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毕业设计(外文翻译)题 目: 轮辐柔性变形效果和滚动接触的潜变力追踪 轮辐的柔性变形结构的效果和在滚动接触的轮/ 轨道的潜变力的追踪 摘录:在这一篇论文中,对滚动接触机械装置上的滚动接触体结构柔性变形的效果简短地分析。轮副和轨道对轮的潜变力的结构变形的效果和轨条详细地被分析研究。轮副的一般结构柔性变形和轨道首先分别用有限元的机械要素方法和关系一起分析,从而获得表达滚动方向和轮副的横方向的结构柔性变形和对应的负载。按照它们之间的关系,我们计算轮和轨条的在一点相接接触的影响力系数。影响力系数代表发生在轮/轨道接触的一个小的矩形面积上的单位面积的牵引力引起的结构柔性变形。他们习惯校订一些与Kalker的无赫兹的形状滚动接触的三维空间的有柔性体的理论 Bossinesq 和 Cerruti 的公式一起获得的影响力系数。在潜变力的分析中, 利用了修正的 Kalker 的理论。从轮副和轨道的结构柔性变形中获得的数字结果表明潜变力发挥的很大影响力。2002 Elsevier 科学出版社版权所有。关键字: 轮/轨条; 滚动接触;潜变力;柔性变形结构1.介绍由于火车轮副和轨道之间的很大相对运动作用力引起轮副和轨道的结构较大的柔性变形。大的结构变形极大影轮和轨条响滚动接触的性能,如潜变力,波形 1 3 ,黏着,滚动接触疲劳, 噪音 4,5 和脱轨6等等. 到现在为止在轮/ 轨道的潜变力的分析中广泛应用的滚动接触理论是以柔性一半的空间假定为基础的 7 12. 换句话说,轮/ 轨道的一个接触的柔性变形和牵引之间的关系可以用Bossinesq 和 Cerruti 的理论公式表达。实际, 当轮副在轨道上持续运动,接触的柔性变形是比那些以滚动接触的现在理论公式计算的更大。因为轮副/ 轨道的挠性是比柔性一半的空间更加大 。由对应的负荷所引起的轮副/ 轨道柔性变形结构在图中被显示。如 1 和 2. 在图中轮副弯曲变形被显示出来。在图 1a 中被显示的轮副弯曲变形主要由车辆和轮副/轨条的垂直动载荷所引起。在图 1 b 中描述的轮副扭转的变形是由于轮和轨道之间的纵潜变力的作用生产的。在图 1 c 中显示的轮副斜角弯曲变形和在图 2 中显示的轨道翻折变形主要地由交通工具和轮副/轨道的横动态负荷所引起。在轮副 (图 1 d) 的轴周围的和旋转装置相同方向的扭转变形,火车可以使用的,主要在电动机的轮/ 轨条和驱动扭矩的接触补缀上的牵引所引起。到目前为止很少的出版物讨论滚动接触的轮副和轨道之间的爬动和潜变力的效果。 事实上,上面提到轮副/ 轨道的柔性变形结构是在轮/轨道的常态和切线的接触刚性以下运动。轮/ 轨道的正常的接触点的刚性通常低于轨道的下沉位置。低于正常接触点的刚性很少的影响接触面积上的正常压力。那低于切线的接触刚性很大影响接触面积的黏结/ 滑移面积状态和牵引力。如果滚动接触的柔性变形结构的影响被对于轮/轨道的分析考虑进去,一对接触面积的全体微粒滑移与用现在滚动接触理论计算的结果不同。所有的连络颗粒和摩擦功的总的滑移比那在分析轮/轨道浅动力的时候,被忽略的柔性变形结构更小。同样一个接触面积的根/ 转差面积的比率比没有考虑的柔性变形结构的效果更大。在这一篇论文中,在滚动接触性能上的滚动接触的车体柔性变形机构的装置被简短地分析,而且和Kalkers 无赫兹的形状滚动接触的三度空间的有柔性车体的理论模型用来分析在轮副和轨道之间的潜变力。在数值分析中挑选的轮副和轨条分别地,是货车轮副的锥形轮廓,中国 兆位元组 和钢轨条的质量是60 公斤/m 。有限元分析方法用来决定他们的柔性变形结构。依照柔性变形结构的关系和对应的由于 FEM 获得负荷, 表示轮副的柔性变位的影响系数是由轮/ 轨条的接触单位面积密度有所反应的牵引生产的轨条所决定。这些影响系数用来代替一些与 Kalkers 的理论 Bossinesq 和 Cerruti 的公式一起计算的影响系数。在图 1a 中被显示的轮副弯曲变形的效果和在轮副轨道的柔性变形结构之中的横断的影响力在研究中被疏忽。获得的数字结果表明在轮副/轨道柔性变形结构的潜变力效果考虑和疏忽的条件之间的显着差别。 2. 减少连络刚性机构增加接触面积的根粘滞/滑动比为了要使轮副/ 轨道关于滚动接触的轮/ 轨的的柔性变形结构的效果较好的理解, 我们必需简短地解释减少的接触刚性的机构增加在没有饱和的潜变力的状态下面的接触面积的粘滞/ 滑移面积的比。通常在一个接触面积的一对接触颗粒之间的总的滑移含有刚性的滑移,局部一个接触面积和柔性变形结构的柔性变形。图 3 a一描述一对滚动接触车体和没有柔性变形接触颗粒, A1 和 A2 的状态 。在图 3 a中的线A1A 1 和 A2A 2, 为了要作描述的让大家接受而被作记号。在车体的形变发生之后,线的位和形变,A1A 1 和 A2A2,在图 3 b 中被显示。位移差别 , w1, 在图 3 b 的二个划线之间由车体的刚性运动和所引起(滚动或变化). 局部点 A1 和 A2 的柔性变形,被 u11 和 u21 指示,与基于有柔性- 半份空间的假设滚动接触的一些现代的理论一起决定,他们有差别在于点 A1 和点A2之间的有柔性位移 u1= u11- u21。如果车体的结构柔性变形的效果和被忽视的A1 和 A2点之间的总转差 , 能用公式: S1 = w1 u1 = w1 (u11 u21)表示。柔性变形结构车体 1 和 2 主要地由牵引力所引起,p 和 p 代表接触插线和车体的其他边界条件1和 2,他们做线,A1A 1 和 A2A 2 产生与接触面积的局部的坐标 (ox1x3,图 3 a) 无关的刚性运动。u10 和 u20 用来表达点 A1 和点A2的位移,各自归于结构柔性变形。在任何的荷载阶段他们为规定的边界条件和车体 1 和 2 的几何学可能被当做有不防碍局部的坐标常数。在点 A1 和点 A2 之间的位移差别取决于 u10 和 u20, 应该是 u0= u10-u20。如此在考虑车体 1 和 2的柔性变形结构的条件之下,在点之间的总滑移 , A1 和 A2,同样地用公式:S*1 = w1 - u1 - u0表示。明显的 S1 和 S?1 是不同的。在一对接触颗粒之间的牵引 ( 或潜变力)非常仰赖 S1( 或 S?1) 。当 |S1|0(或 |S?1|0)那对接触颗粒是在滑移中和牵引力进入饱和。在进入饱和的情形中, 依照库伦摩擦定律的如果一样的磨擦力系数而且正常的压力被假定的二个条件,牵引是相同的。如此对 u1 的牵引影响在二个条件之下也是相同的。如果 |S1|=|S?1|0,|w1| 在 (2) 必须是比在(1)更大。即没有 u0 的影响的那对接触颗粒比有 u0 的影响的滑移更快。相应地没有 u0 的影响整个的接触面积进入滑移情况快于有 u0 的影响。