機(jī)械設(shè)計(jì)外文翻譯-礦井提升機(jī)和數(shù)值的摩擦熱分析模擬墊片的溫度場(chǎng)【中文4130字】【PDF+中文WORD】,中文4130字,PDF+中文WORD,機(jī)械設(shè)計(jì),外文,翻譯,礦井,提升,數(shù)值,摩擦,分析,模擬,墊片,溫度場(chǎng),中文,4130,PDF,WORD 【中文4130字】 礦井提升機(jī)和數(shù)值的摩擦熱分析模擬墊片的溫度場(chǎng) 機(jī)電工程，礦業(yè)，江蘇徐州221008，中國的中國大學(xué)學(xué)院 摘要:密封墊圈的摩擦性能影響礦井提升機(jī)，摩擦熱基于摩擦機(jī)制和傳熱理論，礦山的數(shù)學(xué)模型對(duì)聚氯乙烯墊片的溫度場(chǎng)進(jìn)行了研究，根據(jù)基本假設(shè)，利用ANSYS數(shù)值模擬給出溫度和熱通量的分布，該結(jié)果表明，溫度逐漸減小，模型半徑增加而等溫線是同心半圓的圓弧，熱通量是雙側(cè)對(duì)稱的模型并且徑向減小。當(dāng)鋼絲繩滑動(dòng)時(shí)，該理論值與很短的時(shí)間測(cè)量值相對(duì)應(yīng)（t<=100次）。 關(guān)鍵詞: 礦井提升機(jī)；摩擦熱；墊片；數(shù)值模擬；溫度場(chǎng) 1 引言 礦用提升機(jī)的墊片主要由PVC塑料和PU制成，其有聚合物性能。熱導(dǎo)率PVC塑料和PU相對(duì)較小，該材料溫度因而上升，由于摩擦熱而引起的滑動(dòng)，將導(dǎo)致相位狀態(tài)的改變與結(jié)構(gòu)的變化。以前實(shí)驗(yàn)證明，影響摩擦熱的最重要因素之一是墊圈。在很大程度上是由指示的摩擦系數(shù)，從而降低與一個(gè)在折合在聚合物密封墊圈的溫度[1]。聚合物對(duì)熱敏感，這可以改變摩擦表面狀況，加劇磨損，結(jié)果脫礦或脫落表面層[2]。因此，在研究摩擦?xí)r應(yīng)考慮鋼絲繩之間的機(jī)制墊片的摩擦熱，主要步驟是在墊片摩擦?xí)r了解溫度場(chǎng)的變化，以便獲得影響摩擦的各種因素。 2 滑動(dòng)摩擦熱的機(jī)構(gòu) 2.1 滑動(dòng)模式 一般情況下，礦井提升機(jī)在操作時(shí)，絕對(duì)和相對(duì)滑動(dòng)因?yàn)槟承┰蚨嬖谧饔肹3]。絕對(duì)（純滑動(dòng)）采用下進(jìn)行兩種情況：第一種是，該鋼絲繩在摩擦輪轉(zhuǎn)動(dòng)時(shí)，就在該點(diǎn)如不能解除重量，同時(shí)提升；另一種是，該鋼絲繩上滑動(dòng)的摩擦墊圈，類似于在緊急制動(dòng)電的情況。相對(duì)滑動(dòng)是在摩擦副工作時(shí)引起的差值，絕對(duì)速度通常也發(fā)生兩種情況：在第一個(gè)是該鋼絲繩的速度比該摩擦輪的大，這相當(dāng)于為滑動(dòng)卸載它的重量和減慢，另一條件是速度小于鋼絲繩，這相當(dāng)于滑動(dòng)時(shí)升降在過載運(yùn)行。 2.2 鋼絲繩和墊片摩擦熱產(chǎn)生機(jī)理 摩擦熱摩擦過程中的主要作用為滑動(dòng)，熱量從摩擦工作產(chǎn)生，這直接關(guān)系到了摩擦力和滑動(dòng)速度。歐拉公式是摩擦提升機(jī)的主要驅(qū)動(dòng)原理[4]。 1.它可寫為： （1） 鋼絲繩的拉伸力的限制比例在摩擦輪的兩側(cè)，如圖所示： 圖1 鋼絲繩兩側(cè)拉力 (1) 其中e是自然對(duì)數(shù)2.71828，α0封閉鋼絲繩相對(duì)于所述摩擦輪的角度來看，μ鋼絲繩和墊圈和T1和T2之間的摩擦系數(shù)是在重量的拉伸力。拉伸力和正常壓力之間的關(guān)系是 Ni = Tdθ （2） (2) 其中Ni是正常的氣壓，T為拉伸力和dθ對(duì)應(yīng)的接觸弧度為單位的微角。在滑動(dòng)時(shí)，總摩擦力（T1- T2），并且如果滑動(dòng)速度υ，總摩擦實(shí)際功（Wf）是許多小曲線的總和摩擦功（Wi）[5]： （3） (3) 滑動(dòng)中墊圈的接觸面始終加熱，一般情況下，如果兩個(gè)對(duì)象紋理和幾何形狀彼此相似，摩擦熱通常是良好的顯示分布式[6]，否則，更多的熱量會(huì)傳導(dǎo)至對(duì)象具有良好的導(dǎo)電性。在滑動(dòng)鋼絲繩和墊圈，鋼絲之間繩子將獲得更多的熱量，但只有墊片的5％的摩擦熱主要是產(chǎn)生于分離表面，該表面容易磨損，因此它不利地影響襯墊。為了充分理解摩擦熱效應(yīng)，摩擦產(chǎn)生熱應(yīng)該考慮對(duì)整個(gè)接觸面積。 鋼絲繩和之間的導(dǎo)通的墊片是不穩(wěn)定的，摩擦熱的條件，滑動(dòng)過程中的鋼絲繩示于圖2(1)，這是相當(dāng)復(fù)雜的，因?yàn)樵摪肴κ羌訜幔渌糠轴尫艧崃俊Ｔ诮佑|的橫截面的傳熱條件，鋼絲繩與襯墊之間的區(qū)域顯示圖2(2)，這表明了熱q是良好的顯示分布式上的聯(lián)系方式與圓弧半徑為r0，外加面對(duì)熱源會(huì)在接觸區(qū)域中創(chuàng)建在整個(gè)摩擦輪的滑動(dòng)，以熱鋼絲繩和墊圈加熱表面的接觸面積。根據(jù)摩擦角變化，熱源強(qiáng)度增加在滑動(dòng)方向上，如圖2（3）和所述熱在入口Q''始終是較大的比熱在出口Q'[1-2]。在研究中，墊圈通常被采用為目標(biāo)，作為一個(gè)結(jié)果的復(fù)雜性和該結(jié)構(gòu)的均質(zhì)性鋼絲繩，它是更方便的考慮墊片為連續(xù)均質(zhì)材料[7]。 (1) 墊片 (2) 摩擦熱條件 圖2 鋼絲繩和襯墊滑動(dòng)時(shí)的摩擦熱條件 3 溫度分布模型 3.1 基本假設(shè) 考慮到熱是不可改變的，它只有在封閉時(shí)鋼絲繩和襯墊的某些接觸面積角度改變，作為滑動(dòng)條件是不變的，下面假設(shè)： 1)我們忽略了滑動(dòng)時(shí)墊片的磨損，鋼絲繩的接觸形式在一定的工作條件不變。該整個(gè)表面是一個(gè)大圓弧半徑R和當(dāng)?shù)亟佑|面積是半徑為r0的圓?。ㄤ摻z繩半徑）； 2)墊片各向同性聚合物具有恒定的熱傳導(dǎo)性，是一種均勻連續(xù)的熱擴(kuò)散率，比熱容和密度； 3)非接觸表面，其被暴露在空氣中，是隔熱的，也就是說，它不會(huì)傳遞熱量到空氣； 4)在接觸弧的任何橫截面的熱是恒定的，均勻分布的小接觸圓弧半徑為r0； 5)熱傳遞的方向進(jìn)行半徑r和等溫線是同心的，半圓中心是鋼絲的軸線。 3.2 控制方程 基于以上假設(shè)，我們得到如圖所示，如圖物理模型。該模型具有三面與周圍環(huán)境接觸，鋼絲繩與墊圈的接觸面這是直接由摩擦加熱，其中所述熱量Q是均勻分布，墊圈接觸面和其周圍的空氣，在其上的熱量有上一層極薄的效果，因此溫度變化小，熱對(duì)流的空氣可以忽略不計(jì)；墊片接觸面和接觸區(qū)域的沉積，對(duì)于基于同樣的理由，熱可以忽略。該坐標(biāo)的三維模型的系統(tǒng)是與坐標(biāo)R，θ和φ確定。?是墊圈和一個(gè)繩芯橫截面的距離是特定之間的，θ為該角度從點(diǎn)到對(duì)稱平面和φ是墊圈和其水平位置之間的橫截面為逆時(shí)針角。 圖3 墊片的物理模型 摩擦熱的擴(kuò)散是不穩(wěn)定的，因而我們有數(shù)學(xué)傳熱模型[5]如下： （4） 其中，λ是熱傳導(dǎo)率，T溫度，τ時(shí)間，R絞盤軸之間的距離鋼絲繩芯，這是常數(shù)，表示熱擴(kuò)散。該邊界條件和初始條件是: （5） 方程（4）是一局部方程，由于傳熱在密封墊被認(rèn)為是一個(gè)整體。