Dynamic and Vibration Analysis of a Vehicle Rear Axle System

A detailed finite element model for the rear axle system of a sport utility vehicle is developed in this investigation. The axle system is treated as a multibody system that consists of nine bodies that include the input shaft, two output shafts, the carrier and tube system, four control arms and a track bar. The rotating input and output shafts are mounted on the carrier and tube system using six bearings. The four control arms and the track bar are connected to the carrier system and the frame of the vehicle using rubber bushings. In the model developed in this investigation, three dimensional beam elements are used to develop the finite element model for the input and output axle shafts, the control arms, and the track bar. A non-conventional finite element formulation is used to develop the equations of motion of the rotating input and output shafts in order to account for the effect of their angular velocities. These equations are expressed in terms of inertia shape integrals that depend on the assumed displacement field. The inertia shape integrals are first evaluated for each finite element. The inertia shape integrals of the rotating shafts are obtained by assembling the inertia shape integrals of its finite elements using a standard finite element assembly procedure. A conventional finite element formulation is used for the control arms and the track bar. The model developed in this investigation includes the effect of the bearing stiffness, the effect of the stiffness of the helical springs of the suspension system, and the effect of the stiffness of the tires. Using the Lagrangian dynamics and the finite element method, the equations of motion of the axle system are developed and expressed in terms of the nodal coordinates of the shafts, the control arms and the track bar as well as the degrees of freedom of the carrier. This finite dimensional model is used to determine the mode shapes and the natural frequencies of the axle system. The discrepancies between several of the natural frequencies predicted using the dynamic model developed in this investigation and natural frequencies determined experimentally are found to be less than 2%. A parametric study is performed in order to investigate the effect of the axle system parameters on the natural frequencies and mode shapes. Using the modal transformation, a set of differential equations of motion of the axle system is developed and used to examine the system dynamics under given loading conditions. The solutions of the resulting equations of motion are obtained using numerical methods.     

Investigation of the effects of sleeper-passing impacts on the high-speed train

The sleeper-passing impact has always been considered negligible in normal conditions, while the experimental data obtained from a High-speed train in a cold weather expressed significant sleeper-passing impacts on the axle box, bogie frame and car body. Therefore, in this study, a vertical coupled vehicle/track dynamic model was developed to investigate the sleeper-passing impacts and its effects on the dynamic performance of the high-speed train. In the model, the dynamic model of vehicle is established with 10 degrees of freedom. The track model is formulated with two rails supported on the discrete supports through the finite element method. The contact forces between the wheel and rail are estimated using the non-linear Hertz contact theory. The parametric studies are conducted to analyse effects of both the vehicle speeds and the discrete support stiffness on the sleeper-passing impacts. The results show that the sleeper-passing impacts become extremely significant with the increased support stiffness of track, especially when the frequencies of sleeper-passing impacts approach to the resonance frequencies of wheel/track system. The damping of primary suspension can effectively lower the magnitude of impacts in the resonance speed ranges, but has little effect on other speed ranges. Finally, a more comprehensively coupled vehicle/track dynamic model integrating with a flexible wheel set is developed to discuss the sleeper-passing-induced flexible vibration of wheel set.     

Influence of polygonal wear of railway wheels on the wheel set axle stress

The coupled vehicle/track dynamic model with the flexible wheel set was developed to investigate the effects of polygonal wear on the dynamic stresses of the wheel set axle. In the model, the railway vehicle was modelled by the rigid multibody dynamics. The wheel set was established by the finite element method to analyse the high-frequency oscillation and dynamic stress of wheel set axle induced by the polygonal wear based on the modal stress recovery method. The slab track model was taken into account in which the rail was described by the Timoshenko beam and the three-dimensional solid finite element was employed to establish the concrete slab. Furthermore, the modal superposition method was adopted to calculate the dynamic response of the track. The wheel/rail normal forces and the tangent forces were, respectively, determined by the Hertz nonlinear contact theory and the Shen–Hedrick–Elkins model. Using the coupled vehicle/track dynamic model, the dynamic stresses of wheel set axle with consideration of the ideal polygonal wear and measured polygonal wear were investigated. The results show that the amplitude of wheel/rail normal forces and the dynamic stress of wheel set axle increase as the vehicle speeds rise. Moreover, the impact loads induced by the polygonal wear could excite the resonance of wheel set axle. In the resonance region, the amplitude of the dynamic stress for the wheel set axle would increase considerably comparing with the normal conditions.     

