實(shí)驗(yàn)（DOE）研究盤式制動(dòng)器制動(dòng)尖叫摘要：本文提出了研究結(jié)合有限元模擬與統(tǒng)計(jì)回歸技術(shù)的制動(dòng)片上的盤式制動(dòng)器制動(dòng)尖叫的影響因素探討。復(fù)雜的特征值分析（CEA）已被廣泛用于在制動(dòng)系統(tǒng)模型預(yù)測的不穩(wěn)定頻率、有限元模型與實(shí)驗(yàn)?zāi)B(tài)試驗(yàn)的相關(guān)性。 “制動(dòng)器和制動(dòng)盤的幾何形狀之間的輸入輸出關(guān)系的構(gòu)建可以利用各種幾何配置預(yù)測盤式制動(dòng)器的尖叫。影響的各種因素，即；楊氏模量背板，背板厚度，槽，兩槽間的距離，槽的寬度和角度，槽所使用的設(shè)計(jì)研究實(shí)驗(yàn)（DOE）技術(shù)等。預(yù)測在數(shù)學(xué)模型的基礎(chǔ)上已開發(fā)的最有影響的因素驗(yàn)證，仿真實(shí)驗(yàn)證明了它的充分性。預(yù)測結(jié)果表明，制動(dòng)尖叫傾向可以通過增加的楊氏模量的背板和添加修改倒角形狀減少摩擦材料雙方的摩擦。通過引入槽結(jié)構(gòu)，制動(dòng)尖叫使用建模相結(jié)合的方法CEA和美國能源部被發(fā)現(xiàn)通過驗(yàn)證試驗(yàn)的統(tǒng)計(jì)學(xué)足夠。這種組合方式會(huì)有用到盤式制動(dòng)器的設(shè)計(jì)階段。關(guān)鍵詞：盤式制動(dòng)器的制動(dòng)尖叫，有限元分析，實(shí)驗(yàn)?zāi)B(tài)分析，實(shí)驗(yàn)設(shè)計(jì)1、引言：制動(dòng)器尖叫是因?yàn)槟Σ亮δ軌蛘T導(dǎo)的動(dòng)態(tài)不穩(wěn)定性引起的振動(dòng)引起的噪聲問題（Akay，2002）。制動(dòng)操作期間，墊和盤之間的摩擦力可以誘導(dǎo)系統(tǒng)中的動(dòng)態(tài)不穩(wěn)定性。通常制動(dòng)尖叫發(fā)生在1和20千赫之間的頻率范圍。尖叫聲是一個(gè)復(fù)雜的現(xiàn)象，部分原因是因?yàn)樗膹?qiáng)烈的依賴于許多參數(shù)，部分原因是因?yàn)檫@些機(jī)械相互作用在制動(dòng)系統(tǒng)。機(jī)械的相互作用被認(rèn)為是由于在摩擦界面接觸的非線性影響非常復(fù)雜。發(fā)生尖叫是間歇性的或隨機(jī)的。在一定的條件下，即使當(dāng)汽車是全新的，它也往往產(chǎn)生尖叫噪聲，以消除噪聲為目標(biāo)進(jìn)行廣泛的研究。然而，對(duì)噪聲的機(jī)理細(xì)節(jié)沒有完全理解。幾個(gè)理論已制定解釋制動(dòng)尖叫機(jī)制，和無數(shù)的研究已經(jīng)取得了不同程度的成功將其應(yīng)用到盤式制動(dòng)器的動(dòng)力學(xué)（金凱德等人。，2003）。不穩(wěn)定的發(fā)病原因已被歸因于不同的原因。一些主要的原因的變化與新的接觸點(diǎn)的速度摩擦特性（易卜拉欣，1994；歐陽等人。，1998；Shin等人。，2002）的變化、磁盤的相對(duì)取向和摩擦片的摩擦力修改導(dǎo)致（米爾納，1978）一種不穩(wěn)定性，事實(shí)上發(fā)現(xiàn)即使是一個(gè)恒定的摩擦系數(shù)（喬德哈里等人。，2001；chakrabotry等人，2002；馮瓦格納。等人。，2003；瓦格納等人，2004），最近的文獻(xiàn)回顧（金凱德等人。，2003；papinniemi等人。，2002）對(duì)報(bào)道的復(fù)雜性和制動(dòng)尖叫問題缺乏了解。雖然大部分的工作是尖叫的問題，它需要不斷的調(diào)查研究，完善預(yù)測制動(dòng)組件的有限元模型，給制動(dòng)器的設(shè)計(jì)工程師的合適的工具來設(shè)計(jì)安靜的制動(dòng)精度。還有的數(shù)值計(jì)算方法，用于研究這一問題，兩大類：（1）瞬態(tài)動(dòng)力學(xué)分析（Hu等人。，1999；布巴卡爾等人。，2006）（2）復(fù)特征值分析。經(jīng)常地，復(fù)特征值的方法是首選廣泛用于（萊爾斯，1989；Lee等人。，1998；Blaschke等人。，2000；拜爾等人。，2003；布巴卡爾等人。，2006；劉等人，2007；馬里奧。等人。，2008；戴等人。，2008）預(yù)測的制動(dòng)系統(tǒng)包括阻尼和接觸引起的尖叫傾向快速，它可以分析及其在不同運(yùn)行分析提供設(shè)計(jì)指導(dǎo)作用參數(shù)幾乎。對(duì)制動(dòng)系統(tǒng)的動(dòng)力學(xué)研究的許多研究人員試圖通過改變相關(guān)的因素減少制動(dòng)尖叫。例如（萊爾斯，1989）發(fā)現(xiàn)，短墊，阻尼，軟盤和較硬的背板可降低對(duì)比度惡化，同時(shí)更高的摩擦系數(shù)和磨損的摩擦材料容易尖叫。（李等人。，1998）報(bào)道，降低背板厚度導(dǎo)致接觸壓力分布均勻的改變，從而增加尖叫傾向。（胡等人。，1999）基于DOE分析發(fā)現(xiàn)，優(yōu)化設(shè)計(jì)是一個(gè)使用原來的手指長度，垂直槽，倒角盤墊，28毫米的厚度，和摩擦材料厚度10mm。（布魯克斯等人。，1993）發(fā)現(xiàn)，通過移動(dòng)活塞遠(yuǎn)離主導(dǎo)了通用電氣焊盤的系統(tǒng)不穩(wěn)定性。他們還報(bào)告該預(yù)測系統(tǒng)的不穩(wěn)定是由于TR anslational和旋轉(zhuǎn)盤的特別高的耦合模式的剛度值。從敏感性的研究，他們建議泰德，墊的有效長度減為一半，活塞MAS的SES，有效質(zhì)量，慣量和接地剛度盤和第二電路驅(qū)動(dòng)的剛度也有潛在的對(duì)盤剎車不穩(wěn)定。（Shin等人。，2002）已經(jīng)表明，阻尼墊和盤在導(dǎo)致不穩(wěn)定性方面是重要的。他們的分析也表明，證實(shí)了增加阻尼或盤或墊可能導(dǎo)致系統(tǒng)的不穩(wěn)定。（劉等人。，2007）發(fā)現(xiàn)，噪聲可以通過減小摩擦系數(shù)，增加該盤的剛度，使用的墊采用回阻尼材料和修改的剎車片的形狀等來降低。（Dai等人。，2008）研究結(jié)果表明，徑向槽焊盤的設(shè)計(jì)具有的不穩(wěn)定的模式數(shù)量最少，這意味著較小的傾向，尖叫。在本研究中，盤式制動(dòng)器尖叫的調(diào)查采用有限執(zhí)行復(fù)雜的特征值分析元軟件ABAQUS /標(biāo)準(zhǔn)。一個(gè)復(fù)雜的特征值的一個(gè)正實(shí)部被視為不穩(wěn)定的指示。通過有限元模擬可以提供指導(dǎo)，而將被審判和錯(cuò)誤的方法，以達(dá)到最佳的配置和也可能需要運(yùn)行多個(gè)計(jì)算密集型的分析制定的“輸入”的關(guān)系可能的預(yù)測。因此，在本研究中，通過復(fù)雜的特征值E F提出了一個(gè)新的方法結(jié)構(gòu)化分析與設(shè)計(jì)。該方法的目的是向最佳墊設(shè)計(jì)預(yù)測通過各種剎車片的幾何結(jié)構(gòu)的各種因素。本文的組織如下，在該領(lǐng)域在最近一段時(shí)期，它提出了一個(gè)詳細(xì)的文獻(xiàn)調(diào)查。從文學(xué)調(diào)查的主要目的是形成建立盤式制動(dòng)器的有限元模型的方法，該方法被提出并隨后采用實(shí)驗(yàn)?zāi)B(tài)分析驗(yàn)證。為了預(yù)測制動(dòng)尖叫是CEA的方法，然后對(duì)其用DOE方法進(jìn)行計(jì)算。還討論了測試開發(fā)的統(tǒng)計(jì)模型的充足的方法2、相關(guān)的有限元模型和組件盤式制動(dòng)系統(tǒng)由一個(gè)繞輪的軸線轉(zhuǎn)動(dòng)的圓盤，卡尺活塞組件，活塞SL IDE內(nèi)卡鉗被安裝到車輛的懸掛系統(tǒng)，和一對(duì)剎車片組成。當(dāng)液壓施加壓力，活塞被推壓在盤的內(nèi)墊同時(shí)卡尺卡在盤的外墊。圖1（a）顯示，在考慮汽車前制動(dòng)器有限元模型，使用ABAQUS建立有限元軟件包。在這項(xiàng)研究中采用的制動(dòng)模型是一個(gè)簡化的模型組成的兩個(gè)主要組成部分有助于尖叫：光盤和墊（圖1（b）。 （a）一個(gè)有限元模型 （b）簡化盤式制動(dòng)器模型圖1一個(gè)簡化的模型，本研究采用以下原因：1、 制動(dòng)尖叫的非線性分析，最重要的來源是盤之間的摩擦滑動(dòng)接觸墊。2、 仿真包括幾何簡化以減少CPU時(shí)間，讓更多的配置來計(jì)算。該盤是由鑄鐵、剎車盤副，由摩擦材料和背板，再次按下ST盤以產(chǎn)生摩擦力矩的緩慢的旋轉(zhuǎn)盤。摩擦材料是由有機(jī)摩擦材料和后面板用鋼。有限元網(wǎng)格生成我們19000固體元素。摩擦系數(shù)是摩擦接觸相互作用該盤和摩擦片材料的兩側(cè)之間定義。一個(gè)恒定的摩擦系數(shù)和恒定角該盤的速度是用于模擬目的。圖2給出的約束和載荷的焊盤。