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中文翻译 应用热工三维制动器瞬态温度场的紧急制动 为了准确掌握在葫芦的紧急制动蹄片的温度场的变化规律，制动时，三维（3- D）的瞬态温度场的理论模型，根据热传导，能量转换和分布规律的理论，以及矿山提升机运行的紧急情况制动。一种温度场的解析推导了采用积分变换法。此外，温度模拟实验场进行了温度场和温度梯度和内部的变化规律获得。同时，通过模拟葫芦的紧急制动条件下，实验测量制动蹄的温度，同时进行。结果发现，通过比较模拟结果与实验数据，即三维瞬态温度场模型的制动蹄片是有效和实用，和分析解决方案解决了积分变换方法是正确的。1、 简介提升机的紧急制动是一个转变过程机械能转化为对制动摩擦热能量。该矿山提升机紧急制动过程中具有以下特点高速，重载，而这种情况更糟糕的是比刹车条件的车辆，火车等1-3,6,10,11。以前对刹车片的温度场的重点工作1-4,10,12,13。特别是，由于制动蹄是固定的过程中紧急制动，所以有更强烈的温度上升制动器蹄片。制动蹄片是一种复合材料，以及温度上升，从摩擦产生的热能是最重要的因素影响制动器蹄片摩擦磨损性能同制动安全性能5-10。因此，有必要调查关于制动器蹄片的温度场来调查刹车片的。制动器蹄片的温度场目前的理论模型基于一维或二。 Afferrante11建立了一个二维（2- D）的多层模型来估计瞬态演化在多盘离合器温度扰动和在操作过程中刹车。纳吉12建立了一维数学模型来描述一个制动热行为系统。 Yevtushenko和Ivanyk13推导了瞬态温度场的一轴对称热传导问题2三维坐标。这是困难的这些模式，以反映制动器蹄片真实温度场的三维几何图形。解决的方法刹车片的三维瞬态温度场集中有限元法1-3,14-17，近似集成的方法4,18，格林函数法12和Laplace变换方法9,13等，前三者方法是数值求解方法和低是相对的准确性。例如，有限元方法可以解决复杂热传导问题，但计算精度解决方案是比较低，这是影响网密度，步长等。虽然拉普拉斯变换解决方法是分析方法，它是难以解决的方程复杂边界的热传导。因此，所谓的解析解积分变换方法通过19，因为它是解决问题的合适非均质瞬态热传导。为了掌握制动器蹄片的温度变化规律在葫芦的紧急制动领域，提高安全可靠性制动，一个3- D的制动器蹄片瞬态温度场研究了在积分变换方法的基础上，和有效性证明了数值模拟和实验研究。2、 理论分析2、1理论模式图1显示了葫芦的制动摩擦副示意图。为了分析制动器蹄片的三维温度场，圆柱坐标（r，z）是通过结构来描述几何如图所示。 2，其中R是刹车点之间的距离和制动盘的旋转轴; 为圆心角;这三者之间的制动蹄摩擦点和表面的距离。至于几何结构参数和图2所示。它看到，显然，这是制动器蹄片的温度T是函数的圆柱坐标（r，z）和时间（t）。根据热理论传导，三维瞬态热传导微分方程是获得如下： （1）其中a是热扩散，；是热导率；为密度；是比热容量。2.2、边界条件2.2.1、热流量及其分布系数 这是在紧急制动产生的摩擦热难要在短时间内发出，因此它几乎完全吸收刹车对。由于制动器蹄片是固定的，摩擦温度多面大幅上升，这最终会影响其摩擦学更严重的行为。为了掌握真实该制动器蹄片温度场在紧急制动时，热流量及其分布系数摩擦表面必须确定准确。根据操作紧急制动，条件假设制动速度光盘随时间呈线性，热流量，得到公式 （2） 其中q为热摩擦表面流动; P是比压之间的制动对; 的和是最初的线性和角速度在制动盘; l是刹车副之间的摩擦系数; 是整个制动时间，k是热分布流系数。假设摩擦热量转移到完全制动运动鞋和制动盘，分布的热流量系数根据得到的一维热传导分析。图。 3显示了联系两个半平面示意图。在一维瞬态热传导的条件，对摩擦表面（z = 0处）的温度上升，得到公式 （3） 其中q为在平面吸收一半热流。和热流量是从Eq获得的 （4）假设两个半飞机具有相同的温度上升，对摩擦表面，然后在热流量比进入两个半平面可表示为 其中下标S和D意味着制动器蹄片和制动盘，分别。