A simulation model for the prediction of the ground pressure distribution under tracked vehicles

A computer based simulation model for the prediction of the ground pressure distribution beneath tracked vehicles under static conditions has been developed. The model can differentiate between various track designs and is based on an analytical method developed and described by Garber and Wong. Simulating the model with the parameters of a rubber tracked forestry vehicle (FARMI TRAC 5000) led to several conclusions. The road wheel arrangement has a considerable effect on the ground pressure distribution: increasing the number of road wheels reduces the maximum ground pressure and improces the uniformity of the pressure distribution. The radius of the road wheel, the stiffness of the suspension and the stiffness of the track tensioning device have an insignificant effect on the ground pressure distribution. In contrast, the initial track tension and the width of the track have a significant effect on the ground pressure distribution: increasing the initial track tension reduces the maximum ground pressyre and improves the uniformity of the pressure distribution. The same conclusions are valid for an increase of the track width. This model can be used as a tool to assist in the design of off-road vehicles, and is currently being used in the design of forestry vehicles in Ireland.     

A spatial motion analysis model of tracked vehicles with torsion bar type suspension

A spatial motion analysis model for high-mobility tracked vehicles was constructed for evaluation of ride performance, steerability, and stability on rough terrain. Ordinary high-mobility tracked vehicles are equipped with independent torsion bar type suspension system, which consists of road arms and road wheels. The road arm rotates about the axis of torsion bar, and rigidity of the torsion bar and cohesion of damper absorb sudden force change exerted by interaction with the ground. The motion of the road arms should be considered for the evaluation of off-road vehicle performance in numerical analysis model. In order to obtain equations of motion for the tracked vehicles, the equations of motion for the vehicle body and for the assembly of a road wheel and a road arm were constructed separately at first. Two sets of equations were reduced with the constraint equations, which the road arms are mechanically connected to the vehicle body. The equations of motion for the vehicle have been expressed with minimal set of variables of the same number as the degrees of freedom for the vehicle motion. We also included the effect of track tension in the equations without constructing equations of motion for the tracks. Numerical simulation based on the vehicle model and experiment of a scale model passing over a trapezoidal speed bump were performed in order to examine the numerical model. It was found that the numerical results reasonably predict the vehicle motion.     

Terrain-vehicle systems modelling using a multi-body dynamics program

A general purpose vehicle dynamics modelling capability is described. The development of suspension system superelements as standard elements in a general multi-body dynamics program is discussed. Terrain interaction models for wheeled vehicles with deformable tires operating on rigid pavement are described. A track vehicle suspension superelement is also described that includes a loop force element model of tracks and the use of terramechanical relations to describe soil compliance.     

A method for predicting the internal motion resistance of rubber-tracked undercarriages,Pt. 2. A research on the motion resistance of road wheels

In spite of an increasing number of rubber-tracked crawlers, the literature provides few guidelines and calculation models suitable for minimizing their internal motion resistance. This article presents a model where the internal resistance of double-flanged road wheels for rubber-tracked vehicles is calculated as a sum of the losses resulting from the indentation of the wheels into the track surface and friction of the wheels against the track guide lugs. The model allows for vertical and lateral load of the wheels, the non-uniform distribution of the wheel pressure on the track, and the relationship between the friction coefficient and normal reaction force in the interface between the wheel and track guide lugs. The model has been verified by experiments. According to the results of model computations and experiments discussed in the article, the internal losses of a given rubber-tracked undercarriage might be reduced if: the road wheels are covered with a material that exhibits low friction coefficient and mechanical hysteresis, the vehicle suspension system features oscillating bogie wheels, the undercarriage is fitted with the largest possible number of road wheels, and the vehicle weight is evenly distributed to all of the road wheels.     

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.     