該盤是完全固定在四計(jì)數(shù)器的螺栓孔和焊盤的耳朵被限制只允許軸向位移NTS?？ㄣQ活塞組件不在盤式制動(dòng)系統(tǒng)的簡化模型定義內(nèi)，因此液壓壓力直接應(yīng)用于背板的內(nèi)墊和活塞和外墊之間的接觸區(qū)域和他游標(biāo)卡尺，它是假定每個(gè)墊力大小相等的 圖2約束和簡化的制動(dòng)系統(tǒng)加載驗(yàn)證的目的，主制動(dòng)部件，頻率響應(yīng)函數(shù)（FRF）在自由邊界條件下的每個(gè)組件與10mVN靈敏度和硬頭錘測量小的影響。一個(gè)輕小的加速度計(jì)的靈敏度達(dá)到10mVg，通過動(dòng)態(tài)信號(hào)分析儀的類型dewe-41-t-dsa測量加速度響應(yīng)。FRF測量記錄每個(gè)組件的SISO配置使用。然后，每個(gè)迪尤頻響函數(shù)使用軟件來識(shí)別模態(tài)參數(shù)，即；處理后的共振頻率，模態(tài)振型和阻尼值。圖3顯示了實(shí)驗(yàn)?zāi)B(tài)測試組件。圖3實(shí)驗(yàn)?zāi)B(tài)分析組件頻率測量盤上通過仿真模型計(jì)算出的自由邊界條件模式如表1所示。它可以觀察到的測量和模擬頻率具有良好的協(xié)議。圖4顯示模式有淋巴結(jié)直徑的轉(zhuǎn)子形狀。以類似的方式，在墊的參數(shù)估計(jì)和基于實(shí)測數(shù)據(jù)表2所示，測量和模擬頻率也具有良好的協(xié)議。圖5顯示模式形狀的墊。表1在自由邊界條件下的轉(zhuǎn)子的模態(tài)結(jié)果振形實(shí)驗(yàn)頻率（Hz）有限元分析的頻率（Hz）差異（%）第二彎曲122013036.8第三彎曲255126363.3第四彎曲400341082.6第五彎曲57745591-3.1第六彎曲78737790-1第七彎曲900892092.2表2. 在自由邊界條件的板模態(tài)結(jié)果振形實(shí)驗(yàn)頻率（Hz）有限元分析的頻率（Hz）差異（%）第一彎曲305132315.8第二彎曲84598381-1 第二節(jié)經(jīng)型 (1303Hz) 第三節(jié)經(jīng)型(2636 Hz) 第四節(jié)經(jīng)型(4108 Hz) 第五節(jié)經(jīng)型(5591 Hz)圖4. 在自由邊界條件下的轉(zhuǎn)子模態(tài) 第六節(jié)經(jīng)型(7790 Hz) 第七節(jié)經(jīng)型(9209 Hz) 第一彎曲模態(tài)(3231 Hz) 第二彎曲模態(tài)(8381 Hz)圖5. 在自由邊界條件的板模式的形狀畢業(yè)設(shè)計(jì)(論文)開題報(bào)告題目：某中級(jí)轎車前輪制動(dòng)器設(shè)計(jì) 系 別 機(jī)電信息系 專 業(yè) 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 班 級(jí) 姓 名 學(xué) 號(hào) 導(dǎo) 師 2012年12月26日一、畢業(yè)設(shè)計(jì)（論文）綜述1. 題目背景制動(dòng)器在車輛安全性方面起著相當(dāng)重要的作用，直接影響到車輛的正常行駛，因而制動(dòng)器及其零部件的安全可靠性倍受關(guān)注1。本課題根據(jù)別克君威轎車的主要行駛參數(shù)和運(yùn)動(dòng)要求，對(duì)前輪制動(dòng)器進(jìn)行整體結(jié)構(gòu)設(shè)計(jì)，然后在三維軟件環(huán)境下實(shí)現(xiàn)對(duì)制動(dòng)器虛擬模型的建立，最終實(shí)現(xiàn)汽車良好的制動(dòng)性能，保證其安全性和操控性。 2. 研究意義從汽車誕生時(shí)起，車輛制動(dòng)系統(tǒng)在車輛的安全方面就扮演著至關(guān)重要的角色。制動(dòng)器是車輛的關(guān)鍵部件之一,其性能的好壞直接影響整車性能的優(yōu)劣,因此,制動(dòng)器的設(shè)計(jì)在整車設(shè)計(jì)中顯得相當(dāng)重要2。近年來，隨著車輛技術(shù)的進(jìn)步和汽車行駛速度的提高，這種重要性表現(xiàn)得越來越明顯。眾多的汽車工程師在改進(jìn)汽車制動(dòng)性能的研究中傾注了大量的心血。目前關(guān)于汽車制動(dòng)的研究在制動(dòng)器方面取得了較大成果，包括制動(dòng)控制的理論和方法，以及采用新的技術(shù)3。3國內(nèi)外相關(guān)研究情況3.1制動(dòng)系統(tǒng)的功用制動(dòng)系統(tǒng)的功用實(shí)施汽車以適當(dāng)?shù)臏p速度行駛至停車；在下坡行駛時(shí)，是汽車保持適當(dāng)?shù)姆€(wěn)定的車速；是汽車可靠的停在原地或坡道上4。3.2制動(dòng)器的分類目前，汽車所用的制動(dòng)器幾乎都是摩擦式的，可分為鼓式和盤式兩大類。具體見圖1，圖2。 圖1 鼓式制動(dòng)器示意圖 圖2 盤式制動(dòng)器鼓式制動(dòng)器根據(jù)其結(jié)構(gòu)都不同，又分為雙向自增力蹄式制動(dòng)器、雙領(lǐng)蹄式制動(dòng)器、領(lǐng)從蹄式制動(dòng)器、雙從蹄式制動(dòng)器5.6。盤式制動(dòng)器根據(jù)摩擦副中的固定摩擦元件的結(jié)構(gòu)來分，分為鉗盤式制動(dòng)器和全盤式制動(dòng)器兩大類。3.3鼓式制動(dòng)器鼓式制動(dòng)是早期設(shè)計(jì)的制動(dòng)系統(tǒng)，其剎車鼓的設(shè)計(jì)1902年就已經(jīng)使用在馬車上了，直到1920年左右才開始在汽車工業(yè)廣泛應(yīng)用?，F(xiàn)在鼓式制動(dòng)器的主流是內(nèi)張式，它的制動(dòng)塊(剎車蹄)位于制動(dòng)輪內(nèi)側(cè)，在剎車的時(shí)候制動(dòng)塊向外張開，摩擦制動(dòng)輪的內(nèi)側(cè)，達(dá)到剎車的目的。鼓式制動(dòng)器的旋轉(zhuǎn)元件是制動(dòng)鼓，固定元件是制動(dòng)蹄。制動(dòng)時(shí)制動(dòng)蹄在促動(dòng)裝置作用下向外旋轉(zhuǎn)，外表面的摩擦片壓靠到制動(dòng)鼓的內(nèi)圓柱面上，對(duì)鼓產(chǎn)生制動(dòng)摩擦力矩7.8。 鼓式制動(dòng)器因其具有制動(dòng)力矩大,制動(dòng)性能好,有較好的密封性等優(yōu)點(diǎn)。但也存在不少缺點(diǎn):蹄式制動(dòng)器都在不同程度上利用了磨擦增勢作用來保證一定的制動(dòng)效能,而在使用中,因磨擦系數(shù)并不穩(wěn)定,所以制動(dòng)效能的穩(wěn)定性較差9。3.4盤式制動(dòng)器盤式制動(dòng)器又稱為碟式制動(dòng)器，顧名思義是取其形狀而得名。主要零部件有制動(dòng)盤、分泵、制動(dòng)鉗、油管等。盤式制動(dòng)器是由摩擦襯塊從兩側(cè)夾緊與車輪共同旋轉(zhuǎn)的制動(dòng)盤來產(chǎn)生制動(dòng)的。浮動(dòng)鉗式盤式制動(dòng)器的制動(dòng)鉗體可作軸向平行滑動(dòng)，油缸設(shè)置在制動(dòng)盤的內(nèi)側(cè)，兩個(gè)制動(dòng)塊分裝在制動(dòng)盤的內(nèi)外側(cè)，制動(dòng)塊是由鍛壓成形的金屬背板和摩擦襯塊構(gòu)成，兩者直接牢固地壓嵌、鉚接或粘接在一起。制動(dòng)時(shí)高壓油從制動(dòng)鉗上的進(jìn)油孔進(jìn)入油缸后，在油液壓力作用下，推動(dòng)活塞前進(jìn)使其內(nèi)側(cè)的摩擦襯塊壓在制動(dòng)盤上，而反作用力則推動(dòng)制動(dòng)鉗體連同固定于其上的外側(cè)制動(dòng)塊向與活塞前進(jìn)方向的反方向滑動(dòng)并壓向制動(dòng)盤的另一側(cè)，直到兩側(cè)的制動(dòng)塊受力均等為止，在很短的時(shí)間內(nèi)制動(dòng)力矩便使制動(dòng)盤停止轉(zhuǎn)動(dòng)，從而使汽車停下來10。盤式制動(dòng)器散熱快、重量輕、構(gòu)造簡單、調(diào)整方便。特別是高負(fù)載時(shí)耐高溫性能好，制動(dòng)效果穩(wěn)定，而且不怕泥水侵襲，能在冬季和惡劣路況下行車。很多轎車采用的盤式制動(dòng)器有平面式制動(dòng)盤、打孔式制動(dòng)盤以及劃線式制動(dòng)盤，其中劃線式制動(dòng)盤的制動(dòng)效果和通風(fēng)散熱能力均比較好。盤式制動(dòng)器沿制動(dòng)盤軸向施力，制動(dòng)軸不受彎矩，徑向尺寸小，制動(dòng)性能穩(wěn)定11。相比較而言鼓式制動(dòng)器的制動(dòng)效能和散熱性都要差許多，鼓式制動(dòng)器的制動(dòng)力穩(wěn)定性差，在不同路面上制動(dòng)力變化很大，不易于掌控。而由于散熱性能差，在制動(dòng)過程中會(huì)聚集大量的熱量。制動(dòng)塊和輪鼓在高溫影響下較易發(fā)生極為復(fù)雜的變形，容易產(chǎn)生制動(dòng)衰退和振抖現(xiàn)象，引起制動(dòng)效率下降12.13.14。