中雙鏈刮板輸送機設計【8張cad圖紙+文檔全套資料】

喜歡就充值下載吧。。資源目錄里展示的文件全都有，，請放心下載，，有疑問咨詢QQ:414951605或者1304139763 ======================== 喜歡就充值下載吧。。資源目錄里展示的文件全都有，，請放心下載，，有疑問咨詢QQ:414951605或者1304139763 ======================== 中文翻譯 應用熱工 三維制動器瞬態(tài)溫度場的緊急制動 為了準確掌握在葫蘆的緊急制動蹄片的溫度場的變化規(guī)律，制動時，三維（3- D）的瞬態(tài)溫度場的理論模型，根據(jù)熱傳導，能量轉(zhuǎn)換和分布規(guī)律的理論，以及礦山提升機運行的緊急情況制動。一種溫度場的解析推導了采用積分變換法。此外，溫度模擬實驗場進行了溫度場和溫度梯度和內(nèi)部的變化規(guī)律獲得。同時，通過模擬葫蘆的緊急制動條件下，實驗測量制動蹄的溫度，同時進行。結(jié)果發(fā)現(xiàn)，通過比較模擬結(jié)果與實驗數(shù)據(jù)，即三維瞬態(tài)溫度場模型的制動蹄片是有效和實用，和分析解決方案解決了積分變換方法是正確的。 1、 簡介 提升機的緊急制動是一個轉(zhuǎn)變過程機械能轉(zhuǎn)化為對制動摩擦熱能量。該礦山提升機緊急制動過程中具有以下特點高速，重載，而這種情況更糟糕的是比剎車條件的車輛，火車等[1-3,6,10,11]。以前對剎車片的溫度場的重點工作[1-4,10,12,13]。特別是，由于制動蹄是固定的過程中緊急制動，所以有更強烈的溫度上升制動器蹄片。制動蹄片是一種復合材料，以及溫度上升，從摩擦產(chǎn)生的熱能是最重要的因素影響制動器蹄片摩擦磨損性能同制動安全性能[5-10]。因此，有必要調(diào)查關(guān)于制動器蹄片的溫度場來調(diào)查剎車片的。 制動器蹄片的溫度場目前的理論模型基于一維或二。 Afferrante[11]建立了一個二維（2- D）的多層模型來估計瞬態(tài)演化在多盤離合器溫度擾動和在操作過程中剎車。納吉[12]建立了一維數(shù)學模型來描述一個制動熱行為系統(tǒng)。 Yevtushenko和Ivanyk[13]推導了瞬態(tài)溫度場的一軸對稱熱傳導問題2三維坐標。這是困難的這些模式，以反映制動器蹄片真實溫度場的三維幾何圖形。 解決的方法剎車片的三維瞬態(tài)溫度場集中有限元法[1-3,14-17]，近似集成的方法[4,18]，格林函數(shù)法[12]和Laplace變換方法[9,13]等，前三者方法是數(shù)值求解方法和低是相對的準確性。例如，有限元方法可以解決復雜熱傳導問題，但計算精度解決方案是比較低，這是影響網(wǎng)密度，步長等。雖然拉普拉斯變換解決方法是分析方法，它是難以解決的方程復雜邊界的熱傳導。因此，所謂的解析解積分變換方法通過[19]，因為它是解決問題的合適非均質(zhì)瞬態(tài)熱傳導。為了掌握制動器蹄片的溫度變化規(guī)律在葫蘆的緊急制動領域，提高安全可靠性制動，一個3- D的制動器蹄片瞬態(tài)溫度場研究了在積分變換方法的基礎上，和有效性證明了數(shù)值模擬和實驗研究。 2、 理論分析 2、1理論模式 圖1顯示了葫蘆的制動摩擦副示意圖。為了分析制動器蹄片的三維溫度場，圓柱坐標（r，，z）是通過結(jié)構(gòu)來描述幾何如圖所示。 2，其中R是剎車點之間的距離和制動盤的旋轉(zhuǎn)軸; 為圓心角;這三者之間的制動蹄摩擦點和表面的距離。至于幾何結(jié)構(gòu)參數(shù)和圖2所示。它看到，顯然，這是制動器蹄片的溫度T是函數(shù)的圓柱坐標（r，，z）和時間（t）。根據(jù)熱理論傳導，三維瞬態(tài)熱傳導微分方程是獲得如下： （1） 其中a是熱擴散，；是熱導率；為密度；是比熱容量。 2.2、邊界條件 2.2.1、熱流量及其分布系數(shù) 這是在緊急制動產(chǎn)生的摩擦熱難要在短時間內(nèi)發(fā)出，因此它幾乎完全吸收剎車對。由于制動器蹄片是固定的，摩擦溫度多面大幅上升，這最終會影響其摩擦學更嚴重的行為。為了掌握真實該制動器蹄片溫度場在緊急制動時，熱流量及其分布系數(shù)摩擦表面必須確定準確。根據(jù)操作緊急制動，條件假設制動速度光盤隨時間呈線性，熱流量，得到公式 （2） 其中q為熱摩擦表面流動; P是比壓之間的制動對; 的和是最初的線性和角速度在制動盤; l是剎車副之間的摩擦系數(shù); 是整個制動時間，k是熱分布流系數(shù)。假設摩擦熱量轉(zhuǎn)移到完全制動運動鞋和制動盤，分布的熱流量系數(shù)根據(jù)得到的一維熱傳導分析。圖。 3顯示了聯(lián)系兩個半平面示意圖。在一維瞬態(tài)熱傳導的條件，對摩擦表面（z = 0處）的溫度上升，得到公式 （3） 其中q為在平面吸收一半熱流。和熱流量是從Eq獲得的 （4） 假設兩個半飛機具有相同的溫度上升，對摩擦表面，然后在熱流量比進入兩個半平面可表示為 其中下標S和D意味著制動器蹄片和制動盤，分別。根據(jù)Eq。（5），分配系數(shù)熱流根據(jù)這個公式獲得進入制動器蹄片。 2.2.2、在邊界系數(shù)對流換熱 至于側(cè)面和頂面制動器蹄片，得到他們的對流換熱系數(shù)，分別按自然對流換熱邊界條件直立板和橫板 圖1-制動摩擦副示意圖 圖2、三維幾何模型的制動器蹄片。 圖3、兩個半平面示意圖 其中下標L和U代表側(cè)面和頂部表面，h分別為對流換熱系數(shù)在邊界上，DT是之間的溫差邊界和環(huán)境，L是較短維邊界。 2.2.3、初始和邊界條件 制動器蹄片之間的接觸和制動盤表面受到不斷熱流在緊急制動過程qs的。 制動蹄片的邊界都用空氣的自然對流。邊界和初始條件可以表示為 其中是制動器蹄片在t=0的初始溫度。 2.3。積分變換求解方法 積分變換的方法有兩個解決問題的步驟。首先，只有作出適當?shù)姆e分變換空間 變量，熱傳導原方程可以簡化由于考慮到時間與常微分方程變量t然后，通過采取逆變換關(guān)于解常微分方程的解析解在關(guān)于空間和時間變量溫度場可以得到的。積分變換方法應用于求解方程。 （1）邊界條件方程。（8）。用積分變換有關(guān)空間變量（r，，z）的反過來，他們可能會偏微分方程是''消滅“。編寫公式來表示的運作采取逆變換與積分變換方面到Z，這些被定義為 其中是的積分變化，是特征函數(shù)。 提交Eq，獲得以下方程： 以同樣的方式，逆變換與積分變換關(guān)于和r分別定義 最后，根據(jù)上面的積分變換，方程1）（8）可以簡化為如下： 解決方案可以獲得通過解式。(16)。以反變換關(guān)于根據(jù)Eqs。(九)、(12)和(14),的解析制動器的三維瞬態(tài)溫度場分布 3.仿真和實驗 圖4顯示了一半的制動器剖面樣品。線c、d的中心線,底線的橫截面上的分別。樣品的尺寸是:一個= 137.5 mm,b = = 1 / 6毫米,半162.5 rad,l = 6毫米。閘瓦的材料和盤式制動器是石棉和16Mn,分別。他們的參數(shù)和條件的緊急制動見表1。 假設摩擦系數(shù)和制動襯墊比壓在緊急制動過程是不變的?；谝陨戏治瞿Ｐ?模擬閘瓦的三維溫度場進行與到…= 7.23 s。溫度的變化規(guī)律 圖4 把剖面的一半剎車蹄的樣品 表1剎車副的基本參數(shù)和緊急制動條件 與內(nèi)部溫度梯度場進行了分析。什么是顯示在無花果里都是片面的。5 - 9的仿真結(jié)果相符合。 什么是顯示在圖5是閘瓦的三維溫度場當時間7.23 s。它被認為是從圖5的最高溫度是396.534閘瓦制動,其K后最低溫度和熱是能量293歐幾里得主要集中 圖5 三維溫度場的剎車蹄(t = 7.23 s) 圖6 溫度的改變對摩擦表面與時間t 圖7 溫度的改變對線d用時間t 圖8 溫度梯度的變化與時間線c t 圖9 溫度的改變不同深度隨時間的線c t 層上的摩擦表面的熱影響層(命名),既體現(xiàn)了熱diffusibility閘瓦的很差。為了靈便的溫度變化規(guī)律的摩擦表面,在緊急制動過程的摩擦表面的變化的溫度與時間t進行了模擬。什么是在圖6中顯示,揭示了摩擦表面的溫度,然后增加首先減小的趨勢。