Vertical Wheel-rail Contact Force Research Articles

Dynamic responses of the high-speed train with polygonal wheels considering gear transmissions

To examine the influence of polygonal wheels on the dynamic responses of high-speed train, a vehicle-track dynamics model was developed. This model incorporated gear transmissions using multibody dynamics methodology and gear dynamics theory. The effect of gear transmissions on the dynamic responses of the high-speed train was evaluated by comparing the results of the developed model with those of a non-geared traditional model. The dynamic responses of the train were studied by examining the combined effects of wheel polygonal excitation and time-varying mesh stiffness excitation. The results indicated that the vertical wheel-rail contact force and vibration amplitude of the model with polygonal wheels were larger than those of the normal model. Similarly, the geared transmission model exhibited greater contact force and vibration amplitude compared to the non-geared transmission model, attributed to the increased excitation. The evolution of the wheel polygon’s order and wear depth could significantly increase the vertical wheel-rail contact force and the wheel load reduction rate. The safety limits for wheel polygon order and wear depth were established. The model with gear transmissions is more closely aligned with the actual situation and exhibits higher safety performance, providing valuable reference for wheel turning.

Research on the traction characteristic evaluation of urban rail vehicles based on entropy weight TOPSIS

This paper aims to investigate the influence of different speed at the end of the constant power section of the traction characteristic curve (TCC) on the vehicle dynamic performance and evaluate the TCC. A dynamics co-simulation model is developed in SIMPACK and MATLAB for dynamic analysis of the urban rail vehicle (URV) under different traction characteristics. Then it is used to investigate how acceleration distance and vehicle dynamic performance varies with the speed at the end of the constant power section of the TCC under different starting torques. Moreover, the entropy weight TOPSIS method which is widely used to solve the multi-objective decision-making problem is chosen to evaluate the traction characteristics based on various dynamic performance indexes over 25 test sections and acceleration distance. The results show that under traction conditions, the starting torque has effects on the lateral and vertical accelerations of car body, lateral and vertical wheel-rail contact forces, derailment coefficient and wheel unloading factor. The higher the torque, the greater the value of each index, that means the poorer the vehicle ride characteristics and running safety. For a given starting torque, the dynamic performance indexes increase with the increase of the speed at the end of the constant power section from 50 km/h to 80 km/h during the vehicle speed-up process. The maximum growth rate of the lateral and vertical accelerations of car body, lateral and vertical wheel-rail contact forces are 17%, 8%, 8% and 2%, respectively, when the speed at the end of the constant power section increases from 50 km/h to 80 km/h. Last, the comprehensive evaluation of traction characteristics using entropy-weight TOPSIS method reveals when the starting torque is 800 [Formula: see text], 1000 [Formula: see text], 1200 [Formula: see text] and 1400 [Formula: see text], the corresponding optimal speed at the end of the constant power section is 80 km/h, 80 km/h, 70 km/h and 50 km/h, respectively. The result of the study can provide theoretical support for traction characteristic design and traction control for URVs.

Influence of shortwave irregularity on increasing the vehicle running speed on bi-block ballastless track lines

Compared with slab ballastless track, bi-block ballastless track has the advantages of simpler constructed components and better economy, and has been used in high-speed railways for nearly 20,000 km in China. During the construction, the position deviation between sleepers and the disturbance of sleeper position caused by track bed concrete pouring can easily lead to shortwave irregularity with wavelength of 1 ∼ 2 m of bi-block ballastless track. Massive detection data on several high-speed railway lines showed that the standard deviation of vertical wheel-rail contact forces on bi-block ballastless track was about 58% higher than that on slab ballastless track. In this paper, a vehicle-track coupled dynamic analysis model was established, which can consider 1 ∼ 2 m shortwave irregularities of the track. Under the current construction and operation control standards, the dynamic responses of vehicles and tracks under different running speeds were studied. The results showed that vertical shortwave irregularity mainly affected the dynamic response of the wheel and rail, and rarely affected the dynamic response in other components. Compared with no shortwave irregularity, when the track had shortwave irregularity with σv = 0.8 mm, the peak value of the vertical acceleration of wheelset increased by 4.1 times, the standard deviation of wheel-rail contact force increased by 3.9 times, the vertical acceleration of frame increased by 1.7 times, and the vertical acceleration of track bed increased by 1.8 times, while the vibration acceleration of car body had almost no effect. When the track had shortwave irregularity with σh = 0.8 mm, the lateral acceleration of wheelset increased by 2.3 times. When the track had shortwave irregularity with σv = 0.8 mm and the vehicle speed increased to 450 km·h−1, the wheel load reduction rate reached 0.85, which exceeded the safety limit. Consider the results of this study, following suggestions can be obtained:(1) the shortwave irregularity with wavelength of 1 ∼ 2 m can be measured indirectly by the standard deviation of wheel-rail vertical contact force or wheelset vibration acceleration. (2) To control the wheel load reduction rate within 0.6, the standard deviation of random vertical irregularity should be controlled within 0.6 mm when running speed is 350 km/h, and within 0.4 mm when running speed is 400 km/h or above.