Vertical Vibration Analysis of Vehicle/Imperfect Track Systems

Summary This paper studies the vertical vibration of a vehicle traveling on an imperfect track system. The car body and sleepers are modeled as Timoshenko beams with finite length, and the rail is assumed as an infinite Timoshenko beam with discrete supports. Imperfection of the track system comes from a sleeper lost partial support by the ballast. Since deflection of the rail is limited within a certain interval where the vehicle is passing over, the infinite domain problem can be transformed into a finite domain problem with moving boundary. In this work, the equations of motion of the car body, rail and sleepers are discretized first by the finite element method. The discretized equations of motion for the vehicle and track systems are then assembled, respectively. Finally, the Newmark method is applied to obtain the response of the vehicle and track systems at each time step. The effect of the vehicle speed on the response of the vehicle and track systems is investigated.     

Simulation of the vertical bending fatigue test of a five-link rear axle housing

This study seeks a practical method for simulating the vertical bending fatigue test of the BANJO housing of a five-link rear axle. Linear static and transient dynamic finite element models are constructed for the rear axle in which the rubber bushings and the bearings of the axle shafts are reasonably modeled with solid and shell elements, respectively, for simplicity. The calculated results are compared with the measured strain histories, and the results indicate that the finite element models constructed are reasonable. The hypothesis of equal fatigue damage is applied to determine the Hainan proving ground driving life prediction that is equivalent to the constant amplitude fatigue life in the vertical bending fatigue test.     

Steady-State Curving Performance of Railway Freight Truck with Damper-Coupled Wheelsets

The focus of this paper is on the steady-state curving behaviour of a freight car system with Damper Coupled Wheelset (DCW), where the wheels of conventional shape within an axle are coupled through a damper element. A freight truck model with two DCW and pseudo-car body on curved track is developed to study the influence of wheelset coupler parameter on the curving response and performance. The response is primarily evaluated in terms of wheelset tracking error and yaw misalignment in response to track curvature and cant deficiency. The curving performance is evaluated in terms of slip and flange boundaries. The results in general, indicate that when the value of coupler parameter is reduced, the wheelset response to track curvature increases, and results in flanging and wheel slip on a less tighter curve than those corresponding to conventional rigid axled wheelsets.     

Effect of vehicle vibration environment of high-speed train on dynamic performance of axle box bearing

In this study, we developed a comprehensive three-dimensional vehicle–track coupled dynamics model considering the traction drive system and axle box bearing. In this model, dynamic interactions between the axle box bearing and other components, such as the wheelset and bogie frame, are considered based on a detailed analysis of the structural properties and working mechanism of the axle box bearing. A few complicated dynamic excitations, such as the time-varying mesh stiffness of gears, time-varying stiffness of bearing, bearing gaps and track irregularities, are considered. Then, the dynamic responses of the vehicle–track system are demonstrated via numerical simulations based on the established dynamics model. The results indicate that the traction drive system and track irregularities can significantly influence the dynamic interactions of the axle box bearing. The necessity of considering the excitation caused by gear meshing and track irregularities when assessing the dynamic performance of the axle box bearing is demonstrated.     

Steady-State Curving Performance of Railway Freight Truck with Damper-Coupled Wheelsets

SUMMARY

The focus of this paper is on the steady-state curving behaviour of a freight car system with Damper Coupled Wheelset (DCW), where the wheels of conventional shape within an axle are coupled through a damper element. A freight truck model with two DCW and pseudo-car body on curved track is developed to study the influence of wheelset coupler parameter on the curving response and performance. The response is primarily evaluated in terms of wheelset tracking error and yaw misalignment in response to track curvature and cant deficiency. The curving performance is evaluated in terms of slip and flange boundaries. The results in general, indicate that when the value of coupler parameter is reduced, the wheelset response to track curvature increases, and results in flanging and wheel slip on a less tighter curve than those corresponding to conventional rigid axled wheelsets.     

Dynamic analysis of spiral bevel geared rotor systems applying finite elements and enhanced lumped parameters

The dynamics of spiral bevel gears like most high-speed precision gears employed in motor vehicles and off highway equipments are substantially affected by the structural characteristics of the shafts and bearings. The lumped parameter model is one of the common tools applied to perform gear dynamic analysis. Even though the lumped parameter approach is computationally fast and conveniently efficient, it typically uses limited number of coordinates and may not fully account for the shaft-bearing structural characteristics accurately. In this analysis, the finite element formulation, that can generally represent more complete characteristics of the shaft-bearing assembly, is employed to enhance the current lumped parameter synthesis theory using the concept of effective mass and inertia elements. Computational output shows that the enhanced lumped parameter synthesis model is capable of predicting sufficiently accurate dynamic response when compared to the direct dynamic finite element calculations, and much more precise response than previous lumped parameter results, especially when the gear dynamics are associated with the pinion or gear bending modes. Even though this analysis focuses primarily on the spiral bevel geared rotor systems, the proposed methodology and analysis results can be easily extended to other types of gears.     

