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.     

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 systematic approach to reliably characterize soils based on Bevameter testing

Although a lot of information about soil parameter identification exists in literature, there is currently no algorithm who makes use both of state of the art identification methodologies and incorporating statistical analysis. In this paper a state of the art soil parameter identification method is presented including the calculation of its standard deviations and a proper weighting of the objective function. With this algorithm and a Bevameter with advanced sensor and actuator technology a test campaign is started to find a reliable soil preparation, which is applicable to a large planetary rover performance testbed. Furthermore, the preparation method has to be valid and stable for various types of dry, granular and frictional soils, typically used for planetary rover testing in space robotics, since the result of pre-tests show that the soil parameters are highly depending on the preparation. Besides preparation, the soil parameters are also influenced by different Bevameter test setup variables. Thus, the effect of the penetration velocity as well as the penetration tool geometry for pressure–sinkage tests on soil parameters is investigated. For shear tests the influence of the dimension of the shear ring is analysed as well as the variation of the grouser height, the number of the grousers and the increase of the rotational shear velocity. The results of the extensive test campaign are evaluated by the proposed identification algorithms.     

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.     

Sinkage tests for mobility study, modelling and experimental validation

The sinkage of the bearing tracks or wheels of a vehicle in soil induces a resistance to travel motion. Usually it is determined with methods based on the modelling of soil pressure-sinkage curves. This article presents a new method for modelling soil penetration tests as a result of experimental study of three standard soils. These soils have been chosen to represent the mechanical properties of a range of soils: a sand for frictional soils, a silt for cohesive soils and a silty sand for cohesive frictional soils. The models take into account the mechanical behaviour of soils where a small vertical sinkage can be assumed analogous to elastic behaviour, while for large sinkage, the analogy is with plastic behaviour. A New Model of Mobility (N2M) is proposed. A new equation relating the pressure p and the sinkage z is governed by four parameters which are constant for a specific soil in a given physical state. These parameters can be calculated with two sinkage tests made with two different plate diameters and are particularly stable: a small change of one of them involves a small change of the modelling. They are independent of the size of the sinkage plate and hence could pave the way for the extrapolation to the scale of full size vehicles. For the tested soils, comparison of the model results with experimental tests is very promising.     

Rolling resistance and sinkage analysis by comparing FEM and experimental data for a grape transporting vehicle

In this study a 2D FEM model was developed to analyze ruts formation, rolling resistance, and power loss for a grape transporting cart aimed to replace the use of heavy tractors while harvesting grape. The model was supported by experiments in a vineyard in South Italy. Cone penetration tests were conducted to estimate frictional and cohesive properties in three soil conditions: firm, soft, and wet saturated. A tractor pulled test rig for a single wheel was developed to measure rolling resistance and sinkage, and complete the selection of the soil parameters. Completed the model, the analysis was conducted for a range of different wheel dimensions, and the outputs analyzed through response surfaces. The results showed the different impacts that width and diameter have on ruts formation and rolling resistance for different soil conditions. Wider wheels determined a main reduction of the sinkage, while the width contribution to the rolling resistance was affected by the total soil volume deformed. Larger diameters led to lower rolling resistance, with a higher impact on more deformable soils. Contact stress was compared with the thresholds recommended in the literature to determine the acceptable designs. This analysis represents a tool to select the running gear dimensions.     

The Bekker theory of rolling resistance amended to take account of skid and deep sinkage

The Bekker theory of rolling resistance of free rolling, towed, rigid wheels is amended to take account of both skid and deep sinkage without leading to excessive complexity in the predictive equations. Theoretical relationships between skid and sinkage are derived for a free rolling, towed, rigid wheel on a purely cohesive soil ( = 0) and on a purely frictional soil (c = 0) with a sinkage exponent of unity. Generally, good agreement is found between predicted and measured values of rolling resistance and sinkage at a given vertical load, on both sand and clay soils, at shallow and deep sinkage.     

Slip sinkage effect in soil-vehicle mechanics

The paper presents an analysis and quantitative evaluation of the slip sinkage and its effect on the tractive performance of wheeled and tracked vehicles in different soils. The results of this study indicated that to accurately predict the sinkage and motion resistance of a vehicle in a given soil and operating conditions, the slip sinkage effect should be taken into account. An effective analytical formula that takes into consideration the slip sinkage effect on sinkage of plates and vehicles is developed. The formula was validated in different soil conditions and compared with other formulae used in terramechanics for slip sinkage effect predictions.     

Traction prediction using soil parameters obtained with an instrumented analog device

A fully instrumented device capable of measuring soil sinkage and shear parameters developed at the Agricultural Engineering Department, University of California, Davis was employed to conduct in situ sinkage and shear tests in a tilled and a farm, dry, Yolo loam soil. Similar tests were also conducted in a tilled, moist Yolo loam soil. An 18.4R38 tire was tested at different levels of inflation pressure and axle loads in these soil conditions. Soil parameters obtained using the instrumented device were related to the traction prediction equation parameters using traction mechanics, principle of conservation of energy and dimensional analysis.     

