轮和轨道的结构弹性变形对滚动接触的轮、轨蠕变力的影响外文文献翻译、中英文翻译

1、附录II：外文文献翻译原文及其译文Effects of structure elastic deformations of wheelset and track on creep forces of wheel/rail in rolling contactAbstractIn this paper the mechanism of effects of structure elastic deformations of bodies in rolling contact on rolling contact performance is briefly analyzed. Effects o

2、f 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 th

3、e 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 deformation

4、s 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

5、 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; Rol

6、ling contact; Creep force; Structure elastic deformationIntroduction During 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

7、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 betwe

8、en 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 t

9、heories 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 mainl

10、y 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 o

11、f 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 dri

12、ving 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

13、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

14、. 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

15、 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 mechanis

16、m 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 tra

17、ck. 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 wit

18、h 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 Bo

19、ssinesq 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 forc

20、es 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

21、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 t

22、he 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 o

23、f 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 el

24、astic 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

25、 of structure elastic deformations 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 o

26、f 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 loadin

27、g 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 el

28、astic 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

29、 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 the same frictional coefficients and the normal pressures are assumed. So the contribution of the traction to u1 is also same under

30、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

31、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.

32、 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 F

33、ig. 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

34、 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

35、 given in 7,8 and results of contact geometry of wheel/rail.When a wheelset is moving on a tangent track the rigid creepages of wheelset and rails read as where i = 1, 2, it has the same meaning as subscript i in (3). The undefined parameters in (4) can be seen in the Nomenclature. It is obvious tha

36、t the creepages depend on not only the parameters of contact geometry, but also the status of wheelset motion. Since the variation of the parameters of contact geometry depend mainly on y with prescribed profiles of wheel/rail some of their derivatives with respect to time can be written asPutting (

37、5) into (4), we obtain:In the calculation of contact geometry and creepage of wheel/rail, the large ranges of the yaw angle and lateral displacement of wheelset are selected in order to make the creepage and contact angle of wheel/rail obtained include the situations producing in the field as comple

38、tely as possible. So we select y = 0, 1, 2, 3, . . . , 10 mm, = 0.0, 0.1, 0.2, 0.3, . . . , 1.0, y/v = 0, 0.005 and r0 /v = 0, 0.001. riy, /y and i/y are calculated with center difference method and the numerical results of ri , and i versus y. l0 = 746.5mm, r0 = 420mm.Using the ranges of y, , y/v a

39、nd r0 /v selected above we obtain that i 1 ranges from 0.0034 to 0.0034, i 2 ranges from 0.03 to 0.03, i 3 ranges from 0.00013 to 0.00013 (mm1), and contact angle i is from to 2.88 to 55.83. Due to length limitation of paper the detailed numerical results of creepage and contact geometry are not sho

40、wn in this paper.4. Conclusion (1) The mechanism of effects of structure elastic deformation of the bodies in rolling contact on rolling contact performance is briefly analyzed. It is understood that the reduced contact stiffness of contacting bodies increases the stick/slip area of a contact area u

41、nder the condition that the contact area is not in full-slip situation. (2) 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 analysis, finite element method is used to de

42、termine the influence coefficients expressing elastic displacements of wheelset/rail produced by unit traction acting on each rectangular element, which are used to replace some of the influence coefficients calculated with the formula of Bossinesq and Cerruti in Kalkers theory. The numerical result

43、s obtained show the differences of the creep forces of wheelset/rail under two kinds of conditions that effects of structure elastic deformations of wheelset/rail are taken into consideration and neglected. (3) The structure elastic deformations of wheelset and track run low the contact stiffness of

44、 wheelset and track, and reduce the creep forces between wheelset and track remarkably under the conditions of unsaturated creep force. Therefore, the situation is advantageous to the reduction of the wear, rolling contact fatigue of wheel and rail. (4) In the study the effect of the bending deforma

45、tion of wheelset shown in Fig. 1a is neglected, and the crossed influence coefficients AIiJj(i _= j ; i, j = 1, 2) are not revised. So, the accuracy of the numerical results obtained is lowed. In addition, when the lateral displacement of center of the wheelset, y 10mm, the flange action takes place

46、. In such situation the contact angle is very large and the component of the normal load in the lateral direction is very large. The large lateral force causes track and wheelset to produce large structure deformations, which affect the parameters of contact geometry of wheel/rail and the rigid cree

47、pages. Therefore, the rigid creepages, the creep forces, the parameters of contact geometry, the SED and the motion of wheelset have a great influence upon each other. It is necessary that they are synthetically put into consideration in the analysis. Numerical results of them can be obtained with a

