Vertical Contact Forces Research Articles

Coupling Vibration Research on Vehicle-Bridge System

Take vehicle running through a long-span cable-stayed bridge as an example to study the vibration rule of vehicle and bridge in the process of vehicles running on the large span bridge. Vehicle-bridge coupling numerical analysis model is established to study the changing rule of vertical displacement of the vehicle, vehicle wheel vertical contact force, the vertical displacement of the bridge and the impact coefficients of bridge while different quality of vehicles running on the bridge. The results show that, the heavier the vehicle, the greater and the more obvious wave of the vertical displacement change of bridge main-span across. The heavier the vehicles, the more obvious the change of the vertical displacement and torsion angle of cable-stayed bridge main-span across.

Signal interference of non-uniform tire load on stress-in-motion sensing element

ABSTRACT Sensing elements in Stress-In-Motion (SIM) system were designed to measure vertical and tangential tire-pavement contact forces under uniform loading conditions. However, in reality, the contact forces are not uniformly distributed. Compared with tangential shear force, non-uniform vertical contact force causes a bending moment which may take significant errors to tri-axial contact stress measurements. In the research, three tire thread-sensing element contact conditions (uniform, non-uniform and point load) were applied and influences of the non-uniformity on vertical and tangential stress signals were determined by finite element method. It was found that significant errors may occur as a result of the contact force non-uniformity. The error of the vertical contact force measurement was up to 65% (non-uniform load). In extreme situation with point load, the error would be greater. The errors caused by vertical contact force non-uniformity to the tangential contact stress measuring signals were 15% (non-uniform force) and 60% (point load). So designing of the SIM sensing element and decoupling method between measuring signals should be carefully reconsidered.

Estimation of dynamic tire force by measurement of vehicle body responses with numerical and experimental validation

Abstract Bridge modal parameters, including modal mass, are important factors that directly affect the bridge responses under various excitations. To identify these parameters, the simultaneous measurement of the bridge excitation and its corresponding bridge responses is typically required. However, traditional methods of exciting a bridge using a hammer or a shaker have the limitations of small impact energy, narrow frequency range, and other site-specific difficulties. However, the vehicle-induced load, which excites the bridge through the vehicle-bridge interaction, can be used in bridge parameter identification if the vehicle-bridge contact force is estimated well. In this paper, an algorithm is proposed to estimate the dynamic components of the vertical tire contact forces by measuring the vehicle body acceleration and angular velocity at selected locations on an ordinary vehicle. A Kalman filter with augmented tire forces in the system state vector is employed. Observability and sensitivity analyses provide the method’s theoretical foundation. Numerical examples for different road roughness conditions demonstrate that the proposed algorithm has good accuracy and robustness against noise and modelling error. A commercial light vehicle was used in the conduct of field measurement to validate the proposed method. The estimated dynamic tire forces are in good agreement with reference measurements.

A new strain gauge configuration on the rail web to decouple the wheel–rail lateral contact force from wayside measurement

The simultaneous presence of bending moments and torques produced by the lateral and vertical contact forces between the wheel and the rail generates a complex strain state on the rail surface, which makes it difficult to identify the strain signals produced purely from the lateral contact force. In this study, a new strain gauge configuration is proposed to decouple strain signals of the wheel–rail lateral contact force from wayside measurements by analyzing the bending strains on the rail web using a full Wheatstone bridge. For this purpose, a finite element modeling of the wheel–rail contact is performed to analyze the bending strains on the rail web and to optimize two instrumented sections for eight electric resistance strain gauges. Laboratory testing is also used to examine the installation scheme of the strain gauges at the two optimal instrumented sections. A good agreement is observed between the experimental data and the simulation results. Strain signals are evenly distributed for about 10 cm in the middle region between the two optimal instrumented sections and only account for the lateral contact force.

