Combined lateral and longitudinal forces on driven angled tractor tyres

With the single wheel tester of Hohenheim University, tractive and side forces have been measured on driven tractor tyres of different sizes on a hard stubble field and on a tilled field with higher moisture content. It was found that the lateral forces are diminished as the tractive forces increase. The maximum lateral force was at little negative tractive force, corresponding with small negative wheelslip.     

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.     

The effect of velocity on rigid wheel performance

A simulation model to predict the effect of velocity on rigid-wheel performance for off-road terrain was examined. The soil–wheel simulation model is based on determining the forces acting on a wheel in steady state conditions. The stress distribution at the interface was analyzed from the instantaneous equilibrium between wheel and soil elements. The soil was presented by its reaction to penetration and shear. The simulation model describes the effect of wheel velocity on the soil–wheel interaction performances such as: wheel sinkage, wheel slip, net tractive ratio, gross traction ratio, tractive efficiency and motion resistance ratio. Simulation results from several soil-wheel configurations corroborate that the effect of velocity should be considered. It was found that wheel performance such as net tractive ratio and tractive efficiency, increases with increasing velocity. Both, relative wheel sinkage and relative free rolling wheel force ratio, decrease as velocity increases. The suggested model improves the performance prediction of off-road operating vehicles and can be used for applications such as controlling and improving off-road vehicle performance.     

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.     

Equilibrium of a Prestressed Strip Reinforced with Elastic Plates

The contact problem for a prestressed elastic strip reinforced with equally spaced elastic plates is considered. The Fourier integral transform is used to construct an influence function of a unit concentrated force acting on the infinite elastic strip with one edge constrained. The transmission of forces from the thin elastic plates to the prestressed strip is analyzed. On the assumption that the beam bending model and the uniaxial stress model are valid for an elastic plate subjected to both vertical and horizontal forces, the problem is mathematically formulated as a system of integro-differential equations for unknown contact stresses. This system is reduced to an infinite system of algebraic equations solved by the reduction method. The effect of the initial stresses on the distribution of contact forces in the strip under tension and compression is studied     

A Prestressed Elastic Strip with Elastic Reinforcements

A contact problem is studied for a prestressed elastic strip with an elastic reinforcement. The integral Fourier transform is used to construct an influence function for an infinite strip with one face fixed. A unit concentrated force is applied to the strip at an arbitrary angle. The contact problem on force transfer from a thin infinite stringer to the prestressed strip is solved. The problem is mathematically formulated as a system of integro-differential equations for the unknown contact stresses on the assumption that the beam bending model and the uniaxial stress model are valid for the stringer, which is subjected to both vertical and horizontal forces. This system is solved in a closed form using the integral Fourier transform. The contact stresses are expressed in terms of Fourier integrals in a quite simple form. The influence of the initial stresses on the contact stress distribution is analyzed, and effects of concentrated load are revealed     

2D FE–DEM analysis of contact stress and tractive performance of a tire driven on dry sand

Normal and tangential stresses acting over a contact interface of a tire driven on dry sand were investigated to expand the applicability of our model incorporating 2D FE–DEM with proportional–integral–derivative (PID) control. A simple averaging method for contact reaction was introduced: computational segments were defined over the lower half part of the tire circumference that translates without rotation with the tire; then the contact stresses were calculated segment by segment. For the analysis, it was assumed that the tire was in rigid contact mode and that it would travel on the model sand terrain in stationary condition. The integration of normal and tangential contact stresses with respect to the angle of rotation was then applied to calculate the vertical contact load, gross tractive effort, net traction, and running resistance of the tire by parametric (or semi-empirical) analysis. The result of tractive performance obtained through the parametric analysis was found to be similar to the result of tractive performance obtained directly using FE–DEM analysis. A forward shift of the consistent angle of rotation for maximum normal contact stress and that for maximum tangential contact stress with the increase of slip from 22% was also observed in the FE–DEM result.     

