Three-dimensional dynamic model for off-road vehicles using discrete body dynamics

This paper presents a simple, reliable dynamics model of off-road vehicle operation in real-time (RT) on terrain with obstacles. The numerical model was formulated by a new method – DBD (Discrete Body Dynamics). The new method is based on a discrete-element method, where the equations of motion are linear and simple to solve.In this new method, the suspension systems are composed of soft and stiff springs and dampers (instead of suspension arms and joints constrains), to present the kinematics and dynamics of real suspension. Reduction of the number of bodies and avoidance of constraints significantly improves model efficiency and simplicity.The tires–soil interaction was modeled using Brixius prediction. Specific soil properties were obtained from the classification system for each tire–soil interaction, size, and geometric area. The tire–ground contact was determined by topographic surface and adjustment of the forces and direction acting on the tires.The proposed method allows quick and simple definition of a vehicle. The model is written as an independent software infrastructure, enabling easy integration with any other software component.Simulation results were compared with Siemens' VL commercial multibody dynamics program. The performance of the proposed method was very similar to the commercial program (R² > 0.9), with the significant advantage of much higher RT performance.     

Evaluation of link-track performances using DEM

A two-dimensional discrete-element model for the interaction between link-track and soil is presented. The model was developed using commercial PFC2D code. Two different particles, sphere and clump of two spheres, were used to represent the soil. The soil parameters of the model were determined using Hertzian contact theory. Based on the model and soil parameters, simulations of biaxial tests and calculations of the internal angle of friction and cohesion were preformed. The simulation results showed that the internal angle of friction should not exceed the value of 0.65 when using the spherical particles. Based on the clumped particles model, simulations of shear tests with two grouser plates (lengths 100 and 150 mm) were performed under different soil conditions, normal pressures, and cleat heights. A curve fitting of the simulation results was performed using three semi-empirical models from Bekker, Janosi, and Wong for representing the shear stress–displacement relationship. The best fitting was achieved using Wong’s approach. The simulation results of the cleat effects were compared with Bekker’s grouser approach and McKyes’s formulation for soil–blade interaction. In most of the cases, the results of Bekker’s model were the lower bound and McKyes’s model, the upper bound of the DEM simulation results. The properties of the soil model for the DEM were determined using simulation results of shear tests by grouser plate. In the range investigated, the size of the shearing grouser plate is not significant in determining the soil model properties.     

基于小波有限元的车辆-轨道-桥梁系统竖向振动分析

基于小波有限元建立了车辆-轨道-桥梁系统竖向运动方程。将车辆、轨道和桥梁作为一个整体系统,钢轨和桥梁采用区间B样条小波单元离散,钢轨与桥梁之间的钢轨基础采用均布的弹簧和阻尼模拟,采用虚功原理建立了基于小波有限元的四轴车辆-轨道-桥梁竖向振动分析模型。结果表明,采用区间B样条小波单元可较大程度上减小系统的自由度数,缩减计算量,节省计算时间。     

Semi-active rotary damper for a heavy off-road wheeled vehicle

The development, simulation and laboratory testing of two-state discrete adjustable semi-active rotary dampers for heavy off-road wheeled vehicles, which is a joint venture between the South African based company Reumech Ermetek and Horstman Defence Systems from the UK, is described. A brief history of semi-active damping and rotary dampers is given, after which the working principle and features of combining the two technologies is outlined. Three dimensional simulation is used to determine the ride comfort gains achievable with semi-active rotary dampers compared to the conventional translational dampers currently used on the vehicle under consideration. Simulations are performed over different terrains, including the APG track and discrete obstacles. Semi-active rotary dampers were integrated on the 6×6 GV6 Self-propelled Gun Howitzer in order to quantify the improvements in ride comfort, transient response and handling of the vehicle as indicated by the simulation results. The control system, control strategies and characterisation tests, which includes determination of on and off characteristics as well as valve response times, are discussed.     