這是因為,高速度的盤式制動器是在開始的時候,結(jié)果造成大heat-flow而對流換熱系數(shù)低邊界上的那一刻,所以溫度增加;后期的制動的heatflow量減少的速度,而對流換熱系數(shù)高,由于溫差較大的差異,從而導致減少邊界溫度。無花果。6、7,反映了溫度變化規(guī)律進行了徑向尺寸:在外面的溫度高于閘瓦里面,并且外面的溫度變化較大。 圖8論證了溫度梯度的變化規(guī)律的方向沿z。最高溫度梯度的摩擦層是由3.739 105 K / m與方向會急驟下降沿z。最低價值只是4.597 1011 K / m。在開始的時候,溫度梯度的熱影響層是最高,而溫度接近周圍的溫度。象剎車的推移,溫度梯度漸次降低,直到最后。圖9所示的是變化的溫度不同深度隨時間的線c t。溫度會急驟下降隨著z,、邊界條件等影響有窩內(nèi)部溫度。溫度增高但z P0.0006米。一旦z是由0.002米,制動過程中溫度的差別小于3 k .這表明,熱能集中在熱影響層,其厚度是關(guān)于0.002米。 為了證明的解析模型,實驗進行了摩擦試驗機,如圖10。實驗原理如下:當剎車開始,兩種制動蹄制動圓盤也要被推遲到一定壓力p和溫度點e在摩擦表面熱電偶測量。因為試樣厚度太厚,而且摩擦試驗機的結(jié)構(gòu)是有限的,很難固定熱電偶在剎車蹄。因此,熱電偶是固定的直接對盤式制動器是封閉,點e列圖。10。圖11顯示的溫度變化規(guī)律的兩種情況下點在e的緊急制動。 從圖11,觀察點e增加時的溫度,在第一,然后減少,最高溫度低于,通過仿真實驗數(shù)據(jù)也落后。在圖11a,模擬溫度達到最大427.14凱西在3.6 s而來的實驗數(shù)據(jù)和最大435.65凱西在3.8秒。在圖11b,仿真結(jié)果達到最大469.55凱西在4.5 s而來到479.68實驗數(shù)據(jù)K在5秒。它被認為是從圖11,通過實驗測量溫度低于仿真結(jié)果,在第一,然后它相反的。這是因為熱電偶本身的能量吸收熱量閘瓦在開始,然后將其釋放到剎車蹄當溫度下降。對比實驗數(shù)據(jù)和仿真結(jié)果表明,仿真結(jié)果表明,兩者吻合較好,誤差的實驗,他們的最高溫度是1.99% 圖10 圖解的摩擦測試儀。 圖11a 溫度的變化規(guī)律與時刻t的e點(p = 1.38 = 0 - 1兆帕,證明米/秒)。 圖11b 溫度的變化規(guī)律與時刻t的e點(p = 1.5895%兆帕,證明=長1 - 2.5米/秒)。 和2.16%,分別。這表明,解析解的三維瞬態(tài)溫度場是正確的。 4.結(jié)論 (1)的理論模型建立了三維瞬態(tài)溫度場的理論根據(jù)熱傳導及緊急制動條件的礦山提升機。這個積分變換方法應用于解決的理論模型,并對溫度場的解析解,推導出。這表明,積分變換方法是有效解決這一問題的三維瞬態(tài)溫度場。 (2)基于解析解的理論模型,并采用數(shù)值分析模擬溫度分布的變化規(guī)律下緊急制動狀態(tài)。仿真結(jié)果表明:摩擦表面溫度的增加降低;首先,然后在開始的溫度梯度的熱影響層的最高,其次是溫度增加迅速,正如制動過程正在進行中,溫度梯度溫度的增加呈減少趨勢;窩;邊界條件影響了內(nèi)部溫度上升;熱能量都集中在熱影響層,其厚度約2毫米。 (3) 實驗數(shù)據(jù)與仿真結(jié)果吻合良好,誤差對他們的最高溫度是大約2%,這證明了積分變換方法的正確性求解理論模型的三維瞬態(tài)溫度場。解析模型能夠反映出的變化規(guī)律閘瓦的三維瞬態(tài)溫度場在緊急剎車。 出處 本項目是支持的重點工程,中國教育部(批準號:)資助107054)和程序為新世紀優(yōu)秀人才(批準號:)資助的大學。NCET-04-0488)。 參考 [1] y .楊、江康鈺周、數(shù)值模擬研究的三維熱應力場與復雜邊界問題,《工程熱27(3)(2007)487-489。 [2] l . j .的歌,Z.Y.李郭的研究;(3)快速有限元的仿真模型,對車輛制動熱分析系統(tǒng)仿真學報,17(12)(2005)。2877 2869-2872。 [3] 邱智賢高,X.Z.林、瞬態(tài)溫度場分析剎車在引入非完全軸對稱三維模型、期刊的材料加工技術(shù)129(1 - 3)(2002)513-517。 [4] 應用文獻的理發(fā)師,李,并沒有變法防守的瞬態(tài)熱彈性接觸問題解的速度膨脹法,穿265(3勝4敗)(2008)402-410。 [5] 張亞蘭,Z.C. 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Thuresson、穩(wěn)定的滑動contact-comparison銷釘,并且建立有限元模型,穿261(7 - 8)(2006)896-904。 [17] H.S.氣、陳護升的一天,調(diào)查的閥瓣/襯墊摩擦界面溫度,穿262制動(5 - 6)(2007)505-513。 [18] D.P.劉、懸,近似計算方法,梅摩擦摩擦溫度在絡筒機上襯砌雜志》、《中國礦業(yè)大學及技術(shù)26(1)(1997)70 - 72。(在中國)。 [19] 《孫子兵法》Z.Y.摩擦學行為研究對提升機的制動蹄機盤式制動器(論文)、中國礦業(yè)大學,2007年,pp.103-109技術(shù)(中文)。(4)。 14 中期檢查表 指導教師： 職稱： 副教授 所在院（系）： 機械與動力工程系 教研室（研究室） 機械制造 題 目 刮板輸送機 學生姓名 專業(yè)班級 學號 一、選題質(zhì)量：（主要從以下四個方面填寫：1、選題是否符合專業(yè)培養(yǎng)目標，能否體現(xiàn)綜合訓練要求；2、題目難易程度；3、題目工作量；4、題目與生產(chǎn)、科研、經(jīng)濟、社會、文化及實驗室建設等實際的結(jié)合程度） 1.刮板輸送機非常適合作為畢業(yè)設計的課題，所選題目與書本學習知識聯(lián)系緊密；選題比較貼近生產(chǎn)實際情況，比較具有代表性；適合中批量生產(chǎn)，具有非常大的發(fā)揮空間和巧活多樣的設計思路，對于本科機制專業(yè)的學生來說； 2.題目難度相對適中；課題對學生的專業(yè)素質(zhì)要求較高； 3.該題目由該同學單獨完成，經(jīng)由嚴謹?shù)臄?shù)學計算，具有較高的工作量； 4.選題完全符合專業(yè)培養(yǎng)目標，屬于機械設計制造工藝的一種,對即將畢業(yè)的學生的再學習有著較好的指引作用, 不僅僅局限在機械基礎知識上，更涉及了有關(guān)材料學、力學等多學科知識，使我們對交叉學科有了一定的涉足，綜合訓練的要求也得到充分的體現(xiàn)。 二、開題報告完成情況： 開題報告已完成 三、階段性成果： 1.開題報告和實習報告已完成； 2.英文摘要完成； 3.部分零件圖已完成 四、存在主要問題： 1. 專業(yè)基礎知識學習不夠深入； 2.設計經(jīng)驗欠缺； 3.參考資料收集有限； 4.設計思路不是很清晰； 5..繪圖軟件操作不是很熟 五、指導教師對學生在畢業(yè)實習中，勞動、學習紀律及畢業(yè)設計（論文）進展等方面的評語 指導教師： （簽名） 年 月 日 3 本科畢業(yè)設計（論文）開題報告 題目名稱 刮板輸送機 學生姓名 專業(yè)班級 學號 一、 選題的目的和意義： 刮板輸送機作為煤礦工作面運輸設備，不僅擔負著運煤的作用，而且作為采煤機的運行軌道、液壓支架的推移支點、還要懸掛工作面設備的電纜、水管等。所以，刮板輸送機的可靠、穩(wěn)定、高效運行將直接影響著礦井的生產(chǎn)能力和煤礦企業(yè)的經(jīng)濟效益。 刮板輸送機主要供采煤工作面使用。它要求機身高度小，便于裝載；運輸能力滿足使用地點的生產(chǎn)需要；結(jié)構(gòu)堅固，能抵抗壓、砸和碰撞；變更運輸距離時，加長和縮短方便；能夠不拆卸用機械移置。 單鏈刮板輸送機結(jié)構(gòu)簡單，沒有鏈子受力不均現(xiàn)象，裝載面積大，彎曲性能好。當采用特殊的導向裝置時，可以轉(zhuǎn)彎90°，它的拐彎部分代替了順槽轉(zhuǎn)載機，可以直接將工作面的煤炭卸到順槽可伸縮膠帶輸送機上，減少了輸送環(huán)節(jié)，實現(xiàn)了一機多用。