Dynamic response of vehicle-track interaction at the bolted rail joint in the presence of the polygonal wheel

Rail joints are the weakest link in the railway track structure due to the presence of discontinuities in the track stiffness and wheel-rail contact geometry. This paper presents the dynamic response of vehicle-track interaction at the bolted rail joint (BRJ) in the presence of polygonal wheel wear. A three-dimensional coupled vehicle-track dynamic model was established using the finite element method (FEM) and the multi-body system (MBS) approach, in which the flexibilities of the wheelset and track are taken into account. The proposed dynamic model is validated by the comparisons of field measurement and calculated vertical axle-box acceleration in time and frequency domains. The effects of the flexible wheelset in the presence of polygonal wear on the vehicle-track dynamic interaction at the BRJs are illustrated through comparisons with those obtained using without polygonal wheel model. The results show that the polygonal wheel wear and the rail joint irregularities can induce high-magnitude vertical wheel-rail contact force, and exacerbate the vibration responses of the axle box, the wheelset, and the rails. The simulation results also indicate that the wheelset bending modes, the P2 resonance due to rail joint excitation, and the track vibration modes have significant effects on the vertical vehicle-track dynamic interaction at the supported and suspended BRJs.

The Effect of Interface Damage between Slab and Mortar Layer on the Dynamic Performances of Vehicle and Track Systems under the High Frequency Train Loads

To investigate the influences of through-transverse mortar disengagement with different lengths and heights on the dynamic responses of vehicle and track systems under the high frequency train loads, a coupled rigid vehicle–flexible track multi-body dynamics (MBD) model with mortar disengagement was established in SIMPACK platforms with the help of ANSYS software. The results indicate that when the mortar disengagement length is no more than 1 m, the responses of vehicle and track systems are hardly influenced by mortar disengagement with an increase rate of no more than 10% except for the slab displacement. When LMD reaches 1.5 m, the maximum slab displacement exceeds the safety limit of 0.5 mm. The vertical wheel–rail contact force and the rail displacement exceed the safety limit with the mortar disengagement length of 2 m and the mortar disengagement height of 1.5 mm. The most increase rates induced by mortar disengagement are 190% and 272% with regards to the slab displacement and the longitudinal tension stress of slab, respectively, which is significantly detrimental to the service life of slab. The proposed approach has the potential to preliminarily determine the critical mortar disengagement size, which is conductive to relieving the pressure of track maintenance while ensuring the service life of track structures and the operation safety and riding comfort of the vehicle.

Condition Monitoring of Railway Crossing Geometry via Measured and Simulated Track Responses.

