Article

A Comparison of Alternative Creep Force Models for Rail Vehicle Dynamic Analysis

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... running speed m/s a 0 , a 1 , a 2, a 3 coefficients of the wheel rolling radius polynomial / c 0 , c 1 , c 2 , c 3 coefficients of the contact angle polynomial / e 0 , e 1 , e 2 , e 3 coefficients of the wheel lateral radius polynomial / ξ xl,r , ξ yl,r , ξ sl,r Longitudinal, lateral, and spin creepage / C 11 , C 22 ...
... The models used for rail vehicle bifurcation analysis vary a lot due to the analysis target. Among them, there are single wheelset models with 2 degrees of freedom (DOFs) [6][7][8]12,[15][16][17], rigid-steering bogie model with 2 DOFs [10,18], soft-steering bogie model with 6 DOFs [19], 10 DOFs bogie model [20], half-car model with 11 DOFs [21], half-car model with 17 DOFs [22], and simplified vehicle model with 17 DOFs [23,24]. While a 17 DOFs vehicle model usually decreases the computational efficiency and requires more work to reveal the mechanism of hunting motion. ...
... The creep forces are frictional, and the resultant force shall not exceed μN (μ represents the friction coefficient). Then the Shen-Hedrick-Elkins (S.H.E) model is used to consider the saturation of creep forces, and a modification coefficient α i is defined as [22], ...
... The normal contact force is generally described by the nonlinear Hertz contact theory. 22,23 The mathematical description of tangential creep force is more complex. Kalker 22 described the relationship between creepage and wheel-rail creep force during wheelrail rolling contact under low creepage conditions, and gave a specific numerical solution of creep. ...
... Kalker 22 described the relationship between creepage and wheel-rail creep force during wheelrail rolling contact under low creepage conditions, and gave a specific numerical solution of creep. Shen et al. 23 gave a nonlinear approximation of creep saturation. ...
... Kalker 22 described the relationship between wheelrail creep force and creepage in rolling contact at low creepage, and proposed a detailed method for numerical solution of creep force. Shen et al. 23 gave the following nonlinear approximate calculation formula of creep force saturation: ...
Article
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Polygonalization of the wheel describes the growth of out-of-round profiles of the wheels of railway vehicle. This problem was identified in the 1980s but its mechanism is still not well understood. The wheel-rail disturbance formed by wheel polygonalization will accelerate the fatigue fracture of the key parts of rail vehicles and seriously threaten the safety of rail vehicle. This fact has led to significant efforts in detecting and diagnosing wheel polygonalization, in particular in setting the criteria for health monitoring. Currently, the time-domain feature parameters extraction method based on data statistics and frequency-domain feature parameters extraction method based on spectrum estimation are widely applied to detect wheel polygonalization. However, the basis of spectral estimation is the Fourier transform, which is not good at dealing with non-linear vibration systems (such as vehicle-track coupled system). Aiming at the wheel polygonalization problem existing in high-speed train, the non-linear extent of vibration response of vehicle system caused by wheel polygonalization is analyzed based on vehicle-track coupled dynamics and adaptive data analysis method. A typical high-speed train model is established according to the vehicle-track coupled dynamics theory. The wheel polygonalization model is introduced and vehicle system vibration response is calculated by numerical integration. The vibration response signal is decomposed by empirical mode decomposition (EMD) to produce the intrinsic mode functions (IMFs). By calculating the intra-wave frequency modulation of IMFs, that is, the difference between instantaneous and mean frequencies and amplitudes, the non-linearity of the dynamic response is quantified. Influences of wheel polygonalization on the non-linearity of steady-state and unsteady vibration responses of vehicle system are analyzed in detail. An objective criterion for wheel polygonalization health monitoring based on Degree of Non-linearity is proposed, which provides an effective tool for prognostics and health management of trains.
... The F ASTSIM algorithm is discussed in Appendix C. Alternatively, if the spin effect is small, the Shen-Hedrick-Elkins formula [38] is an appropriate analytical model for cases with creepages and small spin. This is described in Appendix A. In Figure 2-7, using the parameters in Table C-l, it is shown that their results are quite consistent at small spin Y6 = 0.076 m-1 (wheel/rail contact angle is 2' and wheel rolling radius is 0.46 m), but very different at large spin Y6 = 1.7 m-1 (wheel/rail contact angle is 45' ...
... If the spin is large, the friction is also non-linear. For vehicle dynamic analysis on straight track, the Shen-Hedrick-Elkins formula [38] is an appropriate creep-force model. This is analytical and includes the effects of small spin but is not accurate enough for the case with large spin. ...
... If the creepages are in the saturated zone but no spin is involved, the non-linear V-J formula, as given in Eq.(A.3), can be adopted. Alternatively, if the spin exists but its value is small, as applies for the general case of wheel and rail contacting on the tread, the formulation developed by Shen, Hedrick and Elkins[38] can be applied. The Shen-Hedrick-Elkins formula is improved from the V -J formula by including the spin effect. ...
Thesis
p> Railway curve squeal is an environmental noise problem occurring occasionally when a vehicle is negotiating a sharp curve. A theoretical study is carried out to develop a complete model, which can predict curve squeal and may provide useful approaches to control it. The curve squeal results from a kind of self-excited vibration existing in the wheel/rail contact system, mainly due to the falling friction coefficient when sliding occurs between the wheel and rail surfaces. The central work of this thesis is to build a self-excited feedback loop model, representing relations between the wheel/rail motions and the contact forces. The stability analysis of this loop can predict the possibility of squeal, while the time-domain integration of the loop can provide the intensity of squeal. A twin-disc rig, with a wheel disc rolling on a rail disc, was used to investigate the squeal phenomenon and validate the wheel/rail squeal model. With this rig, the lateral forces acting on the discs due to varying amounts of lateral creepage can be measured in a controlled environment, as well as the acoustic and vibration responses of the discs. According to the experimental results, the falling friction in sliding is closely related to the self-excited vibration and hence the occurrence of squeal. The curve squeal prediction is applied for all four wheel/rail contacts in a bogie. The results show that squeal is prone to occur at the leading wheels of a bogie, mainly due to the large lateral steady-state creepage. The leading outer wheel in flange contact has less possibility for squeal than the leading inner one. The trailing wheels are unlikely to squeal. Both a wheel damping treatment and friction modification can be used to control the squeal, but will not always be effective. </p
... Wheel-rail contact is usually regarded as the contact between two quasi-identical bodies [4], which can be separated into the normal contact problem and the tangential contact problem. Hertzian theory [4,5] and the Hertzian-based tangential contact models [6][7][8][9][10] are adopted in traditional railway vehicle dynamics simulation [11,10]. These tangential contact models include the FASTSIM model [6], the FaStrip model [7,8], the Polach model [9], and the Shen-Hedrick-Elkins model [10]. ...
... Wheel-rail contact is usually regarded as the contact between two quasi-identical bodies [4], which can be separated into the normal contact problem and the tangential contact problem. Hertzian theory [4,5] and the Hertzian-based tangential contact models [6][7][8][9][10] are adopted in traditional railway vehicle dynamics simulation [11,10]. These tangential contact models include the FASTSIM model [6], the FaStrip model [7,8], the Polach model [9], and the Shen-Hedrick-Elkins model [10]. ...