因此,在接触面积上的粘滞/ 滑移面积的比率和在上面被讨论的二个类型的总牵引是不同的,他们只是被图 4a 和 b一起被简单描述。图 4a表明粘滞/ 滑移面积的情况。图 4a 的号讯 1 表明不考虑 u0 和 2的效果而指示外壳 即用 u0 的效果指示。图 4 b表示在接触面积上总的接触牵引力F1和车体的滑动关系的一种规律。在图 4 b 中的号讯 1 和 2 和图 4 中的意义相同。从图 4 b 中已知 , 在一点相接牵引力 F1 在 w1=w 时到达它的最大值 F1max 不考虑 u0 和 F1 接触的效果在 w1=w 它的最大 F1max 仅由于 u0 的效果来看w10 的左边变档的时候 ,在顺时针方向,在轮副的轴线和左边的轨道的横向方向之间,我们定义那 y0。叁数仰赖y 和,轮和轨条的轮廓。但是如果轮和轨条的轮廓被指定他们主要地仰赖 y16. 详细的讨论用数字的方法被屈服16,17 和轮/轨条的接触几何学的结果。当一个轮副移动到一个正切追踪刚性蠕动轮副和轨条的时候当做 17:i=1,2时它有如同写在底下在(3)的 i 一样的意义。在 (4)的不明确的叁数能在命名法中看到。很明显蠕动不仅与接触几何学的叁数有关, 而且也与轮副运动的状态有关。因为接触几何学的叁数变化主要依靠一些他们的导出于计时轮/ 轨条的规定轮廓y的变化有关被记做:把(5)放进(4)之内我们获得:在轮/轨条的接触几何学和滑移的计算,大范围的偏角和轮副的横向位移被选用以便轮辐的滑移和接触角含尽可能完全地在磁场中被产生的情况被获得。因此我们选择 毫米 和 与中央的用不同的方法和ri, 和 ?i 和 y l0=746.5mm , r0=420mm比较的数字结果一起计算。使用选择的y , y/ v 和 r0 / v 的范围在我们获得上面 i 1个范围从 ?0.0034 到 0.0034, i 2个范围从 ?0.03 到 0.03, i 3 排列从 ?0.00013 到 0.00013(毫米?1), 和接触角 i 是从到 2.88 到 55.83度。由于论文的长度限制滑动和接触几何学的详细数字的结果不被在这篇论文中显示。4结论(1). 在滚动接触性能上的滚动接触车体的柔性变形结构的效果机构被简短地分析。一般了解连络车体的接触刚性减少则接触面积在不全滑移情形中的粘滞/ 滑移面积增加。(2). Kalkers 的和无赫兹的形状滚动接触的三度空间的弹性体的理论模型被用来分析在轮副和轨道之间的潜动力。在分析中,有限元法被用决定作用于每个矩形元件单位牵引生产的轮副/轨道有柔性位移表达的影响系数,用来代替一些与 Kalkers 的理论 Bossinesq 和 Cerruti 的公式一起计算的影响系数。被获得的数字结果表明在轮副/ 轨条结构柔性变形的效果被考虑和忽略的两种情况之下轮副/ 轨条类型的潜动力的差别。(3). 轮副和轨道的柔性变形结构低于运行轮副和轨道的接触刚性, 而且在没有饱和的潜动力的条件之下显着地减少在轮副和轨道之间的潜动力。因此,这种情况有利于减少磨损和轮与轨条的滚动接触疲劳。(4).在研究中,在图 1 中显示的轮副弯曲形变的因素被忽略,而横断的影响系数 不被修正。因此,获得数字结果的精确度很低。除此之外, 当轮副中心的横向位移, y10 mm,凸圆作用发生。在如此的情形中,接触角非常大,而且横的方向正常负载的元件也非常大。大的横力引起轨道和轮副产生大的结构形变,影响轮/ 轨条的接触几何学的叁数和刚性的滑动。因此,刚性滑动,潜动力, 接触几何学的叁数,柔性变形结构和轮副的运动彼此有很大的影响。他们必需综合地分析考虑。他们的数字结果能与一个其它可能的迭代法一起获得。或许共形的接触或轮和轨条之间的点接触在凸圆的作用期间发生。滚动接触的轮副和轨条的现象是非常复杂的, 而且可能与可能是包括结构形变和包括轮副和轨道的所有边界条件在不久的将来内的效果 FEM 模型的滚动接触的一个新的理论被分析。 这一个工作被研究计划的中国自然的科学基础委员会支持了: 轮和轨条和滚动接触疲劳的接触表面的波形。(59935100)国家牵引动力实验室,西南交通大学。它也被中国的教育部键老师大学也提供基金支持。参考文献1 K. Knothe, S.L. Grassie, Modeling of railway track and vehicle/track interaction at high frequencies, Vehicle Syst. Dynam. 22 (3/4) (1993) 209262.2 K. Hempelmann, K. Knothe, An extended linear model for the prediction of short pitch corrugation, Wear 191 (1996) 161169.3 W.F. Hayes, H.G. Tucker, Wheelsettrack resonance as a possible source of corrugation wear, Wear 144 (1991) 211226.4 P.J. Remington, Wheelrail noise. Part IV. Rolling noise, J. Sound Vibrat. 46 (1975) 419436.5 D. Thompson, Wheelrail noise generation, J. Sound Vibrat. 161 (Part 3) (1993) 387482.6 V.G. Krivonogov, V.S. Lysyuk, S.N. Sharapov. Critical displacement of the rail head under action of wheels, in: Proceedings of the conference IHHA, June 1417 1999, Moscow, Russia, pp. 537540.7 F.W. Carter, On the action of a locomotive driving wheel, Proc. R. Soc. Lond. A 112 (1926) 151157.8 J.K. Vermeulen, K.L. Johnson, Contact of non-spherical bodies transmitting tangential forces, J. Appl. Mech. 31 (1964) 338340.9 J.J. Kalker. On the rolling contact of two elastic bodies in the presence of dry friction, Ph.D. thesis, Delft University, The