根据Eq。（5），分配系数热流根据这个公式获得进入制动器蹄片。2.2.2、在边界系数对流换热至于侧面和顶面制动器蹄片，得到他们的对流换热系数，分别按自然对流换热边界条件直立板和横板 图1-制动摩擦副示意图 图2、三维几何模型的制动器蹄片。 图3、两个半平面示意图其中下标L和U代表侧面和顶部表面，h分别为对流换热系数在边界上，DT是之间的温差边界和环境，L是较短维边界。2.2.3、初始和边界条件制动器蹄片之间的接触和制动盘表面受到不断热流在紧急制动过程qs的。制动蹄片的边界都用空气的自然对流。边界和初始条件可以表示为其中是制动器蹄片在t=0的初始温度。2.3。积分变换求解方法积分变换的方法有两个解决问题的步骤。首先，只有作出适当的积分变换空间变量，热传导原方程可以简化由于考虑到时间与常微分方程变量t然后，通过采取逆变换关于解常微分方程的解析解在关于空间和时间变量温度场可以得到的。积分变换方法应用于求解方程。 （1）边界条件方程。（8）。用积分变换有关空间变量（r，z）的反过来，他们可能会偏微分方程是消灭“。编写公式来表示的运作采取逆变换与积分变换方面到Z，这些被定义为其中是的积分变化，是特征函数。提交Eq，获得以下方程：以同样的方式，逆变换与积分变换关于和r分别定义最后，根据上面的积分变换，方程1）（8）可以简化为如下：解决方案可以获得通过解式。(16)。以反变换关于根据Eqs。(九)、(12)和(14),的解析制动器的三维瞬态温度场分布3.仿真和实验图4显示了一半的制动器剖面样品。线c、d的中心线,底线的横截面上的分别。样品的尺寸是:一个= 137.5 mm,b = = 1 / 6毫米,半162.5 rad,l = 6毫米。闸瓦的材料和盘式制动器是石棉和16Mn,分别。他们的参数和条件的紧急制动见表1。假设摩擦系数和制动衬垫比压在紧急制动过程是不变的。基于以上分析模型,模拟闸瓦的三维温度场进行与到= 7.23 s。温度的变化规律图4 把剖面的一半刹车蹄的样品表1刹车副的基本参数和紧急制动条件与内部温度梯度场进行了分析。什么是显示在无花果里都是片面的。5 - 9的仿真结果相符合。什么是显示在图5是闸瓦的三维温度场当时间7.23 s。它被认为是从图5的最高温度是396.534闸瓦制动,其K后最低温度和热是能量293欧几里得主要集中图5 三维温度场的刹车蹄(t = 7.23 s)图6 温度的改变对摩擦表面与时间t图7 温度的改变对线d用时间t图8 温度梯度的变化与时间线c t图9 温度的改变不同深度随时间的线c t层上的摩擦表面的热影响层(命名),既体现了热diffusibility闸瓦的很差。为了灵便的温度变化规律的摩擦表面,在紧急制动过程的摩擦表面的变化的温度与时间t进行了模拟。什么是在图6中显示,揭示了摩擦表面的温度,然后增加首先减小的趋势。这是因为,高速度的盘式制动器是在开始的时候,结果造成大heat-flow而对流换热系数低边界上的那一刻,所以温度增加;后期的制动的heatflow量减少的速度,而对流换热系数高,由于温差较大的差异,从而导致减少边界温度。无花果。6、7,反映了温度变化规律进行了径向尺寸:在外面的温度高于闸瓦里面,并且外面的温度变化较大。图8论证了温度梯度的变化规律的方向沿z。最高温度梯度的摩擦层是由3.739 105 K / m与方向会急骤下降沿z。最低价值只是4.597 1011 K / m。在开始的时候,温度梯度的热影响层是最高,而温度接近周围的温度。象刹车的推移,温度梯度渐次降低,直到最后。图9所示的是变化的温度不同深度随时间的线c t。温度会急骤下降随着z,、边界条件等影响有窝内部温度。温度增高但z P0.0006米。一旦z是由0.002米,制动过程中温度的差别小于3 k .这表明,热能集中在热影响层,其厚度是关于0.002米。为了证明的解析模型,实验进行了摩擦试验机,如图10。