Rolling Contact Theory Research Articles

Effects of decarburized Layer's material property on the rail corrugation development

A rail corrugation development calculation model that can consider the non-uniformity of material properties near rail surface was established to study the effects of rail decarburized layer on the corrugation growth. Firstly, the elastic modulus and hardness at different vertical positions in the rail decarburized layer were measured using nano-indentation technique. Then a two-dimensional wheel-rail rolling contact theory model that can consider the non-uniformity of material properties was established based on elasticity theory and hierarchical model. A numerical table for fast calculation of wheel-rail contact was established. Finally, the rail corrugation development with the presence of rail decarburized layer was simulated by considering wheel-rail contact with non-uniform material properties in the vehicle-track dynamic simulation. The results show that the decrease of elastic modulus and hardness of rail decarburized layer material would accelerate the development of corrugation. The corrugation growth rate with the presence of rail decarburized layer increases 43%. The maximum peak-to-valley depth of rail corrugation is about 9 times larger on the rail with decarburized layer than that on the rail without decarburized layer. Although the hardness plays a much more significant role in the corrugation development than the elastic modulus, the elastic modulus still has some influence on the growth rate of corrugation depth. The maximum depth of corrugation considering the non-uniformity of both elastic modulus and hardness is 11.7% larger than that considering only the non-uniformity of hardness.

A new prediction model for disc cutter wear based on Cerchar Abrasivity Index

The wear evolution indicated that abrasive wear is the dominant wear mechanism for disc cutter wear. Considering the uneven rolling force distribution on the cutterhead, the relative installation radius is introduced to reflect the influence of installation radius on the rolling force, and the CSM rolling force model is corrected based on linear assumption. To accurately predict disc cutter wear, the relative sliding distance between disc cutters and rock is derived based on corrected rolling force and contact theory. The effect of installation radius, cutters radius and penetration on the relative sliding distance is investigated, the results illustrated that the relative sliding distance increase with the installation radius and penetration, conversely, the relative sliding distance increase with the disc cutter radius decrease. In addition, the relationship between wear coefficient and Cerchar Abrasivity Index (CAI) is analyzed by a series CAI test. According to CAI change trend as stylus sliding distance, the effect of stylus shear failure on the abrasivity property within initial test stage was excluded. Furthermore, A new model is proposed to predict disc cutter wear based on the relative sliding distance and wear coefficient. And the effect of installation radius, cutters radius, Uniaxial Compressive Strength (UCS), CAI et al. on the disc cutter wear is investigated, the results illustrate that the disc cutter wear increase with installation radius, penetration, UCS, CAI and spacing between adjacent cutter, conversely, the disc cutter wear increase with the cutter radius and thickness decrease. Finally, the accuracy of proposed model is verified by Yintao water conveyance tunnel project. The research of parameters provides a theoretical basis for optimizing excavation parameters and reducing cutters wear.

A linear non-Hertzian unsteady tangential wheel-rail contact model

The increase in computational capacity has considerably reduced the use of linear models for wheel/rail tangential contact, being currently replaced by theories that adopt non-linear formulations able to address the most complex conditions realistically. However, linear formulations are difficult to replace in certain applications such as acoustic problem modelling, in which case a linear formulation of the track-contact-vehicle system is needed. The vibration that appears in this type of problem covers a wide range of audible frequencies, so, in addition to linearity, these theories are required to be non-stationary. The literature in contact mechanics gives response to this problem through models that consider low creepage levels, but it remains to cover other conditions in which the mean creepage is not small, such as when a railway vehicle negotiates a curve.This work presents a new theory of unsteady linear tangential rolling contact for non-Hertzian areas that considers kinematics as the sum of a constant creepage resulting from large stationary forces (such as those that occur when the vehicle negotiates a curve with constant radius) and small variable creepage due to a high-frequency phenomenon (e.g. the dynamic interaction between the vehicle and the track). The model is based on the Variational Theory (i.e. the CONTACT method for tangential problems), from which a linear formulation with variable creepage is deduced. According to this formulation, the non-steady state contact problem can be solved for any shape of the wheel/rail contact region, requiring a much smaller computational effort than the general unsteady CONTACT approach. The results show a satisfactory agreement of the proposed model to the unsteady CONTACT version, hence confirming the soundness of the proposed contact model.

