机械毕业设计英文外文翻译317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

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 contact

Abstract

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 Kalker’s 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.

Keywords: Wheel/rail; Rolling contact; Creep force; Structure elastic deformation

Introduction

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 in rolling contact, such as creep forces, corrugation [1–3], 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 [7–12]. 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 doesn’t 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 Kalker’s 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 Kalker’s 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 area

In 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 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 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: S?1 = w1 ? u1 ? u0 (2) It is obvious that S1 and S?1 are different. The traction (or creep-force) between a pair of contact particles depends on S1 (or S?1 ) greatly. When |S1| > 0 (or |S?1 | > 0) the pair of contact particles is in slip and the traction gets into saturation. In the situation, according to Coulomb’s 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 the two conditions. If |S1| = |S?1 | > 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 < w__ 1 . u0 depends mainly on the SED of the bodies and the traction on the contact area. The large SED causes large u0 and the small contact stiffness between the two bodies in rolling contact. That is why the reduced contact stiffness increases the ratio of stick/slip area of a contact area and decreases the total tangent traction under the condition of the contact area without full-slip.

3. Calculation of structure deformation of wheelset/rail

In order to calculate the SED described in Fig. 1b–d, and Fig. 2, discretization of the wheelset and the rail is made. Their schemes of FEM mesh are shown in Figs. 5, 7 and 9. It is assumed that the materials of the wheelset and rail have the same phy sical properties. Shear modulus: G = 82,000 N/mm2, Poisson ratio: μ = 0.28. Fig. 5 is used to determine the torsional deformation of the wheelset. Since, it is symmetrical about the center of wheelset (see Fig. 1b), a half of the wheelset is selected for analysis. The cutting cross section of the wheelset is fixed, as shown in Fig. 5a. Loads are applied to the tread of the wheelset in the circumferential direction, on different rolling circles of the wheel. The positions of loading are, respectively, 31.6, 40.8 and 60.0 mm, measured from the inner side of the wheel. Fig.

6 indicates the torsional deformations versus loads in the longitudinal direction. They are all linear with loads, and very close for the different points of loading. The effect of the loads on the deformation of direction of y-axis, shown in Fig. 5a, is neglected.

Parameters of contact geometry of wheelset/rail to be used in the latter analysis read as:

ri =ri(y,ψ)

δi = δi(y,ψ)

?i = ?i(y,ψ)

ai = ai(y,ψ)

hi = hi(y,ψ)

z = z(y,ψ)

φ = φ(y, ψ) (3)]

where i = 1, 2 stand for the left and right side wheels/rails, respectively. The parameters in (3) are defined in detail in the Nomenclature of the present paper.We define thaty > 0

when the wheelset shifts towards the left side of track and ψ > 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 ψ. But if profiles of wheel and rail are prescrib ed they mainly depend on y [7]. Detailed discussion on the numerical method is 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 that 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 as

Putting (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 completely as possible. So we select y = 0, 1, 2, 3, . . . , 10 mm, ψ = 0.0, 0.1, 0.2, 0.3, . . . , 1.0?, ˙ y/v = 0, 0.005 and r0 ˙ ψ/v = 0, 0.001. ?ri?y, ?φ/?y and ??i/?y are calculated with center difference method and the numerical results of ri , φ and ?i versus y. l0 = 746.5mm, r0 = https://www.360docs.net/doc/0013444673.html,ing the ranges of y, ψ, ˙ y/v and r0 ˙ ψ/v selected above we obtain that ξ i 1 ranges from ?0.0034 to 0.0034, ξ i 2 ranges from ?0.03 to 0.03, ξ i 3 ranges from ?0.00013 to 0.00013 (mm?1), and contact angle δi is from to 2.88 to 55.83?. Due to length l imitation of paper the detailed numerical results of creepage and contact geometry are not shown 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 under the condition that the contact area is not in full-slip situation.

