Algorithms for a Vehicle Dynamics Monitoring System,Based on Model Reference Structure

Vehicle control depends heavily on the knowledge of the vehicle operatingconditions. One of the most important parameters for its control is thetyre–road friction coefficient (µ). An appropriate way toestimate the vehicle operating conditions is the Model Reference Approach.This technique requires a model that provides estimated states which can becompared with the measured states, the difference is used to determine thereal operating conditions. This paper presents two different applications ofthe Model Reference Techniques to estimate tyre–road frictioncoefficient; these are based on the relation between tyre forces and slip,and on the vehicle lateral behaviour using an extended Kalman filter.Experimental data from the test vehicle confirms the good results obtainedin the friction estimation based on the tyre slip–force relation. Theestimation using an extended Kalman filter on lateral behaviour showsaccurate tracking. The next step to be taken is to integrate all thealgorithms in the test vehicle and to validate them for a wide range ofoperating conditions, in order to have reliable information for the activesystem control.     

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.     

Full-field and point strain measurement via the inner surface of a rolling large lug tyre

Vehicle safety and performance can be dramatically improved if force or friction measurement of the tyre-terrain interface is known. Since the tyre-terrain interface is responsible for the majority of forces acting on the vehicle, this region has received a lot of attention in vehicle dynamics. Direct measurement of the tyre-terrain interface is difficult since it is hidden by the tyre and terrain. A lot of research has been conducted on the inside of tyre using accelerometers or strain gauges with research more focussed on passenger car tyres and very little work performed on agricultural tyres with larger lugs. This study performs strain measurements using point measurement, from strain gauges, and full field measurement, using a stereo camera measurement system, of the inside of an agricultural tyre on a drum test rig during vertical and lateral loading. Results show similar trends when compared to results on passenger car tyres, however the mounting of the strain gauge relative to the lug is shown to play a large role in the developed strain. Linear relationships between the applied tyre force and strain were obtained in different direction with R² values above 0.97.     

Off-road tyre modelling II: effect of camber on tyre performance

The problem of off-road vehicle tyre-terrain interaction is that it is difficult to model accurately. For an off-road vehicle over medium to firm terrain, the tyre load may be entirely supported by the tips of the lugs, or with a minimum carcass contact with the terrain. In this case, the effect of the lugs should be taken into consideration. The forces at the interface between lugged tyre and the soil, including normal and shear stresses, are discussed in this paper. The multi-spoke tyre model was developed to study the effect of tyre lugs on the forces between tyre and terrain and it has been extended to predict the tyre forces and moments in the case of combined lateral and longitudinal slip for a cambered tyre. The influence of slip angle, camber angle and soil hardness on off-road tyre performance has been investigated. A computer program was developed using MATLAB software. The results were derived as tyre forces and moments in the three directions along the tyre contact length. A comparison between the results of the multi-spoke tyre model of a smooth off-road tyre and an off-road tyre with straight lugs, in the cambered case, has been made. The results indicated that slip angle, camber angle and soil characteristics have a strong effect on off-road tyre performance. The modified mathematical model results help the off-road tyre engineering designers to predict accurate values of tyre forces and moments in this complex case.     

The problems of multi-axle vehicle drives

The multi-axle drive provides for maximum traction of the vehicle. However, this mode of driving, apart from the complicated design of the driving mechanism, is connected with major problems due to the so-called kinematic discrepancy encountered by a vehicle under operation. In certain conditions, the kinematic discrepancy results in the phenomenon of so-called circulating power which causes, first of all, additional loading on the drive system, then increased energy loss and tyre wear and, in the case of an articulated frame-steer vehicle, the substantial growth of steering resistance.The paper reviews some examples of results of the studies on wheel slips, load on the drive system, and on the 4-wheel-drive articulated frame-steer vehicle's steering gear. The author also discusses a new concept for determining kinematic discrepancy. The suggested equations, when applying the present mathematical models which express the dependence of a tyre's slip rate on longitudinal forces, permit to solve the statically undeterminable problem concerning the distribution of the wheel's longitudinal forces in any multi-axle vehicle.     

