Shakedown Maps Research Articles

Research on the wheel wear and rolling contact fatigue of metro vehicle induced by the rail corrugation

The rail corrugation is a common disease on the track, which exacerbates the wheel-rail interaction and accelerates wheel wear and crack propagation. This study focuses on the wheel wear and rolling contact fatigue of metro vehicle under the rail corrugation. Firstly, the characteristics of the rail corrugation under service conditions are determined by the statistical analysis of the field data, and the rail corrugation is applied to the established vehicle-track coupled dynamics model. Then, the wear index and the work of friction force as indicators of wheel wear are studied. Finally, based on the Shakedown Map and the criterion of maximum amplitude of shear stress, the simulation analysis of wheel-rolling contact fatigue under the rail corrugation is carried out. The results show that the increases in superficial fatigue index and accumulated fatigue are 1.52 and 6.16 times in the wavelength range of 30-90 mm larger than those in the range of 90-210 mm, respectively. Furthermore, the cracks more easily occur 2-4 mm from the outer surface of wheel, and expand along the wheel tread.

A novel prediction method for rolling contact fatigue damage of the pearlite rail materials based on shakedown limits and rough set theory with cloud model

Evaluation and prediction of wheel-rail rolling contact fatigue (RCF) damage can provide important theoretical guarantees for the service safety of wheels and rails and help make maintenance easier to plan. This study aims to develop a novel method for evaluating and predicting RCF damage of the pearlite rail materials with various initial shear yield strengths (ke). Based on the rough set mathematical theory incorporated within the cloud model of the comprehensive evaluation index (P0/ke*μt), a novel evaluation and prediction method for RCF damage states of various pearlite rail materials was constructed using the shakedown limits for pearlite rail materials with various initial shear yield strengths. To develop this novel prediction method, different evaluation indices for RCF damage states were designed. A comprehensive certainty approach was introduced to quantitatively analyze the actual measured values of distinct evaluation indices that corresponds to different RCF damage states, wherein the maximum value rule was applied. Moreover, the prediction results were confirmed after further verifying using the actual measured value of the P0/ke*μt. The results indicated that the predicted results were consistent with the test outcomes. The key feature of this prediction method was that it involved both the intrinsic shear yield strength of evaluated pearlite rail materials and wheel-rail rolling contact variables. On the basis of the two-dimensional classical shakedown map, a three-dimensional shakedown limit diagram for rail materials with varying initial shear yield strengths was further constructed using this novel prediction method. The three-dimensional shakedown limit diagram featured an inclined curved surface. As the initial shear yield strength of the pearlite rail materials increased, the curved surface tilted downward, indicating that an increase in the initial ke value of the pearlite rail materials could result in a lower shakedown limit.

Rail surface damage management through monitoring and modelling

ABSTRACT Rolling contact fatigue (RCF) cracking and wear significantly impact rail surfaces. The interaction between them is crucial; wear dominance can remove initiated cracks, while low wear rates may escalate crack propagation, elevating rail failure risks. Grinding, a preventive maintenance technique, removes remaining cracks, applied in fixed-interval or condition-based regimes. Operational constraints, favouring cyclic regimes, may potentially reduce rail life and increase costs. Thus, an optimal asset management strategy involves grinding based on current RCF condition and its predicted growth rate, considering its interaction with wear. London Underground employs diverse rail inspection methods, including advanced MRX-RSCM technology, to measure crack depth. Research used its measurements, developing a novel Combined Shakedown Map and Tγ approach. This predicts RCF growth under wear interaction, indicating the material to be removed by grinding. Its results are displayed for high and low rails of curved track sites, compared with monitoring measurements, enabling observation of changes in damage susceptibility and related grinding requirements over different rails.