实验原理如下:当刹车开始,两种制动蹄制动圆盘也要被推迟到一定压力p和温度点e在摩擦表面热电偶测量。因为试样厚度太厚,而且摩擦试验机的结构是有限的,很难固定热电偶在刹车蹄。因此,热电偶是固定的直接对盘式制动器是封闭,点e列图。10。图11显示的温度变化规律的两种情况下点在e的紧急制动。从图11,观察点e增加时的温度,在第一,然后减少,最高温度低于,通过仿真实验数据也落后。在图11a,模拟温度达到最大427.14凯西在3.6 s而来的实验数据和最大435.65凯西在3.8秒。在图11b,仿真结果达到最大469.55凯西在4.5 s而来到479.68实验数据K在5秒。它被认为是从图11,通过实验测量温度低于仿真结果,在第一,然后它相反的。这是因为热电偶本身的能量吸收热量闸瓦在开始,然后将其释放到刹车蹄当温度下降。对比实验数据和仿真结果表明,仿真结果表明,两者吻合较好,误差的实验,他们的最高温度是1.99%图10 图解的摩擦测试仪。 图11a 温度的变化规律与时刻t的e点(p = 1.38 = 0 - 1兆帕,证明米/秒)。 图11b 温度的变化规律与时刻t的e点(p = 1.5895%兆帕,证明=长1 - 2.5米/秒)。和2.16%,分别。这表明,解析解的三维瞬态温度场是正确的。4.结论 (1)的理论模型建立了三维瞬态温度场的理论根据热传导及紧急制动条件的矿山提升机。这个积分变换方法应用于解决的理论模型,并对温度场的解析解,推导出。这表明,积分变换方法是有效解决这一问题的三维瞬态温度场。 (2)基于解析解的理论模型,并采用数值分析模拟温度分布的变化规律下紧急制动状态。仿真结果表明:摩擦表面温度的增加降低;首先,然后在开始的温度梯度的热影响层的最高,其次是温度增加迅速,正如制动过程正在进行中,温度梯度温度的增加呈减少趋势;窝;边界条件影响了内部温度上升;热能量都集中在热影响层,其厚度约2毫米。 (3) 实验数据与仿真结果吻合良好,误差对他们的最高温度是大约2%,这证明了积分变换方法的正确性求解理论模型的三维瞬态温度场。解析模型能够反映出的变化规律闸瓦的三维瞬态温度场在紧急刹车。出处 本项目是支持的重点工程,中国教育部(批准号:)资助107054)和程序为新世纪优秀人才(批准号:)资助的大学。NCET-04-0488)。参考1 y .杨、江康钰周、数值模拟研究的三维热应力场与复杂边界问题,工程热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,对车辆制动热分析系统仿真学报,17(12)(2005)。2877 2869-2872。3 邱智贤高,X.Z.林、瞬态温度场分析刹车在引入非完全轴对称三维模型、期刊的材料加工技术129(1 - 3)(2002)513-517。4 应用文献的理发师,李,并没有变法防守的瞬态热弹性接触问题解的速度膨胀法,穿265(3胜4败)(2008)402-410。5 张亚兰,Z.C. Z.Y.朱,G.A.陈,实验研究对摩擦材料行为的葫芦制动蹄络筒机上盘式制动器、润滑工程(12)(2006)99-101。(在中国)。6 B.Y.谢会文,问:5张,Y.F.鲁李,研究鼓式制动器的摩擦系数的紧急刹车衬基于课程,交易的中国农机协会37(12)(2006)33-35。(在中国)。7 Z.J.王建民,王建民,d李,部件wh鲁王,研究应用的影响机理的温升及摩擦系数对制动闸瓦的矿井提升机的杂志 中国煤炭社会30(B08 149-152)(2005)。(在中国)。8 王,一个试验Z.G.加热温度分解的制动摩擦材料的研究J,辽宁工大杂志(自然科学版)24(2)(2005)265-266。(在中国)。9 李宗Matysiak A.A. Yevtushenko,例如,Ivanyk,接触温度和摩擦磨损等元素在复合材料制动、国际期刊上发表的传热、传质的45(1)(2002)193-199。10 Mackin T.J.南卡罗来纳州,等K.J.球之间,在热裂解盘式制动器、工程失效分析9(1)(2002)63-67。