This paper presents methods for continuous condition monitoring of railway switches and crossings (S&C, turnout) via sleeper-mounted accelerometers at the crossing transition. The methods are developed from concurrently measured sleeper accelerations and scanned crossing geometries from six in situ crossing panels. These measurements combined with a multi-body simulation (MBS) model with a structural track model and implemented scanned crossing geometries are used to derive the link between the crossing geometry condition and the resulting track excitation. From this analysis, a crossing condition indicator is proposed. The indicator is defined as the root mean square (RMS) of a track response signal γ that has been band-passed between frequencies corresponding to track deformation wavelength bounds of and for the vehicle passing speed (f = v/). In this way, the indicator ignores the quasi-static track response with wavelengths predominantly above and targets the dynamic track response caused by the kinematic wheel-crossing interaction governed by the crossing geometry. For the studied crossing panels, the indicator ( and ) was evaluated for γ = u, v, or a as in displacements, velocities, and accelerations, respectively. It is shown that this condition indicator has a strong correlation with vertical wheel–rail contact forces that is sustained for various track conditions. Further, model calibrations were performed to measured sleeper displacements for the six investigated crossing panels. The calibrated models show (1) a good agreement between measured and simulated sleeper displacements for the lower frequency quasi-static track response and (2) improved agreement for the dynamic track response at higher frequencies. The calibration also improved the agreement between measurements and simulation for the crossing condition indicator demonstrating the value of model calibration for condition monitoring purposes.

Identification of vertical wheel-rail contact force based on an analytical model and measurement and its application in predicting ground-borne vibration

Wheel-rail interaction plays an important role in the study of railway engineering. The wheel-rail contact forces (WCFs) are the key factors in the models addressing wheel-rail interaction. However, it is sometimes difficult to be measured, so an indirect identification methodology is proposed in this paper. Based on an analytical model and measurement, the vertical WCF can be determined. Using measured rail accelerations as input data, a calculation program is developed. The vertical WCF and the excitation forces transmitted from the vehicle-rail system to the roadbed can be obtained. The latter forces are used to predict the train-induced ground-borne vibrations. A case study of predicting ground-borne vibration in Beijing Metro is presented to verify the effectiveness of this method. The results show that the vertical WCF can be obtained efficiently and accurately, and the predicted ground-borne vibrations have good agreement with the measured ones.

Optimization on the Crosswind Stability of Trains Using Neural Network Surrogate Model

Under the influence of crosswinds, the running safety of trains will decrease sharply, so it is necessary to optimize the suspension parameters of trains. This paper studies the dynamic performance of high-speed trains under crosswind conditions, and optimizes the running safety of train. A computational fluid dynamics simulation was used to determine the aerodynamic loads and moments experienced by a train. A series of dynamic models of a train, with different dynamic parameters were constructed, and analyzed, with safety metrics for these being determined. Finally, a surrogate model was built and an optimization algorithm was used upon this surrogate model, to find the minimum possible values for: derailment coefficient, vertical wheel-rail contact force, wheel load reduction ratio, wheel lateral force and overturning coefficient. There were 9 design variables, all associated with the dynamic parameters of the bogie. When the train was running with the speed of 350 km/h, under a crosswind speed of 15 m/s, the benchmark dynamic model performed poorly. The derailment coefficient was 1.31. The vertical wheel-rail contact force was 133.30 kN. The wheel load reduction rate was 0.643. The wheel lateral force was 85.67 kN, and the overturning coefficient was 0.425. After optimization, under the same running conditions, the metrics of the train were 0.268, 100.44 kN, 0.474, 34.36 kN, and 0.421, respectively. This paper show that by combining train aerodynamics, vehicle system dynamics and many-objective optimization theory, a train’s stability can be more comprehensively analyzed, with more safety metrics being considered.

Indirect identification of wheel rail contact forces of an instrumented heavy haul railway vehicle using machine learning

Rail car safety and stability are important factors for good performance. The most used safety index to quantify railway safety is the ratio between the lateral and vertical wheel rail contact forces (L/Q). This study aims to use machine learning (ML) models to evaluate the viability of estimating the wheel rail contact forces from sensors in a regular instrumented railway vehicle (IRV). A virtual model of a BRA1 railway vehicle was created to generate an artificial dataset with variables measured with the actual BRA1 vehicle plus different variables measured by other IRVs found in the literature. The desired output variable is the L/Q ratio for each wheel of the leading bogie. Exploratory data analysis was done to clarify the correlation between the variables while model explainability techniques were applied to evaluate the contribution of these input variables to the output (L/Q). A total of 24 embedded machine learning models were trained and optimized using the tree-based pipeline optimization tool (TPOT) to generate a ML pipeline capable of producing an accurate L/Q ratio as the output for different cases of sampling rate, input variables and track irregularities. The results show that machine learning models can predict the wheel rail contact forces indirectly – without using instrumented wheelsets – with the highest mean squared error being equal to 0.01113.