Examining Wear Mechanisms in Railway Wheel Steels: Experimental Insights and Predictive Mapping

Railway systems play a pivotal role in modern transportation networks, contributing to both efficiency and environmental sustainability. This study investigated the multifaceted aspects of wear phenomena in railway engineering, focusing on their significant implications for environmental costs and operational efficiency. Experimental trials were conducted using a high-performance bi-disc apparatus, evaluating a range of materials, contact pressures, and lubrication conditions. Shakedown maps were employed to assess ratcheting behaviour, while the wear rate was analysed as a function of the fatigue index (FI). The results reveal the intricate interplay of contact pressure, slip ratio, material properties, and lubrication in determining wear and ratcheting behaviour. Oxidative and mild wear mechanisms were identified, and wear debris composition and morphology were characterised. The outcomes from this research clarify the pivotal role that wear processes play within railway systems and the far-reaching environmental repercussions they entail. This exploration contributes to the ongoing optimisation of railway operations, offering valuable insights aimed at mitigating unavoidable pollution sources and strengthening sustainability efforts. By delving into the intricate dynamics of wear phenomena within wheel–rail material, this research paves the way for innovative solutions that not only enhance operational efficiency but also minimise the ecological footprint of railway transportation.

Influence of shear yield strength of rail material on the shakedown limit in shakedown map

Rail materials with different shear yield strengths can exhibit different rolling contact fatigue (RCF) damage response during cyclic contact loading. The objective of this work is to achieve the actual shakedown limits in the shakedown map for rail materials with different shear yield strengths through RCF simulation tests of wheel-rail, and to investigate the relationship between the shear yield strength (ke) and the shakedown limit. Rolling-sliding tests were performed to investigate the RCF damage states of three types of rail materials with different shear yield strengths. Then, according to the differences of RCF damage states for each rail material and the method of nonlinear curve fitting, the actual shakedown limits for three types of rail materials were obtained. The actual shakedown limits for the three types of rail materials were lower than the original one in the classical shakedown map. With an increase in the shear yield strength (ke) of the rail material, the actual shakedown limit is reduced. Moreover, a relationship emerged which allowed a simple method to be proposed to obtain the actual shakedown limit based on the shear yield strength. The changing process and differences in the impact of different shear stress levels on the microstructural damage transformation of rail materials from the perspective of contact mechanics have been discussed. The behavior of severe accumulation of residual stresses during cyclic loading and more likely initiation of microcracks are the main reasons why rail materials with a higher shear yield strength (ke) under great contact loads are more prone to developing RCF crack damages. That is, the shakedown limit for the material with a higher shear yield strength (ke) is much lower. In view of the application of the shakedown map in the evaluation and prediction for RCF damage of rail materials with different shear yield strengths, different shakedown limits should be applied to different rail materials when analyzing their likely performance.

Investigation of rail damage considering impact at a welded joint under wet condition

PurposeThe purpose of this study is to develop a transient wheel–rail rolling contact model to primarily investigate the rail damage under wet condition when the train passes through the welded joints.Design/methodology/approachThe impact force induced by welded joints is obtained through vehicle–track coupling dynamics. The normal and tangential wheel–rail contact pressures were solved by elastohydrodynamic lubrication (EHL) theory and simplified third-body layer theory, respectively. Then, the obtained tangential pressure and normal pressure were applied to the finite element model as moving loads, simulating cyclic loading. Finally, the shakedown map and critical plane method were used to predict rolling contact fatigue (RCF) and the initiation of fatigue cracks.FindingsThe results indicate that RCF will occur and fatigue cracks are more prone to appear on the subsurface of the rail, specifically around 2.7 mm below the rail surface in the vicinity of the welded joint and its heat-affected zone.Originality/valueThe cosimulation of numerical model and finite element model was implemented. The influence of surface roughness and fluids was considered. In this model, the normal and tangential wheel–rail contact pressure, the stress and strain and the rail fatigue cracks were obtained under a rail-welded joint excitation.