也就是說，刮板輸送機在生產(chǎn)中占有非常重要的地位，而單鏈刮板輸送機又有著結(jié)構(gòu)簡單、裝載面積大、彎曲性能好等優(yōu)點，在實際生產(chǎn)中有著十分優(yōu)越的性質(zhì)，所以通過本次設計，完成單鏈刮板輸送機的結(jié)構(gòu)設計具有很大的實用意義。 二、 國內(nèi)外研究綜述： 我國綜采機械化的應用始于20世紀70年代末，經(jīng)過20多年的發(fā)展，目前我國中、小功率刮板輸送機已具備成型技術(shù)，并有成熟的制造能力，完全能夠滿足國內(nèi)市場的需求。大功率刮板輸送機通過成套引進國外的裝備和技術(shù)，成功地進行了國產(chǎn)化研制工作，并相繼推出了一些產(chǎn)品。從總體水平上看，我國刮板輸送機發(fā)展現(xiàn)狀與國外相比還存在一些差距，主要表現(xiàn)在：基礎研究薄弱，缺少強有力的理論支持，計算少，靠經(jīng)驗取值多，缺乏專門的開發(fā)分析軟件；受基礎工業(yè)水平的制約，國產(chǎn)輸送機制造質(zhì)量不穩(wěn)定，元部件的可靠性還有待提高；大功率刮板輸送機的關(guān)鍵部件仍需進口，有待進一步研發(fā)并國產(chǎn)化；安全性和可靠性的不穩(wěn)定，直接制約了煤礦的生產(chǎn)效率，從而不能從根本上降低使用成本；煤礦管理水平落后，資金不足，礦工不按操作規(guī)程操作等，也間接增加了輸送機發(fā)生故障的機會，從而不能最大限度地發(fā)揮設備的設計能力。 自世界上第一臺刮板輸送機誕生以來，經(jīng)歷了半個多世紀的不斷研究、試驗、改進，刮板輸送機已成為煤礦運輸?shù)闹饕O備。目前世界上生產(chǎn)刮板輸送機的國家主要有德國、美國、英國、澳大利亞、日本等，機型從輕型、中型到重型、超重型，裝機功率已發(fā)展到3×700kW。保護形式有：彈性聯(lián)軸器、限矩型液力耦合器、雙速電機、調(diào)速型液力耦合器、軟啟動(CST可控傳動裝置、閥控調(diào)速型液力耦合器、交流電機變頻調(diào)速技術(shù)三種軟啟動裝置)等等。 三、 畢業(yè)設計（論文）所用的主要技術(shù)與方法： 1， 畢業(yè)設計所用方法：類比設計、優(yōu)化設計、經(jīng)驗設計以及數(shù)據(jù)計算等方法。在資料和信息獲取過程進行了實地考察和調(diào)研。 2， 在繪圖過程中運用計算機繪圖。 3， 在外型設計中運用運用人機工程學方法 四、 主要參考文獻與資料獲得情況： 金曉穎．刮板輸送機的發(fā)展趨勢．中州煤炭，2007，(4)：43-45 韓幼祥．刮板輸送機的改進．煤礦機械，2005，(6)：106-107 孫幼蘭，廖建勇．國外工作面刮板輸送機發(fā)展動向．煤礦機械，1990，（10）：1-4 薛金河，張秀全，李精草．刮板輸送機發(fā)展概況．煤礦機械，2002．（1）：4-5 王琳．刮板輸送機的優(yōu)化設計．煤礦機械，2007，28(10)：19-21 張超軍，張志民，王宏洋．刮板輸送機中部槽的耐磨處理．煤礦機械，2007，28(6)：109-110 羅慶吉，石國祥．綜采工作面刮板輸送機的現(xiàn)狀和發(fā)展趨勢．煤礦機電，2000．（5）：54-57 五、 畢業(yè)設計（論文）進度安排（按周說明） 第4～5周 調(diào)研、查資料、完成畢業(yè)實習報告 第6～8周 總體方案確定、系統(tǒng)總體設計 第9～12周 詳細設計 第13～14周 編制設計說明書，準備答辯 六、 指導教師審批意見： 指導教師： （簽名） 年 月 日 4 Three-dimensional transient temperature field of brake shoe during hoistsemergency brakingZhen-cai Zhu, Yu-xing Peng*, Zhi-yuan Shi, Guo-an ChenCollege of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, Chinaa r t i c l ei n f oArticle history:Received 22 November 2007Accepted 27 April 2008Available online 6 May 2008Keywords:Brake shoeThree-dimensionalTransient temperature fieldIntegral-transform methodEmergency brakingHoista b s t r a c tIn order to exactly master the change rules of brake shoes temperature field during hoists emergencybraking, the theoretical model of three-dimensional (3-D) transient temperature field was establishedaccording to the theory of heat conduction, the law of energy transformation and distribution, and theoperating condition of mining hoists emergency braking. An analytic solution of temperature field wasdeduced by adopting integral-transform method. Furthermore, simulation experiments of temperaturefield were carried out and the variation regularities of temperature field and internal temperature gradi-ent were obtained. At the same time, by simulating hoists emergency braking condition, the experimentsfor measuring brake shoes temperature were also conducted. It is found, by comparing simulation resultswith experimental data, that the 3-D transient temperature field model of brake shoe is valid and prac-tical, and analytic solution solved by integral-transform method is correct.? 2008 Elsevier Ltd. All rights reserved.1. IntroductionThe hoists emergency braking is a process of transformingmechanical energy into frictional heat energy of brake pair. Theemergency braking process of mining hoist has the characteristicof high speed and heavy load, and this situation is worse than brak-ing condition of vehicle, train and so on 13,6,10,11. The previouswork focused on the brake pads temperature field 14,10,12,13.Especially, because the brake shoe is fixed during the process ofemergency braking, so there is more intense temperature rise inbrake shoe. The brake shoe is kind of composite material, and