Numerical simulation and testing verification of the interaction between track and sandy ground based on discrete element method

Tractive effort of tracked vehicles plays an important role in military and agricultural fields. In order to solve the problem of low precision in numerical simulation of the interaction between track and sandy ground, a systematic and accurate discrete element modeling method for sandy road was proposed. The sandy ground was modeled according to the mechanical parameters measured by soil mechanics tests. The interaction coefficients of sandy soil were measured by the repose angle test and triaxial compression test combined with the corresponding simulation. On this basis, a discrete element interaction model of track-sandy ground was established, which can be used to test the tractive effort of track. Numerical simulation calculation of track model at different speeds was carried out, and the simulation results were compared with the results of indoor soil bin test for verification. The verification results show that the interaction between track and sandy ground based on DEM simulation is consistent with the actual soil bin test. The discrete element modeling method in this paper can be used to model the track and sandy ground accurately, and the simulation model can be used to test the tractive effort of tracked vehicle.     

Effect of rail corrugation on vertical dynamics of railway vehicle coupled with a track

The effect of rail corrugation on the vertical dynamics of railway vehicle coupled with a curved track is investigated in detail with a numerical method when a wheelset is steadily curving. In the calculation of rail corrugation we consider the combination of Kalker‘s rolling contact theory modified, a model of material loss on rail running surface, and a dynamics model of railway vehicle coupled with a curved track. In the establishment of the dynamic model, for simplicity, one fourth of the freight car without lateral motions,namely a wheelset and the equivalent one fourth freight car body above it, is considered. The Euler beam is used to model the rails and the track structure under the rails is replaced with equivalent springs, dampers and mass bodies. The numerical results show the great influence of the rail corrugation on the vibration of the parts of the vehicle and the track, and the some characters of rail corrugation in development.     

Finite element analysis for train–track–bridge interaction system

This article deals with the dynamic analysis of train–track–bridge interaction system using the finite element method. In this interaction system, each four-wheelset vehicle in the train is modeled by a mass–spring–damper system with 10 degrees of freedom; the rails and the bridge decks are modeled as a number of Bernoulli–Euler beam elements, while the elasticity and damping properties of the rail bed are represented by continuous springs and dampers. The equation of motion for the interaction system is presented in matrix form with time-dependent coefficients. The correctness of the proposed procedure is illustrated by a comparison with the numerical result from the existing literature. Several numerical examples are chosen to investigate the effect of two types of vehicle models, two types of bridge models and three damping values of bridge on the maximum dynamic responses of train, track and bridges.     

The effect of cell irregularity on the high strain compression of 2D Voronoi honeycombs

The in-plane compression of low-density irregular Voronoi honeycombs with periodic boundary conditions has been simulated to engineering strains of 0.6 using finite element analysis. Different degrees of geometric irregularity in the honeycomb cells, as quantified using a regularity parameter, have been employed. The stress–strain predictions reveal that, for a fixed relative density, a more irregular honeycomb has a higher tangential modulus at low strain but supports a lower compressive stress at higher strain (above approximately 0.04) when compared with a more regular honeycomb. A combined ‘springs in parallel’ and ‘springs in series’ model has also been compared quantitatively with the simulation stress–strain results, the relative importance of the ‘springs in series’ mechanism having been found to increase with the irregularity of the honeycomb and, in many cases, with the applied compressive strain. In addition, the dependency of the Poisson’s ratio, the maximum bending strain in the cell walls, and the mean junction rotation upon the applied compressive strain have also been determined for a range of honeycomb irregularities.     

Soft soil track interaction modeling in single rigid body tracked vehicle models

Single rigid body models are often used for fast simulation of tracked vehicle dynamics on soft soils. Modeling of soil-track interaction forces is the key modeling aspect here. Accuracy of the soil-track interaction model depends on calculation of soil deformation in track contact patch and modeling of soil resistive response to this deformation. An algorithmic method to calculate soft soil deformation at points in track contact patch, during spatial motion simulation using single body models of tracked vehicles, is discussed here. Improved calculations of shear displacement distribution in the track contact patch compared to existing methods, and realistically modeling plastically deformable nature of soil in the sinkage direction in single body modeling of tracked vehicle, are the novel contributions of this paper. Results of spatial motion simulation from a single body model using the proposed method and from a higher degree of freedom multibody model are compared for motion over flat and uneven terrains. Single body modeling of tracked vehicle using the proposed method affords quicker results with sufficient accuracy when compared to those obtained from the multibody model.     

