Simulation of Multibody Vehicles Moving over Elastic Guideways1

SUMMARY

This paper describes the present state of a general purpose computer program for calculating the dynamic response of vehicles travelling over guideways which may be elastic.

The linearized state-equations of motion for general multibody vehicles are constructed automatically by the program, these equations are supplemented by the equations for the active subsystems. Finally, the vehicle system equations are combined with the modal equations for elastic guideways and the complete set of coupled equations is solved simultaneously by numerical integration.     

Design and validation of a slender guideway for Maglev vehicle by simulation and experiment

Normally, Maglev (magnetic levitation) vehicles run on elevated guideways. The elevated guideway must satisfy various load conditions of the vehicle, and has to be designed to ensure ride quality, while ensuring that the levitation stability of the vehicle is not affected by the deflection of the guideway. However, because the elevated guideways of Maglev vehicles in South Korea and other countries fabricated so far have been based on over-conservative design criteria, the size of the structures has increased. Further, from the cost perspective, they are unfavourable when compared with other light rail transits such as monorail, rubber wheel, and steel wheel automatic guided transit. Therefore, a slender guideway that does have an adverse effect on the levitation stability of the vehicle is required through optimisation of design criteria. In this study, to predict the effect of various design parameters of the guideway on the dynamic behaviour of the vehicle, simulations were carried out using a dynamics model similar to the actual vehicle and guideway, and a limiting value of deflection ratio of the slender guideway to ensure levitation control is proposed. A guideway that meets the requirement as per the proposed limit for deflection ratio was designed and fabricated, and through a driving test of the vehicle, the validity of the slender guideway was verified. From the results, it was confirmed that although some increase in airgap and cabin acceleration was observed with the proposed slender guideway when compared with the conventional guideway, there was no notable adverse effect on the levitation stability and ride quality of the vehicle. Therefore, it can be inferred that the results of this study will become the basis for establishing design criteria for slender guideways of Maglev vehicles in future.     

Stability Criteria for Articulated Railway Vehicles Possessing Perfect Steering

The general form of the equations o f motion o f multi-body articulated railway vehicles are used to establish the conditions which the elastic stiffness matrix, which describes the nature and configuration o f the suspension elements connecting the various bodies, must satisfy in order to achieve both perfect steering on circular curves and dynamic stability. The resulting criteria are then used to discuss the properties of various multi-axle configurations which are either typical of current practice or possibilities for future designs.     

Stability Criteria for Articulated Railway Vehicles Possessing Perfect Steering

SUMMARY

The general form of the equations o f motion o f multi-body articulated railway vehicles are used to establish the conditions which the elastic stiffness matrix, which describes the nature and configuration o f the suspension elements connecting the various bodies, must satisfy in order to achieve both perfect steering on circular curves and dynamic stability. The resulting criteria are then used to discuss the properties of various multi-axle configurations which are either typical of current practice or possibilities for future designs.     

Track Induced Heave-Pitch Dynamics of Vehicles with Variable Section Flexible Attachments

Multi-wheeled vehicles travelling on a rough track are subjected to unequal inputs at different wheel locations and are set to oscillate in various combinations of possible modes. Elastic bending and torsional deformations may be critical in design for vehicles with slender flexible body and components. In the present study, an analytical approach has been developed to study the track induced heave-pitch dynamics of a linear vehicle model composed of lumped masses and slender, non uniform section elastic attachments in coupled bending-torsion modes. Exact modal solutions for the variable section beam member with general end conditions have been derived and utilised to develop the second order response statistics for the system. Results are presented for an aircraft model with tapered flexible wings during ground runs on a non homogeneously profiled track supported by elastic foundation.     

Exact Equations for Tractrix Curves Associated with Vehicle Offtracking

Vehicle offtracking behavior at low speeds is closely approximated by a geometric entity called a tractrix. This paper presents differential equations for generalized coordinates of a planar multibody vehicle model based on tractrix behavior. The equations are exact, can be used with any type of input path, are valid for forward and backward movements, and are much simpler than previously published formulations used to compute transient offtracking. The differential equations can be integrated using conventional numerical integration algorithms to obtain plots of the low-speed tracking performance of articulated vehicles. The equations were formulated symbolically by a computer program used to analyze the kinematic and dynamic behavior of multibody systems. Example numerical results are plotted.     