盤式制動(dòng)器一般無摩擦助勢作用，因而制動(dòng)器效能受摩擦系數(shù)的影響較小，即效能較穩(wěn)定；浸水后效能降低較少，而且只須經(jīng)一兩次制動(dòng)即可恢復(fù)正常；在輸出制動(dòng)力矩相同的情況下，尺寸和質(zhì)量一般較??；制動(dòng)盤沿厚度方向的熱膨脹量極小，不會(huì)象制動(dòng)鼓的熱膨脹那樣使制動(dòng)器間隙明顯增加而導(dǎo)致制動(dòng)踏板行程過大；較容易實(shí)現(xiàn)間隙自動(dòng)調(diào)整，其他保養(yǎng)修理作業(yè)也較簡便15。根據(jù)我們汽車制動(dòng)器的技術(shù)條件和市場情況，對(duì)于兩種制動(dòng)形式的比較，得出結(jié)論，本轎車前輪應(yīng)采用盤式制動(dòng)，以達(dá)到良好的制動(dòng)性能和操控性能。3.5制動(dòng)系統(tǒng)發(fā)展展望歐、美、日等發(fā)達(dá)國家已把盤式制動(dòng)器作為標(biāo)準(zhǔn)件裝備在多級(jí)別的轎車、客車、中型、重型汽車上。我國的轎車、微型車已廣泛應(yīng)用液壓盤式制動(dòng)器,開發(fā)應(yīng)用盤式制動(dòng)器是現(xiàn)代汽車的發(fā)展趨勢之一16?，F(xiàn)代汽車盤式制動(dòng)器的研究和開發(fā)應(yīng)注重的問題主要是, 提高制動(dòng)器的制動(dòng)效能、防止塵污和銹蝕, 減輕重量、簡化結(jié)構(gòu)、降低成本, 電子報(bào)警和智能化系統(tǒng)的發(fā)展, 實(shí)用性更強(qiáng)與壽命更長17。液壓制動(dòng)現(xiàn)在已經(jīng)是非常成熟的技術(shù),隨著汽車技術(shù)的進(jìn)步,一些提高制動(dòng)性能的技術(shù)如防抱死制動(dòng)系統(tǒng)、驅(qū)動(dòng)防滑控制系統(tǒng)、電子穩(wěn)定性控制程序等已經(jīng)融人到制動(dòng)系統(tǒng)當(dāng)中,這就使得制動(dòng)系統(tǒng)結(jié)構(gòu)復(fù)雜化,增加了液壓回路泄漏的可能以及裝配、維修的難度。制動(dòng)系統(tǒng)要求結(jié)構(gòu)簡單,功能全面,可靠性高。因此電子技術(shù)的應(yīng)用是大勢所趨。目前制動(dòng)系統(tǒng)的各個(gè)組成部分,都不同程度地實(shí)現(xiàn)了電子化。綜上所述，現(xiàn)代汽車制動(dòng)控制技術(shù)正朝著電子制動(dòng)控制方向發(fā)展。全電制動(dòng)控制因其巨大的優(yōu)越性，將取代傳統(tǒng)的以液壓為主的傳統(tǒng)制動(dòng)控制系統(tǒng)18。二、本課題研究的主要內(nèi)容和擬采用的研究方案、研究方法或措施1. 主要內(nèi)容1.1 制動(dòng)器簡介1.2 制動(dòng)器的方案分析及確定 1.2.1 盤式制動(dòng)器1.2.2 鼓式制動(dòng)器1.3 盤式制動(dòng)器零部件結(jié)構(gòu)方案分析1.3.1 固定鉗式 1.3.2 浮動(dòng)鉗式 1.4 制動(dòng)器主要參數(shù)確定 1.4.1制動(dòng)盤制定1.4.2制動(dòng)盤厚度1.4.3摩擦襯塊外半徑與內(nèi)半徑1.4.4制動(dòng)襯塊工作面積A 1.5 制動(dòng)器的設(shè)計(jì)計(jì)算 1.5.1 制動(dòng)器制動(dòng)力矩計(jì)算 1.5.2 制動(dòng)盤設(shè)計(jì) 1.5.3 制動(dòng)鉗設(shè)計(jì) 1.6 制動(dòng)操縱系統(tǒng)的選型 1.6.1制動(dòng)驅(qū)動(dòng)機(jī)構(gòu)的選型1.6.2分路系統(tǒng)的選型1.7液壓制動(dòng)操縱系統(tǒng)整體的設(shè)計(jì)1.7.1液壓操縱系統(tǒng)參數(shù)的設(shè)計(jì)1.7.2制動(dòng)主缸設(shè)計(jì)1.7.3真空助力器的設(shè)計(jì)計(jì)算1.7.4踏板機(jī)構(gòu)設(shè)計(jì)1.8制動(dòng)性能的校核 1.8.1制動(dòng)距離與制動(dòng)減速度 1.8.2同步附著系數(shù) 1.8.3最大駐坡度2.采用的研究方案、研究方法或措施 2.1研究方案 （1）了解汽車制動(dòng)系統(tǒng)的現(xiàn)狀，熟悉其發(fā)展?fàn)顩r、詳細(xì)構(gòu)造和工作原理； （2）根據(jù)別克君威GS2.0T轎車的主要參數(shù)，對(duì)其前輪制動(dòng)器進(jìn)行結(jié)構(gòu)設(shè)計(jì)，實(shí)現(xiàn)汽車的制功能并滿足操控性能； （3）運(yùn)用AutoCAD軟件繪制制動(dòng)器總裝配圖以及主要部件的零部件； （4）運(yùn)用三維設(shè)計(jì)軟件，對(duì)制動(dòng)器的主要部件進(jìn)行三維建模與裝配。 2.2本次設(shè)計(jì)別克君威GS2.0T轎車的基本參數(shù)見表1.1表1.1 基本參數(shù)排量2.0整備質(zhì)量1650 kg最高車速180 km/h軸距2737 mm前輪輪距1585 mm后輪輪距1587 mm最大功率162 kw最大功率轉(zhuǎn)速5300 r/min最大扭矩350 Nm最大扭矩轉(zhuǎn)速2000-4000 r/min三、本課題研究的重點(diǎn)及難點(diǎn)，前期已開展工作1重點(diǎn)及難點(diǎn)（1）重點(diǎn)掌握制動(dòng)器的動(dòng)力傳遞路線及其結(jié)構(gòu)設(shè)計(jì)；（2）了解制動(dòng)操縱機(jī)構(gòu)的功能與要求、構(gòu)造形式及操縱原理；（3）制動(dòng)器主要零部件的設(shè)計(jì)計(jì)算（4）運(yùn)用三維軟件建立制動(dòng)器的三維模型并進(jìn)行裝配。2. 前期已開展工作 在撰寫開題報(bào)告之前已在圖書館等查閱了大量關(guān)于汽車制動(dòng)器方面的書籍、期刊和手冊(cè)，并且在互聯(lián)網(wǎng)上搜索了一些汽車制動(dòng)器及其零部件的視頻、圖片和文字等信息，通過進(jìn)行了這些前期工作，我對(duì)汽車制動(dòng)器的功用、結(jié)構(gòu)和工作原理都有了進(jìn)一步的了解和認(rèn)識(shí)，相信能成功地完成這次畢業(yè)設(shè)計(jì)。四、完成本課題的工作方案及進(jìn)度計(jì)劃第1-3周：消化課題題目，搜集資料，明確設(shè)計(jì)的任務(wù)及要求，撰寫開題報(bào)告；第4周：熟悉AutoCAD軟件和確定設(shè)計(jì)方案；第5-8周：設(shè)計(jì)計(jì)算制動(dòng)器的主要零部件，熟悉三維建模軟件；第9-11周：應(yīng)用AutoCAD軟件繪制制動(dòng)器總裝配圖以及主要部件的零件圖；第11-13周：運(yùn)用三維設(shè)計(jì)軟件，對(duì)制動(dòng)器主要部件進(jìn)行三維建模與裝配；第14-15周：進(jìn)行畢業(yè)設(shè)計(jì)總結(jié)，編寫畢業(yè)設(shè)計(jì)論文，并作好答辯的準(zhǔn)備。5 指導(dǎo)教師意見（對(duì)課題的深度、廣度及工作量的意見） 指導(dǎo)教師： 年 月 日 6 所在系審查意見： 系主管領(lǐng)導(dǎo)： 年 月 日參考文獻(xiàn)1 王滿祥,蘇小平,王東方,汽車浮鉗式盤式制動(dòng)器有限元分析 A 機(jī)械設(shè)計(jì)與制造 2009.32 陳效華,昌慶齡,制動(dòng)器參數(shù)化設(shè)計(jì)系統(tǒng)概念設(shè)計(jì) A 南京理工大學(xué)學(xué)報(bào) 2001.83 D. V. Tretyak , V. G. Ivanov Study of hysteresis of disk brake mechanism for heavy-duty vehicles J Belarus National Technical University Journal of Friction and Wear Springer Journal4 王望予 汽車設(shè)計(jì) M 機(jī)械工業(yè)出版社2004.85 張文春.汽車?yán)碚揗.北京.機(jī)械工業(yè)出版社.2005：70836 王國權(quán),龔國慶 汽車設(shè)計(jì)課程設(shè)計(jì)指導(dǎo)書 M 機(jī)械工業(yè)出版社 2009.117 劉惟信.汽車設(shè)計(jì)M.北京.清華大學(xué)出版社.2001：1582008 張洪欣.汽車設(shè)計(jì)M.北京.