... Hertzian theory [4,5] and the Hertzian-based tangential contact models [6][7][8][9][10] are adopted in traditional railway vehicle dynamics simulation [11,10]. These tangential contact models include the FASTSIM model [6], the FaStrip model [7,8], the Polach model [9], and the Shen-Hedrick-Elkins model [10]. However, since the wheel and rail profiles are composed of several curves with different radii, the wheel-rail contact is essentially a non-Hertzian contact problem. ...
Article
Relative to the Hertzian theory, the non-Hertzian contact model (NHM) can better reflect the contact characteristic between wheel and rail in railway vehicle dynamics simulation. In this paper, an optimal wheel-rail tangential contact model is determined for vehicle dynamics simulation. First, based on i) the modified Kik–Piotrowski (MKP) contact model, ii) four different ellipse-equivalent methods, and iii) the modified FASTSIM model or modified FaStrip model, eight NHMs are proposed. Then, taking the Kalker's variational method (KVM) as a reference, the computational accuracies of the eight NHMs for calculating the linear creep coefficient and the tangential forces for the typical tangential contact scenarios are compared. NHM II, that is, the model coupled with the MKP model, the ellipse-equivalent method adopted in the Kik–Piotrowski (KP) model, and the modified FaStrip model, shows the best computational accuracy. Finally, the traditional Hertzian & FASTSIM model, the NHM II model, and KVM model are applied to the vehicle-track coupled dynamics simulations, and the dynamics response of a high-speed train running on a slab track is calculated by different contact models. The comparison results show that the NHM II model exhibits better agreement with the KVM compared with the Hertz & FASTSIM model.
... Both FASTSIM and FaStrip are iterative algorithms that 22 require a discretisation of the contact ellipse into rectangular elements, and express the tangent forces by integrating the tangential shears over the discretised contact area. As opposed to this, fast analytical methods such as the Vermeulen-Johnson model [60], the Shen-Hedrick-Elkins model [61] and Polach's model [62] use formulas giving the tangent forces directly as a function of the unsaturated shears. Approaches such as the Book of Tables by Kalker (USETAB) [63] use detailed methods like Kalker's complete theory [21] to develop lookup tables that are used in vehicle dynamics simulations. ...
... Broadly, two approaches may be used to extend FASTSIM type algorithms to non-elliptical contact cases [74]. The first approach consists of regularising the non-Hertzian contact patch to a single equivalent ellipse and using the global creepages to determine the creep forces using one of the various Hertzian approaches [55,60,61,62]. While this approach works well in dynamic studies, it cannot be used to study the contact stresses. ...
... Several heuristic solutions for the creep forces have been presented in the literature. In the following sections, two of these heuristic approaches, namely the one by Shen et al. [61] and Polach's model [62], are outlined briefly. ...
Thesis
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Wheel-rail contact modelling is an active field of research, especially in railway dynamics, where a compromise is required between the computational efficiency and the precision of results. The aim of this thesis is to describe, test, and extend the capabilities of the railway dynamics code VOCO. A new semi-analytical approach for determining the wheel-rail contact zone, and the normal stress distribution is developed. Comparisons with methods commonly used in multibody systems codes show a marked improvement in the results. The new method is combined with a new non-Hertzian tangential contact algorithm and provides the possibility of using a more detailed approach in the context of multibody dynamics. Alongside the development of new methods, a comparison of different commercial and academic multibody codes has been carried out in an international benchmark on turnouts, followed by a collaborative study to assess the wheel-rail contact results in detail.
... In addition to the normal force, the creep force of wheel and rail is frequently calculated according to the following formula and corrected by Shen-Hedrick-Elkins method (Shen et al. 2007). ...
... where f ij is the creep coefficient, T x , T y and M z are the transverse creep force, vertical creep force and rotational creep moment respectively, x , y , and sp are the creep rate in the corresponding direction, the parameter values can also be found in the reference (Shen et al. 2007). ...
Article
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The classification and quantitative description of damage of track structure for high-speed railway girder bridges (HRGBs) are still in the exploratory stage, which seriously interferes with the performance-based seismic damage assessment of HRGBs. In view of this, firstly, from the safety and stability of train operation, this paper defines the damage grade of track structure (intact, slight, moderate, severe and complete damage state) by refining the train operation index value. Secondly, based on the simply supported and continuous girder bridge structures of high-speed railway, a train-track-bridge system (TTBS) model is established, and the additional lateral irregularities of the rail caused by the lateral deflection of the girder are induced. Finally, the influence of the lateral displacement amplitude of the rail and the train velocity on the train safety and stability is discussed. The results indicate that the rail lateral displacement by the reverse translation of the adjacent simply supported spans and the reverse rotation of the adjacent simply supported spans have the most powerful influence on the train safety and stability, respectively. The lateral displacement of rail is proposed as an index to measure the damage of the track structure, and its critical values corresponding to each damage grade in the range of train velocity from 200 km/h to 400 km/h are determined, which can be used for the seismic vulnerability analysis of track structures for HRGBs.
... The wheel-rail spatial interactions are formulated based on the nonlinear Hertz contact theory in the normal plane [43], and formulated by Kalker linear rolling contact theory [44] and Shen-Hedrick-Elkins non-linear model [45] in the tangential plane. The wheel-rail interaction forces and torques appearing in Eqs. ...
... where f 11 , f 22 , f 23 and f 33 are the creep coefficients, ξ x , ξ y and ξ sp are the longitudinal, lateral and spin creepages, respectively; F N is wheel-rail normal force; G is wheel-rail contact constant; δZ wr is wheel-rail vertical relative displacement; δ is wheel-rail contact angle; F Cx , F Cy and M Cz are respectively the longitudinal, lateral wheel-rail creep forces and spin creep torque defined in the contact point coordinate system; F mCx , F mCy and M mCz are the corresponding modified wheel-rail creep forces and spin creep torque; ε is the revision coefficient according to Shen-Hedrick-Elkins nonlinear creep model [45]; T ca represents the transform matrix from the wheel-rail contact point coordinate system to the curve coordinate system, given by ...
Article
This paper presents a semi-analytical solution to free and forced vibrations of a pinned–pinned Euler-Bernoulli curved beam, and extends it into train-track spatial interactions. The in-plane and out-of-plane modes of the curved beam are approximated by the partial sums of sinusoidal Fourier series, and the forced vibration equations in a generalized coordinate are formulated by utilizing the Galerkin method and mode orthogonality derived based on the reciprocal theorem of work. Comparisons of natural frequencies and dynamic responses with published results and finite element method (FEM) illustrate the reliability and advancement of current approach, which provides more accurate results for higher frequency analysis and possesses better adaptability to different boundary conditions by supplementing polynomials. Moreover, the influence of radius and subtended angle on the natural frequencies of rails simulated by the straight and curved beam models are also investigated. Finally, the established model is further extended to simulate the curved rails implemented in a train-track coupled dynamics system with consideration of a nonlinear wheel-curved rail contact model, since they used to be idealized as straight beams instead of taking the actual curvature into account. Some new recognitions are gained by examining the effect of rail modelling options and additional creepages on a curved track, which is conducive to more accurate evaluations on curve negotiation effects induced by train-track spatial interactions.
... The simplified theory behind FASTSIM is based on the computation of the coefficients c ij with the help of Kalker's exact linear theory, which are derived from the initial slope of the tangent forces applied on an elliptical contact patch for small creepage values. Other fast methods such as the Vermeulen-Johnson model [3], the Shen-Hedrick-Elkins model [4], the Book of Tables by Kalker (USETAB) [5], Polach's model [6], and the method FaStrip [7] may also be used. The main drawback for all of the above cited methods is that they remain restricted to elliptical contact patches, although FaStrip has been extended to non-Hertzian patches [8]. ...