11 l . Afferrante,m . Ciavarella李晓岚、Demelio,p . Decuzzi frictionally兴奋,瞬态分析的依据multi-disk离合器、制动器的不稳定性,穿254(1 - 2)(2003)136-146。12 m . Naji,m . AL-Nimr、动态热行为的制动系统、国际通信在传热、28日(6)(2001)835-845。14 j . Voldrich热弹性不稳定,Frictionally阀瓣brakes-transient兴奋的问题。在国际期刊上发表的全部接触的政权,机械科学49(2)(2007)129-137。15 J.H.彩、章旭昌、李、有限元分析的瞬态热弹性行为在磁盘制动器,穿257(1 - 2)(2004年)47-58。16 d . Thuresson、稳定的滑动contact-comparison销钉,并且建立有限元模型,穿261(7 - 8)(2006)896-904。17 H.S.气、陈护升的一天,调查的阀瓣/衬垫摩擦界面温度,穿262制动(5 - 6)(2007)505-513。18 D.P.刘、悬,近似计算方法,梅摩擦摩擦温度在络筒机上衬砌杂志、中国矿业大学及技术26(1)(1997)70 - 72。(在中国)。19 孙子兵法Z.Y.摩擦学行为研究对提升机的制动蹄机盘式制动器(论文)、中国矿业大学,2007年,pp.103-109技术(中文)。(4)。14中期检查表指导教师： 职称： 副教授 所在院（系）： 机械与动力工程系 教研室（研究室） 机械制造 题 目刮板输送机学生姓名专业班级学号一、选题质量：（主要从以下四个方面填写：1、选题是否符合专业培养目标，能否体现综合训练要求；2、题目难易程度；3、题目工作量；4、题目与生产、科研、经济、社会、文化及实验室建设等实际的结合程度）1.刮板输送机非常适合作为毕业设计的课题，所选题目与书本学习知识联系紧密；选题比较贴近生产实际情况，比较具有代表性；适合中批量生产，具有非常大的发挥空间和巧活多样的设计思路，对于本科机制专业的学生来说；2.题目难度相对适中；课题对学生的专业素质要求较高；3.该题目由该同学单独完成，经由严谨的数学计算，具有较高的工作量；4.选题完全符合专业培养目标，属于机械设计制造工艺的一种,对即将毕业的学生的再学习有着较好的指引作用, 不仅仅局限在机械基础知识上，更涉及了有关材料学、力学等多学科知识，使我们对交叉学科有了一定的涉足，综合训练的要求也得到充分的体现。二、开题报告完成情况：开题报告已完成三、阶段性成果：1.开题报告和实习报告已完成；2.英文摘要完成；3.部分零件图已完成 四、存在主要问题：1. 专业基础知识学习不够深入；2.设计经验欠缺；3.参考资料收集有限；4.设计思路不是很清晰；5.绘图软件操作不是很熟 五、指导教师对学生在毕业实习中，劳动、学习纪律及毕业设计（论文）进展等方面的评语指导教师： （签名） 年 月 日3本科毕业设计（论文）开题报告题目名称刮板输送机学生姓名专业班级学号一、 选题的目的和意义：刮板输送机作为煤矿工作面运输设备，不仅担负着运煤的作用，而且作为采煤机的运行轨道、液压支架的推移支点、还要悬挂工作面设备的电缆、水管等。所以，刮板输送机的可靠、稳定、高效运行将直接影响着矿井的生产能力和煤矿企业的经济效益。刮板输送机主要供采煤工作面使用。它要求机身高度小，便于装载；运输能力满足使用地点的生产需要；结构坚固，能抵抗压、砸和碰撞；变更运输距离时，加长和缩短方便；能够不拆卸用机械移置。单链刮板输送机结构简单，没有链子受力不均现象，装载面积大，弯曲性能好。当采用特殊的导向装置时，可以转弯90，它的拐弯部分代替了顺槽转载机，可以直接将工作面的煤炭卸到顺槽可伸缩胶带输送机上，减少了输送环节，实现了一机多用。也就是说，刮板输送机在生产中占有非常重要的地位，而单链刮板输送机又有着结构简单、装载面积大、弯曲性能好等优点，在实际生产中有着十分优越的性质，所以通过本次设计，完成单链刮板输送机的结构设计具有很大的实用意义。