thetemperature rise resulting from frictional heat energy is the mostimportant factor affecting tribological behavior of brake shoe andthe braking safety performance 510. Therefore, it is necessaryto investigate the brake shoes temperature field with respect toinvestigating brake pads.Current theoretical models of brake shoes temperature field arebased on one dimension or two. Afferrante 11 built a two-dimen-sional (2-D) multilayered model to estimate the transient evolu-tion of temperature perturbations in multi-disk clutches andbrakes during operation. Naji 12 established one-dimensionalmathematical model to describe the thermal behavior of a brakesystem. Yevtushenko and Ivanyk 13 deduced the transient tem-perature field for an axi-symmetrical heat conductivity problemwith 2-D coordinates. It is difficult for these models to reflect thereal temperature field of brake shoe with 3-D geometry.The methods solving brake pads 3-D transient temperaturefield concentrated on finite element method 13,1417, approx-imate integration method 4,18, Greens function method 12 andLaplace transformation method 9,13, etc. The former threemethods are numerical solution methods and are of low relativeaccuracy. For example, finite element method can solve the com-plicate heat conduction problem, but the accuracy of computa-tional solution is relatively low, which is affected by meshdensity, step length and so on. Though the Laplace transformationmethod is an analytic solution method, it is difficult to solve theequation of heat conduction with complicated boundaries. There-fore, the analytic solution called integral-transform method isadopted 19, because it is suitable for solving the problem ofnon-homogeneous transient heat conduction.In order to master the change rules of brake shoes temperaturefieldduringhoistsemergencybrakingandimprovethesafereliabil-ity of braking, a 3-D transient temperature field of the brake shoewas studied based on integral-transform method, and the validityis proved by numerical simulation and experimental research.2. Theoretical analysis2.1. Theoretical modelFig. 1 shows the schematic of hoists braking friction pair. In or-der to analyze brake shoes 3-D temperature field, the cylindricalcoordinates (r,u,z) is adopted to describe the geometric structureshown in Fig. 2, where r is the distance between a point of brakeshoe and the rotation axis of brake disc; u is the central angle; z1359-4311/$ - see front matter ? 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.applthermaleng.2008.04.022* Corresponding author. Tel.: +86 13805209649; fax: +86 516 83590708.E-mail address: (Y.-x. Peng).Applied Thermal Engineering 29 (2009) 932937Contents lists available at ScienceDirectApplied Thermal Engineeringjournal homepage: the distance between a point of brake shoe and the friction sur-face. As for the geometric structure and parameters shown in Fig. 2,its seen that a 6 r 6 b, 0 6 u 6 u0, 0 6 z 6 l. It is clear that thebrake shoes temperature T is the function of the cylindrical coor-dinates (r,u,z) and the time (t). According to the theory of heatconduction, the differential equation of 3-D transient heat conduc-tion is gained as follows:o2Tor21roTor1r2o2Tou2o2Toz21aoTot;1whereais the thermal diffusivity,a= k /(q? c); k is the thermal con-ductivity;qis the density; c is the specific heat capacity.2.2. Boundary condition2.2.1. Heat-flow and its distribution coefficientIt is difficult for friction heat generated during emergency brak-ing to emanate in a short time, so it is almost totally absorbed bybrake pair. As the brake shoe is fixed, the temperature of the fric-tion surface rises much sharply, and this eventually affects its tri-bological behavior more seriously. In order to master the realtemperature field of the brake shoe during emergency braking,the heat-flow and its distribution coefficient of friction surfacemust be determined with accuracy. According to the operatingcondition of emergency braking, suppose that the velocity of brakedisc decreased linearly with time, the heat-flow is obtained withthe formqsr;t k ?l? p ? v0? 