A simplified analysis framework for assessing overturning risk of high-speed trains over bridges under crosswind

This technical note addresses the overturning risk assessment of high-speed trains over multi-span simply supported bridges under crosswind. A train-bridge coupled system is established to estimate the wheel–rail contact forces from which the overturning risk of train is assessed. The estimation is also compared to that without consideration of bridge vibration. The result shows that the loss of vertical wheel–rail contact force is primarily caused by the crosswind. The influence of track irregularities and bridge vibration on overtuning risk of train is secondary. The bridge deformation can be approximately estimated as static deformation under moving train weight thus a sophisticated dynamic analysis of coupled train and bridge system can be avoided. When the external excitation due to deformation of multi-span bridge has a frequency close to the vertical domain frequency of train system, resonant effect is observed which increases the influence of the bridge deformation on train performance.

A New Switch and Crossing Design: Introducing the Back to Back Bistable Switch

A new track swtich and crossing (S&C), the back to back bistable (B2B) switch, is proposed that has shown potential to significantly reduce the wheel/rail contact forces through the switch due to its more continuous wheel/rail contact interface and more uniform track stiffness arising from the elimination of the crossing nose. This offers a major reduction on maintenance cost of future S&Cs. The paper explains the concept and identifies the design guidelines for a current layout and uses vehicle/turnout dynamic modelling to predict wheel rail forces through a switch to identify performance improvements relative to a conventional S&C. Both multi-body simulation (MBS) and Finite Element (FE) model have been developed to account for dynamic and thermal analysis. The new design has shown improvements in lateral and vertical wheel-rail contact forces and less relative rail displacements due to thermal effect compared to the conventional S&C.

A High Accuracy and High Speed Imaging and Measurement System for Rail Corrugation Inspection

In order to decrease the noise and vibration of operation in railway tracks, it is necessary to inspect the status of them frequently. A main task in inspection of railway tracks is measurement of rail corrugation. The rail corrugation occurs during operation due to wear. The dynamic component of the vertical wheel-rail contact force, as induced by rail corrugation is an important source to vibration. Also, according to the corrugation wavelength and railway vehicle speed, a dynamic excitation is generated which is an important source to noise. It is essential to utilize a system to check the rail corrugation. In this article, a new measurement system based on image processing is proposed to perform the corrugation measurement in a reliable manner, while traditional measurement systems are based on acceleration measurement or chord measurement and they are not reliable due to physical contact or need for knowing the characteristics of the track. The proposed system is based on laser triangulation principle using image processing to measure the rail corrugation precisely and quickly. This approach is an efficient technique for high-speed and high-accurate rail corrugation measurement. Experimental results show the capability of the system for practical usages.

Simulation of wheel–rail impact load and sleeper–ballast contact pressure in railway crossings using a Green's function approach

A method for the simulation of dynamic vehicle–track interaction and evaluation of measures to improve the design of railway crossings is presented. To accurately represent the high-frequency dynamics and non-linear contact conditions of the vehicle–track system, the vertical interaction between a wheelset and the crossing is simulated in the time domain using a Green's function approach based on extensive finite element models of track and wheelset in combination with an implementation of Kalker's variational method to solve the non-Hertzian, and potentially multiple, wheel–rail contact. Both wheels of the wheelset in simultaneous contact with the crossing rail and the outer rail are considered. Rigid and flexible wheelset models are compared. The sampled contact geometry of the crossing, including the discrete irregularity between the wing rail and the crossing nose, is used to determine a three-dimensional surface geometry between each pair of adjacent rail cross-sections. A parameter study is performed to investigate the influence of crossing design on the maximum vertical wheel–rail contact force and the contact pressure generated at the sleeper–ballast interface. It is concluded that a design with a combination of increased sleeper width, softer rail pads and implementation of under sleeper pads (USP) will reduce the track stiffness gradients in the crossing panel and mitigate the risk of differential track settlement by lowering the sleeper–ballast contact pressure.

