Rolling Contact Theory Research Articles

ANALYSIS ON EVOLUTION OF INITIAL RAIL CORRUGATION

A model of rail corrugation calculation is put forward. The model considers a combination of a Non-Hertzian rolling contact theory of wheel/rail system, rail material wear model and a coupling dynamics of rail vehicle/track in the vertical and lateral directions. A corresponding numerical method is developed to analyze evolution of the initial rail corrugation with different wavelength with an increase of passenger car passage. When the 4 wheels of a same bogie roll over the rails with the same initial corrugation, the wave-depth, passing frequencies and phases of the initial corrugation in development are calculated. The numerical results obtained indicate that: ① The wave-depth of the initial corrugation with an fixing wavelength decreases with an increase of the passenger car passage, the initial corrugation passed by the leading wheelset decays much more than that passed by the trailing wheelset ② The evolution of the initial corrugations has a tendency to move forward. ③ After the leading wheelset rolls over the rails with the initial corrugation with a fixing wavelength repeatedly the initial corrugation gradually changes. The new corrugation gradually forms and presents two wavelengths. ④ Under the condition of the passenger car passage increase, the smaller the wavelength of the initial corrugation is, and the faster the wave-depth of the initial corrugation attenuates.

Numerical simulation of rail corrugation on a curved track

The effects of track vibration with its natural frequency in the vertical and lateral directions on the formation and development of rail corrugation are analysed in detail in the present study. Kalker’s rolling contact theory with non-Hertzian form is modified and then used to calculate the frictional work density on the contact area of the wheel and rail in rolling when a wheelset is steadily curving. A model presenting the material loss of unit area proportional to the frictional work density is used to determine the wear of contact surface material of the rail. Due to the continuous and repeated rolling/slip contact of the wheel and rail the accumulation of the wear obtained by calculation reveals a periodical change in the rolling direction of the wheel. The numerical results also show that the track vibration with its natural frequencies can cause the formation of initial corrugation on the smooth contact surface of rail during the first passage of wheelset. The occurring wavelength of the corrugation depends on the frequencies and the rolling speed of the wheelset, and the depth and growth speed of corrugation depend on the vibration amplitude of the contact normal load and the lateral vibration of track.

Effect of passenger car curving on rail corrugation at a curved track

The paper presents a corrugation calculation model, which considers Kalker's non-Hertzian rolling contact theory to be modified, a material wear model and a vertical and lateral coupling dynamics of a half passenger car and a curved track. The dynamics characters of the curved track model in frequency domain were investigated by the commercial finite element code ANSYS, and some results concerning rail corrugation are presented in this paper. During a passenger car passing a curved track the dynamical performance of the vehicle and track and the initiation and growth of the curved rail corrugation are analyzed with the present corrugation calculation model. In the numerical calculation, two track states are investigated. One is that the track does not have any congenital defect except for the discrete rail support by sleepers. The other is that the track has a lateral dent on the gauge corner of the high rail. The rail corrugations analyzed are attributed to the material wear mechanism. The numerical results obtained indicate that (1) a high passing frequency corrugation initiates on the smooth running surface of the curved rail during the first passing of the passenger car through the curved track without defects; (2) the initial corrugation develops quickly and its passing frequencies change with an increase of passenger car passage; (3) the interaction of the leading wheelset of the bogie and the curved rails causes more severe corrugation and wear on the rail running surface than that of the trailing wheelset of the same bogie; (4) discrete rail support by sleepers is the congenital defect leading to rail corrugation formation.

