A method for predicting the internal motion resistance of rubber-tracked undercarriages,Pt. 3. A research on bending resistance of rubber tracks

Optimizing the efficiency of rubber-tracked undercarriages requires models for calculating external and internal motion resistance, including the resistance resulting from bending of rubber tracks. The experiments on the bending resistance of rubber tracks and a new model of this phenomenon are discussed in this article. An empirical model of friction in bearings typically implemented in driving and idler wheels of rubber-tracked undercarriages is also presented. According to the sample computations carried out on the basis of these models, the efficiency of rubber-tracked undercarriages might be improved by minimizing the number and maximizing the diameter of idler wheels. Furthermore, it has been shown that increase in the initial tension and driving force transmitted by rubber tracks does not significantly affect bending resistance of these tracks; however, it results in increased friction in the driving and idler wheels’ bearings. Nevertheless, the higher the driving force transmitted by the rubber tracks, the higher the efficiency of rubber-tracked undercarriages. Consequently, since track systems of vehicles operating at relatively small drawbar pull will manifest exceptionally low efficiency, there is a serious need for optimizing them in terms of energy consumption.     

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.     

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.     

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.     

车辆纵向非光滑多体动力学建模与数值算法研究

在建立车辆纵向多体系统的动力学模型中, 将车身与车轮视为刚体, 两者通过减振器链接; 将传动系统视为一个圆盘通过扭簧和阻尼器与驱动轮连接; 将车轮与路面间的接触力简化为法向约束力、摩擦力和滚阻力偶,其中摩擦力的模型采用库仑干摩擦模型. 采用笛卡尔坐标作为该系统的广义坐标用于描述该系统的位形, 给出系统单双边的约束方程, 应用第一类拉格朗日方法建立了系统的动力学方程. 由于摩擦与滚阻的非光滑性, 使得该系统动力学方程不连续. 为便于计算, 建立了车轮与路面接触点的相对切向加速度与摩擦力余量的互补条件、车轮角加速度与滚阻力偶余量的互补条件, 以及车轮轮心法向加速度与路面法向约束力的互补条件. 将接触—分离、黏滞—滑移的判断问题转化成线性互补问题的求解, 并给出了具有约束稳定化的基于事件驱动法的数值计算方法. 最后, 应用该方法对车辆纵向多体系统进行了仿真, 分析了输出扭矩、摩擦及滚阻系数对其动力学行为的影响.      

Prediction of ground pressure distribution under tracked vehicles—II. Effects of design parameters of the track-suspension system on ground pressure distribution

The effects of vehicle design parameters on ground pressure distribution and track tension are evaluated quantitatively using the analytical method described in Part I of this paper. The ground pressure distribution of a vehicle is closely related to vehicle sinkage and external motion resistance, while the track tension affects the internal resistance of the track-suspension system. It is found that the number of road wheels on the track has a significant effect on both ground pressure distribution and track tension. On the other hand, the diameter of the road wheels has only a moderate influence on track tension and a rather insignificant effect on ground pressure distribution. The stiffnesses of the suspension and the track tensioning springs have varying degrees of influence on ground pressure distribution and track tension dependent upon terrain stiffness. It is also found that the initial track tension has a significant effect on the actual track tension over a wide range of terrain and a slight to moderate influence on ground pressure distribution, dependent upon terrain stiffness.It should be noted that although individually some of the design parameters have only a slight or moderate effect on ground pressure distribution and track tension, their combined effects may be significant. Therefore, in the selection of design parameters of the track-suspension system, their combined influence must be carefully examined.     