Ride dynamics mathematical model for a single station representation of tracked vehicle

Tracked vehicles are exposed to severe ride environment due to dynamic terrain-vehicle interactions. Hence it is essential to understand the vibration levels transmitted to the vehicle, as it negotiates different types of terrains at different speeds. The present study is focused on the development of single station representation of tracked vehicles with trailing arm hydro-gas suspension systems, simulating the ride dynamics. The kinematics of hydro-gas suspension system have been derived in order to determine the non-linear stiffness characteristics at various charging pressures. Then, incorporating the actual suspension kinematics, non-linear governing equations of motion have been derived for the sprung and unsprung masses and solved by coding in Matlab. Effect of suspension non-linear dynamics on the single station ride vibrations have been analyzed and validated with a multi-body dynamics model developed using MSC.ADAMS. The above mathematical models would help in estimating the ride vibration levels of the tracked vehicle, negotiating different types of terrains at various speeds and also enable the designers to fine-tune the suspension characteristics such that the ride vibrations are within acceptable limits. The mathematical ride model would also assist in development of non-linear ride vibration model of full tracked vehicle and estimate the sprung mass dynamics.     

Experimental characterization of dynamic soil-track interaction on dry sand

A set of soil-track interaction relations was made developed for the morbility simulation of tracked or crawler system vehicles on dry, loose sand. These interaction relations were developed specifically for multibody mobility codes in which the soil-vehicle interaction is represented solely by soil-track interaction forces. By employing plate penetration and shear tests, an average pressure-sinkage relation, a shear force-slippage relation, and a sinkage-slippage relation were measured. These plate test data were sufficient only to describe the soil-track interaction on hard ground. On soft ground, however, it was found that intermittent sinkages induced by each passage of the road wheels become important. This dynamic contribution is called “agitation sinkage.” Based on this observation, the sinkage rate (velocity) was decomposed into elastic and plastic rates; the plastic part consists of normal force-induced, slip-induced, and agitation-induced components. Whereas the elastic and the first two components of the plastic sinkage rate were characterized by the conventional plate penetration and plate shear tests, the last term, agitation sinkage, required a new dynamic test in which the sinkage of the track after successive passages of moving road wheels was measured. It is recommended that this new field measurement technique be adopted to characterize the agitation sinkage for various terrains.     

A new contact & slip model for tracked vehicle transient dynamics on hard ground

This study presents a new general transient contact and slip model for tracked vehicles on hard ground which is simple, accurate, and in agreement with the test results to a satisfactory level. Simulating zero track speed instances become possible with the new contact/shear model which is the major proposed improvement in addition to more accurate results for transient steering and tractive inputs. The model represents a general tracked vehicle having rear or front sprockets, with parameters for center of gravity, wheel positions, number of wheels, and track-pretention. To calculate longitudinal and lateral forces, a transient shear model is used. Shear stress under each track pad is assumed to be a function of shear displacement. The contact time formulation used in shear displacement calculation is improved to gain accuracy for transient and zero track speed conditions.The model is implemented on the Matlab/Simulink platform and verified with a comprehensive program of road tests composed of transient steering and tractive/braking scenarios. The results of the simulations and the road tests are satisfactorily similar for both constant and transient input maneuvers. Moreover, sensitivity simulations for vehicle parameters are conducted to show that the model responses are inline with the expected vehicle dynamics behaviours.     

An optimization method designed to improve 3-D vehicle comfort and road holding capability through the use of active and semi-active suspensions

The primary purpose of this paper is to analyze the effects of vibrations on the comfort and road holding capability of road vehicles as observed in the variation of different parameters such as suspension coefficients, road disturbances, and the seat position. This study required the development of a mathematical model to simulate the dynamic behavior of a 3-D vehicle. With this model, various types of non-linear suspensions such as active and semi-active suspensions may be investigated. The results obtained from the simulation of the 3-D vehicle demonstrate that the use of active and semi-active suspension models on road vehicles prove to be beneficial for comfort without unduly compromising road holding capability.     