1 ? t=t0 k ?l? p ? w0? r:1 ? t=t0;2where q is the heat-flow of friction surface; p is the specific pressurebetweenbrakepair;v0andw0istheinitiallinearandangularvelocityof the brake disc;listhe frictioncoefficient betweenbrakepair; t0isthe whole braking time, k is the distribution coefficient of heat-flow.Suppose the frictional heat is totally transferred to the brakeshoe and brake disk, and the distribution coefficient of heat-flowis obtained according to the analysis of one-dimensional heat con-duction. Fig. 3 shows the contact schematic of two half-planes.Under the condition of one-dimensional transient heat conduc-tion, the temperature rise of friction surface (z = 0) is obtained withthe formDT qkffiffiffiffippffiffiffiffiffiffiffiffi4atpqffiffiffiffiffiffiffiffiffiffiffiffipqckpffiffiffiffiffi4tp;3where q is the heat-flow absorbed by half-plane. And the heat-flowis gained from Eq. (3)q ffiffiffiffiffiffiffiffiffiffiffiffipqckpDT=ffiffiffiffiffi4tp:4Suppose the two half-planes has the same temperature rise onthe friction surface, and then the ratio of heat-flow entering thetwo half-planes is given asqsqdffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipqscskspDT=ffiffiffiffiffi4tpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipqdcdkdpDT=ffiffiffiffiffi4tpffiffiffiffiffiffiffiffiffiffiffiffiffiqscskspffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqdcdkdp;5where the subscript s and d mean the brake shoe and brake disc,respectively. According to Eq. (5), the distribution coefficient ofheat-flow entering brake shoe is obtained with the formk qsqaqsqs qd 1 ?qdqs qd 1 ?1qsqd 1 1 ?11 qscsksqdcdkd?12:62.2.2. Coefficient of convective heat transfer on the boundaryWith regard to the lateral surface and the top surface of thebrake shoe, their coefficients of convective heat transfer are ob-tained, respectively, according to the natural heat convectionboundary condition of upright plate and horizontal platehl 1:42DTl=Ll14;7ahu 0:59DTu=Lu14;7bFig. 1. Schematic of hoists braking friction pair.Fig. 2. 3-D geometrical model of brake shoe.Fig. 3. Contact schematic of two half-planes.Z.-c. Zhu et al./Applied Thermal Engineering 29 (2009) 932937933where the subscript l and u represent the lateral surface and the topsurface, respectively; h is the coefficient of convective heat transferon the boundary,DT is the temperature difference between theboundary and the ambient, L is the shorter dimension of theboundary.2.2.3. Initial and boundary conditionContact surface between brake shoe and brake disc is subjectedto continuous heat-flow qsduring emergency braking process.Brake shoes boundaries are of natural convection with the air.The boundary and initial condition can be represented by? koTor h1T h1T0 f1t;r a; t P 0; 0 6u6u0;0 6 z 6 l;8akoTor h2T h2T0 f2t;r b; t P 0; 0 6u6u0;0 6 z 6 l;8b? koToz h3T qs h3T0 f3t;z 0; t P 0;0 6u6u0; a 6 r 6 b;8ckoToz h4T h4T0 f4t;z l; t P 0; 0 6u6u0;a 6 r 6 b;8d? k1roTou h5T h5T0 f5t;u 0; t P 0; 0 6 z 6 l;a 6 r 6 b;8ek1roTou h6T h6T0 f6t;uu0; t P 0; 0 6 z 6 l;a 6 r 6 