(2) Kalker’s 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 determine 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 Kalker’s theory. The numerical results 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 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 deformation 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. 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 creepages. 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 an 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 model 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。

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面粘/滑率的机械装置

为了更好地了解轮/轨滚动接触的轮/轨SED的影响，我们有必要简要地了解不饱和蠕变力条件下减少接触刚度增加接触面粘/滑率的机械装置。一般来说，接触面的一对接触粒子之间的总滑动，包含刚性滑移，接触面接触处的弹性变形和SED。图3A描述接触对粒子的情形，A1和A2，滚动接触体且没有弹性变形。线A1-A1和A2-A2标记于图3A中，以便更好的理解说明。机构发生变形后的位置和变形线，A1-A1和A2-A2，列于图3A中。位移差异，W1，图3B中两个破折号之间的线是由机构的硬性的运动和滚动或滑动所造成的。该处的弹性变形点，A1和A2，是靠u11和u21表示的，这是由一些依据弹性半空间假设的滚动接触理论确定的，他们导致了点A1和点A2的弹性位移之间的差异，U1= u11 - u21。如果机构的结构弹性变形的影响被忽视，总滑点之间，A1和A2 ，可以理解为：S1= w1?u1=w1?(u11 ? u21)（1）。机构的结构弹性变形的主要由牵引力所造成的，p和p_作用于接触点和机构的其他边界条件，它们导致线，A1_A1和A2_A2产生不受接触面的坐标（ox1x3，见图3A）约束的刚性运动。u10和u20是用来分别表示点A1和点A2由于结构弹性变形的位移。在任何载荷下，他们可以视为与该处给定边界条件下的坐标和机构的几何形状保持一致。点A1和点A2位移差异，取决于u10和u20，应为u0 = u10 - u20 。这样的条件下，考虑机构的结构弹性变形，总滑点之间，A1和A2 ，可以写成：S1= w1?u1?u0（2）。很明显S1和S*1是不同的。接触粒子对之间的牵引力（或蠕变力），极大地取决于S1（或S * 1 ）。当|S1| > 0 (or |S1 | > 0)接触粒子对是打滑且牵引进入饱和。在这种情况下，根据库仑摩擦定律，如果摩擦系数与假设的法向压力相同，上述两个条件下牵引力相同。这样牵引力对U1的作用在上述两个条件下也是相同的。如果|S1| = |S1 | > 0, |w1| 在（2）中要大于（1）中。即接触粒子对在没有u0的影响时进入滑动形势快于有u0的影响时。相应的整个接触面在没有u0的影响时进入滑动形势快于有u0的影响时。因此，粘/滑区比率和接触处的总牵引力在上述两种条件下是不同的，在图4a和b对他们进行了简单的描述。4A表明了粘/滑区的情况。图4A中的标志表明了考虑与不考虑u0的影响的情形。图4B 表示接触面的总切线牵引F1积和1机构的蠕动W之间关系。图4A中的标志和图4B中的具有相同的含义。从图4b可知，切线牵引力F1达到最大值F1max在W1= w_1而不考虑u0作用时和F1达到最大值F1max在W1= w_1考虑u0的影响，并w_1 ＜w__ 1 。u0主要取决于机构的SED和接触面的牵引力。大的SED 导致大的u0和这两个机构之间的滚动接触小的接触刚度。这就是为什么减少接触刚度增加接触面粘/滑区的比率，降低接触面不充分滑条件下的总切线牵引力

3.轮/轨结构变形的计算

为了计算图1b – d和图2中所描述的SED，定义了轮及铁路的离散化。他们的有限元网格图解显示于图5，第7和第9中。假定轮和铁路的材料具有同样的物理特性。剪切模量：G= 82000 N/mm2 ，泊松比：μ= 0.28 。图5用于确定轮的扭变形。因为，它是中心对称轮（见图1b），半轮被选中进行分析。轮的切割截面是固定，所显示的图5a示。负载圆周方向作用于轮对的踏面，从不同圆周出作用于车轮。载荷作用点从车轮内侧测量分别是31.6 ，40.8和60.0毫米。图6表明，扭变形与载荷在纵向相对。他们都是线性的负荷，不同点的载荷大小很接近。负载对Y轴方向的变形的影响（图5a示）忽略不计。