双曲冷却塔塔筒水平地震响应分析

为明确冷却塔在水平地震下的内力环向分布特征及内在原因,同时探究不同地震波时程与规范反应谱所得内力差异的原因,以某大型双曲冷却塔为例,在动力特性分析的基础上,通过反应谱方法和时程方法的水平地震响应计算及对比分析,对上述两个问题进行了研究。研究表明:由于仅侧弯振型对水平地震有贡献,而塔筒的侧弯振型和实际响应均表现为整体侧倾并伴随微弱的截面“流动”变形,这也使塔筒各内力的环向分布分别呈现正弦、余弦分布特征;其整体侧倾可类比于悬臂杆结构,塔筒子午向轴力FY、子午向弯矩MY、剪力FXY和扭矩MXY的环向分布可借助悬臂杆侧倾时截面正应力和剪应力分布来解释;而截面“流动”变形则决定了环向轴力FX和环向弯矩MX的环向分布;整体侧移显著而截面变形极小也使FY和FXY的幅值在塔筒中下部明显大于FX;由于冷却塔第1阶侧弯振型在水平地震响应中往往起绝对主导作用,因此可先对所选地震波计算得到其反应谱,对比第1阶侧弯振型周期对应的水平地震影响系数α值,即可初步推断不同时程及规范反应谱方法所得结果的大小关系。     

The tractive performance of a wide, low-pressure tyre compared with conventional tractor drive tyres

The NIAE single-wheel test vehicle was used to compare the tractive performance of a 67 × 34.00-25 tyre at 0.34 bar inflation pressure with that of 20.8–38 radial tyre at 0.6 bar inflation pressure and a similar 18.4–34 tyre at 0.8 bar inflation pressure. All tyres had similar tread patterns and were tested at the same vertical load of 2250 kg. The best performance was achieved by the 20.8–38 tyre. There was little difference in performance between the other two tyres. When compared with empirical predictions of performance derived from previous work, the two narrower tyres were found to perform approximately as predicted, but the performance of the wide, low-pressure tyre was considerably worse than predicted. This was thought to be due to bulldozing, because of the great width and increased wheel-slip caused by deformation of the soft side-wall and also due to the relatively short ground contact area. It was concluded that wide, low-pressure tyres are only suitable for fitting to vehicles requiring a very low draught capability.     

Development of a solution method for frictional contact problems with complex loading

In this work, solution methods for frictional contact problems are extended to the case of moving punches and to the external loading history-dependent system states. To solve the frictional contact problems in the contact area, an iterative method is developed and implemented. Solutions of two-dimensional problems are constructed using the boundary element method. Numerical analysis is aimed at the quantitative study of effects such as the interaction of contact pressure and friction forces, estimates of the friction force differences due to the differences in the choice of local basis for the calculation of normal pressure and friction forces, and evaluation of the effects of complex loading (rotation of the rigid punch after its preliminary penetration into the solid). We find that, for the same definition of the friction force, different initial approximations lead to the same solution. At the same time, the friction forces defined either as projections onto the common tangent plane or as projections onto the plane tangent to the punch can differ quite substantially. Similar conclusions are derived for the solutions corresponding to single or multiple loading steps. The work relies on the variational principle for the solution of contact problems and numerical algorithms developed for the problems with one-sided constraints. The variational principle was first applied by Signorini [1] to the determination of the stress-strain state in a linearly deformed body in a rigid smooth shell. The modern view of the problem and its generalizations to the frictional problems and some other problems involving unilateral constraints in given in the monograph [2]. Finite difference and finite element methods in application to the problems with unilateral constraints are described in [3]. Analytical solution methods are developed in the monographs [4–6].     