Impacts of vehicle light-weighting on wheel wear and RCF and a novel ultralight vehicle design

Vehicle light-weighting is a critical design target for rail vehicles, as it reduces energy consumption and enhances the vehicle capacity and dynamic performance, making the railway system more attractive in addressing the rising environmental challenges and increasing demand in transportation. This paper presents a quantitative analysis of the impact of vehicle light-weighting on wheel wear and rolling contact fatigue (RCF), using the USFD wear law, the shakedown map and the Tγ approach. A conventional metro vehicle is utilized as a baseline model, and the mass reductions from different vehicle components (i.e., car-body, bogie frame and wheelset) are implemented for the simulation considering various running scenarios. The effect of mass reduction on wheel wear can be divided into two aspects: quasi-static wheel load and wheel-rail dynamic interaction. In short-radius curves, the change in static axle-load predominantly determines wheel wear, whereas in large-radius curves and tangent track, the wheel-rail dynamic interaction plays an important role, thus showing different rates of wear reduction when mass reduction is achieved respectively from car-body, bogie frames and wheelsets. Reducing vehicle mass can significantly reduce wheel damage of RCF on short-radius curves with curve radii above 400 m, while there is a risk of increasing RCF on tight curve R250, due to the impaired function of wear to counteract the crack propagation. This work also exhibits a specific innovative ultralight vehicle design, where the linear synchronous motor technology is applied to reduce substantially the mass of the vehicle without impairing the capability to provide the required amount of tractive effort. The proposed ultralight vehicle can reduce the wheel wear by approximately 40% and shows substantial benefit for preventing RCF damage, compared to a conventional vehicle.

Rail rolling contact fatigue response diagram construction and shakedown map optimization

The shakedown map is one of the key prediction models used in railway engineering to evaluate rolling contact fatigue (RCF) damages of wheels and rails. The objective of this work is to construct the response diagram of RCF and optimize the classical shakedown map based on the rolling-sliding tests. A method based on rolling-sliding tests for constructing the response diagram was presented. Firstly, the traction coefficient (μ) and load factor (P0/ke) were taken as the X-axis coordinate and Y-axis coordinate of the coordinate system of the classical shakedown map, respectively. Then, test parameters (P0 and μ) were designed and obtained using the various X and Y coordinate in four different regions of shakedown map (i.e., different plots of μ versus P0/ke). After that, for various test parameters, the rolling-sliding tests were carried out using a twin-disc testing apparatus under dry condition to investigate the RCF damages of U75V rail steel. The results showed that three types of damage states could be observed after rolling-sliding tests under different test parameters: (I) neither plastic flow of materials nor fatigue cracks, (II) plastic flow, and (III) fatigue cracks with plastic flow. Thus, the response diagram consists of the above three damage regions. Furthermore, with the increase of P0 and μ, all the depth of plastic flow, the length of fatigue cracks and the wear rates were increased. Moreover, materials were work hardened in the damage states of plastic flow and fatigue cracks. The hardness increment was increased with P0 and μ. In addition, the boundary of ratchetting region (i.e., shakedown limit) in the classical shakedown map for partial slip was optimized based on the RCF damages and the new response diagram. The shape of optimized shakedown limit curve was same as that of the classical one, whereas the position of the optimized curve was decreased.

Predictive maps for the rolling contact fatigue and wear interaction in railway wheel steels

Rolling contact fatigue (RCF) and wear are competing phenomena in railway wheels, but they are typically studied as independent events. In this work, preliminary tests are carried out with a twin-disc bench to explore the relationship between RCF and wear. First, the collected tests are reported on the shakedown maps to assess the cyclic response and calculate the fatigue index parameter used to predict the surface-initiated fatigue damage. Second, the fatigue index and material cyclic yield strength are related to the experimental wear rate. This work proposes maps to predict how the wear rate and cyclic response change by varying the contact conditions (clean or contaminated with water or sand), slip ratio and extraction position of specimens. Furthermore, the estimated wear rate is superimposed to the shakedown map to investigate a possible relationship between RCF and wear. The proposed approach allows to understand how a railway wheel steel behaves as a function of the working conditions and whether some working parameters can be changed without compromising the material performance.