方程（4）是通過分析或數(shù)值非常復(fù)雜技術(shù)，并在實(shí)踐中加以簡化。該摩擦熱表面層是很薄的，因此熱影響??；并且進(jìn)一步地和之間的同一個(gè)差別系數(shù)較小時(shí)，是非常小的，和之間的影響是小的，只要它們之間存在一定的距離。因此，值被認(rèn)為是一個(gè)常數(shù)和熱傳導(dǎo)可以轉(zhuǎn)化為一種不穩(wěn)定的熱傳導(dǎo)，一維中空?qǐng)A柱體的內(nèi)壁具有同等熱。簡化的物理模型被示為圖4，并在任何數(shù)學(xué)模型角被計(jì)算如下： 圖4 墊片的簡化物理模型 (6) 其中在任何時(shí)間，t是在半徑r處的溫度，是單位長度上電弧的接觸面的熱流量。 4 在溫度場(chǎng)的數(shù)值模擬 4.1 有限元分析 墊片的傳熱分析通過有限元軟件分析，溫度模擬其特殊多場(chǎng)耦合功能。傳熱分析過程中使用分析如下：首先，劃分對(duì)象，以有限的單位（內(nèi)包括一些結(jié)點(diǎn)）[8] ；第二，根據(jù)給定的平衡解決散熱，每個(gè)結(jié)點(diǎn)的方程邊界條件和初始條件根據(jù)能量守恒原理；第三，制定出溫度在每一個(gè)點(diǎn)和最后解決其他相關(guān)變量[9]。簡化的模型是一個(gè)三維中與內(nèi)壁等于熱通量的非穩(wěn)定熱傳導(dǎo)問題，因此只有一個(gè)橫截面需要分析。在這的橫截面，所述內(nèi)半徑等于所述鋼絲繩半徑，即R0= 1.9毫米，其厚度為2.1毫米，橫截面為半環(huán)形，其橫截面面積和網(wǎng)格分布示于圖5。有半徑20等分和在外圍80等分。 圖5 物理模型尺寸和網(wǎng)格分布 4.2 墊片的屬性和初始邊界條件 1) 材料特性：PVC塑料與密度（ρ）1390千克/平方米，比熱（Cp）1842.2焦耳/（千克·℃），熱導(dǎo)率（λ）0.145（W/（平方米·℃）; 2) 大小和動(dòng)態(tài)參數(shù)：內(nèi)徑為1.9毫米，外半徑為4毫米，T2=217.56 N和V=69.33毫米/秒; 3) 邊界條件：AB，BC和CD邊隔熱有相等的熱通量;初始條件：T=0，T0 =20℃，R= 4毫米，Q =0 R=1.9毫米，q = q0。 我們采取鋼絲的外殼角繩索和摩擦輪作為和摩擦力 圖6 溫度和熱通量在一定時(shí)間分布 溫度和熱流量的變化過程在某個(gè)時(shí)間點(diǎn)被顯示在圖7，在不同的距離選擇沿著從靠近半徑的點(diǎn)。前40秒鐘該曲線在小的徑向點(diǎn)是大，這表明當(dāng)溫度上升并相對(duì)于所述墊圈3鋼絲繩的系數(shù)為0.35，在假定的摩擦力的5％熱傳導(dǎo)到墊片和熱通量墊片是每單位長度的圓的摩擦熱。其計(jì)算公式可以推導(dǎo)出公式（1）和（3） 因?yàn)殡p方的熱通量為零，則該計(jì)算值可以直接加入到在橫截面擴(kuò)大的每個(gè)結(jié)點(diǎn)[10]。 4.3 結(jié)果與分析 結(jié)果如溫度場(chǎng)，熱通量場(chǎng)，熱梯度場(chǎng)可以在繪圖上顯示，這可以使各物理量的變化與時(shí)間或空間更直觀[11]。 溫度和熱通量的分布在一定時(shí)間清楚地顯示在圖6，這表明溫度逐漸降低在半徑折痕，等溫線是同心圓弧半圈，熱通量具有對(duì)稱分布和徑向減小。 熱通量梯度大，所以熱傳導(dǎo)是在不正常的階段。過一會(huì)兒的斜坡曲線接近一個(gè)固定的值，這意味著熱通量在這些點(diǎn)是恒定的，溫度升高和每個(gè)點(diǎn)的熱通量梯度成為濃度恒定，從而使熱傳導(dǎo)是在一個(gè)穩(wěn)定的階段。 圖7 變化的溫度和熱流量的過程在一個(gè)特定的時(shí)間點(diǎn) 圖7a為線1，2，3，4比理論值，而線1’，2’，3’，4’代表測(cè)試溫度）。 從圖中可以看出圖7b，該熱流的折痕半徑逐漸日益增加，這是節(jié)能減排的結(jié)果。作為在熱流的邊界的模型內(nèi)進(jìn)行，其中的一部分傳輸?shù)絾卧臒岜挥糜谀茉醋兓膯卧?；換句話說，它提供了能量使溫度上升，而其他部分出口到其他單位，這些結(jié)果表明墊圈的瞬態(tài)溫度場(chǎng)可準(zhǔn)確地模擬，由計(jì)算機(jī)和數(shù)字仿真可以反映但不能在實(shí)踐中測(cè)量(例如墊圈的內(nèi)側(cè))部分溫度場(chǎng)的變化趨勢(shì)。 5 測(cè)試 該實(shí)驗(yàn)進(jìn)行了驗(yàn)證結(jié)果的模擬，該實(shí)驗(yàn)裝置的設(shè)計(jì)以同樣的方式作為真正的懸掛狀態(tài)。鋼絲繩上滑動(dòng)實(shí)驗(yàn)輪是一個(gè)卷軸由直流電動(dòng)機(jī)驅(qū)動(dòng)旋轉(zhuǎn)，滑動(dòng)速度是由直流電動(dòng)機(jī)的電壓控制，通過一個(gè)變壓器和應(yīng)力對(duì)墊片調(diào)節(jié)是由不同的配重調(diào)整。該條件的絕對(duì)滑動(dòng)化可以實(shí)現(xiàn)，同時(shí)實(shí)驗(yàn)絞盤是固定的，條件相對(duì)滑動(dòng)也可以實(shí)現(xiàn)。同時(shí)，不同速度由兩個(gè)直流電機(jī)驅(qū)動(dòng)閥芯和絞盤，絕對(duì)滑動(dòng)或相對(duì)速度滑動(dòng)可以由測(cè)速發(fā)電機(jī)進(jìn)行測(cè)量和光電傳感器的拉伸力，在進(jìn)口和測(cè)試部分的出口通過拉伸來測(cè)量力傳感器和溫度通過以下方式測(cè)定淹沒熱電偶溫度計(jì)。已被證明，鋼絲繩滑動(dòng)在很短的時(shí)間，理論值和測(cè)量值基本上匹配，因此，在滑動(dòng)的開始，熱量從墊片被轉(zhuǎn)到接觸面積和溫度的分布在所述墊圈可以用數(shù)值計(jì)算仿真。滑動(dòng)的后期可以理解積累的熱量已經(jīng)影響了墊片表面，并導(dǎo)致其熱的放大電導(dǎo)率[12]，這說明不符合同情形測(cè)得的溫度與理論之間在后期的價(jià)值。 6結(jié)論 建立鋼絲繩和墊圈之間的熱傳遞模型，這可用于不同的密封墊。模擬后期的溫度場(chǎng)重量和速度，氣溫逐漸取消折痕，模型半徑增加，而模型中的等溫線的同心半圓弧線熱焊劑具有對(duì)稱分布并徑向減小，鋼絲繩滑動(dòng)時(shí)理論值吻合。 參考文獻(xiàn) [1] Liu D P.Studies on Friction Heat Partition for Friction Hoist .Xuzhou:China University of Mining and Technology,1989.(In Chinese). [2] Xiao G R,Wang Z G.Superficial view on friction heat effect. Journal of Sichuan University of Science and Technology,1995,14(3):74–77.(In Chinese). [3] Liu D P.Some problems of frictional heat effects.Lubrication Engineering,1994,15(6):6–14. (In Chinese). [4] Yang Z J.Studies on Tribology Characteristics of Gasket Material of Multiple-cable Friction Hoist [Master dissertation].Xuzhou:China University of Mining and Technology,1987.