Horizontal Redistribution of Two Fluid Phases in a Porous Medium: Experimental Investigations

Classical models for flow and transport processes in porous media employ the so-called extended Darcy’s Law. Originally, it was proposed empirically for one-dimensional isothermal flow of an incompressible fluid in a rigid, homogeneous, and isotropic porous medium. Nowadays, the extended Darcy’s Law is used for highly complex situations like non-isothermal, multi-phase and multi-component flow and transport, without introducing any additional driving forces. In this work, an alternative approach by Hassanizadeh and Gray identifying additional driving forces were tested in an experimental setup for horizontal redistribution of two fluid phases with an initial saturation discontinuity. Analytical and numerical solutions based on traditional models predict that the saturation discontinuity will persist, but a uniform saturation distribution will be established in each subdomain after an infinite amount of time. The pressure field, however, is predicted to be continuous throughout the domain at all times and is expected to become uniform when there is no flow. In our experiments, we also find that the saturation discontinuity persists. But, gradients in both saturation and pressure remain in both subdomains even when the flow of fluids stops. This indicates that the identified additional driving forces present in the truly extended Darcy’s Law are potentially significant.     

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.     

Lateral tyre dynamic characteristics

The ability to model the ride vibration of unsuspended vehicles is at present seriously limited by lack of knowledge about the lateral and longitudinal dynamic characteristics of rolling tyres and the interaction of these characteristics with the ground surface. In this paper, models for the lateral dynamic behaviour of a rolling tyre are reviewed. The beam model, string model and spring-damper models are described and compared. A new lateral tyre model is introduced and tested against experimental results. This model comprises a parallel spring and hysteretic damping unit, representing the tyre carcass, in series with a viscous damper representing the interaction between the tyre and ground. Model justification was made against the measurements of lateral tyre response. The results showed that the proposed model provided more accurate prediction of lateral dynamic tyre response than the other spring-damper models.     

Effect of interfacial contact forces in radial contact wire strand

A new mathematical model has been developed to predict the behaviour of a stranded cable assembly under the influence of interfacial radial contact forces and radial contraction of the core. A single layered cable assembly with six helical wires and a straight cylindrical core, all made with the same material, Steel has been chosen to explain this phenomenon when the assembly is under the influence of core–wire radial contact. An attempt is made in this paper to model the strand with a radial (core–wire) contact and deduce its equations of equilibrium. Numerical analysis of strand force, twisting moment, strand stiffness, contact force and contact stresses is carriedout based on the equilibrium of thin rods, and the results are compared with the earlier research work. The importance of the inclusion of interfacial forces at the contact locations and their associated effects of axial and twist slip of the helical wires on the core, is highlighted. The behaviour of the stranded cable assembly due to the contact force in the radial direction and its associated effects on the axial strain of the core due to Poisson’s effect is one more additional feature incorporated in the present work.     

Effect of inflation pressure on motion resistance ratio of a high-lug agricultural tyre

A single wheel tyre facility at University Putra Malaysia (UPM) was used to check the validity of Wismer–Luth and Brixius equations in predicting the motion resistance ratio of a high-lug agricultural tyre and to investigate the effect of inflation pressure. A Bridgestone 5-12, 4 ply, lug M was tested on sandy-clay-loam soil. The experiments were conducted by running the tyre in towing mode. Three inflation pressures (i.e., 166, 193 and 221 kPa) were investigated and wheel numerics ranging between 0 and 70. The analysis of covariance (ANCOVA) revealed that both inflation pressure and wheel numeric have significant effects on tyre motion resistance ratio. Regression analysis was also conducted to determine the closeness of fit for Wismer–Luth’s and Brixius’ equations in predicting the motion resistance ratio of the tested tyre. Finally, three new logarithmic models for tyre motion resistance were formulated. The advantage of reducing tyre inflation pressure from 221 (nominal pressure) to 193 kPa on the motion resistance ratio of the high-lug agricultural tyre was pronounced. However, the tyre’s motion resistance ratio deteriorated with further reduction in tyre inflation pressure from 221 (nominal pressure) to 166 kPa.     

Motion resistance measurements on large lug tyres

Motion resistance of tyres directly contribute to the operational costs of all vehicles. Advances in the design and simulation of large off-road vehicles (construction, mining, agriculture etc.) have increased the need for accurate models of large off-road tyres. Vehicle OEMs use coast down and drawbar pull tests to determine the motion resistance of tyres used. Drum test rigs and motion resistance test trailers can also be used to determine motion resistance. Most research on motion resistance to date have been conducted on passenger car tyres with on-road truck tyres coming into focus. Motion resistance studies on agricultural tyres traversing over deformable terrain have been conducted in the past. However as more off-road vehicle are being used on-road OEMs of off-road vehicle are infesting in motion resistance measurements on non-deformable terrain. This paper compares different methods used to measure the motion resistance of a large lug tyre, as used in agricultural applications, on non-deformable terrain. Some basic considerations that need to be taken into account are the very low longitudinal forces that need to be measured compared to the large vertical load carried by the tyre and tyre operating conditions.     