Conference Paper
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The FASTSIM algorithm is widely used in multi-body simulation (MBS) software packages for the evaluation of the tangential wheel-rail contact forces in a steady state. As the algorithm is restricted to Hertzian contact patches, a strip-based local approach is proposed to extend FASTSIM to non-elliptical contact cases. The paper presents this tangential contact approach in detail, which was briefly introduced by Ayasse & Chollet along with the semi-Hertzian method. The contact stresses and their directions are compared with the reference results from the program CONTACT. Different settings for the traction bound are explored to determine their influence on the contact stresses, creep forces, and the limits of the saturation zone in the case of wheel-rail contact. A design of experiments is constructed for a non-Hertzian contact case, with different combinations of the longitudinal, lateral, and spin creepages. The absolute error in the normalised creep forces is used as the quantity of interest and found to be consistent with results in the literature for Hertzian contact cases using FASTSIM.
... The wheel-rail normal force was calculated by using the Hertz contact theory (Xia, Zhang, & Guo, 2018). The creep force was calculated by the Kalker linear creep force model (Kalker, 1967), and the Shen-Hedrick-Euristic (Shen, Hedrick, & Elkins, 1983) nonlinear creep model was used for correction. ...
Article
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After an earthquake, a track-bridge system may suffer damage and residual deformation, posing a threat for trains passing over a bridge. However, since railway transportation is an important channel for disaster relief, the timely passage of trains is of great significance for the transportation of materials and personnel. In the past, subjective and experience-based judgments were made on whether a train can pass over an earthquake-damaged bridge, and no relevant numerical calculations were carried out. Therefore, a strategy for the evaluation of train performance when passing over existing bridges after earthquakes was proposed. The strategy considers the randomness of track irregularity, and evaluates the running safety performance (RSP) and running comfort performance (RCP) of trains passing over existing bridges from the perspective of probability. The probability law of a lateral residual bridge deformation influence on the RSP and RCP after an earthquake was revealed. Finally, the maximum train passing speed which ensures the RSP was recommended.
... With consideration of the nonlinear creep force-creepage relationship by Shen-Hedrick-Elkins theory [48], the creep coefficients will be modified. ...
Article
This work is devoted to constructing a stochastic analysis model for train-track interaction. The fundamentals of the modelling framework in the establishment of the dynamic model, simulation of system uncertainties and randomness propagation process have been properly illustrated and unified in detail. For modelling train-track interaction, a matrix representation method is developed to depict the displacement compatibility and force equilibrium between the train and tracks. This dynamic model possesses advantages in computational stability and accuracy. Using uncertainty quantification approaches, the randomness of system geometries and longitudinal inhomogeneity of system properties can be simulated properly. Finally, the probabilistic transmission between the system inputs and response outputs are investigated from physical concepts, and a family of probability density evolution methods is introduced. Following the fundamental framework of train-track stochastic analysis, numerical examples are presented in detail to show the efficiency and accurateness of the proposed model. Moreover, the applications and advancements of this model in reliability assessment, response and frequency analysis, derailment, etc., are illustrated.
... The tangential forces between the wheel and rail are determined using Kalker's linear creep theory [30]. Further, they are revised by the Shen-Hedrick-Elkins model [31]. ...
Article
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Irregularities of rail joints ordinarily induce high-frequency impacts on wheel–rail contact systems, which may further influence vehicle–track interaction. In this study, a three-dimensional locomotive-track coupled dynamics model that uses the wheelset flexibility was developed. The wheelset rigid motion and elastic deformation are calculated based on the multi-body dynamics theory and finite element method, respectively. The effectiveness of this model was validated. The effect of wheelset flexibility on locomotive–track interaction due to rail weld irregularities is analysed by comparing the dynamic responses obtained using the rigid model and the proposed rigid–flexible coupled model. The proposed model is applied to the sensitivity analysis of the wheelset response to the rail weld geometry irregularity. The results show that the dominant frequency of the wheel–rail force or axle–box acceleration is 81 Hz, which is the 1st bending modal frequency of the wheelset. The P2 resonance frequency is easily excited owing to impacts of rail weld irregularities, which may induce the formation of locomotive wheel polygonization. The wheelset acceleration was more sensitive to the wavelength than the depth of the rail weld irregularities. The wavelength characteristics can be significant in vehicle vibration-based condition monitoring of rail weld irregularities.
... In the model, the tangential contact forces are evaluated using the Shen-Hedrick-Elkins model, 30 which can be found in. 23,28 Flexible brake disc and wheelset model ...
Article
To study the vibration characteristics and stress state of brake discs during vehicle operations, a spatial trailer car-track coupled dynamics model was developed with the consideration of flexible brake disc. In the model, the components of a trailer car are considered as rigid bodies. Flexible models of the brake disc and wheelset were established using the finite element method. The trailer car-track coupled dynamics model is validated using experimental test results. The effects of wheelset flexible deformation on the dynamic properties of brake discs were investigated with the excitations of track irregularity and wheel flats. Furthermore, the brake disc was systematically evaluated and discussed under the condition of wheel flats in the coupled dynamics system. The results indicate that compared to rigid wheelsets with wheel flats, flexible wheelsets can cause the brake disc to vibrate more severely with higher stress. The severe vibration and high stress state of the brake disc could cause it to crack in the region near the bolts. The established dynamics model can be further developed and employed to assess the dynamics of the brake systems of high-speed trains.
... In the lateral direction, the Kalker creep theory (Shen, Hedrick, & Elkins, 1983), characterising the relation of relative motion and corresponding horizontal force between wheel and rail, is adopted to determine the interactions. It is worthwhile noting that the coupling effects of the sway and yawing movements of the wheel-set are ignored. ...
Article
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Due to unavoidable uncertainties, it is critical to perform probabilistic analysis when examining the safety of coupled train-bridge system based on the dynamic interaction analysis. This paper proposes a novel approach for probabilistic safety analysis of coupled train-bridge system using deep learning based surrogate model. Deep neural network embedded with convolutional neural network is designed and developed to construct the surrogate model substituting the 3D train-bridge interaction system model for reducing the computational efforts and efficiently predicting a series of dynamic indices of the coupled system. Due to the lack of explicit expression of the performance function, automatic differentiation is exploited to derive the surrogate model and further to realise the reliability and sensitivity analysis with the first-order method. The obtained reliability and sensitivity indices are compared to that resulting from the Monte Carlo simulation method with importance sampling and tail modelling. The proposed approach is applied on a high-speed train and bridge system, treating multiple main system parameters as random variables. Effects of the railway operational speed on the system reliability are investigated. The results show that the proposed approach can provide an efficient solution to the probabilistic safety analysis of coupled train-bridge system especially with small failure probability.
... [53,54], but may be avoided using fast approximations. Various approximate formulas are used to assess the creep forces instead, e.g. by Vermeulen and Johnson [55], Shen et al. [56], Polach [57], or using FAST-SIM [40,58], or table-based approaches [59], as compared in [60]. A recent addition is the KBTNH approach, using a table for asymmetric contact patches [61,62]. ...