Wheel-rail impact interaction on the high-speed railroad bridges

The paper describes interaction of high-speed rolling stock and railroad bridge deck and proves the importance of adequate model of wheel (mechanism) and rail (structure) interaction. The model must consist of a rail and slabs of the ballastless deck. The paper characterizes the results of computer simulation of perspective rolling stock passing through high speed railroad bridge, that contains the uniform bridge superstructure for Moscow – Kazan line. The paper shows that in case of resonant bridge superstructure vibration the risk of derailment is high because of the decline of the wheel-rail contact force down to zero, which means wheel uplift. Moreover, the impact of the wheel is the result of uplift and the impact value is similar to the impact from impossible damages of wheels or rail on high speed railroad in consequence of which rail breaking occur. This rail breaking is the most frequent reason of derailment. The impact forces are equivalent to the impact of the fresh flat of the wheel and may be more than 300 kN while static force is equal to 85 kN. The vertical contact force is rising from zero to maximum value for 0.002 to 0.004 s after uplift. The computer simulation results show that it is the bridge superstructure resonance, which leads to impact interaction. The rail fasteners rigidity decline causes vertical interaction force decrease during the impact but the derailment risk still exists during vibration of “bridge – track – train” system.

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.

Finite element model for predicting the initiation of subsurface damage in railway crossings—A parametric study

In this study, the initiation of subsurface damage due to the impact of new and worn wheels on differently deformed crossing nose geometries is calculated using the Dang-Van criterion. Three crossings with different materials (manganese steel, chromium-bainitic steel, and tool steel) were cyclically loaded in an FE crossing model reported in a previous study to evaluate the run-in state of plastic deformation. The impacts of the wheels on the deformed crossings were then calculated by considering the behaviour of an elastic material. This parametric study showed the effects of different velocities, axle loads, and wheel types on the vertical contact forces, contact pressures, and Dang-Van damage parameters. Additionally, the ability of manganese steel crossings to withstand unfavorable load situations was observed by including plastic material behavior and considering material history, such as residual stresses and hardening.

Comparative assessment of vertical vibrations of a vehicle on the road and during the EUSAMA test

The work was undertaken to assess the discrepancies between the vertical vibrations of a motor vehicle examined on an EUSAMA suspension tester and the vibrations that occur during rectilinear motion of the same vehicle with a constant speed on an uneven road. The road surface irregularities were of random type and have been described in accordance with recommendations of the International Organization for Standardization (ISO) specified in the document ISO/TC 108/253: “Reporting vertical road surface irregularities. Generalised vertical road inputs to vehicle”. A largely nonlinear “quarter-car” model with two degrees of freedom (2DoF) was used, where the actual elasticity characteristics of vehicle suspension and tyres, sliding friction in the suspension system, and the phenomenon of tyre separation from the road (“bouncing”) were taken into account. The smoothing properties of the tyres were also represented in the model. The description of these properties exactly corresponded to the results of measurements carried out on a test rig. The calculations were done for various values of the coefficient of viscous damping in the shock absorber. In total, 52 simulations of the EUSAMA test (with both nominal and zero sliding friction in the suspension system) and 26 numerical experiments for an average road (of class “C” according to ISO8608) at a vehicle speed of 90 km/h were carried out. The values of the vertical tyre-road contact force, suspension deflection rate, and suspension damping force were analysed in detail. The results of the tests carried out have been chiefly presented in the form of graphs.

Comparison of Fixation Techniques for Acetabular Fractures Involving the Anterior Column with Disruption of the Quadrilateral Plate: A Biomechanical Study.

