Wanming Zhai

TWO SIMPLE FAST INTEGRATION METHODS FOR LARGE-SCALE DYNAMIC PROBLEMS IN ENGINEERING

A new simple explicit two-step method and a new family of predictor–corrector integration algorithms are developed for use in the solution of numerical responses of dynamic problems. The proposed integration methods avoid solving simultaneous linear algebraic equations in each time step, which is valid for arbitrary damping matrix and diagonal mass matrix frequently encountered in practical engineering dynamic systems. Accordingly, computational speeds of the new methods applied to large system analysis can be far higher than those of other popular methods. Accuracy, stability and numerical dissipation are investigated. Linear and nonlinear examples for verification and applications of the new methods to large-scale dynamic problems in railway engineering are given. The proposed methods can be used as fast and economical calculation tools for solving large-scale nonlinear dynamic problems in engineering.

Fundamentals of vehicle–track coupled dynamics

This paper presents a framework to investigate the dynamics of overall vehicle–track systems with emphasis on theoretical modelling, numerical simulation and experimental validation. A three-dimensional vehicle–track coupled dynamics model is developed in which a typical railway passenger vehicle is modelled as a 35-degree-of-freedom multi-body system. A traditional ballasted track is modelled as two parallel continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The non-ballasted slab track is modelled as two parallel continuous beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The vehicle subsystem and the track subsystem are coupled through a wheel–rail spatial coupling model that considers rail vibrations in vertical, lateral and torsional directions. Random track irregularities expressed by track spectra are considered as system excitations by means of a time–frequency transformation technique. A fast explicit integration method is applied to solve the large nonlinear equations of motion of the system in the time domain. A computer program named TTISIM is developed to predict the vertical and lateral dynamic responses of the vehicle–track coupled system. The theoretical model is validated by full-scale field experiments, including the speed-up test on the Beijing–Qinhuangdao line and the high-speed running test on the Qinhuangdao–Shenyang line. Differences in the dynamic responses analysed by the vehicle–track coupled dynamics and by the classical vehicle dynamics are ascertained in the case of vehicles passing through curved tracks.

Modelling and experiment of railway ballast vibrations

The vibration of railway ballast is a key factor to cause track geometry change and increase of track maintenance costs. So far the methods for analyzing and testing the vibration of the granular ballast have not been well formed. In this paper, a five-parameter model for analysis of the ballast vibration is established based upon the hypothesis that the load-transmission from a sleeper to the ballast approximately coincides with the cone distribution. The concepts of shear stiffness and shear damping of the ballast are introduced in the model in order to consider the continuity of the interlocking ballast granules. A full-scale field experiment is carried out to measure the ballast acceleration excited by moving trains. Theoretical simulation results agree well with the measured results. Hence the proposed ballast vibration model has been validated.

A Detailed Model for Investigating Vertical Interaction between Railway Vehicle and Track

SUMMARY A new detailed model is developed to investigate the vertical interactions between railway vehicles and tracks. The model consists of two subsystems of vehicle and track in which the vehicle subsystem is modelled as a multi-body system with 10 DOFs running on the track with a constant velocity, and the track substructure as an infinite Euler beam supported on a discrete-continuous elastic foundation consisting of the three layers of rail, sleeper, and ballast. The interface between these two subsystems is the wheel / rail interaction described by Hertzian nonlinear elastic contact theory. In order to get numerical results of such a complex system, a new simple fast integration method is adopted. And typical numerical results are compared with field measured data to verify the detailed model. Finally, the model is applied to analysing the wheel / rail dynamic interactions in high-speed rail and in heavy haul railway.

High-speed train-track-bridge dynamic interactions - Part I: theoretical model and numerical simulation

This paper presents a framework to systematically investigate the high-speed train–track–bridge dynamic interactions, aiming to provide a method for analysing and assessing the running safety and the ride comfort of trains passing through bridges, which are critically important for the design of new high-speed railway bridges. Train–track–bridge interactive mechanism is illustrated. A fundamental model is established for analysing the train–track–bridge dynamic interactions, in which the vehicle subsystem is coupled with the track subsystem through a spatially interacted wheel–rail model; and the track subsystem is coupled with the bridge subsystem by a track–bridge dynamic interaction model. Modelling of each subsystem and each interactive relationship between subsystems are presented. An explicit–implicit integration scheme is adopted to numerically solve the equations of motion of the large non-linear dynamic system in the time domain. Computer simulation software named the train–track–bridge interaction simulation software (TTBSIM) is developed to predict the vertical and lateral dynamic responses of the train–track–bridge coupled system.