Article
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This paper surveys advances in the understanding and modelling of wheel–rail creep forces. The main focus is placed on tribological aspects, for which significant progress was made in the past two decades. We emphasise the role played by the surface conditions, i.e. the presence of liquid and solid layers, surface roughness, and near-surface plastic deformation. As these surface conditions may change over time, transient changes may be obtained in the creep force characteristic. This brings feedback into the picture, with consequences and opportunities for optimised adhesion recovery, traction control, and braking systems.
... In the present work, the Kalker linear theory [34][35][36][37], Heuristic method [40], and Polach formulation [41] are implemented. For each contact patch, the tangential forces can be calculated depending on the creepages, radius of the elliptical contact patch, and material properties of the two contact bodies. ...
Article
A novel practical three-dimensional (3D) wheel-rail interaction (WRI) element is developed to simulate the interaction between a fast-moving wheel node and nodes of the rail. Different from most previous methods of wheel-rail contact in multibody dynamics, the wheel-rail relationship in this paper is simulated by the WRI element. The WRI element is implemented into a general finite element software framework (i.e., OpenSees), which allows us study not only the vehicle behavior as the multibody models allow, but also the structure behavior with any degree of complexity. Implemented in a FEM framework with strong nonlinear capabilities, it also allows us to study scenarios with important nonlinearities. Compared to most existing models, the WRI element has a better compatible property and can be easily added to the vast majority of finite element platforms. The wheel-rail contact geometry is calculated efficiently with wheel/rail profiles fitted through linear curves and contact locations solved through algorithms with a higher efficiency. Local curvatures around contact points are calculated differently to avoid discontinuities of the contact force. Movements of a wheelset and of a train are studied to verify the accuracy and capability of the WRI element in the dynamic simulation of vehicle-track systems.
... The normal wheel-rail forces are performed by the nonlinear Hertzian elastic contact theory [30]. The Shen-Hedrick-Elkins model [31] is adopted to simulate the wheel-rail creep force, based on the Kalker's linear creep theory [32]. ...
Article
Gear transmission is an essential element in the motor cars of high-speed trains, as it directly effects the reliability and safety of the vehicle. Based on the classical vehicle–track coupled dynamics theory, and gear and bearing dynamics theory, this investigation develops a novel vehicle–track coupled dynamics model with an enhanced gear transmission subsystem comprising gear pair and bearing. In the model, the enhanced gear transmission and vehicle–track system are coupled through suspension system, gear mesh interface, nonlinear bearing interaction and wheel–rail relationship, which enables detailed analysis of the gear transmission in the whole coupled system. Following the validation of the proposed model, the dynamic interactions between the gear pair and bearing are comprehensively investigated. Besides, the effects of the traction torque and track irregularities on the gear-bearing system are investigated. Results show that the gear meshing has significant influences on the bearings. The vehicle–track coupled environment has non-negligible effects on the dynamic interactions and vibrations of the gear transmission. Moreover, the proposed model is applicable to the further dynamic analysis of gears and bearings of the motor car under gear cracking, bearing failures, wheel defects and other destabilising conditions.
... Kalker's creep theory was used to determine the creep force, which was then modified using the Shen-Hedrick-Euristic nonlinear creep model (Shen, Hedrick, and Elkins 1983). ...
Article
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In the dynamic analysis of railway lines, both lateral and vertical track irregularities should be considered. In addition, uncertainties in the bridge structure and train load will have different effects on the train-bridge coupled system (TBCS). This paper presents a three-dimensional model of the TBCS to study the influence of various sources of randomness on the response of the TBCS. The Karhunen–Loéve expansion is combined with the point estimate method (KLE-PEM) to calculate the statistical moment of the system response with high accuracy and efficiency. Furthermore, applicability of KLE-PEM method is discussed and the influence of different combinations of sources of randomness on the train and bridge responses under different speeds is analyzed according to the maximum range of probability values. Random track irregularities are found to have a much greater influence on the train response than uncertain parameters, whereas uncertain parameters have the greatest influence on the displacement of the bridge.
... where G is the Hertzian wheel-rail constant and δZ(t) is the wheel-rail elastic compression deformation at the contact point in the normal direction. Based on the Kalker's linear creep theory [37], the Shen-Hedrick-Elkins model [38] is adopted here to calculate the tangential forces and moments generated from the wheel-rail interface. ...
Article
For railway locomotive, its motor bearing is one of the key components, which is likely to be damaged due to the intensified vibration conditions caused by the wheel-rail interaction and gear mesh. In this paper, a locomotive-track spatially coupled dynamics model considering the dynamic effect of the traction power transmission is established to investigate the dynamic responses of traction motor bearings. The detailed structure of the traction motor, complex internal interactions of the rolling bearing itself, time-varying gear mesh stiffness, and wheel-rail interaction are considered. The simulated results indicate that the gear mesh excitation and internal interactions of the motor bearings significantly affect the dynamic characteristics of the rotor. The motor bearing at the driving end surfers more dynamic loads, and the internal interactions between the components are more intensified than that of the bearing at the non-driving end. Moreover, the skidding phenomenon of the motor bearing at the driving end is alleviated by the greater radial load. Additionally, the wheel-rail interaction with track random irregularity will deteriorate the working conditions of the motor bearings. The modelling method and results can provide helpful theoretical guidance for the motor bearing design and structure optimization of the locomotive traction motor.
... To calculate the wheel-rail creep force, the Kalker linear creep theory was first used [19]. After the creep between the wheel and rail reached saturation, the Shen-Hedrick-Elkins theory was applied for nonlinear correction [20]. The vehicle-track coupling excitation model adopts the "tracking window" model proposed in Refs. ...
Article
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A coupling dynamic model of a subway train and an embedded track is established to study the safety limits of track irregularities. The simulated vehicle system was a 74-degrees of freedom multi-rigid body model, and the rail was a Timoshenko beam. The slab was a three-dimensional solid finite element model. The sensitive wavelength irregularity was first studied, and then the safety limit of the sensitive wavelength was analyzed. The wheel-rail lateral force exhibited a substantial effect on the track alignment and gauge irregularity safety limit. The wheel-rail vertical force and the rate of wheel load reduction significantly affected the height and cross-level irregularity safety limit. The results demonstrate that the safety limits of the alignment, gauge, height, and cross-level embedded track geometric irregularity are 5.3 mm, [− 10.5, 8] mm, 5.6 mm, and 6 mm, respectively.
... Adopting saturated nonlinear creep theory [17], the wheel-rail creep forces are modified asC ...
Article
To disclose the possible dynamic behaviours of vehicle-track systems subject to an entire railway network, random vibration analysis is of great concern in railway engineering due to the system geometric and parametric uncertainties. In this work, an emphasis is therefore put on the highly efficient simulation and numerical analysis of track geometry excitation and its induced system uncertain behaviours. Considering the spatial variability, frequency coherence and constant evolution of track irregularities, the random analysis of track irregularities belongs to a big data analysis scope. By introducing practical tools of power spectral density (PSD), frequency coherence analysis and correlated variable random simulation method, a strategy for obtaining representative and realistic track irregularity PSD samples is proposed. Besides, the modelling method of vehicle-track interactions, where versatile programming tactics to couple the track slab and subgrade elements with incompatible elemental sizes, is introduced. By combining the simulation methods of track irregularities and vehicle-track dynamic interaction, the dynamic performance of vehicle-track systems can be evaluated efficiently, and the full view of system dynamics is revealed with probabilistic characteristics.
... Then the normal forces and creep forces of the wheel-rail interaction can be calculated. The normal wheel-rail contact forces are calculated using the Hertzian nonlinear contact theory [25], and creep forces are calculated using the Shen-Hedrick-Elkins' model [29]. ...