用于后面分析的轮/轨接触的几何参数：

ri =ri(y,ψ)

δi = δi(y,ψ)

?i = ?i(y,ψ)

ai = ai(y,ψ)

hi = hi(y,ψ)

z = z(y,ψ)

φ = φ(y, ψ) (3)

这里i= 1，2分别表示左、右边轮/轨。（ 3 ）中的参数的定义详细见名为Nomenclature的论文。轮转向轨道的左侧时，我们设定它们大于0，如果是在顺时针方向倾斜ψ＞0，，轮轴和轨道之间横向方向指向左侧。参数依赖于轮轨的外形、Y和ψ。但是，如果轮轨外形已经确定，他们主要依靠Y[7] 。数值的详细讨论方法见[7,8]和轮/轨接触的几何结果。当轮正在轨道上切线运动时轮和钢轨的刚性蠕动改为[8] 。

这里i= 1、2 ，它的涵义相同于（3）。（4）中不确定参数的名称可以在Nomenclature 中看到。很明显，蠕动力不仅取决于接触几何参数，而且还取决于轮的运动的形式。由于当轮/轨外形确定时接触几何参数的变化主要取决Y，一些由时间派生的参数可以写出。在计算轮/轨的几何和接触蠕动时，大范围的偏航角和侧向位移轮被选中，，以使轮/轨的蠕动和接触角即使野外工作环境中也尽可能完全的获得。因此，我们选择y=0、1 、2 、3、、、10毫米，ψ = 0.0、0.1、0.2、0.3、、、1.0 ? y/v = 0, 0.005 和r0 ˙ ψ/v = 0, 0.001. ?ri?y, ?φ/?y 和??i/?y是中心差分法计算的且数值结果φ和Δi相对10=l0 = 746.5mm, r0 = 420mm。用通过以上选定范围的y,ψ,y/v和r0、ψ/v ，我们可得ξi 1 范围从-0.0034至0.0034，ξi 2范围从-0.03到0.03 ，ξi 3范围从-0.00013到0.00013（毫米-1），和接触角δi是2.88至55.83°。由于篇幅限制机构的蠕动和接触几何详细计算结果就不表明本

文中。=

4.总结

（1）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。据了解，在接触面是不完全滑的情况下，减少接触机构的接触刚度增加了接触面粘/滑面积。

（2）在分析蠕动力时应用了Kalker理论。在分析中，有限元方法用于确定影响系数，这些系数表明轮/轨的弹性位移由作用于每个矩形单元单位牵引力所致，这是用来取代一些由Kalker的理论中Bossinesq和切瑞蒂公式计算出的影响系数。数值结果表明轮/轨的蠕变力在两条件下不同种，这两种情况分别考虑到和忽视了轮/轨结构的弹性变形的影响。

（3）轮和轨的结构弹性变形降低道运行的轮和轨道的接触刚度，并在蠕变力不饱和的条件下，明显减少轮和轨道之间蠕变力。因此，形势有利于减少磨损，轮轨滚的动接触疲劳。

（4）在研究时，图1a中显示的是忽视轮弯曲变形影响和交叉影响系数的，AIiJj(i _= j ; i, j = 1, 2)没有修正。因此，数值结果的精确被降低。此外，当轮中心的侧向位移y＞10毫米时，就会产生边缘效应。在这种情况下，接触角是非常大，法向负荷的组成部分在横向方向非常大。大的侧向力使轨道和轮对生产大的结构变形，这将影响轮/轨接触几何参数的和刚性蠕动参数。因此，刚性蠕动，蠕变力，接触几何参数，SED和轮运动相互之间有很大的影响。时很有必要对它们综合考虑。它们的数值结果可以通过替代迭代法得到。产生边缘效应时轮轨间可能形成等角接触或两点接触。轮轨滚动接触的这种现象和是在非常复杂的，在不久的将来，或许可用新滚动接触理论分析，这可能是一种有元模型，包括轮和轨道结构变形的影响和所有边界条件。

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