Investigation of coupled dynamics of a railway tank car and liquid cargo subject to a switch-passing maneuver

The movement of the liquid cargo within a partly filled tank car is known to impose additional slosh forces and moments that may adversely affect the dynamic responses of the vehicle. This study is aimed at analyzing the liquid cargo slosh in a partly filled tank car and its effects on vehicle responses during a switch-passing maneuver. A two-dimensional analytical liquid slosh model is formulated for the analyses of the liquid load shift in the roll plane, lateral slosh force, and roll moment through summation of first four antisymmetric modes of the liquid. The analytical slosh model is integrated to a 114 degrees-of-freedom multibody dynamic model of the railway tank car comprising nonlinear wheel–rail contact and contact pairs of the suspension system. The validity of the slosh model is illustrated by comparing the responses with those reported in other studies and those obtained from a nonlinear computational fluid dynamic model. The coupled fluid–vehicle model is subsequently used to study the effects of fluid slosh during switch-passing maneuvers on different response measures, namely roll motion of the tank car, lateral and vertical wheel–rail contact forces, and derailment ratio. The significance of the liquid cargo slosh in the partially filled state is demonstrated by comparing the responses with those of the car with equivalent rigid cargo. The results show that liquid sloshing within the partly filled car can lead to higher magnitudes of car body roll angle and thereby the unloading ratio compared to the conventional rigid cargo car. Switch-passing critical speeds are further identified for different fill ratios and switch geometries. For fill ratios below 80%, the switch-passing critical speeds of the partly filled car are substantially lower compared to those of the equivalent rigid cargo car. Neglecting the contributions due to dynamic slosh force and roll moment arising from a partially filled railway tank car may thus lead to underestimation of the critical speed in switch-passing maneuvers.

A computational simulation study on the dynamic response of high-speed wheel–rail system in rolling contact

The dynamic wheel–rail responses during the rolling contact process for high-speed trains were investigated using the explicit finite element code LS-DYNA 971. The influence of train speed on the wheel–rail contact forces (including the vertical, longitudinal, and lateral forces), von Mises equivalent stress, equivalent plastic strain, vertical acceleration of the axle, and the lateral displacement of the initial contact point on the tread, were examined and discussed. Simulation results show that the lateral and longitudinal wheel–rail contact forces are very smaller than the corresponding vertical contact forces, and they seem to be insensitive to train speed. The peak value of dynamic vertical wheel–rail contact force is approximately 2.66 times larger than the average quasi-static value. The elliptical wheel–rail contact patches have multiple stress extreme points due to the plastic deformation of the wheel tread and top surface of the rail. The vertical acceleration value of the axle in the steady condition is around ±5 m/s2 for the perfected wheel–rail system with the running speed below 300 km/h.

Optimization of Rail Profiles to Improve Vehicle Running Stability in Switch Panel of High-Speed Railway Turnouts

A method for optimizing rail profiles to improve vehicle running stability in switch panel of high-speed railway turnouts is proposed in this paper. The stock rail profiles are optimized to decrease the rolling radii difference (RRD). Such characteristics are defined through given rail profiles, and the target rolling radii difference is defined as a function of lateral displacements of wheel set. The improved sequential quadratic programming (SQP) method is used to generate a sequence of improving profiles leading to the optimum one. The wheel-rail contact geometry and train-turnout dynamic interaction of the optimized profiles and those of nominal profiles are calculated for comparison. Without lateral displacement of wheel set, the maximum RRD in relation to a nominal profile will be kept within 0.5 mm–1 mm, while that in relation to an optimized profile will be kept within 0.3 mm–0.5 mm. For the facing and trailing move of vehicle passing the switch panel in the through route, the lateral wheel-rail contact force is decreased by 34.0% and 29.9%, respectively, the lateral acceleration of car body is decreased by 41.9% and 40.7%, respectively, and the optimized profile will not greatly influence the vertical wheel-rail contact force. The proposed method works efficiently and the results prove to be quite reasonable.