b;8fTr;u;z;t T0;t 0; a 6 r 6 b; 0 6u6u0;0 6 z 6 l;8gwhere T0is the initial temperature of the brake shoe at t = 0.2.3. Integral-transform solving methodIntegral-transform method has two steps for solving the prob-lem. Firstly, only by making suitable integral-transform for spacevariable, the original equation of heat conduction could be simpli-fied as the ordinary differential equation with regard to the timevariable t. Then, by taking inverse transform with regard to thesolution of the ordinary differential equation, the analytic solutionof the temperature field with regard to the space and time vari-ables could be obtained.Integral-transform method is applied to solve Eq. (1) withboundary condition Eq. (8). By integral-transform with regard tothe space variables (z,u,r) in turn, their partial differential couldbe eliminated”. Writing formulas to represent the operation oftaking the inverse transform and the integral-transform with re-gard to z, these are defined byTr;u;z;t X1m1Zbm;zNbmTr;u;bm;t;9Tr;u;bm;t Zl0Zbm;z0 ? Tr;u;z0;tdz0;10where Tr;u;bm;t is the integral-transform of T(r,u,z,t) withregardtoz;Z(bm,z)isthecharacteristicfunction,Z(bm,z) =cosbm(l ? z); bmis the characteristic value, bmtanbml = H3, andH3h3k; N(bm) is the norm,1Nbm 2b2mH23lb2mH23H3.Submit Eq. (10) into Eqs. (1) and (8), the following equations isobtained:o2Tor21roTor1r2o2Tou2f3kcosl ? bm ? b2m? Tr;u;bm;t1aoTr;u;bm;tot;11a?koTor h1T ?f1t;r a; t P 0; 0 6u6u0;11bkoTor h2T ?f2t;r b; t P 0; 0 6u6u0;11c?k1roTou h5T ?f5t;u 0; t P 0; a 6 r 6 b;11dk1roTou h6T ?f6t;uu0; t P 0; a 6 r 6 b;11eTr;u;bm;t Zl0Zbm;z0 ? T0dz0;t 0;a 6 r 6 b; 0 6u6u0:11fIn the same way, the inverse transform and the integral-transformwith regard to u and r are defined byTr;u;bm;t X1n1Uvn;uNvneTr;vn;bm;t;12eTr;vn;bm;t Zu00u0?Uvn;u0 ? Tr;u0;bm;tdu0;13whereeTr;vn;bm;t is the integral-transform of Tr;u;bm;t with re-gard to u;U(vn,u) is the characteristic function,U(vn,u) = vn? cosvnu +H5? sinvnu; vnis the characteristic value, tanvnu0vnH5H6v2n?H5H6H5h5k;H6h6k; N(vn) is the norm,1Nvn2 v2nH25?u0H6v2nH26?H5hi?1.eTr;vn;bm;t X1i1Rvci;rNcieTvci;vn;bm;t;14eTvci;vn;bm;t ZbaRvci;r0 ?eTr0;vn;bm;tdr0;15whereeTvci;vn;bm;t is the integral-transform ofeTr;vn;bm;t withregard to r; Rv(ci,r) is the characteristic function, Rv(ci,r) = Sv?Jv(ci? r) ? Vv? Yv(ci? r), Jv(ci? r) and Yv(ci? r) are the Bessel functionsof the first and second kind with order v, whereSvci?Y0vci?bH2?Yvci?b;Uvci?J0vci?a?H1?Jvci?a;Vvci?J0vci?bH2?Jvci?b;Wvci?Y0vci?a?H1?Yvci?a;ciis the characteristic value which satisfies the equation Uv? Sv?Wv? Vv= 0; N(ci) is the norm,1Ncip22c2iU2vB2?U2v?B1?V2v, where B1 H21c2i1 ? v=cia2? and B2 H22c2i1 ? v=cib2?.Finally, according to the above integral-transform, Eqs. (1) and(8) can be simplified as follows:deTvdtab2mc2ieTv Aci;vn;bm;t;t 0;16aeTvci;vn;bm;t eTv0;t 0;16bwhere A(ci,vn,bm,t) = g1+ g2+ g3,934Z.-c. Zhu et al./Applied Thermal Engineering 29 (2009) 932937g1a?b ? Rvci;bk?e?f2a ? Rvci;ak?e?f1?;g2Zbavk?f5? r2? Rvci;rdr Zbav ? cosvnu0 H5? sinvnu0k?f6? r2? Rvci;rdr;g3Zbaf3k? cosl ? bm ? sinvnbmH5v1 ? cosvnbm? r? Rvci;rdr:The solutioneTvci;vn;bm;t can be gained by solving the Eq. (16). Bytaking the inverse transform with regard toeTvci;vn;bm;t accordingto Eqs. (9), (12) and (14), the analytic solution of brake shoes 3-Dtransient temperature field is obtainedTr;u;z;t X1m1X1n1X1i1Zbm;zNbmUvn;uNvnRvci;rNcie?ab2mc2it?eTv0Zt0e?ab2mt0Aci;vn;bm;tdt02435:173. Simulation and experimentFig. 