Effect of track lateral geometry defects on corrugations of curved rails

When a passenger car passes through a curved track with lateral geometry defects, the effect of the defects on the formation of curved rail corrugation is investigated with a numerical method. The numerical method of rail corrugation considers a combination of Kalker's rolling contact theory with non-Hertzian to be modified, a rail material wear model, and a vertical and lateral dynamics model of the half passenger car coupled with the curved track. In the calculation the considered lateral geometry defects of the track are random variations of the curved track gauge. The corrugations occurring on the running surfaces of the rails passed by the four wheels of the same bogie are calculated. The important numerical results are obtained as follows: (1) the random variation of the curved track gauge causes contact vibrations of both wheels and rails, and the undulatory wear form on the running surfaces of the rails when the passenger car passes the curved track first. The increase of the passenger car passages leads to a quick development of the corrugation with many different wavelengths. (2) The rail corrugations caused by the track lateral geometry defects present two types of wavelengths. One is concerned in the variation frequency of the track irregularity, and the other concerned in the natural frequencies of the track to be easily excited. With an increase of the passenger car passage, the natural frequencies of the track to be easily excited dominate the wavelengths of the corrugation in development.

Effect of rail corrugation on vertical dynamics of railway vehicle coupled with a track

The effect of rail corrugation on the vertical dynamics of railway vehicle coupled with a curved track is investigated in detail with a numerical method when a wheelset is steadily curving. In the calculation of rail corrugation we consider the combination of Kalker’s rolling contact theory modified, a model of material loss on rail running surface, and a dynamics model of railway vehicle coupled with a curved track. In the establishment of the dynamic model, for simplicity, one fourth of the freight car without lateral motions, namely a wheelset and the equivalent one fourth freight car body above it, is considered. The Euler beam is used to model the rails and the track structure under the rails is replaced with equivalent springs, dampers and mass bodies. The numerical results show the great influence of the rail corrugation on the vibration of the parts of the vehicle and the track, and the some characters of rail corrugation in development.

Effect of track irregularities on initiation and evolution of rail corrugation

The effect of track irregularities on rail corrugation is investigated in detail with the numerical method when a wheelset is steadily curving. The irregularities considered in the analysis include initial running surface of rail with periodically varying and different wave length, stochastic roughness on the rail running surface, and vertical uneven support stiffness of the rail due to the discrete sleeper supports. The numerical method considers a combination of Kalker's rolling contact theory with non-Hertzian to be modified, a linear frictional work model and a vertical dynamics model of railway vehicle coupled with a curved track. The model is also validated by an experiment with a full scale facility. The influence of different speeds of wheelset curving on the development of the corrugation is taken into account in the calculation. The numerical results indicate that (1) for existing of the initial corrugation of new rail with any wavelength the depth from the peak to trough of it decreases gradually with an increase of wheelset passage, but the initial corrugation evolved has a tendency to move in the rolling direction, (2) the amplitude of the initial stochastic roughness of new rail is gradually leveled out and but a corrugation with very small depth and a few fixed passing frequencies is initiated, the passing frequencies are the same as the natural frequencies of the track, and (3) the discrete rail supports by sleepers have a great influence on the formation of the corrugation.

Adhesion experiment on a wheel/rail system and its numerical analysis

The experiment on the adhesion coefficient of a wheel-rail system has been carried out by means of a full-scale test facility under the condition of different axle loads and rolling speeds. The effects of the condition of the wheel-rail contact surfaces, such as a clean and dry surface, water and oil contamination and slip, on the adhesion coefficient have been investigated in the experiment. The experimental results show that, when the rolling speed of the wheelset increases, the adhesion coefficient decreases under the condition of the constant creepage and water contamination on the contact surfaces, but it increases for oil contamination. Using the data obtained by statistics and analysis of the experimental results and Kalker's rolling contact theory with Hertzian form modified by the present authors, a numerical analysis concerning the effect of wheelset rolling speed on the adhesion coefficient and the distribution of the stick-slip area in the contact area has been made. The numerical results are in good agreement with those obtained by experiment. They are very useful in designing the traction power of a locomotive at higher speeds.