Practical wheel/rail tangential contact force model for vehicle dynamics analysis combining Levi-Chartet’s formula with adhesion coefficient-velocity relational expression

This paper describes a practical wheel/rail tangential contact force model for railway dynamics analysis under running in rainy conditions. In our previous studies, it was confirmed that experimental results of tangential contact force measurement are agree well with Kalker’s rolling contact theory under dry condition with low humidity around contact surfaces. Here, it can be considered that if the ambient humidity around the contact surface become high infinity, the contact surface is under wet lubrication conditions. On the basis of this assumption, in this study, a practical estimation model for characteristics of tangential contact force under running in rainy conditions is proposed by combining the relationship between the adhesive coefficient and velocity measured on running experiments using actual railway vehicles and Kalker’s linear rolling contact theory. Therefore, to verify the proposed model, the tangential contact force measurement experiment using a twin-disk rolling sliding machine was carried out. As a result, it is confirmed that estimated formulae based on the proposed model are well agreed with experimental results even under different velocity conditions, comparing the relationship between tangential contact force coefficient and slip ratio. From these verified results, the proposed model is considered to be a practical wheel/rail tangential contact force model for vehicle dynamics analysis under rain conditions, because the proposed model has the advantage of low calculation cost and can be easily applied to vehicle dynamics analysis based on multi-body dynamics theories.

Friction torque analysis of planetary roller screw based on the creepage theory

The creepage characteristics of the contact interface are analyzed based on rolling contact theory in this paper. Moreover, creepage parameters such as creepage rate, spinning rate, and Heathcote slip were obtained. The Kalker creepage theory model is employed to determine the friction force within the thread contact interface. The planetary roller screw (PRS) friction force and dynamics model was established based on the Lagrange method. The PRS friction force model is then experimentally validated. Finally, the influence of working conditions and creepage parameters on the friction torque, transmission efficiency, and relative contact interface sliding velocity are analyzed. The results show that the friction coefficient and creepage parameters have significant effect on the friction torque of the PRS.

Generalisation of the linear theory of rolling contact to a single double-elliptic contact region and its application to solve non-Hertzian contact problems using extended FASTSIM

Most contact models addressing the solution of the tangential problem assume an elliptical shape of the contact patch which is derived from the Hertz theory. In particular, the linear theory of rolling contact developed by Kalker is based on this assumption. However, it is well known that in many practical cases the shape of the contact region formed between the rail and a railway wheel can be far from elliptic. Recently, the Simple Double-Elliptic Contact (SDEC) shape has been proposed as an approximation of a wide variety of non-elliptic patches. In this paper, a formulation of the linear theory of rolling contact for a SDEC shape is proposed. The coefficients of the original linear theory for elliptic patches are maintained and four new coefficients are introduced to consider the effect of non-ellipticity. The coefficients of the theory are derived numerically using software CONTACT. Then, an extension of FASTSIM for a SDEC region is introduced and the obtained creep force curves under various conditions are compared to existing formulations of FASTSIM, using results from software CONTACT as a reference. The comparisons show that the proposed model is as fast as FASTSIM and provides more accurate solutions than existing versions of FASTSIM.

Analysis of Contact Stress Distribution between Rolling Element and Variable Diameter Raceway of Cageless Bearing

The change in contact state between the rolling elements and raceway of a cageless bearing with a variable diameter raceway affect the wear of the bearing, which leads to discrete motion failure of the rolling elements. For this purpose, the contact characteristics as contact form and contact stress between the rolling elements and raceway were determined. A numerical method is proposed to determine the three-dimensional contact stress of a cageless bearing. First, combined with the variable diameter raceway structure characteristics and the motion of rolling elements, the rolling elements and raceway contact stress model was established, and the influence factors of contact stress and the maximum stress distribution were determined. Based on the rolling contact theory, the relative position of the stick-slip region and the tangential stress distribution of the contact area were analyzed. The stress equations for the three-dimensional between rolling elements and variable diameter raceway were obtained by the principle of superposition, and the stress component characteristics of the contact area were numerically simulated. The results show that the main influencing factors of contact stress are: load, structure of variable diameter raceway, spindle speed, friction coefficient µ and the ratio of the stick region and the slip region k. Taking a cageless bearing as an example, the influence of the contact curvature Ri on the contact stress is smaller than that of ri. Increasing ri to make it larger than 1.5 mm and controlling the speed to be lower than 13,950 r/min, the maximum stress appears in the conventional raceway, which is beneficial to alleviate the failure of the variable diameter raceway. There are a slip region and a stick region in the contact area, reducing the friction coefficient µ and increasing the stick-slip coefficient k appropriately can ensure the discrete movement of the rolling elements and reduce the wear of the variable diameter raceway. The error of the stress distribution model is less than 15%, which can predict and characterize the contact stress distribution between the rolling elements and the variable diameter raceway. The theoretical guidance for the development and application of cageless bearings is provided.