機(jī)械工業(yè)出版社.1999：1061269 章 彪 淺析汽車用制動(dòng)器 A 科技創(chuàng)新導(dǎo)報(bào) 2011.1810 趙 波,范平清 盤式制動(dòng)器的制動(dòng)效能和接觸應(yīng)力分析 A 機(jī)械設(shè)計(jì)與制造 2011.911 A. Belhocine , M. Bouchetara Thermal behavior of full and ventilated disc brakes of vehicles J Journal of Mechanical Science and Technology12V. Sergienko , M. Tseluev Effect of operation parameters on thermal loading of wet brake discs. J Part 1. Problem formulation and methods of study Journal of Friction and Wear13臧杰 閻巖 汽車構(gòu)造第2版 M 機(jī)械工業(yè)出版社2010.814吳際璋.汽車構(gòu)造M.北京.人民交通出版社.2004: 356815 潘公宇 盤式制動(dòng)器的特點(diǎn)及其應(yīng)用前景 J 試驗(yàn)與研究16張國強(qiáng),車輛制動(dòng)系統(tǒng)的發(fā)展現(xiàn)狀及趨勢淺析 A 農(nóng)業(yè)與技術(shù) 2009年6月17鄭蘭霞, 張俊海, 陳艷艷 盤式制動(dòng)器在現(xiàn)代汽車上的應(yīng)用與發(fā)展分析 B 農(nóng)業(yè)裝備與車輛工程 2007.918楊達(dá) 汽車制動(dòng)系統(tǒng)展望 J 質(zhì)量論談5 5MultiCraft International Journal of Engineering, Science and Technology Vol. 1, No. 1, 2009, pp. 254-271 INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY www.ijest- 2009 MultiCraft Limited. All rights reserved A combined approach of complex eigenvalue analysis and design of experiments (DOE) to study disc brake squeal M. Nouby 1* , D. Mathivanan 2* , K. Srinivasan 1 1 AU/FRG Institute for CAD/CAM, Anna University, Chennai-600025, India 2 Director of CAE Infotech, Chennai-600020, India E-mails:( (M. Nouby), (D. Mathivanan); * Corresponding authors) Abstract This paper proposes an approach to investigate the influencing factors of the brake pad on the disc brake squeal by integrating finite element simulations with statistical regression techniques. Complex eigenvalue analysis (CEA) has been widely used to predict unstable frequencies in brake systems models. The finite element model is correlated with experimental modal test. The input-output relationship between the brake squeal and the brake pad geometry is constructed for possible prediction of the squeal using various geometrical configurations of the disc brake. Influences of the various factors namely; Youngs modulus of back plate, back plate thickness, chamfer, distance between two slots, slot width and angle of slot are investigated using design of experiments (DOE) technique. A mathematical prediction model has been developed based on the most influencing factors and the validation simulation experiments proved its adequacy. The predicted results show that brake squeal propensity can be reduced by increasing Youngs modulus of the back plate and modifying the shape of friction material by adding chamfer on both sides of friction material and by introducing slot configurations. The combined approach of modeling brake squeal using CEA and DOE is found to be statistically adequate through verification trials. This combined approach will be useful in the design stage of the disc brake. Keywords: Disc brake squeal, finite element analysis, experimental modal analysis, design of experiments 1. Introduction Brake squeal is a noise problem caused by vibrations induced by friction forces that can induce a dynamic instability (Akay, 2002). During the braking operation, the friction between the pad and the disc can induce a dynamic instability in the system. Usually brake squeal occurs in the frequency range between 1 and 20 kHz. Squeal is a complex phenomenon, partly because of its strong dependence on many parameters and, partly, because of the mechanical interactions in the brake system. The mechanical interactions are considered to be very complicated because of nonlinear contact effects at the friction interface. The occurrence of squeal is intermittent or even random. Under certain conditions, even when the vehicle is brand new, it often generates squeal noise, which has been extensively studied with the goal of eliminating the noise. However, mechanistic details of squeal noise are not yet fully understood (Joe et al., 2008). Several theories have been formulated to explain the mechanisms of brake squeal, and numerous studies have been made with varied success to apply them to the dynamics of disc brakes (Kinkaid et al., 2003). The reason for the onset of instability has been attributed to different reasons. Some of the major reasons are the change of the friction characteristic with the speed of the contact points (Ibrahim, 1994; Ouyang et al., 