Near surface deformation of rails and wheels in a curve and during acceleration and braking

A hierarchical concept for describing the rolling/sliding contact of a wheel on a rail is proposed, which is developed to model the near surface deformation of the contacting partners depending on the vehicle system dynamics. In principal the vehicle dynamics simulation delivers the input for a static finite element model for the elastic-plastic rolling/sliding contact investigation. To include also more realistic rough surfaces in the calculations, which is absolutely necessary to predict the highly deformed surface layer as observed in wheels and rails, a further refinement of the mesh is necessary and performed. The output values of the static finite element model are now boundary conditions for the finite element micro-model. The results of this micro-model correspond well with the micro-structural investigations of wheel and rail surfaces.     

On the interest of integrating vehicle dynamics for the ground propagation of vibrations: the case of urban railway traffic

This paper presents a complete numerical model for studying the vertical dynamics of the vehicle/track interaction and its impact on the surrounding soil, with the emphasis on vehicle modelling. A decoupling between the track and the soil is proposed, due to the difficulty of considering all the subsystem components. The train/track model is based on a multibody model (for the vehicle) and a finite element model (for the track). The soil is modelled using an infinite/finite element approach. Simulations of both models are carried out in the time domain, which is better able to simulate the propagation of the vibration waves and to take into account the possible nonlinearity of a component. The methodology is applied in the case of an urban tram track and validated with the available experimental data. Models for the tram, the track and the soil are described. Results from the complete model of the vehicle and a simple model, based on an axle load, are compared with experimental results and the benefits of a complete model in the simulation of the ground vibration propagation induced by railway vehicles are demonstrated. Moreover, a parametric study of the vehicle wheel type is conducted, which shows the advantage of a resilient wheel, for various rail defects.     

Dynamic responses of a high-speed railway car due to wheel polygonalisation

The polygonal wear around the wheel circumference could pose highly adverse influences on the wheel/rail interactions and thereby the performance of the vehicle system. In this study, the effects of wheel polygonalisation on the dynamic responses of a high-speed rail vehicle are investigated through development and simulations of a comprehensive coupled vehicle/track dynamic model. The model integrates flexible slab track, wheelsets and axle boxes subsystem models so as to account for elastic deformations caused by impact loads induced by the wheel polygonalisation. A field-test programme was undertaken to acquire the polygonal wear profile and axle box acceleration response of a high-speed train, and the data are used to demonstrate the validity of the coupled vehicle/track system model. Subsequently, the effects of wheel polygonalisation are evaluated in terms of wheel/rail impact forces, axle box vertical acceleration and dynamic stress developed in the axle considering different amplitudes and harmonic orders of the polygonal wear. The results suggest that the high-order wheel polygonalisation can give rise to high-frequency impact loads at the wheel/rail interface, and excite some of the vibration modes of the wheelset and the axle box leading to high-magnitude axle box acceleration and dynamic stress in the wheelset axle.     

Lane-keeping benefits of practical rear axle steer

The classic two-degree-of-freedom yaw-plane or ‘bicycle’ vehicle model is augmented with two additional states to describe lane-keeping behaviour and further augmented with an additional control input to steer the rear axle. A simple driver model is hypothesised where the driver closes a loop on a projected lateral lane position. The driver can select the preview distance to compensate driver/vehicle dynamics, consistent with the ‘cross-over’ model found in the literature. A rear axle steer control law is found to be a function of the front axle steering input and vehicle speed that exhibits stability similar to a positive-real system, while at the same time improving the ability of the driver/vehicle system to track a complex curved lane and improving steady-state manoeuvrability. The theoretically derived control law bears similarity to practical embodiments allowing a deeper understanding of the functional value of steering a rear axle.     

基于载荷分布预分析的应变传感器布置

采用载荷分布预分析技术,对某MPV汽车后桥进行了有限元分析,得到了该后桥在静载、制动、转向及扭转4种工况下的应变云图和张量图。通过分析应变云图和张量图,确定了该后桥的关键受载部位及其主应力方向,然后处理标定试验数据,线性回归出后桥载荷一应变的函数关系,并通过实车道路试验结果分析验证了通过有限元分析确定出的后桥应变传感器贴片位置的正确性。     

Vehicle Response to Stochastic Roadways

Dynamic response calculations for vehicles traversing irregular surfaces are usually accomplished using frequency domain methods involving spectral densities and transfer functions. Here an alternative procedure is developed which allows direct computation of mean square values and correlations of system variables for both transient and steady-state conditions. The method is based upon the differential equation for the covariance matrix which is directly related to the state equations for the vehicle. Multiple white noise inputs can be incorporated as well as inputs at two wheels which follow the same track at a distance from one another..The method is suitable for computer implementation without the complex algebra associated with finding all necessary transfer functions and the necessity of evaluating integrals in order to find mean square values using the conventional approach. As an illustration, a simple vehicle model is worked out completely and the variation of pitch and heave motion as a function of vehicle speed is plotted.     

