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附錄 II：外文文獻(xiàn)翻譯原文及其譯文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 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.? 2002 Elsevier Science B.V. All rights reserved.Keywords: Wheel/rail; Rolling contact; Creep force; Structure elastic deformation1IntroductionDuring 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 2of 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 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 elastic3deformations 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 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 prescribed 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 5the 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 (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 = 420mm.Using 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 limitation 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 6situation 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.7輪和軌道的結(jié)構(gòu)彈性變形對(duì)滾動(dòng)接觸的輪/軌蠕變力的影響摘要本文簡(jiǎn)要分析了機(jī)構(gòu)的結(jié)構(gòu)彈性變形對(duì)滾動(dòng)接觸時(shí)滾動(dòng)接觸性能的影響。詳細(xì)研究了輪和軌道結(jié)構(gòu)變形對(duì)輪軌滾動(dòng)接觸時(shí)的蠕變力的影響。對(duì)輪和軌道的一般性結(jié)構(gòu)彈性變形進(jìn)行了有限元分析，以及分別獲得了表示結(jié)構(gòu)彈性變形和相應(yīng)的滾動(dòng)方向負(fù)荷和橫向方向輪的關(guān)系。利用這些關(guān)系，我們計(jì)算了輪軌切線接觸的影響系數(shù)。這些影響系數(shù)說(shuō)明結(jié)構(gòu)發(fā)生彈性變形與輪/軌接觸面上一個(gè)小矩形面積內(nèi)的單位密度牽引力有關(guān)。它們被用來(lái)修整一些由在 Kalker 以非赫茲形式的三維彈性體滾動(dòng)接觸理論中提出的 Bossinesq 和 Cerruti 公式得出的影響系數(shù)。在分析爬行力時(shí)就應(yīng)用了修正后的Kalker 理論。獲得的數(shù)值結(jié)果表明輪和軌道的結(jié)構(gòu)性彈性變形對(duì)蠕變力存在很大的影響。? 2002 愛思唯爾科技有限公司保留所有權(quán)利。關(guān)鍵詞：輪/軌;滾動(dòng)接觸;蠕變力;結(jié)構(gòu)彈性變形81.導(dǎo)言 在軌道上運(yùn)行的火車輪和鐵軌之間的激烈行動(dòng)引起輪和軌道的結(jié)構(gòu)出現(xiàn)大量彈性變形。大量結(jié)構(gòu)變形將大大影響車輪和鋼軌的滾動(dòng)接觸性能，如蠕變力，起皺[ 1-3 ] ，粘附，滾動(dòng)接觸疲勞，噪音[ 4,5 ]和脫軌[ 6 ] 。到目前為止，廣泛應(yīng)用于分析輪/ 軌蠕變力的滾動(dòng)接觸理論基于假設(shè)的彈性半空[7-12] 。