2D FE–DEM analysis of tractive performance of an elastic wheel for planetary rovers

We have been developing a simulation program for use with soil–wheel interaction problems by coupling Finite Element Method (FEM) and Discrete Element Method (DEM) for which a wheel is modeled by FEM and soil is expressed by DEM. Previous two-dimensional FE–DEM was updated to analyze the tractive performance of a flexible elastic wheel by introducing a new algorithm learned from the PID-controller model. In an elastic wheel model, four structural parts were defined using FEM: the wheel rim, intermediate part, surface layer, and wheel lugs. The wheel rigidity was controlled by varying the Young’s Modulus of the intermediate part. The tractive performance of two elastic wheels with lugs for planetary rovers of the European Space Agency was analyzed. Numerical results were compared with experimentally obtained results collected at DLR Bremen, Germany. The FE–DEM result was confirmed to depict similar behaviors of tractive performance such as gross tractive effort, net traction, running resistance, and wheel sinkage, as in the results of experiments. Moreover, the tractive performance of elastic wheels on Mars was predicted using FE–DEM. Results clarified that no significant difference of net traction exists between the two wheels.     

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.     

The effect of wheel width on the rolling resistance of rigid wheels in sand

The effect of width on the rolling resistance of rigid wheels in sand is shown to be very strong, coefficient of rolling resistance increasing rapidly with width at each of the sinkage levels used in the experiments. Wheel skid also increased rapidly as wheel width increased. Prediction of measured results on the narrow wheels using the modified Bekker analysis was quite good although this is shown to be partly fortuitous. Poor correlation was found between measured values of coefficient of rolling resistance and the Freitag sand number. Very good prediction of measured values of coefficient of rolling resistance was found using an expression comprising the square root of the sinkage/dia ratio multiplied by a factor correcting for width/dia ratio. The square root of the sinkage/dia ratio is shown to be the value of coefficient of rolling resistance of a narrow wheel at shallow sinkage predicted from the modified Bekker analysis. It is also shown to be identical to the inverse of the Freitag clay number, with soil cone index value replaced by mean soil radial stress.     

Prévision de la répartition de la pression sous des véhicules à chenilles Ilème partie - effects des paramètres de conception du système de suspension des chenilles sur la répartition de la pression sur le sol

The effects of vehicle design parameters on ground pressure distribution and track tension are evaluated quantitatively using the analytical method described in Part I of this paper. The ground pressure distribution of a vehicle is closely related to vehicle sinkage and external motion resistance, while the track tension affects the internal resistance of the track-suspension system. It is found that the number of road wheels on the track has a significant effect on both ground pressure distribution and track tension. On the other hand, the diameter of the road wheels has only a moderate influence on track tension and a rather insignificant effect on ground pressure distribution. The stiffnesses of the suspension and the track tensioning springs have varying degrees of influence on ground pressure distribution and track tension dependent upon terrain stiffness. It is also found that the initial track tension has a significant effect on the actual track tension over a wide range of terrain and a slight to moderate influence on ground pressure distribution, dependent upon terrain stiffness.It should be noted that although individually some of the design parameters have only a slight or moderate effect on ground pressure distribution and track tension, their combined effects may be significant. Therefore, in the selection of design parameters of the track-suspension system, their combined influence must be carefully examined.     

Modeling motion resistance of rigid wheels

A mathematical model was developed to describe the motion resistance of rigid wheels under self-propelled conditions where no drawbar pull is developed. The modeling was based on the concept that the work required to overcome the motion resistance is equal to the energy dissipated in compacting the soil beneath the wheel. Slippage of the wheel was also considered in the modeling. Finally the validity of the proposed model was discussed.     

