Variation of Track Response to Wheel Forces with Bogie Axle Spacing: Apparent Track Stiffness and its Influence on Dynamic Impact Forces on Railway Tracks

Track stiffness is an important parameter that affects railway track response. Axle spacing influences the response of the track to wheel forces and has an effect on track stiffness. Track response to train wheels within a bogie or between neighboring bogies vary in relation to their mutual interference, depending on the mechanical characteristics of the layers composing the track, axle spacing and bogie spacing. This interference affects the force-deflection characteristic of the railway track under a wheel. Dynamic impact forces caused by track and wheel roughness relate to track stiffness. Therefore, everything else being the same, two trains with different bogie spacing may generate different dynamic impact forces on the railway track. As a result, the accumulated damage to a railway track over time can relate not only to cumulative tonnage but also to the axle spacing of the trains operating on the railway track. Through superposition of the estimated track deflections by the beam-on-elastic-foundation theorem and looking at it from a new perspective, this paper discovers a set of relations between the variations of track stiffness with bogie axle spacing. The paper introduces a new concept of apparent track stiffness and hypothesizes that dynamic impact forces on the railway tracks relate to axle spacing. The paper then presents a numerical study and an analytical study that analyzes wheel and track interaction along stiffness transition zones for different values of axle spacing and shows that bogie axle spacing has an effect on dynamic impact forces on railway tracks.

Mechanical Wear Contact between the Wheel and Rail on a Turnout with Variable Stiffness

The operation and maintenance of railroad turnouts for rail vehicle traffic moving at speeds from 200 km/h to 350 km/h significantly differ from the processes of track operation without turnouts, curves, and crossings. Intensive wear of the railroad turnout components (switch blade, retaining rods, rails, and cross-brace) occurs. The movement of a rail vehicle on a switch causes high-dynamic impact, including vertical, normal, and lateral forces. This causes intensive rail and wheel wear. This paper presents the wear of rails and of the needle in a railroad turnout on a straight track. Geometrical irregularities of the track and the generation of vertical and normal forces occurring at the point of contact of the wheel with turnout elements are additionally considered in this study. To analyse the causes of rail wear in turnouts, selected technical–operational parameters were assumed, such as the type of rail vehicle, the type of turnout, and the maximum allowable axle load. The wear process of turnout elements (along its length) and wheel wear is presented. An important element, considering the occurrence of large vertical and normal forces affecting wear and tear, was the adoption of variable track stiffness along the switch. This stiffness is assumed according to the results of measurements on the real track. The wear processes were determined by using the work of Kalker and Chudzikiewicz as a basis. This paper presents results from simulation studies of wear and wear coefficients for different speeds. Wear results were compared with nominal rail and wheel shapes. Finally, conclusions from the tests are formulated.

Investigation of Dynamic Factor, Rail Stress and Track Foundation Modulus of Ballasted Railway Track for Different Bed Conditions Using Numerical Methods

The track stiffness is the primary function of roadbeds thickness and subgrade characteristics. For this purpose, numerical scale track finite element technique representing the ballasted track with multi layered substructure founded on subgrade was simulated. The track deflection, stress was abstracted in static and dynamic conditions. The track significant design parameters: Foundation modulus, rail fatigue strength, rail bending stress and stress on subgrade levels were evaluated by using improved current track design numerical methods and compared against field test results which were carried out on part of MG Double track high speed main line (1600 km). Mathematical equations were developed to correlate the variables; ballast thickness, settlement, track stiffness, rail bending stress and rail fatigue strength on varying subgrade soil modulus. Incorporation of this parametric study will improve and optimise the conventional track design and maintenance standard. A simple improved track design was introduced by using single track stiffness parameter from conventional plate bearing test (PBT) on Force Displacement (FD) conventional curve method. The improved method with deriving equivalent track stiffness from rail pad and track substructure tested C value are accurate and simple. The current test method to determine the track stiffness in live track condition is expensive and unsafe with operational requirements. This PBT is simple, cost saving on labour, safe and without applying live train load.

The improvement of the dynamic behavior of railway bridge transition zone using furnace slag reinforcement: A numerical and experimental study

Transition zones between railway tracks and bridge decks can cause higher dynamic impacts. A solution is smoothly changing the track stiffness by gradually mixing steel furnace slag into the stone ballast. A nominated bridge transition zone is divided into 5 blocks of 7 meters long, with the mixing percentages of 0%, 25%, 50%, 75% and 100%. The mechanical behaviors of furnace slag-ballast combinations (FS-BCs) were studied using experiments of shear strength test, Los Angles abrasion index and plate load test. Furthermore, the dynamic behavior of bridge transition zone with FS-BCs blocks was investigated using a field validated FEM model. Results show that the 100%, 75%, 50% and 25% furnace slag by weight of ballast can increase the shear strength and ballast layer bending modulus by 13%, 12%, 9% and 7% at speed of 300 km/h compared with those of the stone ballast. The FEM study shows that rail deflections are reduced about 20%, 14%, 21% and 16% at speed of 300 km/h corresponding to 100%, 75%, 50% and 25% FS-BCs and accelerations are significantly reduced as well as increasing FS content of each block in bridge transition zone so that a smooth bridge transition zone can be achieved.