Energy integrals for mechanical systems with nonlinear nonholonomic constraints

The work analyzes energy relations for nonholonomic systems, whose motion is restricted by nonlinear nonholonomic constraints. For the mechanical systems with linear constraints, the analysis of energy relations was carried out in [1], [2], [3], [4], [5], [6] …. On the basis of corresponding Lagrange’s equations, a general law of the change in energy dε/dt is formulated for mentioned systems by the help of which it is shown that there are two types of the laws of conservation of energy, depending on the structure of elementary work of the forces of constraint reactions. Also, the condition for existing the second type of the law of conservation of energy is formulated in the form of the system of partial differential equations. The obtained results are illustrated by a model of nonholonomic mechanical system.     

Stability and Hopf Bifurcation of Four-Wheel-Steering Vehicles Involving Driver's Delay

A mathematical model is presented for four-wheel-steeringvehicles, with the time delay in driver's response and the nonlinearityin lateral tyre forces taken into account. It is proved that thevehicle-driver system has a trivial steady state motion, as well aseight non-trivial steady state motions due to the nonlinearity of tyreforces. The asymptotic stability and Hopf bifurcation of the trivialsteady state are analyzed for two control strategies ofrear-wheel-steering. It is shown through the numerical simulations thatthe four-wheel-steering technique based on the bilinear control strategyworks better when the driver's response involves time delay.     

A second strain gradient elasticity theory with second velocity gradient inertia – Part II: Dynamic behavior

This paper is the sequel of a companion Part I paper devoted to the constitutive equations and to the quasi-static behavior of a second strain gradient material model with second velocity gradient inertia. In the present Part II paper, a multi-cell homogenization procedure (developed in the Part I paper) is applied to a nonhomogeneous body modelled as a simple material cell system, in conjunction with the principle of virtual work (PVW) for inertial actions (i.e. momenta and inertia forces), which at the macro-scale level takes on the typical format as for a second velocity gradient inertia material model. The latter (macro-scale) PVW is used to determine the equilibrium equations relating the (ordinary, double and triple) generalized momenta to the inertia forces. As a consequence of the surface effects, the latter inertia forces include (ordinary) inertia body forces within the bulk material, as well as (ordinary and double) inertia surface tractions on the boundary layer and (ordinary) inertia line tractions on the edge line rod; they all depend on the acceleration in a nonstandard way, but the classical laws are recovered in the case of no higher order inertia. The classical linear and angular momentum theorems are extended to the present context of second velocity gradient inertia, showing that the extended theorems—used in conjunction with the Cauchy traction theorem—lead to the local force and moment (stress symmetry) motion equations, just like for a classical continuum. A gradient elasticity theory is proposed, whereby the dynamic evolution problem for assigned initial and boundary conditions is shown to admit a Hamilton-type variational principle; the uniqueness of the solution is also discussed. A few simple applications to wave propagation and dispersion problems are presented. The paper indicates the correct way to describe the inertia forces in the presence of higher order inertia; it extends and improves previous findings by the author [Polizzotto, C., 2012. A gradient elasticity theory for second-grade materials and higher order inertia. Int. J. Solids Struct. 49, 2121–2137]. Overall conclusions are drawn at the end of the paper.     

车辆纵振路面谱及其应用

对车辆纵振路面谱及其在地面-车辆系统中的应用进行了探讨,计算了行车纵剪力及其作用下的路面应力强度因子．与垂向路面谱相比,纵振路面谱代表的路面等级较高．行车纵剪力为均值等于0的平稳随机过程,在它的作用下,路面荷载型裂纹从上到下扩展的速度明显大于从下往上扩展的速度,扩展速度与力的 4次幂成正比．行车纵剪力对路面的裂纹损伤远远大于轮胎路面压力导致的裂纹损伤．