基于FFUKF路面附着系数估计的汽车牵引力控制

以后驱牵引车为研究对象, 设计了基于路面附着系数估计的牵引力控制系统(TCS). 在路面附着系数估计方面, 针对传统卡尔曼滤波难以跟踪时变非线性系统的问题, 本文将模糊控制理论和衰减记忆滤波思想引入无迹卡尔曼滤波, 设计一种基于模糊遗忘因子的无迹卡尔曼滤波路面附着系数估计方法, 提高了算法的跟踪性能. 牵引力控制包括扭矩控制和制动控制. 在TCS扭矩控制方面, 分别利用路面附着系数和驱动轮滑转率在目标滑转率附近时的车辆加速度计算目标基础扭矩, 根据车辆行驶状态和抖振度参量, 基于可拓控制理论划分经典域、可拓域和非域, 通过可拓集的关联函数得到动态权重系数, 将上述两种方法计算得到的目标基础扭矩进行可拓融合设计出基础扭矩. 之后, 以实际滑转率和目标滑转率之间的误差作为输入, 采用模糊自整定PI控制器得到目标反馈扭矩. 在制动控制方面, 针对两种典型路面分别设计了PI控制压力和附着差压力. 实车试验结果表明, 基于模糊遗忘因子的无迹卡尔曼滤波算法能够更加快速地跟踪路面附着系数的变化, 同时基于路面附着系数估计的TCS控制策略能够有效抑制驱动轮过度滑转, 将驱动轮滑转率控制在最佳范围内, 显著提高了车辆的动力性.      

Experimental analysis of soil reaction on a lug of a movable lug wheel

A movable lug wheel was tested in a soil bin test apparatus to determine its traction performance and to measure the soil reaction forces on its lugs. Similar tests were also conducted using a fixed lug wheel. The effects of the lug motion pattern, lug spacing and horizontal load on pull and lift forces were studied. From the experiments it is confirmed that the movable action of the lug plate could generate superior pull and lift forces in comparison with the fixed lug wheel. Among the test wheels, lug motion pattern-2 generated the highest pull and lift forces. Within the range of the test conditions, there was no significant difference in pull and lift forces of the lug plate between the test lug wheels with 12 lugs and 15 lugs at the same level of horizontal and vertical loads. The increase of horizontal load up to 200 N generally increased the pull force and generated smaller rolling resistance before the lug left the soil, but did not increase the lift force significantly. The patterns of pull force, lift force and drawbar pull generated under a constant slip were slightly different from those under a constant horizontal load. Finally, the results were also elucidated by their actual lug trajectories in soil.     

Effects of tire inflation pressure and tractor velocity on dynamic wheel load and rear axle vibrations

The objective of this study was to evaluate the effects of agricultural tire characteristics on variations of wheel load and vibrations transmitted from the ground to the tractor rear axle. The experiments were conducted on an asphalt road and a sandy loam field using a two-wheel-drive self-propelled farm tractor at different combinations of tractor forward speeds of approximately 0.6, 1.6 and 2.6 m/s, and tire inflation pressures of 330 and 80 kPa. During experiments, the vertical wheel load of the left and right rear wheels, and the roll, bounce and pitch accelerations of the rear axle center were measured using strain-gage-based transducers and a triaxial accelerometer. The wavelet and Fourier analyses were applied to measured data in order to investigate the effects of self-excitations due to non-uniformity and lugs of tires on the wheel-load fluctuation and rear axle vibrations. Values for the root-mean-square (RMS) wheel loads and accelerations were not strictly proportional and inversely proportional to the forward speed and tire pressure respectively. The time histories and frequency compositions of synthesized data have shown that tire non-uniformity and tire lugs significantly excited the wheel load and accelerations at their natural frequencies and harmonics. These effects were strongly affected by the forward speed, tire pressure and ground deformation.     

Multi-objective traction optimization of vehicles in loose dry sand using the generalized reduced gradient method

A work optimization strategy is combined with algorithms within the vehicle-terrain interface (VTI) model to maximize the traction of a four-wheel vehicle operating on loose dry sand. The optimization model distributes traction among the steered and non-steered wheels with the work optimum coefficient (WOC) of each wheel treated as an independent design objective. Drawbar pull (DBP), motion resistance (MR), longitudinal traction coefficient (LTC), lateral force coefficient (LFC), tire deflection, and wheel slip are key parameters that appear in the VTI model for traction performance analysis. The analysis includes wheels of different diameters, widths, heights, and inflation pressures, under variable wheel slips. A multi-objective optimization problem is formulated over a thirteen-dimensional search space bounded by eight design constraints. The generalized reduced gradient method is used to predict optimal values of the design variables as well as ground and traction parameters such as DBP, MR, LTC, and LFC for maximum slope climbing efficiency. The WOCs are maximized for lateral slip angles between 0° and 24° to find a set of Pareto optimal solutions over a wide range of weight factors. A method to apply the optimization results for predicting vehicle performance and traction control on dry sand is presented and discussed.     