Practical wheel/rail tangential contact force model for vehicle dynamics analysis under running in rainy conditions

This paper describes a practical wheel/rail tangential contact force model for railway dynamics analysis under running in rainy conditions. In our previous studies, it was confirmed that experimental results of tangential contact force measurement are agree well with Kalker’s rolling contact theory under dry condition with low humidity around contact surfaces. Here, it can be considered that if the ambient humidity around the contact surface become high infinity, the contact surface is under wet lubrication conditions. On the basis of this assumption, in this study, a practical estimation technique for characteristics of tangential contact force under running in rainy conditions is proposed by combining the relationship between the adhesive coefficient and velocity measured on running experiments using actual railway vehicles and Kalker’s linear rolling contact theory. Therefore, to verify the proposed technique, the tangential contact force measurement experiment using a twin-disk rolling sliding machine was carried out. As a result, it is confirmed that estimated formulae based on the proposed technique are well agreed with experimental results even under different velocity conditions, comparing the relationship between tangential contact force coefficient and slip ratio. From these verified results, the proposed technique is considered to be a practical wheel/rail tangential contact force model for vehicle dynamics analysis under rain conditions, because the proposed technique has the advantage of low calculation cost and can be easily applied to vehicle dynamics analysis based on multibody dynamics theories.

Vibration modeling of wind turbine shaft as rigid shaft supported by EHL contact ball bearings with overhung disc system

An investigation into the dynamic behavior of Elastohydrodynamic Lubricated (EHL) angular contact ball bearings employed in wind turbines is given in this paper considering non-linear contact characteristics due to combined dynamic loads, different rotation speeds, hydrodynamic effects and load-deformation relation. In order to investigate the dynamic behavior of shaft-bearing system, a rigid shaft with overhung disk which is supported by a couple of EHL angular contact ball bearings is modeled as a 5 DoF nonlinear system.The contact between the rolling element and running surfaces in the bearing is modeled as an equivalent spring and damper. Hertz contact theory and EHL theory are used to obtain EHL contact characteristics and contact forces. Simplified rolling contact theory is used and pure rolling is assumed in the kinematic analysis. The contact angle and mutual approach of rolling elements are obtained analytically. The contact forces and film thickness are calculated iteratively for the quasi-static case using the Newton–Raphson method. In order to express the dynamic behavior of the system, nonlinear equations of motion are solved by a numerical method using Runge Kutta algorithm. The results indicate that the stiffness in EHL contact increases with the increase in load, the damping decreases with the increase in speed, the vibration behavior of the system is more complicated than the dry contact as the natural frequencies are now dependent on system running speed. It has also been observed that there is a significant decrease in vibration amplitude of the system under lubricated contact conditions as well as the frequencies.

A fast method for determination of creep forces in non-Hertzian contact of wheel and rail based on a book of tables

The Kalker book of tables for non-Hertzian contact described in a previous work from the authors provides creep forces, but the moment generated in the contact patch is not available. The extended Kalker book of tables for non-Hertzian contact (KBTNH) presented in this paper provides creep forces, as well as the moment. The paper presents the simplified linear theory of rolling contact for a simple double-elliptical contact (SDEC) region used for regularisation of contact patches and, resulting from this theory, the full symmetry relations for creep forces and moment. The parameterisation of variables and structure of the extended book of tables are described. The extended Kalker book of tables of moderate volume has been computed in co-simulation Matlab-CONTACT. The creep forces and moment obtained from KBTNH have been compared to those obtained directly by CONTACT program and FASTSIM algorithm. The comparison shows that KBTNH is in good agreement with CONTACT for a wide range of creepage conditions and shapes of the contact patch, whereas the use of FASTSIM may lead to significant deviations from the reference CONTACT solutions. The presented example of application is a realistic case of a freight wagon curving simulation, where KBTNH has been used to assess the contribution of the moment into the unit frictional work dissipated in contacts of wheels and rails. The high calculation speed and good accuracy of determining creep forces for non-Hertzian wheel–rail contact make the proposed method a suitable tool for multibody system (MBS) simulation programs oriented for rail vehicle dynamics.