換言之，輪/軌彈性變形和牽引點(diǎn)的關(guān)系可用該理論的 Bossinesq 和切瑞蒂公式表示。在實(shí)踐中，當(dāng)輪正在軌道上運(yùn)動(dòng)時(shí)，接觸處的彈性變形大于按現(xiàn)有的滾動(dòng)接觸理論所計(jì)算出的值。這是因?yàn)檩?軌的彈性遠(yuǎn)大于半彈性空間。相應(yīng)的負(fù)載造成輪/軌的結(jié)構(gòu)彈性變形（SED ）于圖 1 和 2 所示 。在圖 1A 中顯示的輪輻的彎曲變形，主要是由車輛和輪對(duì)/軌道的縱向動(dòng)態(tài)載荷引起的。圖。圖 1b 中所描述的輪輻扭變形是由車輪和鋼軌之間縱向蠕變力作用產(chǎn)生的。引起圖1C 所示的輪輻斜彎曲變形和圖 2 所示鐵路的傾覆變形的主要原因是輛和輪對(duì)軌道的橫向動(dòng)荷載?？捎糜跈C(jī)車運(yùn)動(dòng)的與旋軸輪轉(zhuǎn)向同一方向的扭變形（見圖。 1 ） ，主要是由輪/軌接觸處的牽引力和電機(jī)驅(qū)動(dòng)力矩引起的。直至目前為止很少有發(fā)表論文討論SED 對(duì)輪和軌道之間的滾動(dòng)接觸的蠕動(dòng)和蠕變力的影響。事實(shí)上，上面提到的輪/軌 SED 降低了輪/軌的法向和切向接觸剛度。輪/軌的法向的接觸剛度，主要是因軌道下沉而減小。法向的接觸剛度降低并不會(huì)影響接觸面的法向壓力很大。該切線接觸剛度降低對(duì)粘附/滑移區(qū)的境況和接觸面的牽引力的影響很大。如果考慮到滾動(dòng)接觸中對(duì)輪/ 軌的滾動(dòng)接觸分析，接觸面一對(duì)接觸粒子的總滑動(dòng)系數(shù)與按本滾動(dòng)接觸理論計(jì)算的是不同的。取得的所有接觸粒子的總滑動(dòng)系數(shù)和摩擦功，小于在忽略 SED 的影響條件下分析輪/ 軌蠕變力時(shí)所得值。接觸面粘/滑區(qū)的比例也大于不考慮 SED 的影響時(shí)的。本文簡(jiǎn)要分析了機(jī)構(gòu)的結(jié)構(gòu)彈性變形對(duì)滾動(dòng)接觸時(shí)滾動(dòng)接觸性能的影響，并在分析輪和軌道蠕變力時(shí)就應(yīng)用了 Kalker 的非赫茲形式三維彈性機(jī)構(gòu)滾動(dòng)接觸理論模型。在分析時(shí)選定的輪和鐵路數(shù)值分別是，一列貨運(yùn)汽車的錐形剖面輪，中國(guó)“TB” ，和 60 公斤/ 米的鋼軌。有限元方法是用來(lái)確定他們的 SED 。根據(jù)SED 和通過(guò)有限元獲得的相應(yīng)的載荷的關(guān)系，確定能表示由接觸面單位密度牽引力產(chǎn)生的輪軌彈性位移的影響系數(shù)。這些影響系數(shù)是用來(lái)取代一些由 Kalker 的理論中的Bossinesq 和切瑞蒂公式計(jì)算出的影響系數(shù)。輪彎曲變形的影響如圖 1A 示，輪和鐵路的結(jié)構(gòu)彈性變形的交叉影響研究時(shí)被忽視。數(shù)值結(jié)果表明，在 SED 的影響是否被考慮的兩種情況下，輪/軌的蠕變力有明顯區(qū)別。2.減少接觸剛度增加接觸面粘/滑率的機(jī)械裝置為了更好地了解輪/軌滾動(dòng)接觸的輪 /軌 SED 的影響，我們有必要簡(jiǎn)要地了解不飽和蠕變力條件下減少接觸剛度增加接觸面粘/滑率的機(jī)械裝置。一般來(lái)說(shuō)，接觸面的一9對(duì)接觸粒子之間的總滑動(dòng)，包含剛性滑移，接觸面接觸處的彈性變形和 SED。圖 3A 描述接觸對(duì)粒子的情形，A1 和 A2，滾動(dòng)接觸體且沒有彈性變形。線 A1-A1 和 A2-A2 標(biāo)記于圖 3A 中，以便更好的理解說(shuō)明。機(jī)構(gòu)發(fā)生變形后的位置和變形線，A1-A1 和 A2-A2，列于圖 3A 中。位移差異，W1，圖 3B 中兩個(gè)破折號(hào)之間的線是由機(jī)構(gòu)的硬性的運(yùn)動(dòng)和滾動(dòng)或滑動(dòng)所造成的 。該處的彈性變形點(diǎn)，A1 和 A2，是靠 u11 和 u21 表示的，這是由一些依據(jù)彈性半空間假設(shè)的滾動(dòng)接觸理論確定的，他們導(dǎo)致了點(diǎn) A1 和點(diǎn) A2 的彈性位移之間的差異 ， U1= u11 - u21。