Application of the Bezgin Method to estimate dynamic impact forces and judge the conditions for ballast pulverization and slab cracking due to abrupt and rapid changes in railway track profile

Dynamic impact forces occur on railway tracks due to the presence of roughness of the track and the wheel and relate to the train speed and the rate of change of roughness. Variations in track profile and track stiffness and variations in wheel circularity are the causes of roughness. Quantification of the dynamic impact forces is not an easy task due to the complexity of the mechanics of the rolling stock interaction with the railway track. A number of experimental studies have led to an understanding of the dynamic impact forces, yielding a set of conservative and case-specific empirical equations. There are also many calculation-intensive numerical techniques, relying on iterative calculations seeking to converge to a state of temporary equilibrium for the analyzed structural domain within small-time increments. These techniques provide detailed and valuable information for the stresses that develop within the many components of the railway track. However, such numerical techniques rely on expensive computational tools that require experienced users to apply and interpret their results. The sheer amount of representative structural and material data input required to define the analyzed structural domain of the railway track properly is also an important task to accomplish in order to conduct a meaningful analysis. The second author developed a simple analytical method that can provide an accurate analysis for the dynamic impact forces on any railway track relying on track stiffness as the only mechanical railway track parameter. This paper introduces an ongoing study led by the second author and provides an insight into how a designer or a track maintainer can apply the Bezgin Method to estimate dynamic impact forces that may occur in rail-ends and within turnouts. This paper will also discuss how one can judge the conditions for ballast pulverization or slab cracking should these conditions exist.

Effect of Longitudinal Fastener Stiffness on Fastening System Loading - Initial Findings

Over the past 20 years, there have been at least 10 derailments due to spike fatigue failures in North America. Researchers believe that fatigue failure is caused by a combination of lateral and longitudinal spike loading. The literature indicates the vertical load and fastener friction must be considered when estimating failure locations. Though the in-track vertical, lateral, and longitudinal fastener forces have been quantified at a location that has experienced spike failures, there is a need to account for additional fasteners and track locations. Fastening systems can affect track stiffness, thus, laboratory experimentation was performed to quantify stiffness of multiple fastening systems. This data was input into an analytical model which quantified the effect of stiffness on longitudinal fastener loading. The data indicate there is significant variance in fastening system stiffness within, and between, systems. However, this variation in fastener stiffness has a reduced effect on the load transferred to the fastening system. More work is needed to validate this in the lab or field given variability within a system could lead to stress concentrations that are not fully captured using the current idealized analytical method.

Modelling the Effect of Track Stiffness Variation on Wheel Rail Interaction Using Finite Element Method

For predictive maintenance purpose, wheel and rail wear evolution models have been developed based on wheel rail contact force calculations. These models are known to assume the wheel rotating on a rigid rail. However recent developments have shown that the flexibility of the track plays an important role in wear evolution. On the other hand, vertical track stiffness variation along the track is known to exist and to affect the track flexibility. The present research work investigates the influence of non-uniform track modulus on the wheel rail contact forces using elasto-plastic explicit dynamic Finite Elements (FE). The FE model is composed of a quarter car model running on a rail supported by three cross-ties. The modulus of elasticity of the cross-ties is calibrated to produce the total track modulus of the railroad track infrastructure. Non-uniformity of the track is modeled by assigning distinct elasticity moduli to the cross-ties. The instantaneous contact physical parameters are extracted from FE models repetitively for various cross-tie modulus ratios. The results show that increase in cross-tie modulus variation results in increased fluctuation amplitudes of wheel-rail contact parameters such as force, stress and contact area. This effect leads to changes of the rate of material removal on the wheels and rails. This research work intends to incorporate the spatial variation of the railroad track stiffness into rail vehicle wheel and track wear prediction models.

A Review of Parameters Affecting Rail Break Gap Size Using Analytical Methods

Management of continuous welded rail (CWR) stress is critical to maintaining railroad safety. To successfully manage the stress-state of the rail, knowing the rail neutral temperature (RNT) is critical. RNT is defined as the temperature at which the net longitudinal force in the rail is zero. If the RNT is set too low/high then the rail would buckle/pull apart and create unsafe operation conditions. To reduce unsafe operating conditions, researchers have previously developed guidelines for managing RNT maintenance activities. However, there remains an opportunity to improve these guidelines given there have been 24 derailments caused by buckled track between 2009 and 2018. Therefore, a research program has been established to improve current guidelines. It is difficult to manage the stress of CWR because the RNT is difficult to quantify, and has been shown to change over time, tonnage, or as a result of maintenance (tamping, etc.). Further, rail breaks may lead to local changes in RNT, leading to the need for RNT readjustment. Current guidelines estimate prevalent RNT before a rail break/cut based on rail gap size. Therefore, as a part of a broader research program, this paper reviews an analytical method presented by Kerr that quantifies rail break gap length and identifies the roles of longitudinal track resistance and stiffness. Results indicate that plastic track displacements driven by longitudinal track resistance dominate, and the longitudinal track stiffness has limited influence. This paper also identifies limitations of this analytical approach and documents recommendations for improved models.

Theoretical Studies on the Longitudinal Inhomogeneity of Track Stiffness and a Track Status Estimation Method

Due to material multiplicity, rigid-flexible hybrid and environmental variations, and so forth, the properties of the tracks will be inevitably changed due to the cyclic loads temporally and spatially. In this paper, a theoretical study is conducted to clarify the influence of the longitudinal inhomogeneity of track stiffness on system responses and then a general state estimation method is proposed to inversely predict the parametric distribution of the tracks. To achieve these purposes, a 3D nonlinear vehicle-track coupled model is firstly constructed, where track systems are established by the finite element method with random parameters. Based on this dynamic model, the distribution characteristics of system responses due to random parametric excitations are properly revealed. The numerical studies show that the longitudinal inhomogeneity of track supporting stiffness has significant effects on system responses; besides, the response distributions are varied against different parametric distributions. Finally, a representative example is demonstrated to show the effectiveness of the proposed track state estimation method.