The stress-strain of thin multilayered coatings covered the surface of the rail is studied near the region of side contact in turning motion. The stress-strain state is studied for various geometric and mechanical coating parameters’ values. A theoretical and a finite element models are developed. Stress-strain state analysis has been made based on models developed and recommendations were given for an optimal coating parameters’ selection

Andrey NASEDKIN

Dmitri SUKHOV

Michail CHEBAKOV

Vladimir KOLESNIKOV

Directory of Open Access Journals

TRANSPORT PROBLEMS                                                                                                               2010 PROBLEMY TRANSPORTU                                                                                       Volume 5 Issue 2   contact problem, finite element method, ANSYS, wheel-rail interaction, thin coating   Vladimir KOLESNIKOV Rostov State Transport University Rostov Strelkovogo Polka Narodnogo Opoltchenia sq. Rostov on Don, 344038, Russia Michail CHEBAKOV*, Andrey NASEDKIN, Dmitri SUKHOV Southern Federal University Miltchakova str., 8a, Rostov on Don, 344090, Russia *Corresponding author. E-mail: chebakov@math.rsu.ru    FINITE ELEMENT MODELLING OF CONTACT INTERACTION BETWEEN WHEEL AND RAIL WITH THREE-LAYERED THIN COATING  Summary. The stress-strain of thin multilayered coatings covered the surface of the rail is studied near the region of side contact in turning motion. The stress-strain state is stu-died for various geometric and mechanical coating parameters’ values. A theoretical and a finite element models are developed. Stress-strain state analysis has been made based on models developed and recommendations were given for an optimal coating parame-ters’ selection.    КОНЕЧНО-ЭЛЕМЕНТНОЕ МОДЕЛИРОВАНИЕ КОНТАКТНОГО ВЗАИМОДЕЙСТВИЯ КОЛЕСА И РЕЛЬСА С ТОНКИМ ТРЕХСЛОЙНЫМ ПОКРЫТИЕМ  Аннотация. Исследуется напряженно-деформированное состояние тонких мно-гослойных покрытий, нанесенных на поверхность железнодорожного рельса в ок-рестности бокового контакта рельса и колеса, при движении в поворотах при раз-личных значениях геометрических и механических параметров покрытий. Разрабо-таны математическая и конечно-элементная модели, на основе которых проведен анализ напряженно-деформированного состояния и даны соответствующие реко-мендации по оптимальному подбору параметров покрытий.   1. PROBLEM STATEMENT   In this paper the interaction between wheel and rail in turning motion is studied. In this case an ad-ditional contact region is appearing at the side surface of the rail apart from contact region at the sur-face of the roll. For the aim of side contact friction reduction the rail was covered by thin antifriction coating of complex structure which could be determined as three-layered coating with each layer differ by mechanical properties and thickness. For evaluation of the stress-strain state in the side contact re-gion, including the thin coating, the investigation of corresponding contact problem is necessary.  Taking into account complicated geometry of rail and wheel system and for simplification of the problem we will use Saint-Venant principle [1] and investigate fragments of wheel and coated rail  participating in side contact. This must be done taking into account real curvatures of corresponding surfaces. In Fig. 1a the rectangular region shows regions of wheel and rail that belongs to plane con-tained the point of initial contact and is located orthogonal to generatrix of the rail, for which a contact 120                                                                V. Kolesnikov, M. Chebakov, A. Nasedkin, D. Sukhov  interaction problem is raised and a finite element model is build. Assume that  z axis directed along the rail and Oxy  plane contains the point of initial contact and is located orthogonal to rail generator. In this case the Oxy  plane is a plane of symmetry. In Fig. 1b fragments of wheel and rail at  0 ≤ z  are presented. Cut volumes are getting into contact after loading while forward approaching each other. With assumption that friction is absent in