Torque distribution influence on tractive efficiency and mobility of off-road wheeled vehicles

Off-road vehicle performance is strongly influenced by the tire-terrain interaction mechanism. Soft soil reduces traction and significantly modifies vehicle handling; therefore tire dynamics plays a strong role in off-road mobility evaluation and needs to be addressed with ad-hoc models. Starting from a semi-empirical tire model based on Bekker–Wong theory, this paper, analyzes the performance of a large four wheeled vehicle driving on deformable terrain. A 14 degree of freedom vehicle model is implemented in order to investigate the influence of torque distribution on tractive efficiency through the simulation of front, rear, and all wheel drive configuration. Results show that optimal performance, regardless vertical load distribution, is achieved when torque is biased toward the rear axle. This suggests that it is possible to improve tractive efficiency without sacrificing traction and mobility. Vehicle motion is simulated over dry sand, moist loam, flat terrain and inclined terrain.     

A simple spinning laminated composite shaft model

A simple spinning composite shaft model is presented in this paper. The composite shaft contains discrete isotropic rigid disks and is supported by bearings that are modeled as springs and viscous dampers. Based on a first-order shear deformable beam theory, the strain energy of the shaft are found by adopting the three-dimensional constitutive relations of material with the help of the coordinates transformation, while the kinetic energy of the shaft system is obtained via utilizing the moving rotating coordinate systems adhered to the cross-sections of shaft. The extended Hamilton’s principle is employed to derive the governing equations. In the model the transverse shear deformation, rotary inertia and gyroscopic effects, as well as the coupling effect due to the lamination of composite layers have been incorporated. To verify the present model, the critical speeds of composite shaft systems are compared with those available in the literature. A numerical example is also given to illustrate the frequencies, mode shapes, and transient response of a particular composite shaft system.     

车-桥-线竖平面振动及其能量转化机制精细建模

建立了考虑车-桥(线)纵向振动及其能量相互转化机制的竖平面内精细耦合运动方程.将车-桥(线)视为一个整体系统,车辆各剐体的纵向运动均作为独立的自由度,考虑到车-桥(线)纵向振动及其能量相互转化机制,车辆驱动或制动作用采用轮轨间的纵向相互作用力和轮对作用力矩模拟,桥梁、线路结构采用梁单元离散,线路与桥梁之间的钢轨基础采用竖向和纵向的均布弹簧阻尼连接,建立了竖平面内精细耦合运动方程,它可合理模拟车桥(线)间能量相互转化的过程.简支梁桥算例表明:车辆在桥上无驱动或制动运行过程中,不考虑轨道结构时车速先增加后减小,而考虑轨道结构时车速只有减小的趋势,轮对还发生了高频的纵向振动,且车体和轮对的纵向振动对轨道竖向不平顺较为敏感;此外,考虑轮轨滚动碾压作用和能量转化机制时,钢轨加速度响应略偏大.本文研究可为实际车辆动态变速运行的模拟和更精细空间耦合模型的建立提供研究基础.     

Suitability of rubber track as traction device for power tillers

Suitability of using rubber tracks as traction device in power tillers replacing pneumatic tires was studied using an experimental setup consisting of a track test rig for mounting a 0.80 m × 0.1 m rubber track and a loading device for applying different drawbar pulls. Tests were conducted in the soil bin filled with lateritic sandy clay loam soil at an average soil water content of 9% dry basis by varying the cone index from 300 to 1000 kPa. Data on torque, pull and Travel Reduction Ratio (TRR) were acquired using sensors and data acquisition system for evaluating its performance. Maximum tractive efficiency of the track was found to be in the range of 77–83% corresponding to a TRR of 0.12–0.045. The Net Traction Ratio (NTR) at maximum tractive efficiency was found to be between 0.49 and 0.36.Using non-linear regression technique, a model for Gross Traction Ratio (GTR) was developed and it could predict the actual values with a maximum variation of 6% as compared to an average variation of 50% with Grisso’s model. Based on this model, tractive efficiency design curves were plotted to achieve optimum tractive performance of track for any given soil condition.     