Multi-step wear evolution simulation method for the prediction of rail wheel wear and vehicle dynamic performance

This paper presents a complete model to estimate the effects of wheel wear on the dynamic behavior and ride comfort of a railway vehicle. A co-simulation of the vehicle dynamics modeled in ADAMS VI-Rail and wear evolution modeled in MATLAB is performed in a loop. The outputs from the vehicle dynamics simulation are used to compute the wear evolution, which in turn affects the vehicle dynamics. The local contact parameters, such as normal contact force, tangential stresses and slip, etc., and wear distribution for each cell of the contact surface are estimated with the help of Kalker’s simplified theory of rolling contact and Archard’s wear model, respectively. The wear distribution and smoothening of the wheel profile are obtained for a short travel distance and are then scaled up for larger travel distance. The worn wheel profile is updated in the vehicle dynamics model after every 10,000 km of travel for further dynamic analysis and this process is repeated until either the critical dynamic performance or wheel wear limits are reached. Several new results emerge by considering both acceleration and braking on a tangent track with sinusoidal irregularities. Critical speed appears to increase initially and then decrease quickly, whereas worn wheels give better ride comfort in both lateral and vertical directions as compared to new wheels. According to the results in this work, wheels may be recommended for re-profiling or replacement much before the critical wear depth recommended in maintenance guidelines is reached.

On the influence of conformity on wheel–rail rolling contact mechanics

The aim of this work is to assess the effects of conformity on local contact related quantities at the wheel–rail interface such as traction distributions, subsurface stresses and frictional work distributions. For this purpose conformal contact analyses are carried out by means of Finite Element (FE) models, and also with the exact rolling contact theory approach developed by Kalker, which has been appropriately adapted by the authors in order to take into account some of the effects of conformity. On the other hand, equivalent cases are analysed without taking into account the effects of conformity. In this way, the validity of the hypothesis of non-conformity is evaluated in different cases with varying degrees of conformity.

Stripe theory based numerical method for solving asymmetrical hysteresis of friction force in linear rolling guideways

Linear rolling guideways (LRGs) play an important role in precision engineering. In the pre-rolling region, the hysteretic friction force exerts great impacts on the positioning accuracy. Numerical and experimental studies of the hysteresis of friction force are presented in this paper. A model, which is based on the stripe theory and the simplified theory of rolling contact, is built to describe the transient hysteresis of the friction force. Then, the model is modified by taking the anelasticity effect into consideration. Experimentally, a linear motor direct-drive setup is utilized to measure the transient asymmetrical hysteresis of the friction force in the pre-rolling region of an LRG. The influences of the pre-rolling displacement and the dwelling time on the asymmetrical hysteresis of the friction force are studied. The numerical and experimental results are well correlated, which shows good accuracy of the model. The transient asymmetrical hysteresis of friction force in the pre-rolling region of LRGs can thus be determined using the model.

Optimal rail profile design for a curved segment of a heavy haul railway using a response surface approach

To determine the optimal design of the rail profile for a curved segment of a heavy haul railway, an optimization method that considers the extent of rail wear over the entire design cycle was developed. The approach is based on wheel–rail rolling contact theory, vehicle–track dynamic theory and nonlinear programming theory. The changes in the rail profile were analyzed using an updating strategy that considers random irregularities in the railway track. The minimum average metal loss from the vehicle in terms of wear and grinding for the whole design cycle was regarded as the design objective, and discrete point coordinates on the rail were regarded as the design variables. A radial basis function was used to establish an approximate model, which formed an explicit function between design variables and design objectives. The optimization model was established on this basis, and a genetic algorithm was used to solve the optimization model for the optimized profile. The maximum passing gross load for the whole design cycle reached 150.74 x106 t, an increase of 139.73% compared with the standard profile, which achieved the purpose of prolonging the service life of the rail.

Analysis and numerical simulation of rolling contact between sphere and cone

In non-conforming rolling contact, the contact stress is highly concentrated in the contact area. However, there are some limitations of the special contact model and stress model used for the theoretical study of the phenomenon, and this has prevented in-depth analysis of the associated friction, wear, and failure. This paper is particularly aimed at investigating the area of rolling contact between a sphere and a cone, for which purpose the boundary is determined by the Hertz theory and the geometries of the non-conforming surfaces. The phenomenon of stick-slip contact is observed to occur in the contact area under the condition of no-full-slip (Q < μ · P). Using the two-dimensional rolling contact theory developed by CARTER, the relative positions of the stick and slip regions and the distribution of the tangential force over the contact area are analyzed. Furthermore, each stress component is calculated based on the McEwen theory and the idea of narrow band. The stress equations for the three-dimensional rolling contact between the sphere and the cone are obtained by the principle of superposition, and are used to perform some numerical simulations. The results show that the stress components have a large gradient along the boundary between the stick and slip regions, and that the maximum stress is inversely proportional to the contact coefficient and proportional to the friction coefficient. A new method for investigating the stress during non-classical three-dimensional rolling contact is proposed as a theoretical foundation for the analysis of the associated friction, wear, and failure.