contact region and load is laid in Oxy  plane we are getting a contact problem for bodies that are symmetric with respect to Oxy  plane. Taking this into account it is possible to study the problem for regions which lay at one side of Oxy  plane with symmetry boun-dary condition on  Oxy  plane and half load applied. It is assumed that three-layered thin coating is fixed on the cylindrical surface of the rail and each layer has different thickness and mechanical prop-erties. Layers are assumed to be rigidly bound among themselves. The symbols for basic geometric dimensions of cut fragments of wheel and rail are presented in Fig. 1b.    b a Fig. 1. Problem geometry: a) Wheel and rail interaction scheme; b) Rail and wheel interaction model during side contact Рис. 1. Геометрия задачи: a) Схема взаимодействия колеса и рельса; b) Модель взаимодействия колеса и рельса во время гребневого контакта  Note that dimensions  i a  ( 7 1 ≤ ≤ i ) signed in Fig. 1b were chosen from the preliminary numeric experiments using a “negligible influence of borders to computation results in contact zone” criterion. Let’s introduce some notations:  pw R ,  pr R  are the radiuses of curvatures of wheel and rail surfac-es, respectively, in contact region on Oxy plane;  w a R  is the radius of wheel along the roll surface; i s h  is the layer thickness of three-layered coating ( 1 = i  is the surface layer,  2 = i  is the middle layer,  3 = i  is the layer connected with rail body);  r E ,  r ν  are Young modulus and Poisson ratio of the rail, respectively;  w E ,  w ν  are Young modulus and Poisson ratio of the wheel, respectively;  i s E , i s ν  are Young modulus and Poisson ratio of the rail coating layer with number i, respectively. We use a finite element method (FEM) for solution of this described problem. For this rail - wheel interaction model we accept the following boundary conditions: – on the Oxy plane of rail and wheel fragments a symmetry condition is specified, i.e. normal dis-placement on the direction of z axis and tangential stresses are absent; – edges of rail fragments for x=0 and y=0 are fixed and edges of wheel and rail with  L z − =  ( 4 a L = ) are free from stresses;  Finite element modelling of contact interaction between wheel and rail…                                         121  –  flat edges of wheel that parallel to  0 = x  and  0 = y  planes after interaction keep flat and have only translation movements; at the same time only shear stresses are allowed and friction is absent for these facets;  – the force laying in the Oxy  plane with magnitude P*=P/2 is applied to the wheel fragment in the point of intersection with two other flat edges; its direction is parallel to common normal of contact surfaces of wheel and rail that belongs to the point of initial contact.   2. FINITE ELEMENT ANALYSIS   The described problem was solved using ANSYS CAE package of version 11.0 [2 – 4]. The pro-gram system was developed using ADPL ANSYS language allows to solve considered problems with using parametric input data. With that, it is possible to conduct research of contact interaction of wheel and rail with different input values of geometric and physical parameters using the same programs. a b Fig. 2. Models of rail-wheel interaction: a) Solid model of contact problem; b) Finite element model of contact problem Рис. 2. Модель взаимодействия колесо - рельс: a) Твердотельная контактная задача; b) Конечно-элемент-ная модель контактной задачи  The solid geometric model of described problem is shown in Fig. 2a, and finite element model for one particular variant of finite element meshing is shown in Fig. 2b. According to methodology of FEM solution of contact problem having significantly non-homogeneous properties [5,6], the meshing thickness is increased in supposed contact region. For that purpose the geometric subregions were ad-ditionally defined; for them a regular less-sized finite element mesh was constructed. In regions occu-pied by elastic materials of wheel and rail the SOLID95 twenty-nodal 3D finite elements of siredipity type with quadratic approximations for each local coordinate were used. Paired quadratic elements TARGE170 and CONTA174 were used fs contact pairs [3].   