Analysis on the effect of starved elastohydrodynamic lubrication on the adhesion behavior and fatigue index of wheel-rail contact

Friction modifiers (FMs) are widely used in wheel-rail applications. This paper presents a method to analyze the starved elastohydrodynamic lubrication (EHL) of the wheel-rail surface coated with FMs. Combined with rough surface simulation techniques, starved EHL analysis and film thickness analysis, the pressure distribution and adhesion coefficient under different film thickness states are obtained. The effect of film thickness of the FM supply layers and surface roughness on the adhesion coefficient is studied. The adhesion coefficient increases with the decrease in the effective FM film thickness and increase in the surface roughness. Based on the subsurface stress model, the subsurface stress distribution is studied. Then the influence of FMs on the fatigue of wheel and rail is analyzed on the basis of the shakedown map. Finally, the fatigue index of rail is explored in starved EHL state.

Thermo-mechanically coupled sliding contact shakedown analysis of functionally graded coating-substrate structures

The sliding contact shakedown map composed of elastic shakedown limit and elastic limit is significant to the further optimization of functionally graded (FG) coating parameters. The friction heat induced by the relative sliding velocity of contact pairs can cause thermal stress and changes in contact parameters. Nevertheless, the influence of thermo-mechanically coupled effect on the sliding contact shakedown map of FG coating-substrate structures keeps unrevealed. Therefore, a mathematical optimization model is proposed to draw the shakedown map considering the temperature-dependent friction coefficient and yield stress. Based on the thermo-elasto-perfectly plastic material model and multilayered approximation of FG coating, the required thermo-elastic stress field with the temperature-dependent friction coefficient is obtained by employing the conjugate gradient method and discrete convolution-fast Fourier transform algorithm. The results show that the friction heat can cause the decreases of elastic shakedown limit and elastic limit, and increasing the sliding velocity can enhance the decreases. Moreover, the friction heat can elevate the residual tensile stress near the surface and weaken the residual compressive stress at a large depth from the surface. Meanwhile, the temperature-dependence of friction coefficient can cause the increases of elastic shakedown limit and elastic limit, but the introduction of temperature-dependent yield stress brings no obvious change to the shakedown curves due to the slight thermally-induced change of yield stress. Additionally, decreasing the distribution gradient index can not only improve elastic limit and elastic shakedown limit at large friction coefficients, but also reduce the distribution of residual tensile stress near the surface.

Prediction of rail surface damage in locomotive traction operations using laboratory-field measured and calibrated data

Rail damage prediction is a complex task because it depends on numerous tribological parameters and the dynamic conditions produced by the vehicles operating at different speeds and configurations. Shakedown maps and Whole-Life-Rail-Model/T-Gamma have been used to predict rail damage, but they involve assumptions that may reduce their accuracy. This paper proposes a simulation modelling method to predict rail surface damage based on a locomotive digital twin, calibrated shakedown maps and friction measurements. The method improves the accuracy of rail damage predictions by including slip-dependent friction characteristics, co-simulation of locomotive traction mechatronic system and the mechanical properties of the wheel and rail materials measured through tensile tests. A set of operating conditions are simulated on a high-performance computing cluster, with stress results being post processed into calibrated shakedown heatmaps. The method clearly indicated the influences of the different operating conditions on rail damage for specific combinations of wheel-rail materials and vehicle-track configurations.

Prediction of rail damage using a combination of Shakedown Map and wheel-rail contact energy

Rolling contact fatigue and wear are two key damage mechanisms that govern rail life. Although there are several different mechanisms affecting both their initiation and propagation, the trade-off between them is important and their accurate predictions can provide significant benefits when planning rail maintenance activities. Through integration with vehicle dynamics simulations, damage models based on the wheel-rail contact energy (Tγ) and Shakedown theory have often been used to predict damage. In this paper, the findings from previous studies were reviewed to identify their limitations. To assess the accuracy of the predictions, their input parameters were compared for sites with and without reported RCF defects from two lines on the London Underground network. The results indicated certain variations and hence, a new wear and RCF damage prediction method was developed using a combined Shakedown Map and Tγ approach. While the wear model predictions were validated by comparison with measured rail wear, the availability of field crack depth measurements enabled the validation of the new RCF crack depth prediction model. Reasonable predictions of crack depth and wear over consecutive intervals have been achieved on various sites which increases the confidence of the models to support future optimisation of maintenance planning.