如果機(jī)構(gòu)的結(jié)構(gòu)彈性變形的影響被忽視，總滑點(diǎn)之間， A1 和 A2 ，可以理解為：S1= w1?u1=w1?(u11 ? u21)（1） 。機(jī)構(gòu)的結(jié)構(gòu)彈性變形的主要由牽引力所造成的，p 和 p_作用于接觸點(diǎn)和機(jī)構(gòu)的其他邊界條件，它們導(dǎo)致線， A1_A1 和 A2_A2 產(chǎn)生不受接觸面的坐標(biāo)（ox1x3，見圖 3A）約束的剛性運(yùn)動(dòng)。u10 和 u20 是用來(lái)分別表示點(diǎn) A1 和點(diǎn) A2 由于結(jié)構(gòu)彈性變形的位移。在任何載荷下，他們可以視為與該處給定邊界條件下的坐標(biāo)和機(jī)構(gòu)的幾何形狀保持一致。點(diǎn) A1 和點(diǎn)A2 位移差異，取決于 u10 和 u20，應(yīng)為 u0 = u10 - u20 。這樣的條件下，考慮機(jī)構(gòu)的結(jié)構(gòu)彈性變形，總滑點(diǎn)之間，A1 和 A2 ，可以寫成：S1= w1?u1?u0（2） 。很明顯 S1 和S*1 是不同的。接觸粒子對(duì)之間的牽引力（或蠕變力） ，極大地取決于 S1（或 S * 1 ） 。當(dāng)|S1| > 0 (or |S1 | > 0)接觸粒子對(duì)是打滑且牽引進(jìn)入飽和。在這種情況下，根據(jù)庫(kù)侖摩擦定律，如果摩擦系數(shù)與假設(shè)的法向壓力相同，上述兩個(gè)條件下牽引力相同。這樣牽引力對(duì) U1 的作用在上述兩個(gè)條件下也是相同的。如果|S1| = |S1 | > 0, |w1| 在（2）中要大于（1）中。即接觸粒子對(duì)在沒有 u0 的影響時(shí)進(jìn)入滑動(dòng)形勢(shì)快于有 u0 的影響時(shí)。相應(yīng)的整個(gè)接觸面在沒有 u0 的影響時(shí)進(jìn)入滑動(dòng)形勢(shì)快于有 u0 的影響時(shí)。因此，粘/滑區(qū)比率和接觸處的總牽引力在上述兩種條件下是不同的，在圖 4a 和 b 對(duì)他們進(jìn)行了簡(jiǎn)單的描述。 4A 表明了粘 /滑區(qū)的情況。圖 4A 中的標(biāo)志表明了考慮與不考慮 u0 的影響的情形。圖 4B 表示接觸面的總切線牽引 F1 積和 1 機(jī)構(gòu)的蠕動(dòng) W 之間關(guān)系。圖 4A 中的標(biāo)志和圖 4B 中的具有相同的含義。從圖 4b 可知，切線牽引力 F1 達(dá)到最大值 F1max在 W1= w_1 而不考慮 u0 作用時(shí)和 F1 達(dá)到最大值 F1max 在 W1= w_1 考慮 u0 的影響，并 w_1 ＜ w__ 1 。u0 主要取決于機(jī)構(gòu)的 SED 和接觸面的牽引力。大的 SED 導(dǎo)致大的u0 和這兩個(gè)機(jī)構(gòu)之間的滾動(dòng)接觸小的接觸剛度。這就是為什么減少接觸剛度增加接觸面粘/滑區(qū)的比率，降低接觸面不充分滑條件下的總切線牽引力3.輪/軌結(jié)構(gòu)變形的計(jì)算為了計(jì)算圖 1b – d 和圖 2 中所描述的 SED，定義了輪及鐵路的離散化。他們的有限元網(wǎng)格圖解顯示于圖 5，第 7 和第 9 中。假定輪和鐵路的材料具有同樣的物理特性。剪切模量：G= 82000 N/mm2 ，泊松比： μ = 0.28 。圖 5 用于確定輪的扭變形。因?yàn)椋?0它是中心對(duì)稱輪（見圖 1b） ，半輪被選中進(jìn)行分析。輪的切割截面是固定，所顯示的圖5a 示。負(fù)載圓周方向作用于輪對(duì)的踏面，從不同圓周出作用于車輪。載荷作用點(diǎn)從車輪內(nèi)側(cè)測(cè)量分別是 31.6 ， 40.8 和 60.0 毫米。圖 6 表明，扭變形與載荷在縱向相對(duì)。他們都是線性的負(fù)荷，不同點(diǎn)的載荷大小很接近。負(fù)載對(duì) Y 軸方向的變形的影響（圖5a 示）忽略不計(jì)。用于后面分析的輪/軌接觸的幾何參數(shù)：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)這里 i= 1，2 分別表示左、右邊輪/軌。 （ 3 ）中的參數(shù)的定義詳細(xì)見名為Nomenclature 的論文。輪轉(zhuǎn)向軌道的左側(cè)時(shí)，我們?cè)O(shè)定它們大于 0，如果是在順時(shí)針方向傾斜 ψ ＞0， ，輪軸和軌道之間橫向方向指向左側(cè)。參數(shù)依賴于輪軌的外形、Y 和ψ 。但是，如果輪軌外形已經(jīng)確定，他們主要依靠 Y[7] 。數(shù)值的詳細(xì)討論方法見[7,8]和輪/軌接觸的幾何結(jié)果。當(dāng)輪正在軌道上切線運(yùn)動(dòng)時(shí)輪和鋼軌的剛性蠕動(dòng)改為[8] 。這里 i= 1、2 ，它的涵義相同于（3） 。 （4）中不確定參數(shù)的名稱可以在 Nomenclature中看到。很明顯，蠕動(dòng)力不僅取決于接觸幾何參數(shù)，而且還取決于輪的運(yùn)動(dòng)的形式。由于當(dāng)輪/ 軌外形確定時(shí)接觸幾何參數(shù)的變化主要取決 Y，一些由時(shí)間派生的參數(shù)可以寫出。在計(jì)算輪/軌的幾何和接觸蠕動(dòng)時(shí)，大范圍的偏航角和側(cè)向位移輪被選中， ，以使輪/軌的蠕動(dòng)和接觸角即使野外工作環(huán)境中也盡可能完全的獲得。因此，我們選擇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 是中心差分法計(jì)算的且數(shù)值結(jié)果 φ 和 Δi 相對(duì)10=l0 = 746.5mm, r0 = 420mm。用通過(guò)以上選定范圍的 y,ψ,y/v 和 r0、ψ/v ，我們可得 ξ i 1 范圍從-0.0034 至 0.0034，ξ i 2 范圍從-0.03 到 0.03 ，ξ i 3 范圍從-0.00013 到0.00013（毫米 -1） ，和接觸角 δi 是 2.88 至 55.83°。由于篇幅限制機(jī)構(gòu)的蠕動(dòng)和接觸幾何詳細(xì)計(jì)算結(jié)果就不表明本文中。=114.總結(jié)（1）本文簡(jiǎn)要分析了機(jī)構(gòu)的結(jié)構(gòu)彈性變形對(duì)滾動(dòng)接觸時(shí)滾動(dòng)接觸性能的影響。據(jù)了解，在接觸面是不完全滑的情況下，減少接觸機(jī)構(gòu)的接觸剛度增加了接觸面粘/滑面積。（2）在分析蠕動(dòng)力時(shí)應(yīng)用了 Kalker 理論。在分析中，有限元方法用于確定影響系數(shù)，這些系數(shù)表明輪/軌的彈性位移由作用于每個(gè)矩形單元單位牽引力所致，這是用來(lái)取代一些由 Kalker 的理論中 Bossinesq 和切瑞蒂公式計(jì)算出的影響系數(shù)。數(shù)值結(jié)果表明輪/軌的蠕變力在兩條件下不同種，這兩種情況分別考慮到和忽視了輪/軌結(jié)構(gòu)的彈性變形的影響。（3）輪和軌的結(jié)構(gòu)彈性變形降低道運(yùn)行的輪和軌道的接觸剛度，并在蠕變力不飽和的條件下，明顯減少輪和軌道之間蠕變力。因此，形勢(shì)有利于減少磨損，輪軌滾的動(dòng)接觸疲勞。（4）在研究時(shí)，圖1a中顯示的是忽視輪彎曲變形影響和交叉影響系數(shù)的，AIiJj(i _= j ; i, j = 1, 2)沒有修正。因此，數(shù)值結(jié)果的精確被降低。此外，當(dāng)輪中心的側(cè)向位移y＞10毫米時(shí)，就會(huì)產(chǎn)生邊緣效應(yīng)。在這種情況下，接觸角是非常大，法向負(fù)荷的組成部分在橫向方向非常大。大的側(cè)向力使軌道和輪對(duì)生產(chǎn)大的結(jié)構(gòu)變形，這將影響輪/軌接觸幾何參數(shù)的和剛性蠕動(dòng)參數(shù)。因此，剛性蠕動(dòng)，蠕變力，接觸幾何參數(shù)，SED和輪運(yùn)動(dòng)相互之間有很大的影響。時(shí)很有必要對(duì)它們綜合考慮。它們的數(shù)值結(jié)果可以通過(guò)替代迭代法得到。產(chǎn)生邊緣效應(yīng)時(shí)輪軌間可能形成等角接觸或兩點(diǎn)接觸。輪軌滾動(dòng)接觸的這種現(xiàn)象和是在非常復(fù)雜的，在不久的將來(lái)，或許可用新滾動(dòng)接觸理論分析，這可能是一種有元模型，包括輪和軌道結(jié)構(gòu)變形的影響和所有邊界條件。