Prediction of sinkage and rolling resistance for off-the-road vehicles considering penetration velocity

The use of plate pressure tests is common for the prediction of sinkage and rolling resistance for off-the-road vehicles. Most of these penetration tests are carried out with small penetration bodies in a quasi-static way. However, when vehicles are rolling on soft soil, the soil is charged dynamically. Consequently, this dynamic effect should be considered by the prediction of sinkage and rolling resistance. At the Institute of Automotive Engineering at Hamburg, tests were carried out with penetration bodies in sizes up to 900 cm², which is comparable to the contact area of wheels. The results confirm the influence of the penetration velocity. With a constant load, the body sinkage is smaller at a higher penetration velocity. Also shear tests with shear rings of different sizes have been carried out and an exponential equation for the shear strength, not depending on the shear ring size, was found. A dynamic pressure-sinkage relationship depending on the penetration velocity or driving speed was derived and transferred to the sinkage and rolling resistance of a rigid wheel.     

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.     

LSA model for sinkage predictions

The paper presents a Load-Sinkage Analytical (LSA) model, its validation and comparison with other models used in Terramechanics. The LSA model predicts sinkage and penetration force as functions of soil parameters and plates (or traction devices) shape and dimensions. This model uses invariant soil parameters that can be given or measured before the calculations by routine methods of classical soil mechanics. Soil parameters can also be obtained by recommended empirical equations using four physical soil parameters measured in the field with hand held instruments without time consuming and costly plate tests. The paper includes also an analysis of capabilities and limitations of the observed models.     

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.     

Prediction of impacts of wheeled vehicles on terrain

Traffic of off-road vehicles can disturb soil, decrease vegetation development, and increase soil erosion. Terrain impacts caused by wheeled off-road vehicles were studied in this paper. Models were developed to predict terrain impacts caused by wheeled vehicles in terms of disturbed width and impact severity. Disturbed width and impact severity are not only controlled by vehicle types and vehicle dimensions, but also influenced by soil conditions and vehicle dynamic properties (turning radius, velocity). Field tests of an eight-wheeled vehicle and a four-wheeled vehicle were conducted to test these models. Field data of terrain–vehicle interactions in different vehicle dynamic conditions were collected. Vehicle dynamic properties were derived from a global position system (GPS) based tracking system. The average prediction percentage error of the theoretical disturbed width model is less than 20%. The average absolute error between the predicted impact severity and the measured value is less than an impact severity value of 12%. These models can be used to predict terrain impacts caused by off-road wheeled vehicles.     

Modelling power requirement for traction tyres with zero sinkage

A model was developed by dimensional analysis to predict the gross traction at zero net traction for traction tyres (11.2–28, 12.4–28, 13.6–28) on a hard surface. Different parameters that affect the torque requirement, namely tyre size, tyre deflection, axle load, and rolling radius, were considered for the analysis. Experiments were conducted to study the effect of various wheel and system parameters on torque and energy consumed per unit distance travelled. The model developed predicts the torque requirement in an acceptable range and can be used as a reference for further traction studies of these tyres in various soils.     

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.     

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.     

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.     

Determination of rating cone index using wheel sinkage and slip

It has been known from empirical equations that soil strength can be determined if wheel sinkage and slip of a vehicle can be measured on a soil surface. In this study, field data of wheel sinkage and slip were collected from two platform tractors of different sizes on gravely sandy and sandy loam soils. Using an empirical equation, the rating cone index was determined using the measured wheel sinkage and slip data. The data demonstrated that the same rating cone index can be obtained although the measuring platforms are different. It was also noted that the rating cone index can be estimated in real time by measuring the sinkage and slippage of a driving wheel.     

The mechanism of sinkage of running gear on sand

This paper presents the results of an investigation into the mechanism of sinkage of running gear on sand. The results indicate that the main reasons for the sinkage on sand are its special mechanical properties as well as the spatial strength characteristics of the sand near the surface of the ground. Sinkage on sand is greatly influenced by the mode of interaction. The “flow confining” action of the running gear could change the flow of sand. If the lateral and upward components of displacement are decreased, the bearing capacity of the sand is increased.     

External motion resistance caused by rut sinkage of a tracked vehicle

This paper deals with the external motion resistance of a tracked vehicle caused by rut formation (sinkage) or compression of soil under the tracks. It is shown that the relationship between the applied load and the sinkage for a loading test using a plate is represented by a hyperbola. Based on the above relationship, the external motion resistance caused by the rut formation of a tracked vehicle is estimated by considering the work done by overcoming the ground pressure and the resistance. Further, measurements of the external motion resistance were carried out by using a tracked vehicle and the experimental results are compared with the theoretical ones, and the reliability of the above method is confirmed experimentally.     

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 deflection and contact characteristics of some agricultural tyres with zero sinkage

The vertical deflection, contact area, and ground pressure of three agricultural tractor rear tyres (11.2–28, 12.4–28, 13.6–28) were investigated at different normal loads and inflation pressures on a firm surface. A linear mathematical model was evolved to establish relationship among different parameters. The model could be used to represent tyre behaviour under varying operational parameters.     

Prediction of ground pressure distribution under tracked vehicles—I. An analytical method for predicting ground pressure distribution

An analytical method for predicting the pressure distribution beneath a tracked vehicle under static conditions is presented. In the analysis, the track-suspension system which consists of the track, the suspension and the track tensioning device, is considered inits entirety. All major design parameters of the vehicle, as well as terrain characteristics, are taken into consideration. It is shown that the analytical method proposed can provide a means whereby the effects of vehicle design parameters and terrain conditions on ground pressure distribution can be assessed quantitatively.     

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.