隨機(jī)方向法減速器優(yōu)化設(shè)計(jì)【單級(jí)圓柱齒輪減速器】【P=10KW n=960r-min i=5】【說(shuō)明書+CAD+SOLIDWORKS】,單級(jí)圓柱齒輪減速器,P=10KW n=960r-min i=5,說(shuō)明書+CAD+SOLIDWORKS,隨機(jī)方向法減速器優(yōu)化設(shè)計(jì)【單級(jí)圓柱齒輪減速器】【P=10KW,n=960r-min,i=5】【說(shuō)明書+CAD+SOLIDWORKS】,隨機(jī) 南昌航空大學(xué)科技學(xué)院學(xué)士學(xué)位論文 畢業(yè)設(shè)計(jì)（外文翻譯） 題 目： 隨機(jī)方法減速器優(yōu)化設(shè)計(jì) 專業(yè)名稱： 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 班級(jí)學(xué)號(hào)： 學(xué)生姓名： 指導(dǎo)教師： 二〇一一 年 三 月 Effects of structure elastic deformations of wheelset and track on creep forces of wheel/rail in rolling contact Xuesong Jin, Pingbo Wu, Zefeng Wen National Traction Power Laboratory, Southwest Jiaotong University, Chengdu 610031, PR China 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 w heels/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]: [7] [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 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. This work was supported by the Natural Science Foundation Committee of China that grant the key research project: “Corrugation of Contact Surface of Wheel and Rail and Rolling Contact Fatigue” (59935100) to the National Traction Power Laboratory, Southwest Jiaotong University. It is also supported by the Foundation for University Key Teacher by the Ministry of Education of China. References [1] K. Knothe, S.L. 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Benchmark test for model of railway track and of vehicle/track interaction at relative high frequencies, Vehicle Syst. Dynam. 24, Suppl. (1995) 355–362. [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) 128–136. [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. 39–53 (in Chinese). 輪輻的柔性變形結(jié)構(gòu)的效果和在滾動(dòng)接觸的輪/ 軌道的潛變力的追蹤 金學(xué)松 吳平博 文澤峰 中國(guó) 成都 600031 西南交通大學(xué) 國(guó)家的牽引動(dòng)力實(shí)驗(yàn)室 摘錄:在這一篇論文中，對(duì)滾動(dòng)接觸機(jī)械裝置上的滾動(dòng)接觸體結(jié)構(gòu)柔性變形的效果簡(jiǎn)短地分析。輪副和軌道對(duì)輪的潛變力的結(jié)構(gòu)變形的效果和軌條詳細(xì)地被分析研究。輪副的一般結(jié)構(gòu)柔性變形和軌道首先分別用