Article
Fastening failures have frequently been found on China high-speed railway curved tracks in recent years. Thus the influence of fastening failures on high-speed train-track interaction in curved track needs to be analyzed. A train-curved slab track interaction model is built, in which the real shape of the curved rail is considered and modeled with reduced beam model (RBM) and curved beam theory, and the slabs are modeled with four-nodes Kirchhoff-Love plate elements. The present model is validated at first with different traditional models. Then the influence of fastening failure in curved slab track on train-track interaction dynamics is studied. A different number of failed fastenings are assumed to occur at the curved track, and different types of fastening failure including the fatigue fracture of the clip structure and failure of the rail pad are considered. Based on the calculation results, the fatigue fracture of the clip structure has little influence on train-track interaction dynamics. But when rail pad failure happens and its equivalent vertical stiffness and damping is less than one-tenth of its original, the fastening failure seriously affects the high-speed train operation safety and it must be prevented.
... The wheel-rail normal force F N wr (t) was calculated using the Hertz nonlinear contact theory [31]. The friction in the tangent direction F T wr (t) was calculated using the Shen-Hedrick formula [32]. The trace curve method [33] was used to find the contact point between wheel and rail. ...
Article
With the rapid expansion of high-speed rail networks, the safety of vehicles against derailment on bridges during earthquakes has become a significant concern in bridge design. The vehicle’s responses are the combined effect of earthquakes and track irregularities, both random processes. But few studies exist on the combination rule of derailment indexes from the two random excitations. In addition, the seismic fragility analysis commonly used in structural engineering was rarely seen in the derailment analysis. In this paper, the probability density evolution method (PDEM) was used to obtain the probability density function (PDF) of wheel unloading extremes by treating the earthquake and track irregularity as random processes. The combination rule of extremes of wheel unloading ratio from the two excitation sources was investigated by comparing the PDFs of combined results with direct simulation. It is shown that the extreme values of wheel unloading under earthquakes and track irregularities approximately satisfy the SRSS formula. In addition, the seismic fragility analysis using the incremental dynamic analysis (IDA) was introduced into the vehicle-bridge interaction (VBI) system to simplify the probabilistic derailment assessment. By comparing with the fragility curve from the PDEM (it can be seen as an accurate solution), the IDA-based seismic fragility curve estimated by twenty or more earthquake samples was found to have adequate accuracy for engineering application.
... The wheel-rail normal force was calculated using the nonlinear Hertz theory [28]. The friction in the tangent direction was calculated using Shen-Hedrick formula [29]. A detailed description of wheel-rail contact model was shown in Appendix. ...
Article
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With the rapid development of high-speed railways around the globe, the safety of vehicles running on bridges during earthquakes has been paid more attention to. In the design of railway bridges, in addition to ensuring the safety of the bridge structure in earthquake, the vehicle safety should also be ensured. Previous studies have focused on the detailed analysis of vehicle derailment on bridges, proposing complex numerical algorithms for wheel–rail contact analysis as well as for parametric analysis, but they are inconvenient for designers. Intensity measure (IM) used in performance-based earthquake engineering is introduced in this study. A method to evaluate the vehicle safety on bridges under earthquakes is proposed with respect to the optimal IM. Then, the vehicle derailment case of the Kumamoto earthquake in Japan verifies the decoupling method of vehicle–bridge interaction model. In the assessment of vehicle derailments, eight IMs are systematically compared: the IMs of bridge deck motion are generally better than those of ground motion; the variation coefficient of spectral intensity of the bridge deck is the smallest at different frequencies. Finally, the derailment fragility cloud map is presented to evaluate the vehicle safety on bridges during earthquakes.
... Considering the tangential problem at wheel-rail contact, Vollebregt et al. [25] have presented an accuracy comparison between different contact models used in multibody software. Vollebregt et al. [25] have analysed Fastsim [26], the Polach model [69], Kalker linear theory [27], the Vermeulen-Johnson model [28], the Shen-Hedrick-Elkins model [29] and USETAB [30] against CONTACT and concluded that Fastsim and USETAB provide good results with 5%-10% root mean square deviations. Recently, an alternative approach to Fastsim called FaStrip has been proposed [31]. ...
... Wheel-rail interaction is the core and link of the vehicle and track system, which has a decisive impact on the dynamic performance of vehicle-track interaction. The 'trace line method' is used to determine the wheel-rail contact geometric relationship [22], the nonlinear Hertz elastic contact theory is introduced to solve the wheel-rail normal force [27], and the tangential creep force is acquired by the Kalker linear creep theory and modified by the Shen-Hedrick-Elkins nonlinear model [28]. The geometric relative relationship between the wheelset and the rail is considered in the wheel-rail contact model as shown in Figure 2(b). ...
... Intrusion or separation between the rim and rail are worked out for every instant when the positions of the wheel rim and rail top are determined by numerically solving the associated motion equations, which are presented. In case of intrusion, rolling contact between the rim and rail occurs and the normal wheel-rail contact force is calculated based on the Hertz contact theory while the tangential wheel-rail contact force is calculated with Shen-Hedrick-Elkins model (Shen et al., 1983). ...
Article
Resilient wheels are extensively used for trams due to the noise reduction they can achieve. However, the effect of the resilient wheels on vehicle dynamics has not been adequately studied. An effort is presented in this paper, trying to bridge this gap. To simulate interactions between vehicle and track, the resilient wheel is modelled as a multi-rigid body system consisting of a rigid wheel core and a rigid rim between which a rubber layer is inserted. The rubber layer is regarded as three-directional spring-damper units, allowing the rim and core to have relative motions, so that the flexibility of the resilient wheel provided by the rubber layer is fully simulated. Then, the dynamics of a vehicle-track coupling system integrated with this resilient wheel model is simulated and compared with in-situ measurement. The simulation results show that, compared with a conventional solid wheel, the vertical vibration of the wheel core is much reduced in the frequency range of 70–300 Hz while the lateral vibration is much reduced in the frequency range of 90–300 Hz. The paper continues with the recommendation of the radial and axial stiffnesses, two key parameters of the resilient wheel, aiming to lower the wheel-rail contact force and carbody vibration.
... The wheel-rail normal contact forces are derived by nonlinear Hertzian elastic contact theory (Zhai et al. 2013). In addition, the tangent wheel-rail creep forces are calculated by Shen-Hedrick-Elkins nonlinear model (Shen et al. 1983). ...
Article
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Running safety of the railway vehicles on the bridge during earthquakes is a major concern for railway engineering. To reduce the derailment risk of railway vehicles on bridges, friction pendulum bearings (FPB) are proposed to be equipped on simply supported bridges in this study. The full nonlinear behavior of the FPB is introduced into the vehicle-bridge interaction model. The effect of FPB’s manufacturing variations, including the shear pin’s strength and friction coefficient, on the misalignment was investigated. The manufacturing variations of the FPB were found to produce large lateral misalignment, which further contributes to large wheel-rail forces when the vehicle passes over the girder ends. It diminishes the improvement in the vehicle’s seismic safety provided by FPBs. Thus, a misalignment control device is proposed to limit the misalignment of the railway bridges equipped with FPBs. The vehicle-bridge interaction analysis results show that no wheel uplift occurred on the bridge equipped with FPBs and misalignment control devices during an earthquake. It indicates that the FPB significantly reduces the vehicle’s derailment risk on bridges compared with the non-isolated bearings.