(In Chinese) [5] Yang S M,Tao W Q.Heat Transfer.Beijing:Higher Education Press,2002.(In Chinese). [6] Liu D P,Mei S H.Approximate method of calculating friction temperature in friction winder lining.Journal of China University of Mining & Technology,1997,15(3):25–29.(In Chinese). [7] Zhang W M.Brake process and friction temperature field of wet disc brake. Nonferrous Metals,1997,16(2):15–17.(In Chinese). [8] Zhang Y M,Song Y P,Zhao Y F.Finite element analysis and linear regression of maximum temperature for Inner wall of chimney foundation.Journal of China University of Mining & Technology,2005,15(3):234–270.(In Chinese). [9] Xia Y M,Ma Z G,Bu Y Y.Simulation of cobalt-rich crust’s crushing process based on ANSYS.Journal of China University of Mining & Technology,2006,16(1):28–32.(In Chinese). [10] Zhang J F,Li Y,Yan B H.Application of ANSYS inheat-analysis.Energy for Metallurgical Industry,2004,15(9):35–38.(In Chinese). [11] Chen Y,Xu C.Application of ANSYS-finite element analysis software to thermal analysis of multichip module.Electronic Engineer,2007,18(2):25–26. (In Chinese). [12] Shang F M,Li Jun,Huang F.The application of ANSYS in numerical heat transmitting.Journal of Changchun Institute of Technology,2004,18(5):17–19.(In Chinese). Received 12 May 2008;accepted 15 August 2008 Projects 50225519 supported by the National Outstanding Youth Science Foundation of China and 0E4458 by the Youth Science Foundation of China Univer-sity of Mining and Technology Corresponding author.Tel:+86-15852498680;E-mail address: Frictional heat analysis of mine hoist and numerical simulation on temperature field of gasket HAN Dong-tai,GE Shi-rong,DU Xue-ping School of Mechanical and Electrical Engineering,China University of Mining&Technology,Xuzhou,Jiangsu 221008,China Abstract:The frictional performance of gaskets is greatly affected by frictional heat in operational mine hoists.Based on frictional mechanism and heat transfer theory,the mathematical model of the temperature field of the PVC gasket in an operational mine hoist was investigated,a numerical simulation using ANSYS is presented and the distribution of the temperature and heat flux were studied under basic assumptions.The results show that the temperature gradually decreases as the radius of the model increases and the isotherms are arcs of concentric semi-circle.The heat flux is of bilateral symmetry in the model and decreases radially.The theoretical values correspond with the measured values for a short time(?100 s)when the steel wire rope slides.Keywords:mine hoist;frictional heat;gasket;numerical simulation;temperature field 1 Introduction These days,gaskets of mine hoists are mainly made of PVC plastic and PU polyurethane which have polymer properties.The thermal conductivity of PVC plastic and PU polyurethane is relatively small,thus the rise of the temperature of the material,caused by frictional heat while sliding,will lead to a change in the phase state and in structure.Previous experiments proved that frictional heat is one of the most important factors affecting the frictional per-formance of the gasket.This is largely indicated by the friction coefficient,which decreases with an in-crease in temperature of the polymer gasket1.Poly-mers are sensitive to heat,which can change the fric-tional condition of its surface,aggravates abrasion and results in the