Netherlands, 1967, pp. 64100.10 J.J. Kalker. Simplified Theory of Rolling Contact, Delft Progress Report, Delft University Press, The Netherlands, 1973, pp. 110.11 J.J. Kalker. Three-Dimensional Elastic Bodies in Rolling Contact, Kluwer Academic Publishers, The Netherlands, 1990.12 Z.Y. Shen, J.K. Hedrick, J.A. Elkins. A comparison of alternative creep-force models for rail vehicles dynamic analysis, in: Proceedings of the Eighth IAVSD Symposium, Cambridge, MA, 1984, pp. 591605.13 S. Guo, C. Cai, W. Zhai. A study of lateral coupling dynamics of vehicle/track system, J. China Railway Soc. Suppl. (1994) 9198 (in Chinese).14 W. Wei, A model of rail track receptance analysis, J. Dalian Railway Inst. 19 (4) (1998) 3338 (in Chinese).15 S.L. Grassie. Benchmark test for model of railway track and of vehicle/track interaction at relative high frequencies, Vehicle Syst. Dynam. 24, Suppl. (1995) 355362.16 X. Jin, W. Zhang, Analysis of creepages and their sensitivities for a single wheelset moving on a tangent track, J. Southwest Jiaotong Univ. 20 (2) (1996) 128136.17 X Jin. Study on creep theory of wheel and rail system and its experiment, Ph.D. thesis, Southwest Jiaotong University, Chengdu, China, 1999, pp. 3953 (in Chinese).Effects of structure elastic deformations of wheelset and track on creep forces of wheel/rail in rolling contactAbstract: In this paper the mechanism of effects of structure elastic deformations of bodies in rolling contact on rolling contact performance is briefly analyzed. Effects of structure deformations of wheelset and track on the creep forces of wheel and rail are investigated in detail. General structure elastic deformations of wheelset and track are previously analyzed with finite element method, and the relations, which express the structure elastic deformations and the corresponding loads in the rolling direction and the lateral direction of wheelset, respectively, are obtained. Using the relations, we calculate the influence coefficients of tangent contact of wheel and rail. The influence coefficients stand for the occurring of the structure elastic deformations due to the traction of unit density on a small rectangular area in thecontact area of wheel/rail. They are used to revise some of the influence coefficients obtained with the formula of Bossinesq and Cerruti in Kalkers theory of three-dimensional elastic bodies in rolling contact with non-Hertzian form. In the analysis of the creep forces, the modified theory of Kalker is employed. The numerical results obtained show a great influence exerted by structure elastic deformations of wheelset and track upon the creep forces. 