二、 国内外研究综述：我国综采机械化的应用始于20世纪70年代末，经过20多年的发展，目前我国中、小功率刮板输送机已具备成型技术，并有成熟的制造能力，完全能够满足国内市场的需求。大功率刮板输送机通过成套引进国外的装备和技术，成功地进行了国产化研制工作，并相继推出了一些产品。从总体水平上看，我国刮板输送机发展现状与国外相比还存在一些差距，主要表现在：基础研究薄弱，缺少强有力的理论支持，计算少，靠经验取值多，缺乏专门的开发分析软件；受基础工业水平的制约，国产输送机制造质量不稳定，元部件的可靠性还有待提高；大功率刮板输送机的关键部件仍需进口，有待进一步研发并国产化；安全性和可靠性的不稳定，直接制约了煤矿的生产效率，从而不能从根本上降低使用成本；煤矿管理水平落后，资金不足，矿工不按操作规程操作等，也间接增加了输送机发生故障的机会，从而不能最大限度地发挥设备的设计能力。自世界上第一台刮板输送机诞生以来，经历了半个多世纪的不断研究、试验、改进，刮板输送机已成为煤矿运输的主要设备。目前世界上生产刮板输送机的国家主要有德国、美国、英国、澳大利亚、日本等，机型从轻型、中型到重型、超重型，装机功率已发展到3700kW。保护形式有：弹性联轴器、限矩型液力耦合器、双速电机、调速型液力耦合器、软启动(CST可控传动装置、阀控调速型液力耦合器、交流电机变频调速技术三种软启动装置)等等。三、 毕业设计（论文）所用的主要技术与方法：1， 毕业设计所用方法：类比设计、优化设计、经验设计以及数据计算等方法。在资料和信息获取过程进行了实地考察和调研。2， 在绘图过程中运用计算机绘图。3， 在外型设计中运用运用人机工程学方法四、 主要参考文献与资料获得情况：金晓颖刮板输送机的发展趋势中州煤炭，2007，(4)：43-45韩幼祥刮板输送机的改进煤矿机械，2005，(6)：106-107孙幼兰，廖建勇国外工作面刮板输送机发展动向煤矿机械，1990，（10）：1-4薛金河，张秀全，李精草刮板输送机发展概况煤矿机械，2002（1）：4-5王琳刮板输送机的优化设计煤矿机械，2007，28(10)：19-21张超军，张志民，王宏洋刮板输送机中部槽的耐磨处理煤矿机械，2007，28(6)：109-110罗庆吉，石国祥综采工作面刮板输送机的现状和发展趋势煤矿机电，2000（5）：54-57五、 毕业设计（论文）进度安排（按周说明）第45周 调研、查资料、完成毕业实习报告第68周 总体方案确定、系统总体设计第912周 详细设计第1314周 编制设计说明书，准备答辩六、 指导教师审批意见： 指导教师： （签名）年 月 日 4Three-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: pengyuxing (Y.-x. Peng).Applied Thermal Engineering 29 (2009) 932937Contents lists available at ScienceDirectApplied Thermal Engineeringjournal homepage: /locate/apthermengis 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 disc78664738Fig. 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, Numerical simulation study of 3-D thermal stress field withcomplex boundary, Journal of Engineering Thermophysics 27 (3) (2007)487489.2 L. Li, J. Song, Z.Y. Guo, Study on fast finite element simu