demineralization or abscission of the surface layer2.Therefore,frictional heat and its effects should be considered in investigating the fric-tional mechanism between the steel rope and the gasket.The primary step is to know about the distri-bution and variation of the temperature field of the gasket during the friction process,in order to obtain an insight of the various factors affecting frictional heat.2 Mechanism of sliding frictional heat 2.1 Sliding modes In general,both absolute and relative slides exist for certain reasons while the mine hoist is in opera-tion3.The absolute slide(pure slide)takes place under two conditions:the first one is that the steel wire rope rests as the friction wheel is rotating,just at the point where it cannot lift the weight while hoisting;the other is that the steel wire rope slides on the frictional gasket,similar to that in the case of emergency brak-ing.The relative slide is caused by the difference of the absolute velocities of the friction pairs while working and usually also takes place under two conditions:the first one is that the speed of the steel wire rope is lar-ger than that of the friction wheel,which is equivalent to the sliding as the hoist unloads its weight and slows down;the other condition is that the speed of the fiction wheel is larger than that of the steel wire rope,which is equivalent to sliding when the hoistoperates under overload.2.2 Mechanism of frictional heat generation be-tween steel wire rope and gasket Frictional heat is the main effect of friction during sliding.The heat is generated from the frictional work which directly relates to the friction force and sliding speed.The Euler formula for soft wire drive is the main driving principle of the friction hoist4.The limit ratio of the stretch forces of the steel wire rope on the two sides of the friction wheel,as seen in Fig.1.It can be written as:Mining Science and Technology 19(2009)00400044MININGSCIENCE AND TECHNOLOGY HAN Dong-tai et al Frictional heat analysis of mine hoist and numerical simulation 41Fig.1 Stretch forces of steel wire rope on both sides of the fiction wheel in its penultimate state 012/eT T=(1)where e is the natural logarithm to the base 2.71828,0 the enclosed angle of the steel wire rope with respect to the friction wheel,the frictional coeffi-cient between steel wire rope and gasket and T1 and T2are the stretch forces on the weight and light side,respectively.The relationship between the stretch force and normal pressure is diNT=(2)where iN is normal pressure,T the stretch force and d the micro-angle corresponding to a unit of con-tact radian.During the sliding,the total frictional force is(T1T2)and if the slide speed is,the total fric-tional work(Wf)is the sum of many mini-curve fric-tional works(Wi)per unit of time5:()f12iWWTT=?(3)The contact surface of the gasket is always heated by frictional heat during the absolute slide.Generally,if the two objects are similar to each other in texture and geometry,the frictional heat is usually well-dis-tributed6;otherwise,more heat will conducted to the object with good conductivity.During the sliding between the steel wire rope and gasket,the steel wire rope will gain more heat,but the gasket gains only 5%.The frictional heat is generated largely on the segregated surface which is easily abraded,so it badly affects the gasket.In order to understand