Monitoring vertical wheel–rail contact forces based on freight wagon inverse modelling

The safety and stability of freight train operations are closely related to the wheel–rail contact dynamic forces. To evaluate and monitor the wheel–rail dynamic forces based on the accelerations on the wagon components, a two-dimensional inverse wagon model has been developed. To verify the inverse modelling, a detailed VAMPIRE wagon model has been used for the simulations on two cases of track rail top surface and cross-level irregularities. The simulated accelerations on wagon components are then the inputs into the inverse wagon model. Reasonable agreement has been achieved in the comparison between the predicted and simulated primary and secondary suspension forces and wheel–rail contact forces. The inverse wagon model is finally simplified into a one-dimensional vertical model for potential online applications. The predicted and simulated wheel–rail contact dynamic forces are also compared due to the random track geometry irregularities.

A hybrid model for prediction of ground-borne vibration due to discrete wheel/rail irregularities

A hybrid model for the prediction of ground-borne vibration due to discrete wheel and rail irregularities, such as wheel flats, dipped welds and insulated rail joints, is presented. The hybrid model combines the simulation of vertical wheel–rail contact force in the time domain, accounting for parametric excitation due to sleeper periodicity and impact excitation induced by loss of wheel–rail contact, and calculation of ground-borne vibration in the frequency–wavenumber domain considering a layered soil model. The model is demonstrated by investigating the influence of wheel flat size and vehicle speed on maximum vertical wheel–rail contact force and free field ground vibration. It is shown that magnitudes of impact load and ground vibration are increasing with increasing wheel flat length (and depth), but the influence of vehicle speed is not as evident. Higher vehicle speeds often lead to loss of wheel–rail contact and severe impact loads but the frequency content of such impact loads is shifted to higher frequencies which may be less significant for ground vibration.

Inverse identification of wheel–rail contact forces based on observation of wheel disc strains: an evaluation of three numerical algorithms

In this paper, three numerical algorithms for the identification of wheel–rail contact forces based on measured wheel disc strains on an instrumented railway wheelset are discussed and compared. The three algorithms include one approach resting on static calibration, one that is applying a Kalman filter and the third is exploiting an inverse identification scheme. To demonstrate and evaluate the alternative methods, two load cases including periodic excitation by sinusoidal wheel–rail irregularities and transient excitation by an insulated rail joint are considered. Based on a previously presented vehicle–track interaction model in the time domain, load scenarios are defined by taking the calculated vertical wheel–rail contact forces as the reference force to be re-identified by the proposed algorithms. The reference contact forces are applied on a finite element model of the wheel to generate synthetic observation data, that is, radial strains at the positions of the strain gauges, serving as input to the identification procedures. It is concluded that the inverse identification scheme leads to superior accuracy at higher computational cost. If on-line implementation and evaluation is required, the Kalman filter generates better accuracy than the static calibration approach.

Acceptance criterion for rail roughness level spectrum based on assessment of rolling contact fatigue and rolling noise

▶ A reference short-pitch rail corrugation spectrum has been derived. ▶ Development of acceptance criterion regarding noise emission and RCF risk. ▶ Demonstration on employing the criterion to analyze altered operational conditions. ▶ Significantly improve means of planning preventive actions, e.g. grinding. The influences of train speed and rail roughness level on rolling noise and subsurface initiated rolling contact fatigue (RCF) impact are studied. In particular, the consequences of short-pitch rail corrugation on tangent track with wavelengths in the interval 3–8 cm are simulated using models of dynamic vehicle–track interaction. Based on the calculated results, a criterion in terms of a limit for maximum levels of rail roughness with respect to the current traffic conditions can be determined. Such a criterion may be useful for planning of rail grinding intervals if used together with a system for regular monitoring of rail roughness levels. It is concluded that the importance of controlling rail roughness increases with increasing train speed. Increasing axle loads on freight vehicles from 22.5 tonnes to 30 tonnes leads to a significant increase in RCF impact. In operational practice, this is usually compensated for by introducing more conformal wheel–rail profile combinations. Calculated vertical wheel–rail contact forces and rolling noise levels show good agreement with field measurements.