Prediction of sinkage and motion resistance of a tracked vehicle using plate penetration test

The relationship between contact pressure and sinkage must be represented by a mathematical model to estimate the sinkage and the motion resistance due to a vehicle. In this study an approximate and simple pressure-sinkage model is proposed. This model takes into account the effect of the size of the penetration plate on soil response, and includes two soil values that can be obtained by a single plate penetration test. It is submitted that the sinkage and the motion resistance of a tracked vehicle can be estimated by means of the proposed model.     

A mathematical model for spatial motion of tracked vehicles on soft ground

A mathematical model which predicts spatial motion of tracked vehicles on non-level terrain has been developed. The motion of the vehicle is represented by three translational and three rotational degrees of freedom. In order to incorporate the inelastic deformation of soil, a soil-track interaction model is introduced; this constitutive model relates the traction exerted on the track by soil to the slip velocity and sinkage of the track. The model is based upon available soil plasticity theories and furnishes mechanics-based interpretation of Bekker's empirical relations. For planar motion the proposed model reduces to the existing equations of motion by introducing kinematic constraints on the vertical translation, pitching and rolling degrees-of-freedom.     

Performance prediction of animal drawn vehicle tyres in sand

Four animal drawn vehicle (ADV) tyres of 5.00–19, 6.00–19, 7.00–19 and 8.00–19 sizes were tested in sand under various but controlled conditions in an indoor soil bin. A tyre test carriage with four-bar parallel linkage was developed for accommodating a single wheel of different sizes. Performance tests were conducted at five levels of inflation pressure and load. The sand compaction level was varied in the range of 3.4–4.5 MPa/m and forward speed of the test carriage was maintained at 3.1 km/h. Performance of the tyres 7.00–19 and 8.00–19 was identical and offered less rolling resistance as compared to other tyres. However, their use in camel carts may not be recommended beyond the payload of 6 kN on single wheel with inflation pressure and sand compaction range of 172–379 kPa and 3.4 –4.5 MPa/m, respectively. Based on the experimental results, empirical models were developed to predict the performance of tyres. The accuracy of prediction of the developed empirical models was compared with that of existing semi-empirical approaches. Model with sand mobility number considered relatively simple and convenient to use in the field and yields reasonably good prediction for rolling resistance and sinkage.     

Using a local-interaction model to determine the resistance to penetration of projectiles into sandy soil

A local-interaction model describing the penetration of axisymmetric projectiles into sandy soil at a constant velocity is studied experimentally and theoretically. Two approaches to the determination of the parameters of the quadratic local-interaction model are considered. The first approach is based on the use of the solution of the problem of spherical-cavity expansion taking into account the dynamic compressibility and shear resistance of soil. In the second approach, model parameters are determined based on the experimental dependence of the resistance to penetration of conical projectiles into a sandy soil on the impact velocity. Good agreement was obtained between the results of experiments, two-dimensional numerical calculations, and calculations for the local interaction model based on the solution of the spherical-cavity expansion problem and used to determine the maximum resistance to penetration of conical and spherical projectiles.     

Deformation processes below a plate sinkage test on sandy loam soil: theoretical approach

Mathematical models to predict the mode and extent of deformation occurring below sinkage plates are presented in the first part of this paper which encompasses the theoretical approach to the subject. These models are based on previous work by Earl (Earl R. Assessment of the behaviour of field soils during compression. Journal of Agricultural Engineering Research 1997;68:147–57)who developed a procedure to predict the likely mode of deformation using confined compression tests carried out alongside plate sinkage tests. This work suggested that soil behaviour, during increasing compression under a sinkage plate, is governed by three processes; (i) compaction below the plate with constant lateral stress, (ii) compaction with increasing lateral stress, and (iii) displacement and compaction of soil laterally. The aim of this second part to the paper is to observe soil deformation processes occurring below a circular sinkage plate to examine (i) whether the three phases of deformation referred to above occur in practice, and (ii) the accuracy of the models for predicting the soil deformation processes that occur. Tests were carried out on sandy loam soil under controlled conditions in a soil bin. Observations of deformation processes, recorded using long-exposure photography, revealed that during the initial stages of sinkage (a few millimetres), the corresponding disturbance of soil below the plate extended disproportionately further and was cylindrical in form. As sinkage progressed, the deformation process went through a transitional stage before reaching the more widely recognised form of the development of an inverted cone of compacted soil directly below the plate which moved with the plate causing lateral soil movement and compaction. Predictions for a medium density sandy loam were found to be in broad agreement with soil behaviour under a semi-circular sinkage plate observed behind a sheet of tempered glass under controlled conditions in a soil tank.     