1998; Shin et al., 2002) the change of the relative orientation of the disk and the friction pads leading to a modification of the friction force (Millner, 1978), and a flutter instability which is found even with a constant friction coefficient (Chowdhary et al., 2001; Chakrabotry et al., 2002; Von Wagner et al., 2003; Von Wagner et al., 2004). In fact, recent literature reviews (Kinkaid et al., 2003; Papinniemi et al., 2002) have reported on the complexity and lack of understanding of the brake squeal problem. Though much work was done on the issue of squeal, it requires continuous study and investigation to refine the prediction accuracy of finite element models of brake assemblies to give brake design engineers appropriate tools to design quiet brakes. There are two main categories of numerical methods that are used to study this problem: (1) transient dynamic analysis (Hu et al., Nouby et al. / International Journal of Engineering, Science and Technology, Vol. 1, No. 1, 2009, pp. 254-271 255 1999; AbuBakar et al., 2006) and (2) complex eigenvalue analysis. Currently, the complex eigenvalue method is preferred and widely used (Liles, 1989; Lee et al., 1998; Blaschke et al., 2000; Bajer et al., 2003; AbuBakar et al., 2006; Liu et al., 2007; Mario et al., 2008; Dai et al., 2008) in predicting the squeal propensity of the brake system including damping and contact due to the quickness with which it can be analysed and its usefulness in providing design guidance by analysing with different operating parameters virtually. Many researchers in their studies on the dynamics of brake system tried to reduce squeal by changing the factors associated with the brake squeal. For example (Liles, 1989) found that shorter pads, damping, softer disc and stiffer back plate could reduce squeal whilst in contrast, higher friction coefficient and wear of the friction material were prone to squeal. (Lee et al., 1998) reported that reducing back plate thickness led to less uniform of contact pressure distributions and consequently increasing the squeal propensity. (Hu et al., 1999) based on the DOE analysis found that the optimal design was the one that used the original finger length, the vertical slot, the chamfer pad, the 28mm thickness of disc, and the 10mm thickness of friction material. (Brooks et al., 1993) found that by shifting the pistons away from the leading edge of the pads the system could destabilise. They also reported that the predicted unstable system was due to the coupling of translational and rotational modes of the disc particularly at high values of pad stiffness. From the sensitivity studies, they suggested that the effective half length of the pad, the piston masses, the effective mass, inertia and grounding stiffness of the disc and the second circuit actuation stiffness also have potential on the disc brake instability. (Shin et al., 2002) have shown that the damping of the pad and the disc were important in reducing instability. Their analysis also has shown and confirmed that increasing damping of either the disc or the pad alone could potentially destabilise the system. (Liu et al., 2007) found that the squeal can be reduced by decreasing the friction coefficient, increasing the stiffness of the disc, using damping material on the back of the pads and modifying the shape of the brake pads. (Dai et al., 2008) have shown that the design of the pads with a radial chamfer possesses the least number of unstable modes, which implies lesser tendency towards squeal. In the present study, an investigation of disc brake squeal is done by performing complex eigenvalue analysis using finite element software ABAQUS /standard. A positive real part of a complex eigenvalue is being seen as an indication of instability. Though the FE simulations can provide guidance, it will rather be trial-and-error approach to arrive at an optimal configuration and also one may need to run many number of computationally intensive analyses to formulate the input-out relationships for possible prediction. Hence, in the present investigation, a novel approach is proposed by integrating