2002 Elsevier Science B.V. All rights reserved.Keywords: Wheel/rail; Rolling contact; Creep force; Structure elastic deformation1. IntroductionDuring running of a train on track the fierce action between wheelset and rails causes large elastic deformations of structure of wheelset and track. The large structure deformations greatly affect performances of wheels and rails in rolling contact, such as creep forces, corrugation 13, adhesion, rolling contact fatigue, noise 4,5 and derailment 6. So far rolling contact theories widely used in the analysis of creep forces of wheel/rail are based on an assumption of elastic half space 712. In other words, the relations between the elastic deformations and the traction in a contact patch of wheel/rail can be expressed with the formula of Bossinesq and Cerruti in the theories. In practice, when a wheelset is moving on track, the elastic deformations in the contact patch are larger than those calculated with the present theories of rolling contact. It is because the flexibility of wheelset/rail is much larger than that of elastic half space. Structure elastic deformations (SED) of wheelset/rail caused by the corresponding loads are shown in Figs. 1 and 2. The bending deformation of wheelset shown in Fig. 1a is mainly caused by vertical dynamic loads of vehicle and wheelset/rail. The torsional deformation of wheelset described in Fig. 1b is produced due to the action of longitudinal creep forces between wheels and rails. The oblique bending deformation of wheelset shown in Fig. 1c and the turnover deformation of rail shown in Fig. 2 are mainly caused by lateral dynamic loads of vehicle and wheelset/rail. The torsional deformations with the same direction of rotation around the axle of wheelset (see Fig. 1d), available for locomotive, are mainly caused by traction on the contact patch of wheel/rail and driving torque of motor. Up to now very few published papers have discussions on the effects of the SED on creepages and creep forces between wheelset and track in rolling contact. In fact, the SED of wheelset/rail mentioned above runs low the normal and tangential contact stiffness of wheel/rail. The normal contact stiffness of wheel/rail is mainly lowed by the subsidence of track. The normal contact stiffness lowed doesnt affect the normal pressure on the contact area much. The lowed tangential contact stiffness affects the status of stick/slip areas and the traction in the contact area greatly. If the effects of the SED on the rolling contact are taken into account in analysis of rolling contact of wheel/rail, the total slip of a pair of contacting particles in a contact area is different from that calculated with the present rolling contact theories. The total slip of all the contacting particles and the friction work are smaller than those obtained under condition that the SED is ignored in the analysis of creep forces of wheel/rail. Also the ratio of stick/slip areas in a contact area is larger than that without consideration of the effects of the SED.In this paper the mechanism of effects of