3. ANALYSIS OF MULTILAYERED COATING’S STRESS-STRAIN STATE IN CONTACT REGION  Using finite element models a calculation of normal stresses distribution in contact region, contact region parameters and effective stresses were made for inner points of interacting bodies. For effective stresses, following formula was used: ( ) ( ) ( ) ) ( 621 2 2 2 2 2 2yz xz xy z x z y x y e τ τ τ σ σ σ σ σ σ σ + + + − + − + − = . 122                                                                V. Kolesnikov, M. Chebakov, A. Nasedkin, D. Sukhov  During the analysis process following input data were taken: applied force Р =70 КН, wheel radius w a R =625 mm, rail surface curvature radius at the point of initial contact  pr R =13 mm, wheel surface curvature radius in Oxy plane on the point of initial contact  pw R =13.5 mm, Young modulus and Poisson ratio of rail and wheel  r E = w E =2.1·105 МПа ,  r ν = w ν =0.3.  Three series of calculations were conducted depending on mechanical properties of the outer coat-ing layer. In the first series of calculations (A) it was assumed:  1 s E = 0.005·105 MPa,  1 s ν =0.47; in the second series (B) –  1 s E = 0.025·105 MPa,  1 s ν =0.35; and in the third series (C) –  1 s E =0.27·105 MPa, 1 s ν =0.4. Simultaneously it was assumed that the outer layer’s thickness  1 s h =0.015 mm; total thick-ness of middle and inner coating layers 0.2 mm  ≤ ≤ h  0.35 mm ( 3 2 s s h h h + = ) taking into account that  6 / 3 h hs = ;  Young modulus and Poisson ratio of the middle coating layer  2 s E =0.9 r E , 2 s ν =0.3; Young modulus of the inner coating layer  r E ≤ ≤ 3 s E 3 r E  and its Poisson ratio  3 s ν =0.3. We introduce also a notation r s E E E / 3 = . The analysis was made by supercomputer system consisting of four T-Platforms Edge-8 computa-tional clusters with top performance at 300 Gigaflops each (total peak performance of the whole sys-tem is 1.2 Teraflops). The ANSYS Multiphysics v. 11.0 licensed software with no restrictions of the number of degrees of freedom and with possibility to parallel computations and commercial use was applied. a     b  Fig. 3. Equivalent stress distribution (h =0.2, E =1.5): a) Equivalent stress distribution in Oxy plane; b) Equiva-lent stress distribution along normal Fig. 3. Распределение эквивалентных напряжений (h =0.2,  E =1.5): a) Распределение эквивалентных на-пряжений в плоскости Oxy; b) Распределение эквивалентных напряжений вдоль нормали  As an example a typical pictures of effective stresses in the Oxy plane are presented in Figs. 3a, 4a for series A with h=0.2 mm, E =1.5 and h=0.2 mm, E =3 ( r s E E E / 3 = ). The typical diagrams of effective stresses distribution in Oxy  plane of the rail on the normal to rail’s cylindrical surface that goes through the initial contact point are presented in Figs. 3b, 4b with the same input values.  The effective stresses’ distribution in Oxy  plane of the rail fragment and in border surface between lower and middle coating layers are presented in Fig. 5a for the case h=0.35, E=3 for series A of nu-meric experiments. In this case, maximum effective stresses are located on the border between lower and middle layers at the some distance from Oxy  plane.  Finite element modelling of contact interaction between wheel and rail…                                         123  a b  Fig. 4. Equivalent stress distribution (h =0.2, E =3): a) Equivalent stress distribution in Oxy  plane; b) Equiva-lent stress distribution along normal Fig. 4. Распределение эквивалентных напряжений (h =0.2,  E =3): a) Распределение эквивалентных на-пряжений в плоскости Oxy; b) Распределение эквивалентных напряжений вдоль нормали  The  contact  stresses’  distribution  for  particular parameters’ values from series A is shown in Fig. 5b. The analysis have also shown that the behaviour of contact stresses’ distribution doesn’t change appreciably both in magnitude and structure for all numerical experiments of all series studied. From Fig. 5b one can also learn about shape and size of contact region, taking into account the height of rectangles that includes the contact region and shown at this figure, which is equal to 16 mm.     