48、n alternative iterative method. Probably conformal contact or two-point contact between wheel and rail take place during the action of flange. Such phenomenon of wheelset and rails in rolling contact is very complicated, and can be analyzed with a new theory of rolling contact, which may be a FEM mo

49、del including effects of structure deformations and all boundary conditions of wheelset and track in the near future.轮和轨道的结构弹性变形对滚动接触的轮/轨蠕变力的影响 摘要 本文简要分析了机构的结构弹性变形对滚动接触时滚动接触性能的影响。详细研究了轮和轨道结构变形对轮轨滚动接触时的蠕变力的影响。对轮和轨道的一般性结构弹性变形进行了有限元分析，以及分别获得了表示结构弹性变形和相应的滚动方向负荷和横向方向轮的关系。利用这些关系，我们计算了轮轨切线接触的影响系数。这些影响系数说明结

50、构发生弹性变形与轮/轨接触面上一个小矩形面积内的单位密度牵引力有关。它们被用来修整一些由在Kalker以非赫兹形式的三维弹性体滚动接触理论中提出的Bossinesq和Cerruti公式得出的影响系数。在分析爬行力时就应用了修正后的Kalker理论。获得的数值结果表明轮和轨道的结构性弹性变形对蠕变力存在很大的影响。 2002爱思唯尔科技有限公司保留所有权利。关键词：轮/轨;滚动接触;蠕变力;结构弹性变形1.导言 在轨道上运行的火车轮和铁轨之间的激烈行动引起轮和轨道的结构出现大量弹性变形。大量结构变形将大大影响车轮和钢轨的滚动接触性能，如蠕变力，起皱 1-3 ，粘附，滚动接触疲劳，噪音 4,5 和

51、脱轨 6 。到目前为止，广泛应用于分析轮/轨蠕变力的滚动接触理论基于假设的弹性半空7-12 。换言之，轮/轨弹性变形和牵引点的关系可用该理论的Bossinesq和切瑞蒂公式表示。在实践中，当轮正在轨道上运动时，接触处的弹性变形大于按现有的滚动接触理论所计算出的值。这是因为轮/轨的弹性远大于半弹性空间。相应的负载造成轮/轨的结构弹性变形（SED）于图1和2所示 。在图1A中显示的轮辐的弯曲变形，主要是由车辆和轮对/轨道的纵向动态载荷引起的。图。图1b中所描述的轮辐扭变形是由车轮和钢轨之间纵向蠕变力作用产生的。引起图1C所示的轮辐斜弯曲变形和图2所示铁路的倾覆变形的主要原因是辆和轮对轨道的横向动荷

52、载。可用于机车运动的与旋轴轮转向同一方向的扭变形（见图。 1 ），主要是由轮/轨接触处的牵引力和电机驱动力矩引起的。直至目前为止很少有发表论文讨论SED对轮和轨道之间的滚动接触的蠕动和蠕变力的影响。事实上，上面提到的轮/轨SED降低了轮/轨的法向和切向接触刚度。轮/轨的法向的接触刚度，主要是因轨道下沉而减小。法向的接触刚度降低并不会影响接触面的法向压力很大。该切线接触刚度降低对粘附/滑移区的境况和接触面的牵引力的影响很大。如果考虑到滚动接触中对轮/轨的滚动接触分析，接触面一对接触粒子的总滑动系数与按本滚动接触理论计算的是不同的。取得的所有接触粒子的总滑动系数和摩擦功，小于在忽略SED的影响条件

53、下分析轮/轨蠕变力时所得值。接触面粘/滑区的比例也大于不考虑SED的影响时的。本文简要分析了机构的结构弹性变形对滚动接触时滚动接触性能的影响，并在分析轮和轨道蠕变力时就应用了Kalker的非赫兹形式三维弹性机构滚动接触理论模型。在分析时选定的轮和铁路数值分别是，一列货运汽车的锥形剖面轮，中国“TB” ，和60公斤/米的钢轨。有限元方法是用来确定他们的SED 。根据SED和通过有限元获得的相应的载荷的关系，确定能表示由接触面单位密度牵引力产生的轮轨弹性位移的影响系数。这些影响系数是用来取代一些由Kalker的理论中的Bossinesq和切瑞蒂公式计算出的影响系数。轮弯曲变形的影响如图1A示，轮和铁路的结构弹性变形的交叉影响研究时被忽视。数值结果表明，在SED的影响是否被考虑的两种情况下，轮/轨的蠕变力有明显区别。2.减少接触刚度增加接触