“Wheels vs. tracks” – A fundamental evaluation from the traction perspective

The issue of wheeled vehicles vs. tracked vehicles for off-road operations has been a subject of debate for a long period of time. Recent interest in the development of vehicles for the rapid deployment of armed forces has given a new impetus to this debate. While a number of experimental studies in comparing the performances of specific wheeled vehicles with those of tracked vehicles under selected operating environments have been performed, it appears that relatively little fundamental analysis on this subject has been published in the open literature, including the Journal of Terramechanics. This paper is aimed at evaluating the tractive performance of wheeled and tracked vehicles from the standpoint of the mechanics of vehicle–terrain interaction. The differences between a tire and a track in generating thrust are elucidated. The basic factors that affect the gross traction of wheeled and tracked vehicles are identified. A general comparison of the thrust developed by a multi-axle wheeled vehicle with that of a tracked vehicle is made, based on certain simplifying assumptions. As the interaction between an off-road vehicle and unprepared terrain is very complex, to compare the performance of a wheeled vehicle with that of a tracked vehicle realistically, comprehensive computer simulation models are required. Two computer simulation models, one for wheeled vehicles, known as NWVPM, and the other for tracked vehicles, known as NTVPM, are described. As an example of the applications of these two computer simulation models, the mobility of an 8 × 8 wheeled vehicle, similar to a light armoured vehicle (LAV), is compared with that of a tracked vehicle, similar to an armoured personnel carrier (APC). It is hoped that this study will illustrate the fundamental factors that limit the traction of wheeled vehicles in comparison with that of tracked vehicles, hence contributing to a better understanding of the issue of wheels vs. tracks.     

Fast dynamic modeling for off-road track vehicles

The paper presents a simple, fast, and reliable dynamic model for an off-road track vehicle operating on terrain with obstacles. The method has been proven previously for wheeled-vehicle formulation. The model is based on a discrete body dynamics (DBD) method, which leads to simplistic linear decoupled motion equations. In this method, joints and bodies with relatively small mass are replaced with stiff springs and dampers, eliminating the system’s constraints and reducing the number of system bodies; this is important for accelerating the simulation runtime of the track vehicle model. The track in this approach is based on modeling each link as a point-mass. Two consecutive links are connected by stiff springs and dampers. This approach reduces the calculation time and increases system stability. The track–soil interaction was modeled using Bekker’s and Janosi’s formulation (Bekker, 1956; Hanamoto and Janosi, 1961). Specific soil properties were obtained for each link–soil interaction from soil classification and GIS. The link–ground contact was determined from topographic surface and adjustment of the force and direction acting on the track. The results of the simulation using the DBD method were compared with Siemens' VL commercial multibody dynamics program and with experiments reported in the literature. Results using the proposed method were found to be similar to the commercial program based on published experiments. The solution runtimes obtained for unpaved soil were two orders faster with the DBD method compared with the Siemens' VL program. The model was written as an independent software infrastructure, enabling easy integration with any other software component, such as a control system. The algorithm is in a suitable form for parallel processing calculation to speed up the runtime simulation close to real-time.     

Analytical track models for ride dynamic simulation of tracked vehicles

This paper presents various modelling strategies to account for track in the ride dynamic simulation of high mobility tracked vehicles negotiating rough off-road terrains. Four analytical track representations of varying complexities are formulated in conjuction with an in-plane ride dynamic model of a typical tracked vehicle. These track models are conceived in view of the tracked vehicle kinematics while ignoring the track belt vibrations. The ride dynamic response of a conventional armoured personnel carrier is evaluated in conjunction with different track methods, and validated against field-measured ride data. The relative performances of these track models are thus assessed based on the accuracy of response predictions, and associated computational time.     

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.     

Interaction of subway LIM vehicle with ballasted track in polygonal wheel wear development

This paper develops a coupled dynamics model for a linear induction motor (LIM) vehicle and a subway track to investigate the influence of polygonal wheels of the vehicle on the dynamic behavior of the system. In the model, the vehicle is modeled as a multi-body system with 35 degrees of freedom. A Timoshenko beam is used to model the rails which are discretely supported by sleepers. The sleepers are modeled as rigid bodies with their vertical, lateral, and rolling motions being considered. In order to simulate the vehicle running along the track, a moving sleeper support model is introduced to simulate the excitation by the discrete sleeper supporters, in which the sleepers are assumed to move backward at a constant speed that is the same as the train speed. The Hertzian contact theory and the Shen- Hedrick-Elkins’ model are utilized to deal with the normal dynamic forces and the tangential forces between wheels and rails, respectively. In order to better characterize the linear metro system (LMS), Euler beam theory based on modal superposition method is used to model LIM and RP. The vertical electric magnetic force and the lateral restoring force between the LIM and RP are also taken into consideration. The former has gap-varying nonlinear characteristics, whilst the latter is considered as a constant restoring force of 1 kN. The numerical analysis considers the effect of the excitation due to polygonal wheels on the dynamic behavior of the system at different wear stages, in which the used data regarding the polygonal wear on the wheel tread are directly measured at the subway site.     