Steering forces on undriven, angled wheels

The steering forces at low speed and zero camber angle were measured on undriven, angled wheels using tyres with no tread. The forces were measured in a soil bin using a moist loam soil at different levels of compaction. It was found that the coefficient of side force relative to the wheel was related to slip angle by an exponential relationship. Coefficient of rolling resistance relative to the wheel was a linear function of slip angle in the region zero to 20° but was an irregular function of slip angle at higher angles. The effects of tyre size, load, inflation pressure and soil condition were modelled well using different versions of the tyre mobility number. The most successful version of mobility number was one which incorporated both soil cohesion and internal friction angle. The coefficients of the exponential and linear relationships mentioned above were predicted with varying degrees of success using mobility number.     

Integration of uniform design and quantum-behaved particle swarm optimization to the robust design for a railway vehicle suspension system under different wheel conicities and wheel rolling radii

This paper proposes a systematic method, inte-grating the uniform design(UD)of experiments and quantum-behaved particle swarm optimization(QPSO),to solve the problem of a robust design for a railway vehicle suspension system. Based on the new nonlinear creep model derived from combining Hertz contact theory, Kalker's linear the-ory and a heuristic nonlinear creep model,the modeling and dynamic analysis of a 24 degree-of-freedom railway vehi-cle system were investigated.The Lyapunov indirect method was used to examine the effects of suspension parameters, wheel conicities and wheel rolling radii on critical hunting speeds.Generally,the critical hunting speeds of a vehicle sys-tem resulting from worn wheels with different wheel rolling radii are lower than those of a vehicle system having origi-nal wheels without different wheel rolling radii.Because of worn wheels, the critical hunting speed of a running rail-way vehicle substantially declines over the long term. For safety reasons,it is necessary to design the suspension sys-tem parameters to increase the robustness of the system and decrease the sensitive of wheel noises.By applying UD and QPSO,the nominal-the-best signal-to-noise ratio of the sys-tem was increased from?48.17 to?34.05 dB.The rate of improvement was 29.31%.This study has demonstrated that the integration of UD and QPSO can successfully reveal the optimal solution of suspension parameters for solving the robust design problem of a railway vehicle suspension sys-tem.     

Experimental and DEM analyses on wheel-soil interaction

In this paper, the wheel-soil interaction for a future lunar exploration mission is investigated by physical model tests and numerical simulations. Firstly, a series of physical model tests was conducted using the TJ-1 lunar soil simulant with various driving conditions, wheel configurations and ground void ratios. Then the corresponding numerical simulations were performed in a terrestrial environment using the Distinct Element Method (DEM) with a new contact model for lunar soil, where the rolling resistance and van der Waals force were implemented. In addition, DEM simulations in an extraterrestrial (lunar) environment were performed. The results indicate that tractive efficiency does not depend on wheel rotational velocity, but decreases with increasing extra vertical load on the wheel and ground void ratio. Rover performance improves when wheels are equipped with lugs. The DEM simulations in terrestrial environment can qualitatively reproduce the soil deformation pattern as observed in the physical model tests. The variations of traction efficiency against the driving condition, wheel configuration and ground void ratio attained in the DEM simulations match the experimental observations qualitatively. Moreover, the wheel track is found to be less evident and the tractive efficiency is higher in the extraterrestrial environment compared to the performance on Earth.