轉(zhuǎn)盤換軌電動平車系統(tǒng)的設(shè)計-電動轉(zhuǎn)盤的設(shè)計,轉(zhuǎn)盤換軌電動平車系統(tǒng)的設(shè)計-電動轉(zhuǎn)盤的設(shè)計,轉(zhuǎn)盤,電動,平車,系統(tǒng),設(shè)計 輪和軌道的結(jié)構(gòu)彈性變形對滾動接觸的輪/軌蠕變力的影響 摘要：本文簡要分析了機構(gòu)的結(jié)構(gòu)彈性變形對滾動接觸時滾動接觸性能的影響。詳細研究了輪和軌道結(jié)構(gòu)變形對輪軌滾動接觸時的蠕變力的影響。對輪和軌道的一般性結(jié)構(gòu)彈性變形進行了有限元分析，以及分別獲得了表示結(jié)構(gòu)彈性變形和相應(yīng)的滾動方向負荷和橫向方向輪的關(guān)系。利用這些關(guān)系，我們計算了輪軌切線接觸的影響系數(shù)。這些影響系數(shù)說明結(jié)構(gòu)發(fā)生彈性變形與輪/軌接觸面上一個小矩形面積內(nèi)的單位密度牽引力有關(guān)。它們被用來修整一些由在Kalker以非赫茲形式的三維彈性體滾動接觸理論中提出的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;滾動接觸;蠕變力;結(jié)構(gòu)彈性變形 1.導(dǎo)言 在軌道上運行的火車輪和鐵軌之間的激烈行動引起輪和軌道的結(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接觸性能，如蠕變力，起皺[ 1-3 ] ，粘附，滾動接觸疲勞，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的關(guān)系可用該理論的Bossinesq和切瑞蒂公式表示。在實踐中，當輪正在軌道上運動時，接觸處的彈性變形大于按現(xiàn)有的滾動接觸理論所計算出的值。這是因為輪/軌的彈性遠大于半彈性空間。相應(yīng)的負載造成輪/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/軌道的縱向動態(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軌道的橫向動荷載。可用于機車運動的與旋軸輪轉(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驅(qū)動力矩引起的。直至目前為止很少有發(fā)表論文討論SED對輪和軌道之間的滾動接觸的蠕動和蠕變力的影響。 事實上，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影響接觸面的法向壓力很大。該切線接觸剛度降低對粘附/滑移區(qū)的境況和接觸面的牽引力的影響很大。如果考慮到滾動接觸中對輪/軌的滾動接觸分析，接觸面一對接觸粒子的總滑動系數(shù)與按本滾動接觸理論計算的是不同的。取得的所有接觸粒子的總滑動系數(shù)和摩擦功，小于在忽略SED的影響條件下分析輪/軌蠕變力時所得值。接觸面粘/滑區(qū)的比例也大于不考慮SED的影響時的。本文簡要分析了機構(gòu)的結(jié)構(gòu)彈性變形對滾動接觸時滾動接觸性能的影響，并在分析輪和軌道蠕變力時就應(yīng)用了Kalker的非赫茲形式三維彈性機構(gòu)滾動接觸理論模型。在分析時選定的輪和鐵路數(shù)值分別是，一列貨運汽車的錐形剖面輪，中國“TB” ，和60公斤/米的鋼軌。有限元方法是用來確定他們的SED 。根據(jù)SED和通過有限元獲得的相應(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)是用來取代一些由Kalker的理論中的Bossinesq和切瑞蒂公式計算出的影響系數(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/滑率的機械裝置 為了更好地了解輪/軌滾動接觸的輪/軌SED的影響，我們有必要簡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/滑率的機械裝置。一般來說，接觸面的一對接觸粒子之間的總滑動，包含剛性滑移，接觸面接觸處的彈性變形和SED。圖3A描述接觸對粒子的情形，A1和A2，滾動接觸體且沒有彈性變形。線A1-A1和A2-A2標記于圖3A中，以便更好的理解說明。機構(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中兩個破折號之間的線是由機構(gòu)的硬性的運動和滾動或滑動所造成的 。該處的彈性變形點，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)的滾動接觸理論確定的，他們導(dǎo)致了點A1和點A2的彈性位移之間的差異 ， U1= u11 - u21。如果機構(gòu)的結(jié)構(gòu)彈性變形的影響被忽視，總滑點之間， A1和A2 ，可以理解為：S1= w1?u1=w1?(u11 ? u21)（1）。機構(gòu)的結(jié)構(gòu)彈性變形的主要由牽引力所造成的，p和p_作用于接觸點和機構(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（ox1x3，見圖3A）約束的剛性運動。u10和u20是用來分別表示點A1和點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和機構(gòu)的幾何形狀保持一致。點A1和點A2位移差異，取決于u10和u20，應(yīng)為u0 = u10 - u20 。這樣的條件下，考慮機構(gòu)的結(jié)構(gòu)彈性變形，總滑點之間，A1和A2 ，可以寫成：S1= w1?u1?u0（2）。很明顯S1和S*1是不同的。接觸粒子對之間的牽引力（或蠕變力），極大地取決于S1（或S * 1 ）。當|S1| > 0 (or |S1 | > 0)接觸粒子對是打滑且牽引進入飽和。