Use of shakedown maps to assess plastic flow in railway curves

Plastic deformation of rails can occur on tight curves, which can significantly reduce the rail life. This paper investigated the phenomena of gross plastic deformation, or plastic flow, using multibody vehicle–track interaction and simplified finite element analysis. The focus is on understanding the contact conditions on the low rail of curves and how these differ from those in shakedown maps. To this end, two trial sites are simulated using multibody vehicle–track software. The contact conditions are then compared against several criteria assumed in the derivation of the shakedown maps. A further assumption implicit in the shakedown maps is also investigated by a non-linear finite element analysis. In this case, a more realistic Chaboche material model is used as opposed to the simple linear elastic–perfectly plastic model in the shakedown theory. The results of the finite element analysis are combined with a bespoke indicator of plastic flow to assess the influence of distance to shakedown limits on the likely plastic flow. Finally, a simple interpolation scheme is used to map the finite element results back to the trial sites. The interpolated results for the sites are used to evaluate the influence of running speed and different levels of wheel profile wear. Results suggest that the bespoke indicator defined in this work can be used as an effective measure of plastic flow; this measure is then used to quantify the influence of cant excess on the rates of plastic flow.

On the wheel rolling contact fatigue of high power AC locomotives running in complicated environments

Severe rolling contact fatigue (RCF), occurring continuously around the nominal rolling circle of a wheel as lateral cracks up to 14.5 mm deep, has been observed on some high-power (≥7200 kW) AC locomotives in China. Its characteristics are first explained with data collected during field observations and monitoring tests. Then, a multi-body dynamic model is developed, in combination with the shakedown map and Tγ model, to reveal its initiation mechanisms. It is found that unqualified sand used for adhesion enhancement and complicated environments such as sharp curves and steep slopes are the main causes for RCF.

A 3D dynamic model to investigate wheel–rail contact under high and low adhesion

In this article the finite element elastic-plastic code ANSYS/LS-DYNA was utilised to investigate the stress states and material response of wheel/rail under three contact situations, which included high and low adhesion, and full slip. Canted and non-canted rails were considered to measure how the cant angle affected the contact stress levels. Furthermore, the effects of the contact curvatures on the contact zone and contact pressure were also examined. The simulation of wheel flange contact was conducted to compare the stress state of the rail head and rail gauge. The results showed that a higher level of adhesion would enlarge the slip region in the stick/slip contact patch and widen the surface damage to a larger area. Moreover, the worn wheel/rail profiles would result in a non-elliptical contact patch and an increase of the contact pressure. Based on the shakedown map, it was anticipated that the rail would be damaged from the ratchetting response of the material. • New and worn profiles of wheel and rail were introduced in the contact analysis. • Canted and non-canted rails were applied to evaluate its influence on the contact stresses. • The stress states were determined under high and low adhesion, and full slip contact conditions. • The material response of rail to contact loading was predicted by the shakedown map.