High-speed wheel/rail contact determining method with rotating flexible wheelset and validation under wheel polygon excitation

A rotating flexible wheelset model is developed and integrated into a vehicle/track dynamic model. Flexible wheelset modes with natural frequencies less than 1000?Hz are considered in the wheelset modelling. An innovation of the paper is that wheel/rail rolling contact calculation considers the effect of the wheelset flexibility and the rotating effect. By introducing two half dummy rigid wheelsets the rolling contact between the flexible wheelset and the two rails can be transformed to that between a rigid wheelset and the rails. As an extension application, the wheel OOR (Out-Of-Round) wears with the 11th, 15th, and 17th orders are used to the vehicle system dynamic model with rigid, flexible and rotating-flexible wheelset model. The results of the three models are compared to study the influence of wheelset flexibility and rotation. The ‘online searching contact method’ developed in this paper is compared with the traditional contact method with considering the rotating flexible wheelset. And then a measured OOR is used to excite the rotating flexible wheelset, the response of which is analysed and verified.     

An investigation into the mechanism of the polygonal wear of metro train wheels and its effect on the dynamic behaviour of a wheel/rail system

This paper presents a detailed investigation conducted into the mechanism of the polygonal wear of metro train wheels through extensive experiments conducted at the sites. The purpose of the experimental investigation is to determine from where the resonant frequency that causes the polygonal wear of the metro train wheels originates. The experiments include the model tests of a vehicle and its parts and the tracks, the dynamic behaviour test of the vehicle in operation and the observation test of the polygonal wear development of the wheels. The tracks tested include the viaducts and the tunnel tracks. The structure model tests show that the average passing frequency of a polygonal wheel is approximately close to the first bending resonant frequency of the wheelset that is found by the wheelset model test and verified by the finite element analysis of the wheelset. Also, the dynamic behaviour test of the vehicle in operation indicates the main frequencies of the vertical acceleration vibration of the axle boxes, which are dominant in the vertical acceleration vibration of the axle boxes and close to the passing frequency of a polygonal wheel, which shows that the first bending resonant frequency of the wheelset is very exciting in the wheelset operation. The observation test of the polygonal wear development of the wheels indicates an increase in the rate of the polygonal wear of the wheels after their re-profiling. This paper also describes the dynamic models used for the metro vehicle coupled with the ballasted track and the slab track to analyse the effect of the polygonal wear of the wheels on the wheel/rail normal forces.     

Vehicle Response to Stochastic Roadways

SUMMARY

Dynamic response calculations for vehicles traversing irregular surfaces are usually accomplished using frequency domain methods involving spectral densities and transfer functions. Here an alternative procedure is developed which allows direct computation of mean square values and correlations of system variables for both transient and steady-state conditions. The method is based upon the differential equation for the covariance matrix which is directly related to the state equations for the vehicle. Multiple white noise inputs can be incorporated as well as inputs at two wheels which follow the same track at a distance from one another..The method is suitable for computer implementation without the complex algebra associated with finding all necessary transfer functions and the necessity of evaluating integrals in order to find mean square values using the conventional approach. As an illustration, a simple vehicle model is worked out completely and the variation of pitch and heave motion as a function of vehicle speed is plotted.     

重载铁路路基动力响应的数值分析

通过大型有限元软件ANSYS,建立轨道-路基三维有限元模型,分析路基动应力沿线路横向和纵向的分布规律,以及不同轴重和基床表层模量对路基动应力的影响,为以后重载铁路基床的设计和养护维修提供参考。研究结果表明:路基面竖向动应力沿线路横向和纵向的分布都不均匀,横向大致呈“M”形。基床表层动应力的衰减最为急剧,约为40%。随着轴重的增加,路基各层竖向动应力都在增加。基床表层弹性模量为150 MPa时,轴重每增加5 t,基床表面竖向动应力最大增加26.1%。40 t轴载下,基床表层弹性模量每增加50 MPa,基床表面竖向动应力最大增加2.68%。