fully the frictional heat effect,the generation of frictional heat should be considered on the entire contact area.The conduction between the steel wire rope and the gasket is unstable.The frictional heat conditions of the steel wire rope during sliding are shown in Fig.2(1).It is rather complex because the semi-circle is heated and the other parts release heat.The heat transfer condition at a cross section of the contact area between the steel wire rope and gasket is shown in Fig.2(2),which shows that the heat q is well-dis-tributed on the contact arc with radius 0r.The sur-face heat source will be created on the contact area during the sliding of the entire friction wheel to heat the steel wire rope and gasket.The heating surface is the contact area.According to the variation of the friction angle,the intensity of the heat source gradu-ally increases in the sliding direction,as shown in Fig.2(3)and the heat at the inlet q is always larger than the heat at the outlet q12.In research,the gasket is usually adopted as the target as a result of the complexity and heterogeneity of the structure of the steel wire rope.It is more convenient to consider the gasket as continuous homogeneous material7.Fig.2 Frictional heat conditions of steel wire rope and gasket during sliding 3 Temperature distribution model of gas-ket 3.1 Basic assumptions Considering that the heat is unchangeable on a certain contact area of the steel wire rope and gasket and that it only changes with the enclosed angle 0as the sliding condition is unchanged,the following assumptions are made:1)We ignore the abrasion of the gasket in the slid-ing process;the contact form of the steel wire rope is unchangeable under certain working conditions.The entire form is a large arc with radius R and the local contact area is an arc with radius 0r(the radius of the steel wire rope);2)The gasket is a homogeneous,continuously iso-tropic polymer with a constant heat conductivity,thermal diffusivity,heat capacity and density;3)The non-contact surface,which is exposed in air,is heat insulation,i.e.,it will not transfer heat to the air;4)The heat?at any cross-section of the contact arc is constant and well-distributed on the small contact arc with radius 0r;5)The heat transfer is conducted in the direction of radius r and the isotherms are pieces of the concentric semi-circle whose centre is the axes of the steel wire rope.3.2 Governing equation Based on the assumptions above,we obtained the physical model as shown as Fig.3.The model has three surfaces in contact with the surroundings:I is the contact surface of the steel wire rope and gasket which is heated directly by friction,where the heat qis well-distributed;is the contact surface of?the gasket and its surrounding air,on which the heat has effect on an extremely thin layer,thus the tempera-Mining Science and Technology Vol.19 No.142ture changes little and the heat convection with the air can be ignored1;is the contact surface of the?gasket and the deposit of the contact area.For the same reasons,the heat transfer can be ignored.The coordinate system of the three-dimensional model is established with the coordinates r,and.ris the distance between a certain point in the cross-section of the gasket and the rope core,is the angle from the point to the symmetric plane and is the counter-clockwise angle between the cross-section of the gasket and its horizontal position.