Chapter
The railway wheel wear prediction is essential in the optimization of the maintenance strategies of the wheel-rail system which have both economic and safety implications. The computation of the stresses across the contact patch is necessary to determine the wear distribution, which makes the wear simulation computationally expensive and challenging. Therefore, a fast wear computation method is highly desirable for wheel wear estimation in the context of multibody railway vehicle dynamics simulations where many contact problems must be solved at each timestep. This paper proposes a fast computation approach to estimating wear distribution over the wheel-rail contact patch. The effectiveness and efficiency of the proposed method are demonstrated with the selected case studies.
Chapter
Simulations of vehicle/track interaction (VTI) in switches and crossings (S&C) require taking into account the complexity of their geometry. The VTI can be handled via a co-simulation process between a finite element (FE) model of the track and a multibody system (MBS) software. The objective of this paper is to reduce the computing effort in the co-simulation process. In the proposed approach, the VTI problem is solved inside the MBS software to reduce the computational effort in the track model as well as the flow of input/output between both modules. The FE code is used to supply the matrices of stiffness, damping and mass at the beginning of the simulation. An explicit time scheme is used with mass scaling. A good agreement is found between both approaches with a reduction of the computing time by a factor of 10. This new approach allows the optimisation of the design of S&C in further studies.
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The near fault (NF) line waves send out signal envelopes that oscillate over lengthy periods of time with periodic impulses. Like train bridges, train tracks demonstrate comparable track-bridge (TB) motion dynamics. Using these coupling dynamics, are the high-speed train-track-bridge (HSTTB) system designs sensitive to those parameters? This research incorporates a Finite Element Analysis (FEA) technique developed for simulating the dynamic reactions of the coupled TB system when faced with simultaneous NF lateral and vertical ground motions (GMs). For the first time, data from the pre-commissioning field testing of the Beijing-Shanghai high-speed train are utilized to validate the Train-Track-Bridge Dynamic Analysis (TTBDA) test. As a matter of fact, the current research has concentrated on the running safety of the high-speed train's operations, as well as the possible derailment mechanism of the high-speed train, in light of the far-field (FF) earthquakes. This analysis reveals that the NF GMs in the bridge structure's seismic reactivity are considerable. Many high-speed train derailments are due to frequent wheel displacement, elevated wheels, and significant lateral motion. The data discovered in the field may give engineers vital information for calculating relevant situations and railroad engineering projects.
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An accurate and high-efficiency contact model is essential for vehicle-track dynamic simulation and wear prediction. The paper attempts to assess the influence of different contact models on the offline and online simulation, as well as wear depth distribution. Taking CONTACT as the reference model, the computational accuracies of contact model combinations (i.e. Hertz + FASTSIM, Kik–Piotrowski (KP) + FASTSIM, modified Kik–Piotrowski (MKP) + FASTSIM and MKP + FaStrip) are evaluated. Typical wheel-rail contact cases and two dynamic simulation cases (track irregularity and curve track) have been studied. Results show that MKP + FaStrip achieves the best computational accuracy in calculating the typical wheel-rail contact situation, besides, the yaw angle has a significant influence on the contact patch shape and pressure distribution, especially when the wheel flange contacts with a rail corner. With regard to the vehicle passing the track with the lateral irregularity, both KP + FASTSIM and MKP + FaStrip models can achieve relatively good agreement on dynamic results and wear prediction with CONTACT. In terms of the curve track, MKP + FaStrip has better accuracy on dynamic results and wear due to a larger yaw angle.
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With the rapid development of subway transportation, it has brought great convenience to us, but the induced vibration has seriously influenced our daily life. The simulation models are the major approach to investigate this problem. However, due to the discreteness and randomness of the physical parameters of various materials and inappropriate simplifications of the finite element (FE) model, the simulated results cannot reflect the actual dynamic responses accurately. To solve this issue, we carried out systematic investigations as follows: (1) conducting in-situ dynamic measurements of the track structure in an operating subway line; (2) establishing a simulation model of the vehicle-track coupled system; (3) proposing the multi-objective functions according to the simulated and measured results; (4) designing and implementing the sensitivity analysis based on the Latin Hypercube Sampling (LHS); (5) devising and performing the model updating process based on the multi-island genetic algorithm (MIGA). The results reveal that the updated model can simulate the dynamic responses accurately, and the simulation results have an excellent agreement with the in-situ measurements. Overall, the developed method in this work can obviously improve the accuracy of the dynamic simulation of the track structure and provide a way for the model updating and vibration analysis of the vehicle-track coupled system.
Thesis
L’aiguillage est un des appareils de voie (ADV) ferroviaire : il assure le support et le guidage du matériel roulant sur un itinéraire donné, lorsque d’autres itinéraires divergent ou le traversent. C’est un élément important et fragile du réseau ferroviaire, et le contact roue-rail y est plus complexe que sur un rail normal. L’objet des travaux présentés est le développement d’outils numériques ayant pour point commun de contribuer à l’optimisation dynamique des ADV. Pour traiter l’interaction véhicule/voie dans un aiguillage, le laboratoire d’accueil a développé une approche de cosimulation entre un code « maison » de dynamique ferroviaire, appelé VOCO, et un logiciel éléments finis tiers modélisant la voie. Avec cette approche, dénommée ‘IVOIE4’, la durée d’une simulation peut être de l’ordre de la journée. Dans cette thèse, on a développé une nouvelle approche ‘IVOIE5’ pour traiter l’interaction véhicule/voie plus rapidement. La nouvelle approche consiste à éviter les entrées/sorties fréquentes dans le processus de cosimulation : la réponse de la voie est calculée directement dans VOCO, en y important les matrices élémentaires du logiciel éléments finis. La nouvelle approche a été testée dans le cas de géométries complexes et les résultats montrent un très bon accord entre les deux approches et un gain de temps important. Durant la thèse, un Benchmark international portant sur la simulation de franchissement d’aiguillages a été organisé par les Universités de Huddersfield (UK) et Chalmers (Suède) entre 2020 et 2021. Dix-neuf équipes ont participé au benchmark, et neuf logiciels ont été utilisés. Pour répondre au cahier des charges du Benchmark, un modèle de voie mobile a été ajouté dans VOCO : ce modèle permet des simulations très rapides, et facilitera le développement de nouvelles méthodes de contact dans VOCO. D’autre part, la modélisation du contre rail a été améliorée à l’occasion du benchmark. Les résultats de VOCO sont en accord avec la tendance moyenne de ceux des autres participants. Quatre participants au benchmark ont ensuite prolongé la comparaison en substituant un modèle éléments finis 3D de l’ADV au modèle mobile. Cela a permis de comparer les approches ‘IVOIE4’ et ‘IVOIE5’ à d’autres approches : les résultats de VOCO sont globalement en accord avec ceux des autres participants. Afin de tenir compte de la multiplicité des paramètres d’entrée qui ont une influence sur la réponse dynamique d’un ADV, la méthode Proper Generalized Decomposition (PGD) a été mise en œuvre pour la première fois dans le contexte de la dynamique ferroviaire, du moins de manière non intrusive. Ce travail a été conduit en partenariat avec la chaire ENSAM/ESI Group. L’un des avantages de la méthode PGD est de traiter un problème paramétrique multivarié comme une série de sous-problèmes unidimensionnels. Ainsi, la méthode permet de contourner la « malédiction de la dimensionnalité », et de prendre en compte des paramètres généralement non considérés dans la conception ou la maintenance. Le modèle réduit résultant peut être manipulé facilement ce qui permet d’envisager d’optimiser la conception de l’ADV en dynamique. Enfin, on a proposé d’améliorer la recherche du point de contact entre la roue et le rail quand les profils du rail sont variables comme c’est le cas des ADV. La nouvelle procédure proposée permet d’obtenir une trajectoire de la roue plus réaliste, et par la même des pics d’effort de contact plus réalistes, tout en conservant le même temps de calcul.Les trois développements effectués (‘IVOIE5’, PGD, approche 3D du contact) doivent permettre à l’avenir de faciliter l’optimisation des ADV. La participation au benchmark a permis quant à elle de se comparer avec les autres approches multicorps de simulations dynamiques d’ADV, et de vérifier la pertinence de notre approche
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Train derailments in railway switches are becoming more and more common, which have caused serious casualties and economic losses. Most previous studies ignored the derailment mechanism when vehicles pass through the turnout. With this consideration, this work aims to research the 3D derailment coefficient limit and passing performance in turnouts through the quasi-static analysis and multi-body dynamic simulation. The proposed derailment criteria have considered the influence of creep force and wheelset yaw angle. Results show that there are two derailing stages in switch panel, which are climbing the switch rail and stock rail, respectively. The 3D derailment coefficient limit at the region of top width 5 mm to 20 mm is much lower than the main track rail, which shows that wheels are more likely to derail in this area. The curve radius before the switch rail is suggested to be set as 350 m. When the curve radius before turnout is 65 m, the length of the straight line between the curve and turnout needs to be larger than 3 m. This work can provide a good understanding of the derailment limit and give guidance to set safety criteria when vehicles pass through the turnout.