Exact Equations for Tractrix Curves Associated with Vehicle Offtracking

Abstract

Vehicle offtracking behavior at low speeds is closely approximated by a geometric entity called a tractrix. This paper presents differential equations for generalized coordinates of a planar multibody vehicle model based on tractrix behavior. The equations are exact, can be used with any type of input path, are valid for forward and backward movements, and are much simpler than previously published formulations used to compute transient offtracking. The differential equations can be integrated using conventional numerical integration algorithms to obtain plots of the low-speed tracking performance of articulated vehicles. The equations were formulated symbolically by a computer program used to analyze the kinematic and dynamic behavior of multibody systems. Example numerical results are plotted.     

A Novel Approach to Vehicle Dynamics using the Theory of a Cosserat Point and its Application to Collision Analyses of Platooning Vehicles

A fully three-dimensional, computationally inexpensive vehicular model is presented. In contrast to traditional rigid body models, the vehicle's sprung mass is modeled as a (nonlinearly) deformable body. The formulation of the equations of motion is based on a continuum theory known as the theory of a Cosserat point. These equations largely preserve the relative simplicity of rigid body dynamics but incorporate deformable features. The ease of computer implementation permits the simultaneous simulation of vehicle and collision dynamics of multiple vehicles and highway objects. In this paper, the theory of a Cosserat point is summarized and its general application to vehicle and collision dynamics is illustrated. A three-dimensional collision algorithm is discussed with emphasis on small closing velocities (negligible residual crush, elastic rebound). The novel model is compared to standard procedures.     

重型汽车荷载作用下简支梁桥的动力反应分析

基于结构动力学理论，视桥梁与车辆为一个相互作用的整体系统，建立了桥梁在移动车辆荷载作用下振动的计算模式。在分析中，汽车采用2轴模型，桥梁结构模拟为梁单元，统一列出车桥系统的动力方程，编制了计算程序。对实际预应力混凝土简支箱梁桥在重型汽车作用下的动力冲击效应进行了计算，并与轻型汽车荷载作用下产生的动力冲击系数进行了比较。     

刚性道面上水泥混凝土加铺层系统的动态设计理论研究

讨论移动荷载下弹性半空间地基上的刚性道面水泥混凝土分离式加铺层的动态设计方法。由系统运动方程出发，利用界面连续条件，通过二维Fourier积分变换，求出加铺层板系统在移动荷载作用下的挠度解析解。然后利用高斯积分求出数值解，并以此为基础通过实测值及目标优化反算加铺层厚度。通过实例计算，按本文方法计算的挠度满足工程精度要求。     

General Purpose Vehicle System Dynamics Software Based on Multibody Formalisms

This paper pursues two objectives: Firstly, to review the state-of-the-art of general purpose vehicle system dynamics software and secondly, to describe two representatives, the program MEDYNA and the program NEWEUL. The general modeling requirements for vehicle dynamics software, the multibody system approach and a comparative discussion of multibody software are given. The two programs NEWEUL and MEDYNA are described with respect to modeling options, computational methods, software engineering as well as their interfaces to other software. The applicability of these programs is demonstrated on two selected examples, one from road vehicle problems and the other from wheel/rail dynamics. It is concluded that general purpose software based on multibody formalisms will play the same role for mechanical systems, especially vehicle systems, as finite element methods play for elastic structures.     

Simulation of Rail Vehicle Dynamics in MATLAB Environment

The following paper describes a general conception and realization of a computer package to predict some aspects of dynamic behaviour of railway vehicles. The package consists of three parts, an interactive pre-processor, the analysis program and an interactive post-processor. MATLAB was used as environment for the realization of the package. In recent versions only passenger vehicles, which have a MD 52 (Minden-Deutz) type trucks, can be analysed but the pre- and post-processor have a general form.     