the complex eigenvalue FE analyses with structured DOE. The proposed approach is aimed towards prediction of optimal pad design through the various factors of the brake pad geometrical construction. The paper is organised as follows, it presents a detailed literature survey in this field in the recent period. From the literature survey the main objectives were formed. Methodology to develop FE model of the disc brake is presented and it was subsequently validated using experimental modal analysis. The CEA approach is presented in order to predict brake squeal. Then DOE approach for soft computing is presented. Also a methodology to test the adequacy of the developed statistical model is discussed. 2. Finite element model and component correlation A disc brake system consists of a disc that rotates about the axis of a wheel, a caliperpiston assembly where the piston slides inside the caliper that is mounted to the vehicle suspension system, and a pair of brake pads. When hydraulic pressure is applied, the piston is pushed forward to press the inner pad against the disc and simultaneously the outer pad is pressed by the caliper against the disc. Figure 1 (a) shows the finite element model of the car front brake under consideration, built using the ABAQUS finite element software package. The brake model used in this study is a simplified model consisting of the two main components contributing to squeal: the disc and the pad (Figure 1(b). (a) (b) Figure 1. Finite element models of a (a) realistic (b) simplified disc brake model Nouby et al. / International Journal of Engineering, Science and Technology, Vol. 1, No. 1, 2009, pp. 254-271 256 A simplified model was used in this study for the following reasons: 1. For brake squeal analysis, the most important source of nonlinearity is the frictional sliding contact between the disc and the pads. 2. The simulation includes geometry simplifications to reduce CPU time, allowing far more configurations to be computed. The disc is made of cast iron. The pair of brake pads, which consist of friction material and back plates, are pressed against the disc in order to generate a friction torque to slow the disc rotation. The friction material is made of an organic friction material and the back plates are made of steel. The FE mesh is generated using 19,000 solid elements. The friction contact interactions are defined between both sides of the disc and the friction material of the pads. A constant friction coefficient and a constant angular velocity of the disc are used for simulation purposes. Figure 2 presents the constraints and loadings for the pads and disc assembly. The disc is completely fixed at the four counter-bolt holes and the ears of the pads are constrained to allow only axial movements. The caliperpiston assembly is not defined in the simplified model of the disc brake system, hence the hydraulic pressure is directly applied to the back plates at the contact regions between the inner pad and the piston and between the outer pad and the caliper, and it is assumed that an equal magnitude of force acts on each pad. Figure 2. Constraints and loading of the simplified brake system For the purpose of validation, the main brake components, Frequency Response Functions (FRFs) were measured at free-free boundary conditions by exciting each component with a small impact hammer with sensitivity of 10mV/N and a hard tip. The acceleration response was measured with a light small accelerometer with sensitivity of 10mV/g through Dynamic Signal Analyzer type DEWE-41-T-DSA. FRF measurements were recorded for each component using SISO configurations. Then, the FRFs were processed using DEWE FRF software in order to identify the modal parameters, namely; resonance frequencies, modal shapes and damping values. Figure 3 shows the experimental modal test components. Figure 3. Experimental Modal Analysis Components The frequencies measured on the disc and calculated by the simulated model for modes with free-free boundary conditions are shown in table 1. It can be observed that the measured and simulated frequencies are in