4 shows the half section view of brake shoe sample. Line cand d are the center line and bottom line of the cross section,respectively. The sample dimension is: a = 137.5 mm, b = 162.5 mm,u0= 1/6 rad, l = 6 mm. The material of brake shoe and brake discare asbestos-free and 16Mn, respectively. Their parameters andthe condition of emergency braking are shown in Table 1.Suppose that the friction coefficient and the specific pressureare constant during emergency braking process. Based on theabove analytic model, simulation of brake shoes 3-D temperaturefield is carried out with t0= 7.23 s. The change rules of temperaturefield and internal temperature gradient are analyzed. Whatsshown in Figs. 59 are partial simulation results.What is shown in Fig. 5 is brake shoes 3-D temperature fieldwhen time is 7.23 s. It is seen from Fig. 5 that the highest temper-ature of the brake shoe is 396.534 K after braking, and its lowesttemperature is 293 K. And the heat energy is mainly concentratedFig. 4. Half section view of brake shoes sample.Table 1Basic parameters of brake pair and the emergency braking conditionq(kg m?3)c(J kg?1K?1)k(W m?1K?1)T0(K)v0(m s?1)p(MPa)lBrake shoe220625300.295293101.380.4Brake disc786647353.212.51.58Fig. 5. 3-D temperature field of brake shoe (t = 7.23 s).Fig. 6. The change of temperature on friction surface with time t.Fig. 7. The change of temperature on line d with time t.Z.-c. Zhu et al./Applied Thermal Engineering 29 (2009) 932937935on the layer of friction surface (named thermal effect layer), whichindicates the thermal diffusibility of the brake shoe is poor. In or-der to mater the temperature change rules of friction surface dur-ing emergency braking process, the variation of friction surfacestemperature with time t is simulated. What is shown in Fig. 6 re-veals that the temperature of friction surface increases firstly, thendecreases. This is because that the speed of brake disc is high in thebeginning and this results in large heat-flow while the coefficientof convective heat transfer is low on the boundary at the moment,so the temperature increases; at the late stage of brake the heat-flow decreases with the speed while the coefficient of convectiveheat transfer is high due to large difference in temperature onthe boundary, which leads to decreasing in temperature. Figs. 6and 7 reflect the temperature change rules in the radial dimension:the temperature at the outside of brake shoe is higher than that in-side, and the outside temperature changes more greatly.Fig. 8 demonstrates the change rules of the temperature gradi-ent along the direction z. The highest temperature gradient of thefriction layer is up to 3.739 ? 105K/m and decreases sharply alongthe direction z. The lowest value is only 4.597 ? 10?11K/m. In thebeginning the temperature gradient of thermal effect layer is thehighest while the temperature is close to the surrounding temper-ature. As the brake goes on, the temperature gradient decreasesgradually until the end. Fig. 9 shows the change of temperatureat different depth on the line c with time t. The temperature de-creases sharply with the increasing z, and the boundary conditionhas litter influence on the inner temperature. The temperature in-creases all the time when z P 0.0006 m. Once the z is up to0.002 m, the difference in temperature during brake is less than3 K. It indicates that the heat energy focuses on the thermal effectlayer, and its thickness is about 0.002 m.In order to prove the analytic model, experiments were carriedout on the friction tester in Fig. 10. The experimental principle is asfollows: when the brake begins, two brake shoes are pushed tobrake the disc with certain pressure