Simulation of Rail Vehicle Dynamics in MATLAB Environment

The following paper describes a general conception and realization of a computer package to predict some aspects of dynamic behaviour of railway vehicles. The package consists of three parts, an interactive pre-processor, the analysis program and an interactive post-processor. MATLAB was used as environment for the realization of the package. In recent versions only passenger vehicles, which have a MD 52 (Minden-Deutz) type trucks, can be analysed but the pre- and post-processor have a general form.     

Identification of Vibration Parameters for Motor Vehicles

Identification of the vibration parameters of motor vehicles, as well as of dynamic systems in general, represents a complex problem. Many experimental-theoretical procedures have been proposed in order to solve the problem but there is no generally accepted method. The development of a method for the identification of the vibration parameters of motor vehicles is described in this paper. The identification of the unknown parameters is achieved by the use of experimental data applied to an vibration model with a known structure but unknown physical parameters. The methods of nonlinear programming are employed in the computations. The elastic and damping elements, including the tyres, are also by assumption nonlinear. Verification of the reliability of the method is carried out by using two vibration models of the vehicle - one with known and the other with unknown values of the vibration parameters.     

General Purpose Vehicle System Dynamics Software Based on Multibody Formalisms

SUMMARY

This paper pursues two objectives: Firstly, to review the state-of-the-art of general purpose vehicle system dynamics software and secondly, to describe two representatives, the program MEDYNA and the program NEWEUL. The general modeling requirements for vehicle dynamics software, the multibody system approach and a comparative discussion of multibody software are given. The two programs NEWEUL and MEDYNA are described with respect to modeling options, computational methods, software engineering as well as their interfaces to other software. The applicability of these programs is demonstrated on two selected examples, one from road vehicle problems and the other from wheel/rail dynamics. It is concluded that general purpose software based on multibody formalisms will play the same role for mechanical systems, especially vehicle systems, as finite element methods play for elastic structures.     

具有模块化结构的汽车动力学仿真模型的初步研究

初步探讨了面向开发型驾驶模拟器的具有模块化结构的汽车动力学仿真模型建立方法，从而可以在此基础上进一步建立一套通用的面向结构的汽车动力学仿真程序，便捷地在开发型驾驶模拟器上实现对不同类型或同类型不同结构车辆性能的仿真。     

弹性需求下高速公路超限补偿费率优化模型

为了准确刻画超限需求弹性对补偿费率的影响,从用户和系统的角度分别对超限运输的收益和成本进行分析和建模,构造超限运输弹性需求函数,反映超限运输需求量与其运输效益之间的变化关系,将超限运输业者运输行为的选择归结为弹性需求下的用户均衡配流问题,进而利用高速公路管理者与超限运输业者之间的Stackelberg博弈关系,建立了基于弹性需求的高速公路超限补偿费率的双层规划优化模型,并设计了基于模拟退火算法求解的优化算法。结果表明：模型能较好地优化超限补偿费率,使之对超限运输业者进行合理补偿收费和适度惩罚,有效遏制超限运输,从而产生更大的社会与经济效益。     

Railway Vehicle Modelling by the Constraint Equation Method*

A method for the dynamic analysis of railway vehicles is proposed. The method is based on both the using of constraint equations, and on the building of the mathematical model by means of the initial data.

The calculation models are nonlinear, due both to the connecting elements, and to the wheel-rail contact modelling. Solving of differential equations is achieved by time step integration. The method has been applied to the analysis of a freight wagon and a train unit.     

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.     

一种考虑纵向连接间隙的带式浮桥变位计算方法

传统的带式浮桥变位的计算都是采用弹性地基梁的方法进行的,舟单元法中有类似算法。本文利用组成浮桥的多个舟体的平衡条件进行求解,并且在平衡方程中考虑了间隙闭合对浮桥变位的影响,编制了相应的求解程序,通过将文中算例与实测结果相比较,验证了该方法正确可行。