Wheel damage on the Swedish iron ore line investigated via multibody simulation

The Swedish iron ore company LKAB uses freight wagons with three-piece bogies to transport iron ore from its mines in Kiruna and Malmberget to the ports at Luleå and Narvik. A simulation model of the freight wagon is built using the multibody simulation code GENSYS. The objective is to investigate possible sources of rolling contact fatigue (RCF) of the wheels given the high level of observed damage. A parameter study is performed on the effects of vertical track stiffness and viscous damping that occur as a result of seasonal variations of the track condition. Another parameter study is carried out on the influence of the wheel/rail friction coefficient as in winter time the climate is very dry along most parts of the Malmbanan line. The impact of track gauge, track quality and cant deficiency on RCF is also studied. Comparing the calculated and observed RCF locations on wheels, attempts are made to find a relation between wear number and RCF damage. To detect the surface-initiated fatigue a so-called shakedown map is used. It is shown that RCF occurs on the tread of the inner wheels while negotiating curves with below an approximately 450 m radius. It is also shown that cant deficiency can be helpful for the vehicles to negotiate curves and to reduce the risk of RCF, however, on the other hand it may increase the track forces and in severe cases result in flange climbing. Lateral track irregularities and a large track gauge result in small contact areas and can lead to a higher risk of RCF. In cold dry climate conditions, as the water content in air drops significantly, the wheel/rail friction coefficient increases and when the material in the wheel begins to behave in a brittle manner, the risk of RCF is significantly increased, especially when the wear rate is not high enough to remove the initiated cracks.

The effect of slip ratio on the rolling contact fatigue property of railway wheel steel

Shelling is one of the typical rolling contact fatigue (RCF) failures of railway wheels. Creepage between wheels and rails due to rolling radius difference in curves is inevitable on railway tracks. Therefore, there are tangential stresses and slip phenomena on wheel treads. Eventually, initiation of RCF cracks being the origin of shelling is accelerated by creepage. The objective of the present paper is to evaluate RCF property of railway wheel steel. The effect of the slip ratio on the RCF strength of the railway wheel steel was evaluated. RCF tests were conducted using two cylindrical contact specimens under water lubrication at a slip ratio of 0.0–1.0%. The range of slip ratio is determined to assume a creepage between wheel and rail during curving. As a result, it was found that the traction coefficient increased with the increase in the slip ratio, and the fatigue strength decreased simultaneously. The results were evaluated by a shakedown map and Hirakawa’s RCF map. Experimental fatigue limits could be expressed more precisely by the criterion of Hirakawa’s RCF map than that expressed by the well-known shakedown map. Stress intensity factors (SIFs) of the cracks produced by the RCF test were calculated by finite element (FE) analysis where the effect of water pressure due to the penetration of water into the cracks is taken into account. Two peaks of the maximum tangential SIF occurred during one cycle of rolling contact. The direction of the crack propagation was estimated by the maximum tangential stress criteria. The results of the RCF test showed that the cracks were initiated at the surface, propagated obliquely in the depth direction and then branched into two directions. One was towards the surface and the other was towards the depth. These two crack directions were inspected experimentally, corresponding to the estimated crack directions from the two peaks of SIF by FE analysis. The effect of slip ratio on RCF crack propagation was discussed by using the SIFs of the RCF cracks where water penetration into the cracks was considered.

Contact fatigue limits of gears, railway wheels and rails determined by means of multiaxial fatigue criteria

In the present paper, the Dang-Van and the Liu-Zenner multiaxial fatigue criteria are applied to gear and wheel/rail contacts in order to determine contact fatigue limits. In the case of gear contacts, a comparison with experimental contact fatigue limits is discussed for various gear steels. In the case of wheel/rail contacts, the influence of thermal stresses on the contact fatigue limits is analyzed. The results of this analysis are summarized in maps, here called contact fatigue maps, similar to the well-known shakedown maps, but drawn to provide fatigue limits

Use of multiaxial fatigue criteria and shakedown theorems in thermo-elastic rolling–sliding contact problems

Abstract In this paper two multiaxial fatigue criteria, the Dang Van and the Liu–Zenner criteria, are applied to rolling–sliding line contact problems taking into account both mechanical and thermal contact loads. The results of this analysis are summarized in maps, here called contact fatigue maps, similar to the so-called shakedown maps introduced by Johnson, but drawn to provide fatigue limits. These maps enable a general comparison of the contact fatigue limits obtained by the two multiaxial fatigue criteria and can be used as a design tool against high-cycle fatigue damage in rolling/sliding contacts. Shakedown maps are also provided and a comparison between contact fatigue and shakedown maps is discussed.