structure elastic deformations of bodies in rolling contact on rolling contact performance is briefly analyzed, and Kalkers theoretical model of three-dimensional elastic bodies in rolling contact with non-Hertzian form is employed to analyze the creep forces between wheelset and track. In the numerical analysis the selected wheelset and rail are, respectively, a freight-car wheelset of conical profile, China “TB”, and steel rail of 60 kg/m. Finite element method is used to determine the SED of them. According to the relations of the SED and the corresponding loads obtained with FEM, the influence coefficients expressing elastic displacements of the wheelset and rail produced by unit density traction acting on the contact area of wheel/rail are determined. The influence coefficients are used to replace some of the influence coeffi- cients calculated with the formula of Bossinesq and Cerruti in Kalkers theory. The effect of the bending deformation of wheelset shown in Fig. 1a and the crossed influences among the structure elastic deformations of wheelset and rail are neglected in the study. The numerical results obtained show marked differences between the creep forces of wheelset/rail under two kinds of the conditions that effects of the SED are taken into consideration and neglected. 2. Mechanism of reduced contact stiffness increasing the stick/slip ratio of contact areaIn order to make better understanding of effects of the SED of wheelset/track on rolling contact of wheel/rail it is necessary that we briefly explain the mechanism of reduced contact stiffness increasing the ratio of stick/slip area in a contact area under the condition of unsaturated creep-force. Generally the total slip between a pair of contact particles in a contact area contains the rigid slip, the local elastic deformation in a contact area and the SED. Fig. 3a describes the status of a pair of the contact particles, A1 and A2, of rolling contact bodies and without elastic deformation. The lines, A1A_1 and A2A_2 in Fig. 3a, are marked in order to make a good understanding of the description. After the deformations of the bodies take place, the positions and deformations of lines, A1A_1 and A2A_2, are shown in Fig. 3b. The displacement difference, w1, between the two dash lines in Fig. 3b is caused by the rigid motions of the bodies and (rolling or shift). The local elastic deformations of points, A1 and A2, are indicated by u11 and u21, which are determined with some of the present theories of rolling contact based on the assumption of elastic-half space, they make the difference of elastic displacement between point A1 and point A2, u1 = u11 u21. If the effects of structure elasticdeformations of bodies and are neglected the total slip between points, A1 and A2, can read as: S1 = w1 u1 = w1 (u11 u21) (1) The structure elastic deformations of bodies and