good agreement. Figure 4 shows the mode shapes of rotor with nodal diameters. In a similar way, the parameters for the pads are estimated based on the measured data indicated in Table 2. The measured and simulated frequencies are in good agreement. Figure 5 shows the mode shapes of the pad. Nouby et al. / International Journal of Engineering, Science and Technology, Vol. 1, No. 1, 2009, pp. 254-271 257 Table 1. Modal results of the rotor at free-free boundary conditions Mode shape Experimental Frequency (Hz) FEA Frequency(Hz) Differences (%) 2 nd bending 1220 1303 6.8 3 rd bending 2551 2636 3.3 4 th bending 4003 4108 2.6 5 th bending 5774 5591 -3.1 6 th bending 7873 7790 -1 7 th bending 9008 9209 2.2 Table 2. Modal results of the pad at free-free boundary conditions Mode shape Experimental Frequency (Hz) FEA Frequency(Hz) Differences (%) 1 st bending 3051 3231 5.8 2 nd bending 8459 8381 -1 2 nd Nodal Diameter Mode (1303Hz) 3 rd Nodal Diameter Mode (2636 Hz) 4 th Nodal Diameter Mode (4108 Hz) 5 th Nodal Diameter Mode (5591 Hz) Figure 4. Mode shapes of the rotor at free-free boundary conditions Nouby et al. / International Journal of Engineering, Science and Technology, Vol. 1, No. 1, 2009, pp. 254-271 258 6 th Nodal Diameter Mode (7790 Hz) 7 th Nodal Diameter Mode (9209 Hz) Figure 4 (contd). Mode shapes of the rotor at free-free boundary conditions 1 st Bending Mode (3231 Hz) 2 nd Bending Mode (8381 Hz) Figure 5. Mode shapes of the pad at free-free boundary conditions. 3. Complex eigenvalue analysis The complex eigenvalue analysis (CEA) has been widely used by researchers. It deals with computation of system eigenvalues which are prove to be complex valuated functions in the general case because friction causes the stiffness matrix to be asymmetric. The real and imaginary parts of the complex eigenvalues are, respectively, responsible for the stability and for the frequency of the corresponding modes. This method was first used on lumped models (Kinkaid et al., 2003; Ibrahim, 1994). Then, improvements in computer systems have made it possible to perform analyses on finite element (FE) models (Liles, 1989; Lee et al., 1998; Blaschke et al., 2000; Bajer et al., 2003; AbuBakar et al., 2006; Liu et al., 2007; Mario et al., 2008; Dai et al., 2008). In order to perform the complex eigenvalue analysis using ABAQUS (Bajer et al, 2003), four main steps are required as follows: (1) nonlinear static analysis for the application of brake pressure; (2) nonlinear static analysis to impose a rotational velocity on the disc; (3) normal mode analysis to extract the natural frequency to find the projection subspace; and (4) complex eigenvalue analysis to incorporate the effect of friction coupling. The governing equation of the system is: 0=+ KuuCuM (1) Where M, C and K are respectively the mass, damping and stiffness matrices, and u is the displacement vector. Because of friction, the stiffness matrix has specific properties: FS KKK += (2) Where S K is the structural stiffness matrix, F K the asymmetrical friction induced stiffness matrix and the friction coefficient. The governing equation can be rewritten as: 0)( 2 =+ KCM (3) Nouby et al. / International Journal of Engineering, Science and Technology, Vol. 1, No. 1, 2009, pp. 254-271 259 Where, is the eigenvalue and is the corresponding eigenvector. Both eigenvalues and eigenvectors may be complex. In order to solve the complex eigenproblem, this system is symmetrized by ignoring the damping matrix C and the asymmetric contributions to the stiffness matrix K. Then this symmetric eigenvalue problem is solved to find the projection subspace. The N eigenvectors obtained from the symmetric eigenvalue problem are expressed in a matrix as ,., 21 N . Next, the original matrices are projected onto the subspace of N eigenvectors ,.,., 2121 * N T N MM = (4a) ,.,., 2121 * N T N CC = (4b) and ,.,., 2121 * N T N KK = (4c) Then the projected complex eigenproblem becomes 0)( *2 =+ KCM (5) Finally, the complex eigenvectors of the original system can be obtained by k N k * 21 ,., = (6) Detailed description of the formulation and the