考虑接触应力非线性分布的接触力元模式及其验证分析

在作者提出的非连续变形计算力学模型中,采用接触力元模型描述多体接触界面上的接触特性．由于这种模型中假定接触应力沿接触界面为线性分布,从而得到的接触界面应力分布往往出现跳跃等非光滑性特征,该文对此进行了改进,采用具有高阶光滑性的非线性函数建立了能够考虑界面上接触应力非线性分布的接触力元模式,以期合理地揭示多体系统中界面的接触特性．对某一典型算例进行了数值计算,通过与大型通用非线性有限元结构分析软件ABASQUS的计算结果对比,验证了所建议计算模型的合理性与有效性．两种方法计算得到的界面接触对上的接触力基本相同;而由于采用的应力分布模式的假定不同,接触应力有所差别,由于在该文计算模型中接触对上的接触应力是按照未知量直接求得的,因此按照所建议的非线性接触力元模式所得到的接触应力更为合理．     

Three-dimensional photoelasticity of the rotating body

Report covers the stress distribution of a hydraulically loaded pump impeller obtained with the aid of the stress-freezing method. The similarity of stress distribution of an actual metallic impeller and the photoelastic model is discussed dynamically and hydrodynamically. From the experiments by freezing stresses under centrifugal force and hydraulic forces, the stress distribution of the actual metallic impeller has been estimated on the basis of similarity.     

Tractive performance of a tread design for improved flexibility

The tractive performance of an 18.4R38 radial-ply tractor tire with increased flexibility in the tread area was compared to that of a standard tread design. Normal soil-tire interface stresses were measured at four locations on the lug surfaces of both tires operating on Decatur clay loam and Norfolk sandy loam soils. There was a tendency for the increased flexibility in the tread area to provide a higher net traction ratio at the same tractive efficiency as the standard tread design, especially on Decatur clay loam soil. The more flexible tread design reduced the magnitude of peak normal contact stresses across the tire width, which may have implications for reducing soil compaction without compromising tractive performance. The more flexible tire reduced the average normal contact stress by approximately 15% in the sandy loam soil and 23% in the clay loam soil for the range of operating conditions investigated.     

An improvement of frozen-image model and its application in a HTS levitation system

This paper mainly reports an improvement of frozen-image model which can qualitatively describe the influence of lateral moving speed on vertical force in a HTS levitation system under lateral movement with field-cooling condition. The model is improved by introducing a dipole which represents the influence of lateral moving speed and modifying the rule of diamagnetic dipole based on frozen-image model. The vertical and lateral forces that are obtained by this improved model agree with the previous measurements qualitatively. This model can also describe the effect of finite scale of superconductor sample in a levitation system.     

Application of material forces to fracture of inhomogeneous materials: illustrative examples

The material forces concept has become an elegant tool in continuum mechanics for the calculation of the thermodynamic driving force of a defect. Based on this concept, we have recently shown that inhomogeneities essentially shield or anti-shield crack tips from applied far-field stresses. The goal of this paper is to illustrate this by considering the model example of a crack in a CT-type specimen that contains a bimaterial interface. The crack driving force is calculated as the sum of the far-field driving force and the crack-tip shielding or anti-shielding. Several cases of inhomogeneity in either thermal or elastic properties are considered. Rather simple hand calculations are provided in addition to numerical results to illustrate the advantages of using the material forces concept.     

Traffic performance of a rubber-tracked vehicle travelling up and down a sloped pavement

The tractive and braking performances of a 40 kN rubber-tracked vehicle travelling up and down a sloped pavement depend on the grouser shape. The purpose of this paper is to find the most suitable grouser shape to obtain the maximum optimum effective tractive effort and the maximum optimum effective braking force and to clarify the several traffic performances of the vehicle travelling up and down sloped concrete and asphalt paved roads. As results, it is verified that the most suitable shape of rubber grouser is an equilateral trapezoid type of contact length 3 cm for concrete pavement and another of contact length 5 cm for asphalt pavement, respectively, and that the effective tractive effort and the effective braking force decrease with the increment of slope angle.     