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The paper demonstrates the possibilities of a scientometric approach using CiteSpace II software analysis of the field of railway dynamics with detection of research front, main clusters of cross-cited papers, their evolution and pivotal points (see terms in Sections 2.1 and 2.2). The initial database contained 5126 Web Of Science records published between 1975 and 2019 (45 years). The linguistic analysis determined the evolution of burst terms and grouped the papers in 14 clusters that corresponded with the view of the specialists in the field. ‘Railway vehicle’, ‘Curved track’ (hunting stability and derailment risk), ‘Unconventional railway truck’, ‘Railway turnout (crossing)’ and ‘Polygonal wear’ clusters were analysed in more detail with a determination of top-cited papers in each cluster and papers that determined connections between clusters (pivotal papers). Two pivotal papers were verified with their authors.
Article
Running safety of the railway vehicles on the bridge during earthquakes is a major concern for railway engineering. To reduce the derailment risk of railway vehicles on bridges, friction pendulum bearings (FPB) are proposed to be equipped on simply supported bridges in this study. The full nonlinear behavior of the FPB is introduced into the vehicle-bridge interaction model. The effect of FPB’s manufacturing variations, including the shear pin’s strength and friction coefficient, on the misalignment was investigated. The manufacturing variations of the FPB were found to produce large lateral misalignment, which further contributes to large wheel-rail forces when the vehicle passes over the girder ends. It diminishes the improvement in the vehicle’s seismic safety provided by FPBs. Thus, a misalignment control device is proposed to limit the misalignment of the railway bridges equipped with FPBs. The vehicle-bridge interaction analysis results show that no wheel uplift occurred on the bridge equipped with FPBs and misalignment control devices during an earthquake. It indicates that the FPB significantly reduces the vehicle’s derailment risk on bridges compared with the non-isolated bearings.
Article
The wheel flat will cause a severe wheel/rail impact, thus aggravating fatigue damage to vehicle and track components. To reveal the characteristics of the coupled vibration response of heavy-haul locomotives and tracks due to actual wheel flat, a fitting model for wheel flat was established based on the field measured data. Using a heavy-haul locomotive-track coupled dynamic model that considers the interaction between the rail pad and fastening clip in detail, the wheel/rail dynamic response caused by locomotive wheel flat was simulated and analyzed in time and frequency domains. The results show that the geometry of the actual wheel flat was not symmetrical. The P2 force induced by the wheel flat had a great influence on the track components. The wheel flat would cause temporary separation between the rail and the fastening system. This research provided a theoretical reference for identifying locomotive wheel tread damages and maintaining heavy-haul track components.
Article
Wheel–rail dynamic interaction under short-wavelength irregularity which has a detrimental effect on the service life of vehicle and track components, is of crucial importance to be estimated accurately. Aiming at this, dissipative contact force models are integrated into a validated vehicle–track coupled dynamics model, which enables to consider the energy dissipation at the wheel–rail interface. Wheel–rail interactions for different dissipative contact force models are evaluated, and the Hu–Guo model is selected as the most suitable one for wheel–rail interaction analysis. The wheel–rail interactions for the Hu–Guo model and Hertz theory are analysed under different track irregularities including sinusoidal rail corrugation and rail welded joints. The simulation results indicate that the Hu–Guo model has little effect on the normal interaction at low frequencies, but reduces the contact force fluctuation amplitude obviously at high frequencies above 600 Hz, with a more significant reduction at the resonance peak of high frequency range. The Hu–Guo model has an obvious contact force phase lead compared with the Hertz theory at higher frequencies above 1250 Hz. The Hu–Guo dissipative contact force model is needed for the wheel–rail interaction analysis at high frequencies above 600 Hz.
Article
When conducting a numerical simulation of a train’s derailment and post-derailment, it is necessary to continuously observe the relative position of the wheel and rail, which is of great significance for the correct evaluation of train safety. In this paper, a non-analytic method is proposed to extend the search range and improve the accuracy of the classical semi-analytical method, i.e. the contact locus method. Based on the point cloud convex hull, a high-density wheel contact locus vertical profile is obtained by projecting the chamfer and internal zone of the flange onto the rail cutting plane. To obtain maximum compression in the normal direction and avoid singularities on both rail head sides in the Cartesian coordinate system the rail surface is interpolated with the polar spline curve. Compared with the classical method used to describe the wheel contact locus, in the proposed hybrid method, potential contact points are provided. Finally, the proposed hybrid method and the classical methods are applied to the wheel track coupling simulation. Numerical results demonstrate the high reliability and effectiveness of the proposed method.
Article
In this note an explanation and the relevance of a couple of singularities in the mathematical models of rolling friction is presented.
Article
The evolution of wheel-rail dynamic interaction of a high-speed railway vehicle is essential for the simulation of wheel-rail rolling contact damage under low adhesion conditions. The main objective of this study is to reproduce the dynamic wheel-rail interaction behaviour under various interfacial contaminations by experimental and numerical modelling methodology. Firstly, the wheel-rail adhesion characteristics under different interfacial contaminations were obtained. Subsequently, a simplified numerical methodology was proposed to extract the parameters from the high-speed adhesion tests to modify the simplified theory of Kalker (FASTSIM). The initial slop reduction factor and the slip-velocity-dependent coefficient of friction (COF) were introduced based on the high-speed experimental curves. Furthermore, the modified wheel-rail rolling contact model was incorporated into a longitudinal vehicle-track coupled dynamic model. The wheel-rail dynamic interaction behaviours under different operational conditions were attained. Finally, the wheel-rail wear performances were primarily investigated for typical traction coefficients under wet conditions. Results show that the wheel-rail creep force drops dramatically when the wheel enters the low adhesion zone (LAZ). There is a sudden increase in the creep force when the adhesion recovers. In addition, the wheelsets begin to slide and have severe wear at LAZ when the traction coefficient is larger than 0.1 at high speed.
