Dynamic behaviour of an open lugged wheel under paddy soil conditions

Many experimental studies of open lugged wheel-soil interaction have been conducted, mainly based on the condition of constant slip and sinkage. As a result the reaction force to lugs seemed to be equal to the soil cutting resistance to a metal surface. However, analyses based on such methods do not appear to represent the actual behaviour of lugged wheel-soil interaction, especially when the lugs are spaced widely. The actual motion the wheel axle. In this study, an experimental device for a model lugged wheel was constructed to investigate the characteristics of the interaction between a lugged wheel and soil. Experiments were conducted under several test conditions of soil including paddy soil with a hard pan. The result of both theoretical and experimental data indicated that slip and sinkage of a lugged wheel showed a fluctuation with rotation angle of which the period is equal to the angular lug spacing. In each test soil condition used, the motion of the lugged wheel and the reaction forces acting on each lug from the soil for a free sinking wheel were different from that of the condition of constant slip and sinkage. It was found that the results obtained from this study could clarify the actual behaviour of lugged wheel-soil interaction.     

Modes of wet clay soil behaviour under a single cage wheel lug

This paper presents the results of studies on the effect of sinkage and slip of a single cage wheel lug on the deformation of wet clay soil. It was observed that the deformation pattern was strongly influenced by lug sinkage and slip. Soil wedge formation on the lug was also found to be a function of sinkage and slip. Four different deformation patterns were identified during this investigation. It seems unlikely that these can be predicted without a more exact knowledge of stress-strain relationships in soils.     

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.     

Effects of a roller and a tracked vehicle on the compaction of a high lifted decomposed granite sandy soil

The aim of this research was to innovate a new compaction machinery by comparing experimentally the effects of a two-axle, two wheel road roller and a tracked vehicle on the compaction of a decomposed granite sandy soil with a high spreading lift. By measuring the amount of sinkage of the terrain surface, the dry density distribution versus depth using a cone penetrometer, the normal earth pressure distribution versus depth using a stress state transducer (SST), the effects of the road roller and the tracked vehicle on the increment of the soil dry density were considered theoretically. It was observed that the tracked vehicle showed a larger amount of sinkage and a larger dry density distribution versus depth than the roller. The ratio of shear stress to normal stress was still large enough at the deep stratum, so that an optimal shear strain was developed on the whole range of the high lifted stratum and it increased the soil compaction density due to the dilatancy effect.     

Development of in-wheel sensor system for accurate measurement of wheel terrain interaction characteristics

Planetary rovers need high mobility on a rough terrain such as sandy soil, because such a terrain often impedes the rover mobility and causes significant wheel slip. Therefore, the accurate estimation of wheel soil interaction characteristics is an important issue. Recent studies related to wheel soil interaction mechanics have revealed that the classical wheel model has not adequately addressed the actual interaction characteristics observed through experiments. This article proposes an in-wheel sensor system equipped with two sensory devices on the wheel surface: force sensors that directly measure the force distribution between the wheel and soil and light sensors that accurately detect the wheel soil surface boundary line. This sensor design enables the accurate measurement of wheel terrain interaction characteristics such as wheel force distribution, wheel–soil contact angles, and wheel sinkage when the powered wheel runs on loose sand. In this article, the development of the in-wheel sensor system is introduced along with its system diagram and sensor modules. The usefulness of the in-wheel sensor system is then experimentally evaluated via a single wheel test bench. The experimental results confirm that explicit differences can be observed between the classical wheel model and practical data measured by the in-wheel sensor system.     

An indoor traction measurement system for agricultural tires

To reliably study soil–wheel interactions, an indoor traction measurement system that allows creation of controlled soil conditions was developed. This system consisted of: (i) single wheel tester (SWT); (ii) mixing-and-compaction device (MCD) for soil preparation; (iii) soil bin; (iv) traction load device (TLD). The tire driving torque, drawbar pull, tire sinkage, position of tire lug, travel distance of the SWT and tire revolution angle were measured. It was observed that these measurements were highly reproducible under all experimental conditions. Also relationships of slip vs. sinkage and drawbar pull vs. slip showed high correlation. The tire driving torque was found to be directly influenced by the tire lug spacing. The effect of tire lug was also discussed in terms of tire slip.     

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.     