Effect of a scratch on curved rail on initiation and evolution of rail corrugation

The effect of a scratch formed on the running surface of a curved rail, due to the slide of a locomotive wheel, on the formation and evolution of rail corrugation is investigated in detail with numerical methods when a wheelset is steadily and repeatedly curving. In the calculation we consider a combination of Kalker’s rolling contact theory with non-Hertzian to be modified, a linear frictional work model and a vertical dynamics model of railway vehicle coupled with a curved track. Also the influence of different speeds of wheelset curving through the scratch on the development of the corrugation is taken into account. The numerical results indicate that a scratch causes strong contact vibration between the wheel and rail, and initiation and development of rail corrugation under the condition of steady creepage occurring between the wheel and curved rail. The wave-length of the corrugation depends on the speed of wheelset curving and the natural frequencies of the track.

A. Yu. Ishlinskii's researches in the field of rolling friction and their development

The results of the research by A. Yu. Ishlinskii and others on the theory of rolling contact of deformable bodies, taking into account their imperfect elasticity and partial slip in the area contact region, are presented.

A Survey of Rail Vehicle Track Simulations and Flexible Multibody Dynamics

The important development in rolling contact theory withthe recent advances made in the field of flexible multibody dynamics canserve as the foundation for developing new analysis and designcomputational methods for railroad vehicle/track systems. Multibody computational methods can be used tosimulate the dynamic effects due to the structural flexibility of thevehicle components and the track, multiple coupled railway carsnegotiating variable track geometry, derailments resulting from gagewidening, three-dimensional wheel/rail contact, vehicle trackinteraction, and vehicle dynamics under high operating speeds. Asdiscussed in this review paper, based on the new development in rollingcontact theory, one can predict the contact forces between the wheel andthe rail when realistic kinematic and dynamic descriptions are providedat the contact points. Basic quantities such as the longitudinal,lateral and spin creepages are essential for the accurate prediction ofthe contact forces. Nonetheless, in many investigations, linearized orpartially linearized kinematic expressions are used to define thecreepages. Using new multibody algorithms which allowfor the analysis of nonlinear models, the linearization schemescurrently employed in railroad vehicle/track research can be evaluated.Other related issues considered in thissurvey article include wheel/track interaction models, safetyconsideration, experimental verification of simulation results, andapplications which can significantly benefit from adopting the moregeneral computational flexible multibody techniques. As oneof the main objectives of this survey article is to shed more light onthe limitations of some of the current simulation tools used by railroadindustry and at the same time demonstrate the benefits of adoptingcomputational flexible multibody methodologies in railroad vehicle/tracksimulations, some future research areas are identified in the Summaryand Conclusions section.

The long road to solution of the railway hunting and curving problems

Two theoretical problems in railway vehicle mechanics required an exceptionally long time-scale for their solution: the ‘hunting’ problem and the prediction of curving behaviour. Here the history of each is recounted from the point of first recognition (in theoretical terms) to effective solution. Also briefly described is the parallel development of rolling contact theory, which is needed in both applications.

A fast non-steady state creep force model based on the simplified theory

In this paper some preliminary results are presented for a fast non-steady state creep force model which is based on Kalker's simplified theory of rolling contact (J.J. Kalker, Vehicle Syst. Dynamics, 11 (1982) 1–13). Problems with moderate non-steady state creepage and small non-steady spin can be treated at a very high speed on a personal computer with this method. Comparison made with CONTACT (J.J. Kalker, Three-Dimensional Elastic Bodies in Rolling Contact, Kluwer, Dordrecht 1990). shows its promise for dynamic simulation. Further effort to reduce its error and to make it suitable for treating non-steady normal force and non-steady varying contact patch is needed.

Wheel-rail rolling contact theory

In this paper the theory of rolling contact is surveyed after a development of over 60 years. Six theories are significant at present: (1) the two-dimensional theory of Carter (1926); (2) the linear theory (Kalker 1967); (3) the complete theory (CONTACT, Kalker 1983–1990); (4) the British Rail Table Book ( ca. 1980); (5) the theory of Shen, Hedrick and Elkins (1984); (6) the simplified theory (Kalker, 1973–1989). Their operation, scope and limitations will be discussed, and it will be indicated to which problem(s) of wheel-rail technology each of these theories is best suited.