()q is the heat at angle.Fig.3 Physical model of gasket The diffusion of the frictional heat is unstable,thus we have the mathematical heat transfer model5 as follows:()()()()222222222 cos11cossin1 coscosRrttttarr Rrrrttr RrRr=+(4)whereis the heat conductivity,t temperature,time,R the distance between the capstan axes and the steel wire rope core,which is constant;()/pac=,denoting thermal diffusion.The boundary conditions and initial conditions are()()00?0,0202?00 ,ltttrrrqrt rt?=?=?=?=?(5)Eq.(4)is a partial equation,since the heat transfer in the gasket is considered as a whole.The solution of Eq.(4)is very complex by analytical or numerical technique and has to be simplified in practice.Thesurface layer affected by the frictional heat is very thin,thus the heat effect is small;and further,the dif-ference between()q and()q+is small when is very small,and the effect between()q and()q+is small as long as there is a certain distance between them.Therefore,()q can be considered as a constant and the heat conduction can be transformed to an unstable heat conduction of a one dimensional hollow cylinder with equal heat flux on the inner wall.The simplified physical model is shown as Fig.4 and the mathematical model at any angle is obtained as follows:Fig.4 Simplified physical model of gasket()20211o0=?rltttttaat ttr rrqrrrrrrrr?=+=?=?=?(6)where t is the temperature at radius r at any time in the gasket;()lq is the heat flow rate of unit arc length on the contact surface.4 Numerical simulation of the tempera-ture field 4.1 Finite element analysis The heat transfer analysis of the gasket is investi-gated by the FEM software ANSYS,which is advan-tageous in temperature simulation for its special multi-field coupling function.The heat transfer analysis process using ANSYS is as follows:first,divide the object to finite units(in-cluding some nodal points)8;second,solve the heat balance equation of each nodal point under the given boundary and initial conditions,according to the en-ergy conservation principle;third,work out the tem-perature at each point and finally,solve for the other relative variables9.The simplified model is an un-stable heat conduction problem of a 3D hollow cyl-inder with equal heat flux on the inner wall;therefore just one cross-section needs to be analyzed.At this cross-section,the inner radius is equal to the steel wire rope radius,that is,r0=1.9 mm,its thickness 2.1 mm and the cross-section is a half annulus whose cross-section area and grid distribution are shown in Fig.5.There are 20 equal divisions in the radius and 80 equal divisions in the periphery.The grid distribu-tions are given by the ANSYS menu:Mesh-Areas.HAN Dong-tai et al Frictional heat analysis of mine hoist and numerical simulation 43?Fig.5 Physical model size and grid distribution 4.2 Gasket properties and initial boundary con-ditions 1)Material properties:PVC plastic with den-sity()1390 kg/m3,specific heat()pc 1842.2 J/(kgC)and heat conductivity()0.145(W/(mC);2)Size and dynamic parameters:inner radius is 1.9mm,external radius is 4 mm,T2=217.56 N and=69.33 mm/s?3)Boundary conditions:the ab,bc and cd sides are thermally insulated,the ad side is of equal heat flux;initial conditions:?