Analysis of Mars Exploration Rover wheel mobility processes and the limitations of classical terramechanics models using discrete element method simulations

A previous three-dimensional discrete element method (DEM) model of Mars Exploration Rovers (MERs) wheel mobility demonstrated agreement with test data for wheel drawbar pull and sinkage for wheel slips from 0.0 to 0.7. Here, results from the previous model are compared with wheel mobility data for non-MER wheels that cover the range of wheel slip from 0.0 to 1.0. Wheel slips near 1.0 are of interest for assessing rover mobility hazards. DEM MER wheel model predictions show close agreement with weight-normalized wheel drawbar pull data from 0.0 to 0.99 wheel slip and show a similar trend for wheel sinkage. The nonlinear increase in MER wheel drawbar pull and sinkage for wheel slips greater that 0.7 is caused by development of a tailings pile behind the wheel as it digs into the regolith.Classical terramechanics wheel mobility equations used in the ARTEMIS MER mobility model are inaccurate above wheel slips of 0.6 as they do not account for the regolith tailings pile behind the wheel. To improve ARTEMIS accuracy at wheel slips greater that 0.6 a lookup table of drawbar pull, wheel torque, and sinkage derived from DEM mobility simulations can be substituted for terramechanics equation calculations.     

Further study of the method of approach to testing the performance of extraterrestrial rovers/rover wheels on earth

The current practice for experimentally evaluating the performance of extraterrestrial rovers/rover wheels is to conduct tests on earth on a soil simulant, appropriate to the regolith on the extraterrestrial body of interest. In the tests, the normal load (force) applied by the rover/rover wheel to the soil simulant is set identical to that expected on the extraterrestrial surface, taking into account its acceleration due to gravity. It should be pointed out, however, that the soil simulant used in the tests is subject to earth gravity, while the regolith on the extraterrestrial surface is subject to a different gravity. Thus, it is uncertain whether the performance of the rover/rover wheel obtained from tests on earth represents that on the extraterrestrial surface. This issue has been explored previously. A method has been proposed for conducting tests of the rover/rover wheel on earth with identical mass to that on the extraterrestrial surface, instead of with identical normal load used in the current practice [1]. This paper provides further evidence to substantiate the merits of the proposed method, based on a detailed analysis of the test data obtained under various gravity conditions, produced in an aircraft undergoing parabolic flight manoeuvres [8]. In the study, the effect of slip on wheel sinkage has been evaluated. It is found that gravity has little effect on the slip and sinkage relationship of the rover wheel under self-propelled conditions.     

Visualization and analysis of wheel camber angle effect for slope traversability using an in-wheel camera

This paper visualizes and analyzes an effect of a wheel camber angle for the slope traversability in sandy terrain. An in-wheel camera developed in this work captures the wheel-soil contact phenomenon generated beneath the wheel through a transparent section of the wheel surface. The images taken by the camera are then analyzed using the particle image velocimetry. The soil flows with various wheel camber angles are analyzed with regard to the soil failure observed on the slope surface. The analysis reveals that the slope failure and soil accumulation in front of the wheel significantly affect the wheel forces and distributions of the wheel sinkage in the wheel width direction. Further, the side force of the wheel in traversing a slope decreases as the slip ratio increases because the shear stress in the slope downward direction decreases owing to the slope failure.     

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.     

The optimum height of application of force and eccentricity of a wheeled vehicle running on a loose sandy soil

In earthmoving sites, multi-wheeled vehicles are used to excavate a sandy soil or to pull other construction machinery. In this paper, the mechanism of a 5.88 kN weight, two-axle, four-wheel vehicle running on a loose sandy soil is theoretically analysed. For given terrain-wheel system constants, the combination of the effective braking force of the front wheel during pure rolling state and the effective driving force of the rear wheel during driving action will clarify the relation between effective effort of the vehicle and slip ratio and the relation between amounts of sinkage the front and rear wheels and slip ratio, etc. The maximum effective tractive effort of the vehicle varies with the height of application force and the position of the center of gravity of the vehicle. The optimum height of application of force and the eccentricity of the center of gravity to obtain the largest value of the maximum effective tractive effort can be explained with an analytical simulation program. Results of this study showed that the optimum height of application force should be 30 cm and the optimum eccentricity of the center of gravity is 0.05 for a vehicle considered for this study.     

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.     

A dynamic terramechanic model for small lightweight vehicles with rigid wheels and grousers operating in sandy soil

This paper presents a validated dynamic terramechanic model for rigid wheels with grousers that may be used for planetary and terrestrial mobile robots operating in loose sandy soil. The proposed model is based on established analytical terramechanic theories and incorporates two new dimensionless empirical coefficients. The additional terms in the model are based on existing soil mechanic theories that vary as a function of soil properties, slip conditions, and vehicle loading. The proposed model was able to capture and predict the dynamic oscillations observed in experimental data from a single-wheel testbed for the sinkage, drawbar pull and normal load. For the operating conditions tested in this research the simulation results using the proposed model show an improvement over traditional terramechanic models for capturing the dynamic effects of grousers.     