Prediction of the tractive performance of a flexible tracked vehicle

In this study, we describe a mathematical model designed to allow for the determination of the mechanical relationship existing between soil characteristics and the primary design factors of a tracked vehicle, and to predict the tractive performance of this tracked vehicle on soft terrain. On the basis of the mathematical model, a computer simulation program (Tractive Performance Prediction Model for Tracked Vehicles; TPPMTV) was developed in this study. This model took into account the characteristics of the terrain, including the pressure-sinkage, the shearing characteristics, and the response to the repetitive loading, as well as the primary design parameters of the tracked vehicle. The efficacy of the developed model was then confirmed via comparison of the drawbar pulls of tracked vehicles predicted using the simulation program TPPMTV, with those determined as the result of traction tests. The results indicated that the predicted drawbar pulls, with the change in slip, were quite consistent with the ones measured in the traction test, for the changes in the weight of the vehicle, the initial track tension, and the number of roadwheels within the entire slip range. Thus, we concluded that the simulation program developed in this study, named TPPMTV, proved useful in the prediction of the tractive performance of a tracked vehicle, and that this system might be applicable to the design of a vehicle, possibly enabling a significant improvement in its functions.     

Model of the UIC link suspension for freight wagons

Summary The paper presents a model of the UIC link suspension for freight wagons with emphasis on its longitudinal and lateral characteristics, which influence the lateral dynamics of the vehicle. The functioning of the suspension in the horizontal plane is realised by a number of technical (pivoted) pendulums composing linkages. The main feature of the joints of linkages is internal rolling/sliding in the presence of dry friction. The dissipation of energy by dry friction in the joints is the only source of damping, which influences the lateral dynamics of the vehicle. After detailed modelling of the technical pendulum, phenomenological models of the suspension are built, which reproduce the characteristics of the suspension using simple elements. A three-parameter model with one dry-friction slider and two linear springs reproduces the lateral characteristic of the suspension. A nine-parameter model with four dry-friction sliders and five springs reproduces the longitudinal characteristic. The models, using a method of non-smooth mechanics, may be directly implemented to vehicle/track dynamic simulations.Professor Hans True of TU Denmark for stressing the importance of the problem of the UIC suspension modelling for successful upgrading of freight wagons.     

基于磁流变阻尼器的多单体组合隔震结构模糊控制研究

提出了一种新的组合结构振动控制体系——多单体组合隔震结构,建立了力学模型及运动方程。基于瞬时最优控制算法,将控制力表达成阻尼力的形式,用磁流变阻尼器充当控制器,运用模糊控制方法对其进行控制。通过计算机仿真分析,并运用LQR控制与之进行对比。研究结果表明,这种组合隔震结构体系的控制效果明显,各结构的地震响应都有明显降低。采用模糊控制不需要建立精确的计算模型,并能达到与LQR控制相接近的控制效果。用磁流变阻尼器充当控制器减少了能量输入,在结构2与结构3之间安装弹簧-阻尼器使控制更容易实现。     

An efficient computational method for vibration analysis of unsymmetric piecewise-linear dynamical systems with multiple degrees of freedom

This paper presents an efficient computational method for determining vibrational responses of piecewise-linear dynamical systems with multiple degrees of freedom (MDOF) and an arbitrary number of gap-activated springs. A time-domain solution is obtained using the Bozzak–Newmark numerical integration scheme. At each time step, an auxiliary displacement vector, complementary to the contact force vector, is introduced. With the help of a simple transformation, the vibration problem is reduced to a standard linear complementarity problem (LCP) for which an accurate solution can be obtained. Responses of an SDOF system with a gap-activated spring and a 3-DOF system with three gap-activated springs under harmonic excitations are obtained using the proposed method, and compared with the results in the literature. Good agreement is observed. The proposed method has also been successfully applied to a piecewise linear dynamical system with 1000 DOF’s and 1000 gap-activated springs under harmonic excitations.     

Study on the subgrade deformation under high-speed train loading and water–soil interaction

It is important to study the subgrade characteristics of high-speed railways in consideration of the water–soil coupling dynamic problem,especially when high-speed trains operate in rainy regions.This study develops a nonlinear water–soil interaction dynamic model of slab track coupling with subgrade under high-speed train loading based on vehicle–track coupling dynamics.By using this model,the basic dynamic characteristics,including water–soil interaction and without water induced by the high-speed train loading,are studied.The main factors-the permeability coefficien and the porosity-influencin the subgrade deformation are investigated.The developed model can characterize the soil dynamic behaviour more realistically,especially when considering the influenc of water-rich soil.