Fig. 5. Equivalent and contact stress distribution (A series, h =0.2,  E =3): a) Equivalent stress distribution be-tween lower and  middle layers of coating; b) Contact stress distribution Fig. 5. Распределение  контактных  напряжений  (A series,  h =0.2,  E =3):  a) Распределение  напряжений             между нижним и средним слоями покрытия; b) Распределение контактных напряжений  In the following table the results of effective and contact stresses’ computations for some parame-ters’ values of three series of analysis are presented. Following notation is used:  maxe σ  is the maximal effective stress in the rail body;  ne σ  is the maximal effective stress in the rail body on the normal that belongs to Oxy  plane and includes the initial contact point of rail and wheel;  maxc σ  is the maximal contact stress. Note that according to the results of analysis increasing of lower layer’s stiffness leads to moving of the zone of maximal effective stresses towards the rail surface in the region of thin coating. At the 124                                                                V. Kolesnikov, M. Chebakov, A. Nasedkin, D. Sukhov  same time, lowering inner and middle layers’ thickness leads to higher effective stresses’ values in the thin coating region, and maximal stresses will not belong to the Oxy  plane but will lie in the same distance from it. The table 1 also demonstrates that contact stresses have relatively the same magni-tudes independently to parameters of coating studied and they increase only slightly with outer layer’s stiffness grow. Table 1 Equivalent and contact stress values (MPa) Se-ries E  1.0  1.0  1.5  1.5  2.0  2.0  3.0  3.0 h  0.2  0.35  0.2  0.35  0.2  0.35  0.2  0.35  A maxe σ   561  560  560  561  559  561  812  753 ne σ   559  559  559  559  588  557  756  588 maxc σ   846  846  849  850  850  852  852  856   B maxe σ   558  557  557  557  556  558  812  753 ne σ   556  556  554  556  554  553  756  589 maxc σ   841  841  844  846  845  848  848  851   C maxe σ   582  583  582  583  582  583  834  772 ne σ   579  579  580  579  578  579  775  601 maxc σ   878  878  881  884  884  887  887  891  From the obtained results the following conclusion can be formulated 1) Using the theory of strength and presented results, the stiffness of inner coating layer bonded with main rail body must be chosen as close to the stiffness of main rail body material as possible.  2) Thin three-layered coating with studied parameters do negligible influence to maximal contact stresses’ values in rail and wheel side contact but the character of stress distribution in the inner points of coating depends on its parameters significantly.  The analysis was made with financial support of Russian Fundamental Research Fund (grants No. 08-08-00873, 09-08-12062)   References  1. Novaczky V. Theory of Elasticity. Moscow, Mir, 1975. (in Russian). 2. ANSYS Rel. 11.0. Basic Analysis Procedures Guide. SAS IP Inc. Canonsburg, 2007. 3. ANSYS Rel. 11.0. Elements Reference. SAS IP Inc. Canonsburg, 2007. 4. ANSYS Rel. 11.0. Theory Reference for ANSYS and ANSYS Workbench. SAS IP Inc. Canonsburg, 2007.  5. Kolesnikov V.I., Nasedkin A.V., Chebakov M.I., Ivanochkin P.G. Contact interaction in double- layered self-smearing cylindrical full-floating bearing. Vestnik RGUPS, vol. 4, 2007, (in Russian), pp. 5-10.  6. Kolesnikov V.I., Nasedkin A.V., Chebakov M.I., Bogush A.I. The study of mechanical properties’  heterogeneousness of near-surface wheel layers influence on rail contact interaction characteris tics. Proc. Int. Sci. Techn. Conf. “Actual problems of tribology”, Samara, June 6-8, 2007, vol. 3, Moscow, Mashinostroenie, 2007, (in Russian), pp. 676-690.    Received 14.06.2009; accepted in revised form 2.06.2010 

Finite element modelling of contact interaction between wheel and rail with three-layered thin coating

Abstract

Similar works

Full text

Available Versions

Directory of Open Access Journals