Article
The simultaneous prediction of wheel surface wear is one of the most challenging tasks in the railway field, which requires the knowledge of vehicle–track dynamics, rolling contact mechanics, and other tribological phenomena. In this paper, a new model for predicting wheel profile wear is presented to study in detail the characteristics of wear in the railway. The model is able to consider the effect of track flexibility on wheel wear evolution. The proposed modelling approach includes a vehicle-track coupled model for vehicle dynamical simulation, the local contact model for wheel-rail interaction, and an energetic approach for surface wear evaluation. The whole model has been validated by the comparison with experimental data coming from Chinese high-speed railway lines. The results show that the new model assures high computational efficiency as well as reaches a good prediction accuracy. The proposed model allows the investigation of the role played by different track parameters related to track flexibility on the wheel and rail wear evolution. The influence of the fastener and railpad stiffness on the wheel wear evolution is presented, using the proposed model.
Article
Excessive vibrations of railway vehicles induced by dynamic impact loadings have a significant impact on train operating safety and stability; however, due to the complexity and diversity of railway lines and service environment, they are extremely difficult to eliminate. A comprehensive overview of recent studies on the impact vibration behavior of railway vehicles was given in this paper. First, the sources of impact excitations were categorized in terms of wheel-rail contact irregularity, aerodynamic loads, and longitudinal impulses by train traction/braking. Then the main research approaches of vehicle impact vibration were briefly introduced in theoretical, experimental, and simulation aspects. Also, the impact vibration response characteristics of railway vehicles were categorized and examined in detail to various impact excitation sources. Finally, some attempts of using the railway vehicle vibration to detect track defects and the possible mitigation measures were outlined.Graphic abstract
Article
Vehicular loads represent one of the most critical external dynamic actions on the bridge structures, especially the short- and medium-span bridges. The dynamic interactions between the vehicle and bridge become more and more significant due to the rapid development of transportation nowadays. This paper proposes a methodological framework for efficient and accurate prediction of dynamic responses of the vehicle-bridge interaction system using artificial neural networks. Based on the developed vehicle-bridge system model composed of 3D train vehicle model, bridge finite element model, and wheel-rail contact model, numerical experiments are carried out to produce data required for training neural networks. Feedforward neural network and deep long short-term memory network are developed and designed to forecast various dynamic responses of both the vehicle and bridge in time- and frequency-domain. The proposed framework is illustrated on a high-speed train vehicle and bridge system. To further examine its robustness, effects of track irregularity and noise level on the prediction performance are investigated. The present framework can provide an efficient alternative to the vehicle-bridge interaction analysis, and has significant ability of inclusion of field measurement data and promising potential for the realization of online response prediction.
Article
In railway transportation, track geometry irregularity is one of the main factors in controlling train safety. At present, railway practitioners typically use the track geometry car (TGC) based on the inertial navigation system to inspect track irregularities. However, TGCs are quite expensive, and their inspection interval is relatively long. Among a variety of emerging methods, using vehicle responses to estimate track irregularities seems very promising as it enables a cheaper and more efficient solution. In this work, an extended auto-encoder (EAE) is proposed to estimate the track longitudinal irregularity through car body acceleration. The mean absolute percentage errors of the estimated results on the simulated and the real-world dataset are 2.67% and 3.75%, respectively, which is 50%–55% lower than the traditional neural network. In the frequency domain, the characteristic wavelengths of 5.4 and 32 m can be effectively identified. Besides, the Bayesian deep learning (BDL) method is introduced to improve the EAE and estimate the confidence interval of the track longitudinal amplitude. A metric (coverage width and error) for evaluating and optimizing the performance of the estimated interval is proposed. The interval estimation result in the time domain has a 98% correct coverage rate of the ground truth and 93% in the frequency domain. Within the error range of plus/minus one standard deviation, the EAE model has an estimation accuracy of 94.2% for the standard deviation of track longitudinal irregularity, and the BDL-EAE can even reach 100%. Compared with the existing methods, our proposed model only requires car body acceleration and has the potential to use ordinary in-service trains for onboard track inspection.
Article
Vehicle actions represent the main operational loading for various types of bridges. It is essential to conduct random vibration analysis due to the unavoidable uncertainties arising from both the vehicle and bridge structure. This paper proposes a novel approach for the vehicle-induced random vibration analysis of bridges integrating Bayesian deep learning. The dynamic equation of the stochastic vehicle-bridge interaction system in state space form is deduced, based on which an ensemble of deep neural network is proposed to construct the surrogate model consisting of two designed functional modules, i.e., convolutional layers for excitation input feature extraction and long short-term memory (LSTM) layers for bridge response time series prediction. According to the deduced state space equation, the conventional LSTM cell is modified by introducing randomness to a portion of cell parameters. Probability distributions of the selected network parameters are then estimated by Bayesian inference, enabling the surrogate model to convey the uncertainties of the vehicle-bridge interaction system and rapidly estimate random vibration responses of the bridge. The proposed approach is applied on a railway bridge under high-speed train loading to demonstrate its efficacy. A deep Bayesian neural network is tailored and developed using the present methodology for the studied train-bridge coupling dynamic system. Time-domain statistics and frequency-domain responses of the bridge are acquired through the Bayesian deep learning model and compared with the results from a validated vehicle-bridge interaction model. Robustness of the Bayesian deep learning approach is further examined by investigating the influence of training dataset size, vehicle speed, and model input noise.
Chapter
A new moving train–track interaction model is shown in the paper to accurately and efficiently determine long-term high-speed train–track interaction dynamic response. In this model, the rail is represented with a reduced beam model (RBM) and the slabs mainly affected by the train–track interaction are modeled with four-node Kirchhoff-Love plate elements. The fastenings are modeled with spring-damper elements and the Concrete Asphalt (CA) layer is modeled with a Winkler foundation. Since only a small part of the rail and a few slabs from the whole slab track are included, the present model has fewer degrees of freedom than the traditional model using the modal superposition method and the simulation time is significantly decreased. The present model is validated by a long-term train–track interaction case where the results are compared with those from the traditional method. The simulation results show that the present model is accurate and efficient and has great advantages in solving high-speed train–track interaction problems.
Article
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.
Article
Improvements have been made to the nonlinear wheel/rail force prediction method of Elkins and Gostling. These improvements are described, along with experimental equipment used in order to provide input data for the predictions, and to validate them. A further series of curing tests, using a laboratory coach equipped with bogies having variable suspension parameters, has been carried out. The prediction method is now used on a regular basis within British Rail, and its use for vehicle design is considered, together with planned extensions to cover calculation of wheel and rail wear and dynamic behavior of railway vehicles on curve and switch entry.
Article
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.
Article
In this paper the computer code Duvorol, dealing with the computation of three-dimensional rolling contact with dry friction, is described. It is based on the variational principle of Duvaut and Lions for dry friction, which leads to an incremental theory. The relevant properties of Duvorol are:1Generality. All half-space steady-state rolling contact problems with Hertzian normal contact can be treated.2Reliability. The total tangential force is always found with reasonable accuracy by a standard discretization.3Speed. On an IBM 370/158 the calculation of a case then takes only several seconds.
The Effect of Surface Condition in Rolling Contact Behavior
• A O Gilchrist