=0,t0=20 C;r=4 mm,q=0;r=1.9 mm,q=0q.We have taken the enclosure angle of the steel wire rope and the friction wheel as?,and the frictional coefficient of steel wire rope relative to the gasket?as 0.35,on the assumption that 5%of the frictional heat is conducted to the gasket and the heat flux on the gasket is the frictional heat per unit circle length.The calculation formula can be deduced from Eqs.(1)and(3)00200.05(e)/?qTTr=?(6)Because the heat flux of the three thermally insu-lated sides is zero,the calculated value 0q can be directly added to each nodal point in the cross sec-tion10.4.3 Results and analysis The results such as the temperature field,heat flux field,heat gradient field can be shown in a drawing which can make the change of each physical quantity with time or space more intuitive11.The distributions of temperature and heat flux at a certain time are clearly shown in Fig.6.It shows that the temperature gradually decreases as the radius in-creases,the isotherms are arcs of concentric semi-circles,and the heat flux has a symmetric distribution and decreases radially.(a)Isotherms (b)In X direction (c)In Y direction Fig.6 Distributions of temperature and heat flux at a certain time The changing process of temperature and heat flow at a certain point in time is shown in Fig.7.Four points were chosen along the radius from near to far at different distances.The slopes of the curves at the small radial points are large at the preceding 40 sec-onds,which indicates that the temperature rise and heat flux gradient are large,so the heat conduction is at an abnormal stage.After a while,the slopes of the curves approach a fixed value which means the heat flux at these points is constant,the rise in temperature and the heat flux gradient of each point become con-stant,so that the heat conduction is at a steady stage.?(a)Temperature (b)Heat flow Fig.7 Changing process of temperature and heat flow at a certain point in time Mining Science and Technology Vol.19 No.144It can be seen from Fig.7b that the heat flow de-creases gradually with the increasing radius,which is the result of energy conservation.As the heat flow on the boundary is conducted inside the model,one part of the heat transferred into the unit is used for energy change of the unit;in other words,it provides the energy for the increase in temperature;the other part is exported to other units.These results indicate that the transient temperature field of the gasket can be accurately simulated by computer and the numerical simulation can reflect the changing trend of the tem-perature field of the part that cannot be measured eas-ily in practice(such as the inside of the gasket).5 Tests The experiment was carried out to verify the result of simulation.The experimental set-up is designed the same way as the real hoisting condition.The steel wire rope slides on the experimental wheel which is rotated by a reel driven by a DC motor.The sliding speed is controlled by the voltage of the DC motor,adjusted by a transformer and the stress on the gasket is adjusted by different balance weights.The condi-tion of absolute sliding can be achieved while the experimental capstan is fixed and the condition of relative sliding can be achieved while the speeds of the spool and capstan driven by two DC motors are different.The speed of absolute sliding or relative sliding can be measured by a tachogenerator and photoelectric sensor;the tensile forces at the inlet and outlet of the test part can be measured by a tensile force sensor and