Contact force and mechanical loss of multistage cable under tension and bending

A theoretical model for calculating the stress and strain states of cabling structures with different loadings has been developed in this paper. We solve the problem for the first-and second-stage cable with tensile or bending strain. The contact and friction forces between the strands are presented by two-dimensional contact model. Several theo-retical models have been proposed to verify the results when the triplet subjected to the tensile strain, including contact force, contact stresses, and mechanical loss. It is found that loadings will affect the friction force and the mechanical loss of the triplet. The results show that the contact force and mechanical loss are dependent on the twist pitch. A shorter twist pitch can lead to higher contact force, while the trend of mechanical loss with twist pitch is compli-cated. The mechanical loss may be reduced by adjusting the twist pitch reasonably. The present model provides a simple analysis method to investigate the mechanical behaviors in multistage-structures under different loads.     

Interlaminar stresses and energy release rates in delaminated orthotropic composite plates

The classical laminated plate theory is applied to calculate the stresses and energy release rate function in symmetrically delaminated orthotropic plates. First, the equilibrium of classical plate forces, moments and interfacial shear stresses is formulated. Second, the displacement continuity between the interface plane of a double-plate model was considered. The governing equation system of the double-plate model consists of ten equations. As an example a delaminated, orthotropic, simply-supported plate subjected to a point force is analyzed. The distribution of the plate forces as well as the interlaminar shear stresses over the uncracked part were determined. Moreover, the mode-II and mode-III energy release rate distributions along the crack front were calculated by the J-integral. The 3D finite element model of the delaminated composite plate was also created. The results indicate a reasonably good agreement between analysis and numerical calculation.     

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.     

Determining forces required to override obstacles for ground vehicles

The military is constantly expanding the use of unmanned ground vehicles in warfighting applications that often involve complex environments. Part of the focus of military research is to improve or validate existing routing algorithms which are used to predict vehicle mobility. Routing algorithms are based on the time required for vehicle movement through a series of obstacles such as trees or fences, thus requiring an assessment of the ability to override such obstacles as compared to finding an alternate maneuver path. The required overriding force can be computed and compared to a vehicle’s tractive force to determine the best viable option. If overriding the obstacle is an option (tractive force exceeds the required overriding force), the delay in overriding can be assessed as compared to the delay in maneuvering around the obstacle. This study provides a quick and reasonable calculation of the force required to override specific types of vertically embedded obstacles to support the determination of movement capabilities for unmanned ground vehicles on the battlefield.     

Multi-pass effect on off-road vehicle tractive performance

The paper presents an analysis and qualitative and quantitative evaluation of the multi-pass effect on off-road vehicle tractive performance in different soils. A literature review and the results of this study indicated that to accurately predict a vehicle’s tractive performance, the multi-pass effect should be taken into account. A new method has been developed on how to calculate the effect in given soil and operating conditions. The method includes consecutive calculation of the tractive performance: (a) for the first vehicle pass using an analytical model with soil input including an initial soil parameters set, (b) for the following vehicle passes using the same analytical model with corresponding soil input for each pass which can be obtained using the new procedure.     

Lateral slide sinkage tests for a tire and a track shoe

Previous field studies have shown the influence of turning vehicles on rut formation or sinkage. In order to further investigate the relationships, laboratory tests were conduced on a 14.5–20.3 6-PR trailer tire and an Armored Personnel Carrier (APC) track shoe in sand. Lateral displacements, and resulting lateral forces, were applied to the tire and track shoe under constant normal forces. The tire was pulled laterally and the track shoe was pulled back and forth to represent actual movement during vehicle turning. Results show that the lateral force and lateral displacement generated by turning maneuver affect sinkage severely for wheeled and tracked vehicles. The final sinkage caused by the lateral force for the tire is 3–5 times to the static sinkage. For the track shoe, the final sinkage caused by the lateral displacement is about three times to the static sinkage.     

Numerical Investigation of the Flow Past a Rotating Golf Ball and Its Comparison with a Rotating Smooth Sphere

Large-eddy simulations are conducted for a rotating golf ball and a rotating smooth sphere at a constant rotational speed at the subcritical, critical and supercritical Reynolds numbers. A negative lift force is generated in the critical regime for both models, whereas positive lift forces are generated in the subcritical and supercritical regimes. Detailed analysis on the flow separations on different sides of the models reveals the mechanism of the negative Magnus effect. Further investigation of the unsteady aerodynamics reveals the effect of rotating motion on the development of lateral forces and wake flow structures. It is found that the rotating motion helps to stabilize the resultant lateral forces for both models especially in the supercritical regime.