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.     

Effect of circumferential angle, lug spacing and slip on lug wheel forces

This study was conducted to investigate the effect of circumferential angle, lug spacing and wheel slip on forces produced by a cage wheel. Experiments were conducted in a laboratory soil bin having Bangkok Clay soil with 51% (d.b.) soil moisture content. Six ring-type loadcells were used to measure the soil horizontal, vertical and transverse reactions on the cage wheel lugs. The circumferential angle was varied from 0, 15, 30 to 45°. The lug spacing and wheel slip were varied from 20, 30 to 40° and 20, 35 to 50% respectively. All the force measurements were done at a constant 7 cm sinkage. The results showed that increasing circumferntial angle up to 45° can reduce variation in lug wheel forces, at the same time it had little effect on the mean pull and lift values. The side force was affected by the changes of circumferential angle. The 20° lug spacing not only gave the minimum variations but also maximum mean lug forces. The highest lug wheel forces occurred at 35% wheel slip.     

Statistical models for predicting compaction generated by off-road vehicular traffic in different soil types

The behaviour of soils under a vehicle wheel was determined by measuring the density, moisture content, and the position of the data point. From the several thousands of data points, statistical models were established for dry density in terms of external pressure, moisture content, and position. The effect of slip was also obtained at the required situations. Separate models were determined for sand, sandy loam, loamy sand, and clay. For every soil type, there exists an optimum moisture content for worst compaction. Considering this, models were obtained for various categories.     

Shape effects of wheel grousers on traction performance on sandy terrain

This paper presents the effects of different wheel grouser shapes on the traction performance of a grouser wheel traveling on sandy terrain. Grouser wheels are locomotion gears that allow small and lightweight exploration rovers to traverse on the loose sand on extraterrestrial surfaces. Although various grouser shapes have been analyzed by some research groups, a more synthetic and direct comparison of possible grousers is required for practical applications. In this study, we developed a single wheel testbed and experimentally investigated the effects of four grouser shapes (parallel, slanted, V-shaped, and offset V-shaped) on the traction performance of linear movement on flat sand. The wheel slip, sinkage, traction and side force acting on the wheel axle, the wheel driving torque, and the efficiency of each wheel were examined. Thereafter, the effects on the lateral slope traversability of a small and lightweight four-wheeled rover with different grouser shapes were also examined. The traversability experiment demonstrated the vehicle mobility performance in order to contribute to the design optimization of rover systems. These experimental results and their comparisons suggested that, of the shapes studies herein, the slanted shape was the optimal grouser design for use in wheeled rovers on lunar and planetary soil.     

Tractive performance of a driven rigid wheel on soft ground based on the analysis of soil-wheel interaction

A new analytical method has been presented to predict the tractive performance of a rigid wheel running on soft ground. The resultant stress of the normal stress and the shear resistance applied around the peripherical contact part of the rigid wheel should be calculated by use of the dynamic pressure-sinkage curve measured from the plate loading and unloading test, considering the rolling locus of the wheel in the direction of the external resultant force of the effective driving force and the axle load. The effective driving force could be calculated as the difference of the driving force, i.e. the integration of shear resistance and the locomotion resistance calculated from the total amount of sinkage. As a result, the analytical relations between the driving force, the effective driving force and the slip ratio, the amount of sinkage and the slip ratio, the amount of eccentricity of resultant force and the slip ratio, and the entry angle, the exit angle and the slip ratio could be verified experimentally.     

Prediction of wheel-soil interaction and performance using the finite element method

In this experimental-analytical study of wheel-soil interaction, a technique based on the finite element method is used for predicting continuous wheel performance and subsoil response behaviour. The evaluation of wheel-soil interaction performance at any degree of slip is performed using energy principles. The analytical technique utilizes experimentally determined wheel-soil particle path as displacement input for load simulation to predict the soil response beneath the wheel.

An incremental loading approach is adopted to satisfy as closely as possible the soil loading path. The solution requires initial conditions which establish the soil at zero energy level (no stress history) and proceeds to stationary wheel positions with wheel-soil penetration equal to its dynamic sinkage. The method of analysis then proceeds to the steady-state wheel travel mode. The predicted drawbar pulls and subsoil behaviour results are presented and shown to compare well with the experimentally measured values.