In elderly patients who have sustained an acetabular fracture involving disruption of the quadrilateral plate (QLP), postoperative loading of the joint beyond the level of partial weight-bearing can result in medial redisplacement of the QLP. The purpose of this biomechanical study was to compare the performances of 4 different fixation constructs intended to prevent medial redisplacement of the QLP. Anterior column posterior hemitransverse (ACPHT) fractures with disruption of the QLP were created on synthetic hemipelves (fourth-generation Sawbones models) and subsequently stabilized with (1) a 12-hole plate bridging the QLP (Group 1), (2) the plate with added periarticular screws along the QLP (Group 2), (3) the plate combined with an infrapectineal buttress plate (Group 3), or (4) the plate with the added periarticular screws as well as the buttress plate (Group 4). The point of load application on the acetabulum was defined to be the same as the point of application of maximum vertical hip contact force during normal walking. Loads were applied to simulate either partial weight-bearing (20 cycles, from 35 to 350 N) or inadvertent supraphysiologic loads (linearly increasing loads until the onset of failure, defined as fragment displacement of >3 mm). A universal testing machine was synchronized with a digital image correlation system to optically track redisplacement at the QLP. The level of significance was set at p < 0.05. During experimental simulation of partial weight-bearing, maximum fracture step openings never exceeded 2 mm. During simulation of inadvertent supraphysiologic load, the median load to failure was higher (p < 0.05) in Group 2 (962 N; range, 798 to 1,000 N) and Group 4 (985 N; range, 887 to 1,000 N) compared with Group 1 (445 N; range, 377 to 583 N) and Group 3 (671 N; range, 447 to 720 N). All 4 fixation constructs performed in an acceptable manner on testing with simulated partial weight-bearing. Only additional periarticular screws along the QLP increased the fixation strength. Redisplacement of the QLP resulting in an incongruency of the hip joint has been associated with poor long-term outcomes. Within the constraints of this study, periarticular long screws were superior to infrapectineal buttress plates in preventing medial redisplacement of the QLP.

Numerical investigation on effect of the relative motion of stock/switch rails on the load transfer distribution along the switch panel in high-speed railway turnout

ABSTRACTIn railway turnout, the stock rail and switch rail are separated to enable the vehicle changing among the tracks, and they are provided with different rail resilience level on the baseplate. Therefore, there will be vertical relative motion between stock/switch rails under the wheel loads, and the relative motion will affect consequentially the wheel–rail contact conditions. A method is developed to investigate the effect of the relative motion of stock/switch rails on the load transfer distribution along the switch panel in high-speed railway turnout. First, the rigid wheel–rail contact points of stock/switch rails are calculated based on the trace line method, and then the contact status is determined by the presented equations, finally, the distribution of wheel–rail contact forces of stock/switch rails is obtained based on the continuity of interface displacements and forces which using an approximate surface deformation method. Some parametric studies have been performed, such as the lateral displacement of wheel set, the vertical contact forces, the wheel profiles and the vertical stiffness of rail pad. The results of the parametric study are presented and discussed.

New Insights into the Short Pitch Corrugation Enigma Based on 3D-FE Coupled Dynamic Vehicle-Track Modeling of Frictional Rolling Contact

A three-dimensional (3D) finite element (FE) dynamic frictional rolling contact model is presented for the study of short pitch corrugation that considers direct and instantaneous coupling between the contact mechanics and the structural dynamics in a vehicle-track system. In this study, we examine the system responses in terms of vibration modes, contact forces and the resulting wear with smooth rail and corrugated rail with progressively increasing amplitude to infer the conditions for consistent corrugation initiation and growth. Wear is assumed to be the damage mechanism, and short pitch corrugation is modeled using wavelengths from field observations of a Dutch railway. The contribution of this paper is a global perspective of the consistency conditions that govern the evolution of short pitch corrugation. The main insights are as follows: (1) the longitudinal vibration modes are probably dominant for short pitch corrugation initiation; (2) during short pitch corrugation evolution, the interaction and consistency between longitudinal and vertical modes should determine the development of short pitch corrugation, and once a certain severity is reached, vertical modes become dominant; and (3) in the case simulated in this paper, corrugation does not grow probably due to not only the different resulting main frequencies of the vertical and longitudinal contact forces, but also the inconsistency between the frequencies of the vertical and longitudinal vibration modes and the resulting wear. It is inferred that in the continuous process of initiation and growth of the corrugation, there should be a consistency between them, and this could be done by the control of certain track parameters.

Modelling vertical human walking forces using self-sustained oscillator

Abstract This paper proposes a model of a self-sustained oscillator which can generate reliably the vertical contact force between the feet of a healthy pedestrian and the supporting flat rigid surface. The model is motivated by the self-sustained nature of the walking process, i.e. a pedestrian generates the required inner energy to sustain its repetitive body motion. The derived model is a fusion of the well-known Rayleigh, Van der Pol and Duffing oscillators. Some additional nonlinear terms are added to produce both the odd and even harmonics observed in the experimentally measured force data. The model parameters were derived from force records due to twelve pedestrians walking on an instrumented treadmill at ten speeds using a linear least square technique. The stability analysis was performed using the energy balance method and perturbation method. The results obtained from the model show a good agreement with the experimental results.