A method for predicting the internal motion resistance of rubber-tracked undercarriages,Pt. 1. A review of the state-of-the-art methods for modeling the internal resistance of tracked vehicles

This article summarizes the known methods for calculating the internal resistance of tracked undercarriages. The values of the coefficient of internal resistance for sample tracked vehicles are available in the literature and presented in this paper. Although they are suitable for simple computations, they cannot be used to optimize the energy efficiency of new generation tracked undercarriages. This problem might be solved by the models where every phenomenon leading to energy dissipation during vehicle motion is described by a separate submodel as a function of vehicle speed, track tension, undercarriage layout, design features of the undercarriage components, etc. This kind of model is still missing for vehicles with conventional rubber tracks. The article presents multiple state-of-the-art models describing rolling resistance of road wheels, bending resistance of rubber belts, etc., including the models of belt conveyors resistance. A vast majority of the phenomena discussed herein are described by several incompatible models whose parameters have not yet been determined for conventional rubber tracks. Consequently, in the second and the third part of the article, the authors have undertaken a theoretical and experimental studies on the methods for calculating and optimizing the internal motion resistance of vehicles with conventional rubber tracks.     

履带车辆路面激励响应的简化计算

为了快速计算履带车辆在路面不平度激励下的动力学响应,基于合理假设采用理论力学方法建立了某履带车辆的简化动力学模型,用ADAMS 软件建立了同种工况下的履带车辆动力学模型,并把两种模型的求解结果进行了对比,验证了简化模型的合理性. 研究结果为基于简化模型的动力学方程对车辆悬挂系统进行优化和逆动力学分析奠定了基础.     

Prediction of track forces in skid-steering of military tracked vehicles

Track forces for outer and inner tracks have been calculated for a military tracked vehicle in a skid-steer situation. The present work is an attempt to improve the understanding of track force variation with turning radius. Furthermore, a reasonable estimate of transmission loads is required for the design of steering transmission for turning a tracked vehicle. This may also be obtained from the track forces. The understanding of track force variation with turning radius has been rather poor. In literature, the reason for lower track force at larger turning radius has been explained in terms of the deflection of the various suspension components like the track shoes, bushings, etc., which are associated with steer action. Deflection of the suspension components does not seem to be an adequate explanation for the variation of track forces with turning radius. In the present work, track forces have been obtained from the dynamics of the moving vehicle. The variation of tractive coefficient (coefficient of friction) due to lateral track slippage has also been considered. This is where the present work differs from the conventional track force estimation where a constant value of coefficient of lateral friction has been used. The estimation of tractive coefficient is made by using pull-slip equation found in literature. The explanation of decreasing track force with increasing radius is given in terms of variation of slip with speed and turning radius. It is found from the study that the concept of variation of coefficient of friction (tractive coefficient) is very important and probably a realistic one in the prediction of track forces. The results of the calculations compare reasonably well with the trends of test result plots obtained in the literature.     

基于智能驾驶电动汽车的多车?桥梁耦合系统动力学特性研究

迫于能源和环保问题的压力, 电动汽车及智能驾驶受到了各国高度重视. 轮毂电机驱动电动汽车车轮振动剧烈, 与桥梁路面动力学相互作用更加突出, 现有研究主要针对传统汽车, 关于电动车轮与公路桥梁接触动力学相互作用及智能驾驶车队的多车?桥梁耦合作用研究尚不多见. 本文以轮毂电机驱动电动汽车为研究对象, 考虑车轮和桥面多点接触关系, 研究了两个智能驾驶汽车过桥时的车桥耦合动力学特性. 分析了电机质量、电机激励、轮胎悬架刚度非线性、车距、车速对系统振动特性的影响, 以及桥面不平顺激励、三重耦合激励对电动汽车平顺性的影响. 研究表明: 车距和车速是影响车?桥系统振动特性的重要因素, 在车?桥耦合动态设计中, 车距和车速的影响应重点关注; 桥面越平坦, 电机激励及桥面二次激励对车辆平顺性和道路友好性影响越加显著, 当汽车行驶在平坦桥面时两种激励对轮毂电机驱动电动汽车的影响不容忽视. 所建模型有望为智能驾驶电动汽车与桥梁的耦合作用研究提供理论参考.