the temperature can be measured by the submerged thermocouple thermometer.It has been proved that the theoretical value and the measured value are basically matched over a short time(?100 s)as the steel wire rope slides(shown in Fig.7a as lines 1,2,3,4 representing theoretical values,while lines 1?,2?,3?,4?represent the test tem-peratures).Therefore,the heat transferred from the contact area to the gasket and the distribution of tem-perature in the gasket can be calculated by numerical simulation at the beginning of sliding.The error in the late period of sliding can be understood as the accumulation of heat on the surface that has affected the gasket and resulted in the enlargement of its heat conductivity12.This indicates the lack of conformity between the measured temperature and the theoretical value in the late period.6 Conclusions The model of heat transfer between steel wire rope and gasket is established,which can be used to simu-late the temperature field of gasket under different weights and speeds.The temperature gradually de-creases as the radius of the model increases and the isotherms are arcs of concentric semi-circles;the heat flux has a symmetrical distribution in the model and decreases radially;the theoretical values agree quite well with the measured values over a short time(?100 s)as the steel wire rope slides.Acknowledgements Financial support for this work,provided by the National Outstanding Youth Science Foundation of China(No.50225519)and the Youth Science Founda-tion of China University of Mining and Technology(No.0E4458),is gratefully acknowledged.References 1 Liu D P.Studies on Friction Heat Partition for Friction Hoist Master dissertation.Xuzhou:China University of Mining and Technology,1989.(In Chinese)2 Xiao G R,Wang Z G.Superficial view on friction heat effect.Journal of Sichuan University of Science and Technology,1995,14(3):7477.(In Chinese)3 Liu D P.Some problems of frictional heat effects.Lubrication Engineering,1994,15(6):614.(In Chinese)4 Yang Z J.Studies on Tribology Characteristics of Gasket Material of Multiple-cable Friction Hoist Master dis-sertation.Xuzhou:China University of Mining and Technology,1987.(In Chinese)5 Yang S M,Tao W Q.Heat Transfer.Beijing:Higher Education Press,2002.(In Chinese)6 Liu D P,Mei S H.Approximate method of calculating friction temperature in friction winder lining.Journal of China University of Mining&Technology,1997,15(3):2529.(In Chinese)7 Zhang W M.Brake process and friction temperature field of wet disc brake.Nonferrous Metals,1997,16(2):1517.(In Chinese)8 Zhang Y M,Song Y P,Zhao Y F.Finite element analysis and linear regression of maximum temperature for Inner wall of chimney foundation.Journal of China University of Mining&Technology,2005,15(3):234270.(In Chi-nese)9 Xia Y M,Ma Z G,Bu Y Y.Simulation of cobalt-rich crusts crushing process based on ANSYS.Journal of China University of Mining&Technology,2006,16(1):2832.(In Chinese)10 Zhang J F,Li Y,Yan B H.Application of ANSYS in heat-analysis.Energy for Metallurgical Industry,2004,15(9):3538.(In Chinese)11 Chen Y,Xu C.Application of ANSYS-finite element analysis software to thermal analysis of multichip mod-ule.Electronic Engineer,2007,18(2):2526.(In Chi-nese)12 Shang F M,Li Jun,Huang F.The application of ANSYS in numerical heat transmitting.Journal of Changchun Institute of Technology,2004,18(5):1719.(In Chinese)