Wheel squeal noise: A simplified model to simulate the effect of rolling speed and angle of attack

The sound pressure level of wheel squeal has been shown to increase with angle of attack and rolling speed in both field and laboratory tests. However, the exact causes behind the manner of increase are still unknown. To investigate this, a simplified analytical vibration model in the time domain is integrated with nonlinear rolling contact theory developed for wheel squeal. This model is used to simulate the vibration velocity of a test rig wheel at different rolling speeds and angles of attack. The simulated vibration velocities correlate well in the trend with the recorded sound pressure levels of wheel squeal in laboratory tests. Lateral creepage and force at various angles of attack and rolling speeds in the rolling contact are simulated. It is found that due to the interaction of wheel vibration, lateral force and creepage, the vibration velocity amplitude of the wheel increases with angle of attack and rolling speed. The generation mechanism of wheel squeal is explained from the view of energy input per cycle of vibration. Furthermore, the reasons why the sound pressure levels of wheel squeal increase with rolling speed and angle of attack are investigated, and these phenomena are explained theoretically based on energy input and the nonlinear creep behaviour.

Research on Finite Element Model of Wheel-Rail Contact

Many researchers applied creepage to calculating creep force, but relation between creepage and creep force are very complex and it has been a major problem for solving rolling contact theory. The paper uses the finite element method for studying directly creep forces and apply it to the studies of wheel-rail rolling contact. Paper establishes the finite element model of wheel-rail rolling contact based on ALE method in ABAQUS, and simulated unsteady state of wheel-rail rolling contact and research normal force of wheel-rail contact pitch. Results show that the normal maximum pressure in left wheel have a trend toward the center of contact pitch and the normal maximum pressure in right wheel have a trend toward the other center of contact pitch with increasement of displacement

Impact of Yaw Motion of Wheelset on Wheel-Rail Contact Creepage

Many researchers applied creepage to calculating creep force, and relation between creepage and creep force are very complex and it has been a major problem for solving rolling contact theory. The paper established the finite element model of wheel-rail rolling contact based on ALE method (Arbitrary Lagrange-Euler method) in ABAQUS, and research impact of yaw motion of wheelset on creepage of wheel-rail contact. Results show that in the yaw movement there are small fluctuations in elastic longitudinal creepage; elastic lateral wheel creepage of left and right wheel appear different, there are small change after yaw angle beyond 2 mrad; spin creepage of left and right wheel have not change with increase of yaw angle

Impact of Lateral Motion of Wheelset on Wheel-Rail Contact Creepage

Many researchers applied creepage to calculating creep force, and relation between creepage and creep force are very complex and it has been a major problem for solving rolling contact theory. The paper established the finite element model of wheel-rail rolling contact based on ALE method (Arbitrary Lagrange-Euler method) in ABAQUS, and research impact of lateral motion of wheelset on creepage of wheel-rail contact. Results show in the lateral movement value difference between their longitudinal creepage is small, and maximum error is less than 20%, there is more distinct change trend about lateral creepage in left contact area than one in right contact area, and spin creepage of left wheel drop down in 4mm lateral displacement.

Analysis on Wheel-Rail Contact and Rail Cracks of 50m Radio Telescope

In order to search the pointing accuracy degradation and the wheel-rail contact of the National astronomical observatory 50m radio telescope, according to the actual wheel-rail structure and design indicators, the wheel rail contact problem with the finite element analysis based on non-Hertz rolling contact theory is analyzed. The results show that the maximum deformation should be less than 1 mm. Then the measurement scheme of rail horizontal error and deformation is formulated. The mean value of the rail horizontal error is 2.89mm, while the maximum rail horizontal error is 1.5mm. The rail maintenance scheme is put forward after the flaw detection which finds large areas of cracks at the rail junction and the welded joint. The measurement is taken after rail maintenance; the experimental data coincide with the simulation results and then verify the correctness of the wheel-rail contact model, also the solution scheme of rail cracks. The reason for the pointing accuracy degradation is verified finally, which also can provide an effective method for the wheel-rail design and maintenance of large radio telescope.