algorithm are presented by Sinou et al. (2003). The eigenvalues and the eigenvectors of Eq. (3) may be complex, consisting of both a real and imaginary part. For under damped systems the eigenvalues always occur in complex conjugate pairs. For a particular mode the eigenvalue pair is iii i = 2,1 (7) Where, i and i are the damping coefficient (the real part) and damped natural frequency (the imaginary part) describing damped sinusoidal motion. The motion for each mode can be described in terms of the complex conjugate eigenvalue and eigenvector. A positive damping coefficient causes the amplitude of oscillations to increase with time. Therefore the system is not stable when the damping coefficient is positive. By examining the real part of the system eigenvalues the modes that are unstable and likely to produce squeal are revealed. An extra term, damping ratio, is defined as /2 . If the damping ratio is negative, the system becomes unstable, and vice versa. 3.1. Complex eigenvalue analysis (CEA) results Since friction is the main cause of instability, which causes the stiffness matrix in Eq. (3) to be asymmetric, complex eigenvalue analysis has been undertaken to assess the brake stability as the friction coefficient values. It was observed that high values for this parameter tend to facilitate two modes merging to form an unstable complex mode. In addition, an increase in the friction coefficient leads to an increase in the unstable frequency. Figure 6 shows the results of a complex eigenvalue analysis with variation of the friction coefficient () between 0.2 and 0.6. As predicted in the complex eigenvalue analysis, as the friction coefficient further increases, real parts of eigenvalues, the values that can be used to gauge the degree of instability of a complex mode, increase further, as well, and more unstable modes may emerge. This is because the higher coefficient of friction causes the variable frictional forces to be higher resulting in the tendency to excite greater number of unstable modes. In the past, a friction coefficient of 0.35 was typical. However, brake compounds today possess coefficient of friction that is 0.45 or higher, which increases the likelihood of squeal. This poses a greater challenge for brake designer to develop a quiet brake system. In an earlier work (Nouby et al., 2009), an attempt was made using parametric study to reduce squeal at 12 kHz. Based on the earlier study, a decision was taken to understand the effects of influencing variables of squeal at 6.2 kHz using DOE. Nouby et al. / International Journal of Engineering, Science and Technology, Vol. 1, No. 1, 2009, pp. 254-271 260 Figure 6. Results of CEA with variation of , and unstable mode at interested Frequency (6.2 kHz) 4. Methodology Human made products or processes can be treated like a system, if it produces a set of responses for a given set of inputs. Disc brake system can also be treated like a system as shown in Figure 7. Some systems like disc brake system produce unwanted outputs namely squeal for a set of inputs parameters. The present study was aimed at establishing the input-output relationships for prediction of brake squeal. Disc brake system has numerous variables. In order to arrive at the most influential variables and its effects a two phase strategies were proposed. In the first phase, initial screening with various variables was taken up. Fractional factorial design (FFD) of experiments was conducted to identify the most influential variables. Subsequently, in the second phase, central composite design (CCD) based Response surface methodology (RSM) was deployed to develop a non-linear model for prediction of disk brake squeal. Figure 7. Disc brake squeal system 4.1 First phase: screening FFD of experiments If any experiment involves the study of the effects of two or more factors, then factorial designs are more efficient than one- factor-at-a-time experiments. Furthermore, a factorial design is necessary when interactions may be present to avoid misleading Nouby et al. / International Journal of Engineering, Science and Technology, Vol. 1, No. 1, 20