are mainly caused by traction, p and p_ acting on the contact patch and the other boundary conditions of bodies and , they make lines, A1A_1 and A2A_2 generate rigid motions independent of the local coordinates (ox1x3, see Fig. 3a) in the contact area. The u10 and u20 are used to express the displacements of point A1 and point A2, respectively, due to the structure elastic deformations. At any loading step they can be treated as constants with respect to the local coordinates for prescribed boundary conditions and geometry of bodies and . The displacement difference between point A1 and point A2, due to u10 and u20, should be u0 = u10 u20. So under the condition of considering the structural elastic deformations of bodies and , the total slip between points, A1 and A2, can be written as: S1 = w1 u1 u0 (2) It is obvious that S1 and S1 are different. The traction (or creep-force) between a pair of contact particles depends on S1 (or S1 ) greatly. When |S1| 0 (or |S1 | 0) the pair of contact particles is in slip and the traction gets into saturation. In the situation, according to Coulombs friction law the tractions of the above two conditions are same if thesame frictional coefficients and the normal pressures are assumed. So the contribution of the traction to u1 is also same under the two conditions. If |S1| = |S1 | 0, |w1| in (2) has to be larger than that in (1). Namely the pairs of contact particles without the effect of u0 get into the slip situation faster than that with the effect of u0. Correspondingly the whole contact area without the effect of u0 gets into the slip situation fast than that with the effect of u0. Therefore, the ratios of stick/slip areas and the total traction on contact areas for two kinds of the conditions discussed above are different, they are simply described with Fig. 4a and b. Fig. 4a shows the situation of stick/slip areas. Sign in Fig. 4a indicates the case without considering the effect of u0 and indicates that with the effect of u0. Fig. 4b expresses a relationship law between the total tangent traction F1 of a contact area and the creepage w1 of the bodies. Signs and in Fig. 4b have the same meaning as those in Fig. 4a. From Fig. 4b it is known that the tangent traction F1 reaches its maximum F1max at w1 = w_1 without considering the effect of u0 and F1 reaches its maximum F1max at w1 = w_1 with considering the effect of u0, and w_1 0 when the wheelset shifts towards the left side of track and 0 if it is inclined, in the clockwise direction, between the axis of wheelset and the lateral direction of track pointing to the left side. The parameters depend on the profiles of wheel and rail, y and . But if profiles of wheel and rail are prescribed they mainly depend on y 7. Detailed discussion on the numerical method is given in 7,8 and
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