Indentation tests and rolling simulations of a compliant wheel on soil at different consistencies

The investigation presented addresses the response of a compliant wheel in interaction with deformable soil dependent on the water content, and accordingly on soil consistency. Two fine soils are considered. The basic soil properties and the soil shear strength are obtained from routine tests. A non-pneumatic Tweel in full size is tested in a loading device against a rigid base and against soil placed in a container in order to assess its stiffness and the compressional behavior of the soil, respectively. The measured pressure sinkage curves are then utilized in conjunction with a standard explicit FEM code to calibrate a hyperelastic model for the Tweel and an elasto-plastic constitutive model for the soil. Soil-tire interface strength is obtained from shear tests on a flat tire section embedded in soil. The numerical model is then applied to investigate how the water content affects the global response of the tire-soil system under different scenarios of free rolling, braking and driving. The methodology followed, complemented by appropriate soil testing, can be used as guide for the implementation of more elaborate models.     

Modeling wheel-induced rutting in soils: Rolling

Theoretical models for predicting penetration of non-driving (towed) rigid cylindrical wheels rolling on frictional/cohesive soils are presented. The models allow for investigating the influence of soil parameters and wheel geometry on the relationship between the inclined rolling force and wheel sinkage in the presence of permanently formed ruts. The rolling process is simulated numerically in three dimensions using the finite element code ABAQUS. The numerical simulations reveal that the advanced three-dimensional process of rutting can be regarded as steady, and an approximate analytic model for predicting sinkage under steady-state conditions, which accounts for three-dimensional effects, is also developed. The differences between wheel rolling and wheel indentation (considered in a separate paper) are discussed. Numerical and analytic results are compared with test results available in the literature and obtained from preliminary small-scale experiments, and general agreement is demonstrated.     

Improved sinkage algorithms for powered and unpowered wheeled vehicles operating on sand

Modeling and simulation of vehicles in sand is critical for characterizing off-road mobility in arid and coastal regions. This paper presents improved algorithms for calculating sinkage (z) of wheeled vehicles operating on loose dry sand. The algorithms are developed based on 2737 tests conducted on sand with 23 different wheel configurations. The test results were collected from Database Records for Off-road Vehicle Environments (DROVE), a recently developed database of tests conducted with wheeled vehicles operating in loose dry sand. The study considers tire diameters from 36 to 124 cm with wheel loads of 0.19–36.12 kN. The proposed algorithms present a simple form of sinkage relationships, which only require the ratio of the wheel ground contact pressure and soil strength represented by cone index. The proposed models are compared against existing closed form solutions defined in the Vehicle Terrain Interface (VTI) model. Comparisons suggest that incorporating the proposed models into the VTI model can provide comparable predictive accuracy with simpler algorithms. In addition to simplicity, it is believed that the relationship between cone index (representing soil shear strength) and the contact pressure (representing the applied pressure to tire-soil interface) can better capture the physics of the problem being evaluated.     

Semi-empirical traction prediction equations based on relevant soil parameters

Extensive single-wheel traction tests were conducted in the vicinity of UC Davis campus using four different radial ply tires, two soil types, four soil conditions, three levels of inflation pressures, and three axle loads. Soil sinkage and shear characteristics were also obtained using an instrumented soil test device in every test condition. These field data were analyzed to obtain semi-empirical traction prediction equations for radial ply tires. In general, these prediction equations were able to predict traction equation parameters with less than 25% error.     

A dynamic model for soil cutting by blade and tine

A dynamic model for soil cutting resistance prediction by blade and tine was developed, taking account of shear rate effects both on soil shear strength and soil-metal friction, besides the conventional soil slice inertia, for both brittle and flow failure of soil. The model was verified with a series of tests in a soil bin with a blade and a tine, and the results were acceptable.     

Longitudinal skid model for wheels of planetary rovers based on improved wheel sinkage considering soil bulldozing effect

To successfully deploy a wheeled mobile robot on deformable rough terrains, the wheel-terrain interaction mechanics should be considered. Skid terramechanics is an essential part of the wheel terramechanics and has been studied by the authors based on the wheel sinkage obtained using a linear displacement sensor that does not consider soil bulldozing effect. The sinkage measured by a newly developed wheel via detecting the entrance angle is about 2 times of that measured by the linear displacement sensor. On the basis of the wheel sinkage that takes the soil bulldozing effect into account, a linear function is proposed to the sinkage exponent. Soil flow in the rear region of wheel-soil interface is considered in the calculation of soil shear displacement, and its average velocity is assumed to be equal to the tangential velocity component of the transition point of shear stress. To compute the normal stress in the rear region directly, the connection of the entrance and leaving points is supposed as the reference of wheel sinkage. The wheel performance can be accurately estimated using the proposed model by comparing the simulation results against the experimental data obtained using two wheels and on two types of sands.