Dynamic Response of a Simplified Turbine Blade Model with Under-Platform Dry Friction Dampers Considering Normal Load Variation

Dry friction dampers are widely used to reduce vibration. The forced vibration response of a simplified turbine blade with a new kind of under-platform dry friction dampers is studied in this paper. The model consists of a clamped blade as two rigidly connected beams and two dampers in the form of masses which are allowed to slide along the blade platform in the horizontal direction and vibrate with the blade platform in the vertical direction. The horizontal and vertical vibrations of the two dampers, and the horizontal and transverse platform vibrations are coupled by friction at the contact interfaces which is assumed to follow the classical discontinuous Coulomb’s law of friction. The vertical motion of the dampers leads to time-varying contact forces and can cause horizontal stick-slip motion between the contact surfaces. Due to the relative horizontal motion between the dampers and the blade platform, the vertical contact forces and the resultant friction forces act as moving loads. The Finite Element (FE) method and Modal Superposition (MS) method are applied to solve the dynamic response, together with an algorithm that can capture nonsmooth transitions from stick to slip and slip to stick. Quasi-periodic vibration is found even under harmonic excitation.

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.

Dynamic Amplification of Bridge-Expansion-Joints considering Roughness induced Vehicle Vibrations

The response of bridge expansion joints to the transient impact induced by crossing vehicles always represent the dynamic reaction of the former to the dynamic wheel contact forces at that particular moment. Separating the dynamic components in the vertical wheel contact forces, the dynamic amplification of the bridge expansion joints response, which is dominated by the driving velocity of the vehicle, its crossing position in lateral direction, the dynamic behavior of the expansion joint itself and most importantly by the interaction between the vehicle tire and the expansion joint’s lamellas can be discussed. Due to the random distribution of the roughness amplitudes a stochastic characterization of the vehicle vibrations is necessary. In addition to the classical frequency approach based on complex transfer matrices completely describing the dynamic behavior of the vehicles and spectral density matrices characterizing the pavement roughness, the numerically efficient covariance analysis is applied. Therefore the spectral characteristics of the roughness amplitudes, which are described on the basis of multi-correlated random processes, are considered by introducing shaping filters in combination with a state space augmentation. The dynamic behavior of the considered bridge expansion joint is dominated by the properties of the discrete elastomeric spring elements. Hence a a non-proportional damping approach has to be applied to analyze the three dimensional finite element model of the structure using a modal superposition.

A MSD model for coupled analysis of pedestrian-footbridge dynamic interaction

Recent footbridges are characterized by long span, light materials and increasing slenderness which make them more sensitive to dynamic forces induced by pedestrians. While walking, the pedestrian adapts his gait to the bridge motion and interacts with the structure. At contact points, the pedestrian transmits contact forces to the bridge that, in turn, imposes a set of displacements and velocities to the pedestrian’s feet. The bridge response accounting for the human-structure interaction depends both on reliable estimates of expected loading scenarios and on the accuracy of the models representing pedestrians.This work presents a complete framework for the analysis of the human-structure dynamic interaction. To properly describe this phenomenon, the coupled equations of motion for the two mechanical systems are derived. To this aim the standard FE modeling of the structure is retained, while a new bipedal mass-spring-damper model is adopted for the pedestrian. The model is able to reproduce the sequence of single and double support phases typical of the human gait and is excited by both an equivalent bio-mechanical force and the motion at contact points with the bridge. The solution of the coupled formulation is based on a forced uncoupling of the equations, possibly associated to an iterative integration procedure. At each time instant the two systems are analyzed separately: the bridge subjected to vertical contact forces, the pedestrian to an imposed motion at his feet.The uncoupled strategy of solution is implemented into a research code. In the case study groups of pedestrians cross a lively footbridge, whose modal properties were experimentally identified. The numerical model was developed with ANSYS. To investigate the potential of the proposed approach, numerical analyses have addressed the effect on the bridge response of both the degree of synchronization and the spatial distribution of groups of nine pedestrians. The bridge vertical accelerations reach values out of the range of comfort and show an high dependency on these parameters. The effectiveness of the proposed approach of modeling and analysis is highlighted.