Dynamic interaction between a lumped mass vehicle and a discretely supported continuous rail track

Abstract This paper describes the formulation and application of a numerical model that simulates the vertical dynamic interaction between a train vehicle and the rail track. The considered vehicle model is supported on two double-axle bogies at each end and is described as a 10-degree-of-freedom lumped mass system comprising the vehicle body mass and its moment of inertia, the two bogie masses and their moments of inertia, and four wheelset unsprung masses. The bogie sideframe mass is linked with the wheel unsprung mass through the primary suspension springs and linked with the vehicle body mass through the secondary suspension springs. In the track model, the rail is treated as an infinitely long beam discretely supported at rail/sleeper junctions by a series of springs, dampers and masses representing the elasticity and damping effects of the rail pads, the ballast, and the subgrade, respectively. Shear springs and dampers are also introduced between the ballast masses to model the shear coupling effects in the ballast. The mass, stiffness and damping values of these track components and the sleeper spacings can be arbitrarily varied, so that variations in track component properties and track geometric errors can be taken into account. The dynamic interaction between the wheelsets and the rail is accomplished by using the non-linear Hertzian theory. Example applications of the model are given.

Coupling Model of Vertical and Lateral Vehicle/Track Interactions

SUMMARY A new dynamic model of vehicle/track interaction is presented. The model considers the vehicle and the track as a whole system and couples the vertical interaction with the lateral interaction. The vehicle subsystem is modeled as a multi-body system with 37 degrees of freedom, which runs on the track with a constant velocity. The track substructure is modeled as a discretely supported system of elastic beams representing the rails, sleepers and ballasts. The normal contact forces between wheels and rails are described by Hertzian nonlinear elastic contact theory and the tangential wheel/ rail forces are decided by the creep theory. Numerical results are compared with those of conventional dynamic models of railway vehicles. Applications of the coupling model to the investigation of safety limits against derailment due to the track twist and the combined alignment and cross-level irregularities are reported at the end of the paper.

A NEW WHEEL/RAIL SPATIALLY DYNAMIC COUPLING MODEL AND ITS VERIFICATION

Based on the theory of vehicle-track coupling dynamics, a new wheel/rail spatially dynamic coupling model is established in this paper. In consideration of rail lateral, vertical and torsion vibrations and track irregularities, the wheel/rail contact geometry, the wheel/rail normal contact force and the wheel/rail tangential creep force are solved in detail. In the new wheel/rail model, the assumption that wheel contacts rail rigidly and wheel always contacts rail is eliminated. Finally, by numeric simulation comparison with international well-known software NUCARS, comparison with vehicle-track vertical coupling model, and comparison with running test results by China Academy of Railway Sciences, the new wheel/rail spatially dynamic coupling model is shown to be correct and effective.

Dynamic effects of vehicles on tracks in the case of raising train speeds

Abstract In order to enhance the efficiency of railway transportation, Chinese Railways has decided to raise the speed of trains on the existing railway main lines. A theoretical model and the corresponding simulation software, VICT, based on the vehicle-track coupling dynamics are employed to analyse dynamic effects of trains on track structures caused by raising train speeds. Chinese passenger cars and freight cars running on the lines where speed has been raised were chosen for investigation. It is shown that raising train speeds on the existing railway lines obviously intensifies the dynamic effects of vehicles on tracks, especially in the turnouts, in the welded rail joints, and in the sections of bridge-subgrade connections. The occurrence of wheel flats becomes more general after raising train speeds. An unfavourable peak of dynamic effects of wheel flats on tracks is observed in the speed range from 140 to 160 km/h, which is just the region of running speeds for passenger trains after the increase in the speed. Some basic countermeasures, including stricter maintenance standards for the speed-raised railways, are proposed to solve these problems, on the basis of dynamic analysis.

High-speed train-track-bridge dynamic interactions - Part II: experimental validation and engineering application

Experimental validation is a precondition for dynamic simulation of high-speed train–track–bridge interaction system to be applied to railway engineering in the field. The paper first presents an onsite experiment of the train–track–bridge interaction dynamics carried out on the Beijing–Tianjin high-speed railway, and then the experimental results are used to validate the train–track–bridge interaction simulation software (TTBSIM). There is a good correlation between the calculated results and the measured data. As a case study, the Yellow River Bridge in the Beijing–Shanghai high-speed railway is studied, from modelling of the bridge structure to evaluating the dynamic performance of the train–track–bridge interaction system under the CRH3 EMU passing through at speeds of 250–375 km/h. The calculated and measured results are also compared in the case of such a large steel bridge under high-speed moving train, demonstrating the effectiveness of the TTBSIM simulation for dynamic evaluation of complex bridge structures in high-speed railways.