在這種情況下，根據(jù)庫侖摩擦定律，如果摩擦系數(shù)與假設(shè)的法向壓力相同，上述兩個條件下牽引力相同。這樣牽引力對U1的作用在上述兩個條件下也是相同的。如果|S1| = |S1 | > 0, |w1| 在（2）中要大于（1）中。即接觸粒子對在沒有u0的影響時進入滑動形勢快于有u0的影響時。相應(yīng)的整個接觸面在沒有u0的影響時進入滑動形勢快于有u0的影響時。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對他們進行了簡單的描述。 4A表明了粘/滑區(qū)的情況。圖4A中的標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機構(gòu)的蠕動W之間關(guān)系。圖4A中的標志和圖4B中的具有相同的含義。從圖4b可知，切線牽引力F1達到最大值F1max在W1= w_1而不考慮u0作用時和F1達到最大值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和這兩個機構(gòu)之間的滾動接觸小的接觸剛度。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)變形的計算 為了計算圖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。因為，它是中心對稱輪（見圖1b），半輪被選中進行分析。輪的切割截面是固定，所顯示的圖5a示。負載圓周方向作用于輪對的踏面，從不同圓周出作用于車輪。載荷作用點從車輪內(nèi)側(cè)測量分別是31.6 ， 40.8和60.0毫米。圖6表明，扭變形與載荷在縱向相對。他們都是線性的負荷，不同點的載荷大小很接近。負載對Y軸方向的變形的影響（圖5a示）忽略不計。 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)的定義詳細見名為Nomenclature的論文。輪轉(zhuǎn)向軌道的左側(cè)時，我們設(shè)定它們大于0，如果是在順時針方向傾斜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)值的詳細討論方法見[7,8]和輪/軌接觸的幾何結(jié)果。當輪正在軌道上切線運動時輪和鋼軌的剛性蠕動改為[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，蠕動力不僅取決于接觸幾何參數(shù)，而且還取決于輪的運動的形式。由于當輪/軌外形確定時接觸幾何參數(shù)的變化主要取決Y，一些由時間派生的參數(shù)可以寫出。在計算輪/軌的幾何和接觸蠕動時，大范圍的偏航角和側(cè)向位移輪被選中，，以使輪/軌的蠕動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是中心差分法計算的且數(shù)值結(jié)果φ和Δi相對10=l0 = 746.5mm, r0 = 420mm。用通過以上選定范圍的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°。由于篇幅限制機構(gòu)的蠕動和接觸幾何詳細計算結(jié)果就不表明本文中。 4.總結(jié) （1）本文簡要分析了機構(gòu)的結(jié)構(gòu)彈性變形對滾動接觸時滾動接觸性能的影響。據(jù)了解，在接觸面是不完全滑的情況下，減少接觸機構(gòu)的接觸剛度增加了接觸面粘/滑面積。 （2）在分析蠕動力時應(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矩形單元單位牽引力所致，這是用來取代一些由Kalker的理論中Bossinesq和切瑞蒂公式計算出的影響系數(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，形勢有利于減少磨損，輪軌滾的動接觸疲勞。 （4）在研究時，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，當輪中心的側(cè)向位移y＞10毫米時，就會產(chǎn)生邊緣效應(yīng)。在這種情況下，接觸角是非常大，法向負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)的和剛性蠕動參數(shù)。因此，剛性蠕動，蠕變力，接觸幾何參數(shù)，SED和輪運動相互之間有很大的影響。時很有必要對它們綜合考慮。它們的數(shù)值結(jié)果可以通過替代迭代法得到。產(chǎn)生邊緣效應(yīng)時輪軌間可能形成等角接觸或兩點接觸。輪軌滾動接觸的這種現(xiàn)象和是在非常復(fù)雜的，在不久的將來，或許可用新滾動接觸理論分析，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。 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. ? 2002 Elsevier Science B.V. All rights reserved. Keywords: Wheel/rail; Rolling contact; Creep force; Structure elastic deformation 1. 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 physical 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 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 [8]: 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 = 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 o