Tire–pavement interaction modelling: hyperelastic tire and elastic pavement

The interaction between deformable tire and pavement was studied using the validated finite element model; the full understanding of tire–pavement contact has implications for pavement damage prediction and pavement life-cycle assessment (fuel consumption estimation). The tire’s rubber and reinforcement were considered hyperelastic and linear elastic, respectively, with material constants obtained from the tire manufacturer (rubber) and laboratory testing (reinforcement). On the other hand, the pavement was assumed linear elastic supported by linear elastic springs. This assumption was made as a first step to examine the impact of using a deformable-on-deformable tire–pavement system to predict energy in the tire and contact stresses. The effect of the pavement stiffness on contact area, tire deflection, three-dimensional contact stresses, surface deflection, internal energy of the tire and its components, the work performed by the contact forces, and dissipation caused by friction was also studied. The elastic modulus of the pavement affected the contact area, while the elastic constants of the springs were more relevant for tire deflection. In addition, stiffness of the pavement had a varying effect on each component of the three-dimensional contact stresses: vertical contact stresses remained almost constant and longitudinal ones were the most affected. The symmetry of the surface deflection decreased and the friction dissipation increased 10.2% as the elastic modulus changed from the smallest to the highest value. Finally, the work performed by the vertical contact forces was significantly higher than by the in-plane loads, and the stiffness of the pavement affected rolling resistance force, which is related to fuel consumption.

Evaluation of Railway Track Safety with a New Method for Track Quality Identification

A new method for track inspection is developed to complement traditional geometric methods. An inertial measuring system and a specialized data treatment method is proposed to evaluate railway track safety, observed from the vehicle dynamic performance point of view. System equations for the inverse vehicle dynamic problem, augmented with the suspension torsion equation, are solved to estimate the wheels driving forces that are directly correlated with the vehicle safety traveling over an irregular track. Results of a measuring campaign on a railway wagon are used to evaluate the present system by direct positional comparison with lateral and vertical contact forces (L/V) safety ratio measured with two instrumented wheelsets (IWS) installed on the leading bogie of the wagon. Also, data collected and treated are compared with track geometry measurements. The results of quantified track safety present good agreement with those found using traditional measuring methods. This confirms the ability of the new method to detect the location of the highest potential hazard region, for optimized track maintenance purposes. The new system proves to be a promising method for track safety evaluation.

Compliant Biped Walking on Uneven Terrain with Point Feet

In this paper, we aim to realize compliant biped walking on uneven terrain with point feet. A control system is designed for a 5-link planar biped walker. According to the role that each leg plays, the control system is decomposed into two parts: the swing leg control and the support leg control. The trajectory of the swing foot is generated in real-time to regulate the walking speed. By considering the reaction torque of the swing leg's hip joint as disturbance, a sliding model controller is implemented at the support leg's hip joint to control the torso's posture angle. In order to make sure the landing foot does not rebound after impact, the vertical contact force control is set as the internal loop of the hip's height control. In simulation, the control system is tested on a virtual 5-link planar biped walker in Matlab. Finally, stable biped walking is realized on uneven terrain with roughness up to 2cm.

An analytical mathematical method for calculation of the dynamic wheel–rail impact force caused by wheel flat

ABSTRACTThe simplified method to determine a vertical impact force of wheel with flat and rail interaction is presented in this article. The presented simplified method can be used to identify maximum contact force and its distribution in the contact length between the damaged wheel and the rail. The vertical impact force depends on geometrical parameters of the rail and wheel with flat, speed of vehicle and the angle of deviation of rail. This article demonstrates the influence of wheel with flat geometrical parameters, speed of vehicle to maximum contact force and its distribution in the contact zone. The obtained values of the simplified method for determination of a vertical contact force are compared with the results obtained from field measurements.