p and the temperature of pointe on the friction surface is measured by thermocouple. Because thespecimen thickness is too thin and the structure of the friction tes-ter is limited, it is difficult to fix the thermocouple in the brakeshoe. Therefore, the thermocouple is fixed directly on the brakedisc which is closed to point e shown in Fig. 10. Fig. 11 showsthe temperatures change rules at point e under two situations ofemergency braking.From Fig. 11, it is observed that the temperature at point e in-creases at first, then decreases; the highest temperature by simula-tion is lower than and also lags behind the experimental data. InFig. 11a, the simulation temperature reaches the maximum427.14 K at 3.6 s while the experimental data comes up to themaximum 435.65 K at 3.8 s. In Fig. 11b, the simulation resultreaches the maximum 469.55 K at 4.5 s while the experimentaldata comes up to 479.68 K at 5 s. It is seen from Fig. 11, the temper-ature measured by experiment is lower than simulation results atfirst, then it inverses. This is because the thermocouple itself ab-sorbs heat energy from the brake shoe in the beginning, then re-leases to the brake shoe when the temperature decreases.Comparison between the experimental data and the simulation re-sults indicates that the simulation shows good agreement with theexperiment, and the errors of their highest temperature are 1.99%Fig. 8. The change of temperature gradient on line c with time t.Fig. 9. The change of temperature at different depth on the line c with time t.Fig. 10. Schematic of friction tester.Fig. 11a. Temperatures change rules at point e with time t (p = 1.38 MPa, v0= 1-0 m/s).936Z.-c. Zhu et al./Applied Thermal Engineering 29 (2009) 932937and 2.16%, respectively. It indicates that the analytic solution of 3-D transient temperature field is correct.4. Conclusion(1) The theoretical model of 3-D transient temperature field wasestablished according to the theory of heat conduction andthe emergency braking condition of mining hoist. The inte-gral-transform method was applied to solve the theoreticalmodel, and the analytic solution of temperature field wasdeduced. It indicates that integral-transform method iseffective to solve the problem of 3-D transient temperaturefield with regard to cylindrical coordinates.(2) Based on the analytic solution of the theoretical model, thenumerical analysis was adopted to simulate the change rulesof temperature distribution under the emergency brakingcondition. Simulation results showed: the temperature offriction surface increased firstly and then decreased; in thebeginning the temperature gradient of thermal effect layerwas the highest, the temperature increased swiftly; as thebrakingprocessgoingon,thetemperaturegradientdecreased while the temperature increased; the boundarycondition had litter influence on the internal temperaturerise; the heat energy was concentrated on the thermal effectlayer and its thickness is about 2 mm.(3) The experimental data has good agreement with the simula-tion results, and the errors of their highest temperature areabout 2%, which prove the correctness of the integral-trans-form method solving the theoretical model of 3-D transienttemperature field. The analytical model can reflect thechange rules of brake shoes 3-D transient temperature fieldduring emergency braking.AcknowledgementsThis project is supported by the Key Project of Chinese Ministryof Education (Grant No. 107054) and Program for New CenturyExcellent Talents in University (Grant No. NCET-04-0488).References1 Y. Yang, J.M. Zhou, Numer