Some New Results in Rolling Contact

SUMMARY In the present paper three problems in the simplified theory of rolling contact are investigated. As to the first problem, three benchmark loadings, derived by Kalker in 1973 for Hertzian rollingcontact, are in existence. Each of these loadings gives rise to a value of the flexibility parameter of the simplified theory. These values are combined to a single, creepage dependent value of the flexibility, which appears to have an error of at most 10 to 15%. Secondly, the law of Coulomb is generalised by introducing two values of the coefficient of friction. The FASTSIM algorithm is adapted to that, and it is found that the traction, and hence the displacement, show a discontinuity inside the contact area. The discontinuity in the displacement is removed by introducing damping in the constitutive relations of the simplified theory. The damping constant is determined experimentally. When the damping coefficient decreases, the damped solution tends to the solution obtained directly without damping. This...

Wheelset Mechanics During Wheelclimb Derailment

An analysis of the mechanics and dynamics of a railroad vehicle wheelset during flange contact and wheelclimb derailment is presented. The theoretical model includes wheelset lateral, vertical, roll, yaw, and axle rotation degrees of freedom, plus lateral displacement of the truck frame. The equations of motion are based on the kinematics and dynamics of the wheelset subject to constraints imposed by wheel/rail contact geometry. These constraints are used to compute creepages and normal forces at the wheel/rail contact points, needed as inputs to the Kalker Simplified Theory of rolling contact. Computational methods for simulation of the nonlinear dynamic model are discussed. Results of the simulation demonstrate the significance of the various degrees of freedom on wheelset motion and on predicted values of the derailment quotient (Q/P).

A Fast Algorithm for the Simplified Theory of Rolling Contact

SUMMARY An algorithm “Fastsim” for the simplified theory of rolling contact is described which is 15-25 times as fast as the existing programs Simrol (Kalker), and 3 times as fast as Rolcon (Knothe). The relative total force computed with Fastsim differs at most 0.2 from that calculated with Simrol, Simcona (Goree & Law), Rolcon, and the “exact” program Duvorol (Kalker). Descriptions and lists of an Algol 60, and HP 67 program version are available upon request: the Fortran IV version is given in the paper.

転がり接解問題解析の一手法 (第3報)

転がり接解問題解析の一手法 (第3報)

Survey of Wheel—Rail Rolling Contact Theory

SUMMARY This paper describes the theory of frictional rolling contact as far as it is significant for the wheel-rail system. It is divided into two parts. The first part, mostly non-mathematical, contains a historical survey from the times of Carter and Fromm (1926) to the present day, in which all aspects of rolling contact theory are discussed. Included are a quantitative account of the results of Hertz theory (Section 3), and a table of the creepage and spin coefficients. The second part gives a present day account of the simplified theory (Section 4), and of the exact linear and non-linear theory (Section 5). The paper closes with some recommendations for future research, of which the most pressing is a thorough investigation of the accuracy of simplified theory.

転がり接触問題解析の一手法 (第2報)

A theoretical approach is presented to the plane theory of rolling contact with friction. An analysis is given of plastic deformation which affects elastic-plastic and residual stress fields in rolling contact. Some effects are discussed of sress fields due to tangential load. In case of static loads, because of friction the tensile zone of residual stress σχis constructed in the neighbourhood of the rear contact area, and the negative shearing residual stress zone is extended widely than that of positive one. The axial residual stress field σz is affected by the secondary plastic flow due to unloading. When the combined loads ran away the values of residual stresses do not vary because of friction, while the tangential load can be understood that specifies the depth of plastic zone.

ころがり接触問題解析の一手法 (第1報)

ころがり接触問題解析の一手法 (第1報)