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.     

Discrete element method-based studies on dynamic interactions of a lugged wheel with granular media

Terramechanics plays an important role in determining the design and control of autonomous robots and other vehicles that move on granular surfaces. Traction capabilities, slippage, and sinkage of a robot are governed by the interaction of a robot’s appendage with the operating terrain. It is important to understand how the terrain flows under this appendage during such an interaction. In this work, dynamics of soil performance and locomotion performance of a lugged wheel travelling on soft soil are numerically investigated. Studies are conducted with a two-dimensional model by using the discrete element method to analyze the interactions between a lugged wheel and the soil. The soil performance is studied by examining the force distribution and evolution of force networks during the course of the wheel travel. For two different control modes, namely, slip-based wheel control and angular velocity-based wheel control, the performance parameters such as, sinkage, traction, traction efficiency, and power consumption of the wheel are compared for various wheel configurations. The findings of this work are expected to be useful for optimal design and control of the lugged wheel travelling on deformable surfaces.     

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.     

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.     

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.     

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.     

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.     

Mobility performance of a rigid wheel in low gravity environments

To investigate influences of gravity on mobility of wheeled rovers for future lunar/planetary exploration missions, model experiments of a soil-wheel system were performed on an aircraft during variable gravity maneuvers. The experimental set-up consists of a single rigid wheel and a soil bed with two kinds of dry sands: lunar soil simulant and Toyoura sand. The experimental results revealed that a lower gravity environment yields higher wheel slippage in variable gravity conditions. In addition to the partial gravity experiments, the same experiments with variable wheel load levels were also performed on ground (1 g conditions). The on-ground experiments produced opposite results to those obtained in the partial gravity experiments, where a lower wheel load yields lower slippage in a constant gravity environment. In low gravity environments, fluidity (flowability) of soil increases due to the confining stress reduction in the soil, while the effect of the wheel load on sinkage decreases. As a result, both of these effects are canceled out, and gravity seemingly has no effect on the wheel sinkage. In the meantime, in addition to the effect of wheel load reduction, the increase of the soil flowability lessens the shear resistance to the wheel rotation, as a result of which the wheel is unable to hold sufficient traction in low gravity environments. This suggests that the mobility of the wheel is governed concurrently by two mechanisms: the bearing characteristics to the wheel load, and the shearing characteristics to the wheel rotation. It appears that, in low gravity, the wheel mobility deteriorates due to the relative decrease in the driving force while the wheel sinkage remains constant. Thus, it can be concluded that the lunar and/or Mars’ gravity environments will be unfavorable in terms of the mobility performance of wheels as compared to the earth’s gravity condition.     

Modeling wheel-induced rutting in soils: Indentation

The analysis of indentation of rigid cylindrical wheels into frictional/cohesive soils is presented. Three- and two-dimensional numerical simulations were performed using the finite element code ABAQUS to assess the influence of soil strength parameters, dilatancy, and wheel geometry on the relationship between the indentation force and wheel sinkage. The effect of three-dimensionality in the indentation process is studied in detail. Three-dimensional effects were found to be minor for clays though significant for sands. An approximate analytic approach is also presented, which relates indentation force and wheel sinkage for given wheel geometry and material parameters. Theoretical results are compared with preliminary experimental data obtained from small-scale indentation tests, and satisfactory qualitative agreement is shown. The results described in the paper are regarded as reference for numerical and analytic modeling of wheel rolling, to be presented in a separate paper.     

The development of a soil trafficability model for legged vehicles on granular soils

This paper extends previous research in planetary microrover locomotion system analysis at the University of Surrey through the development of a legged microrover mobility model. This model compares various two- and three-dimensional soil cutting models to determine the most applicable model to legged locomotion in deformable soils, and is flexible to use any of these models depending on the leg shape, sinkage and other conditions. This baseline draught force model is used for determining the soil forces available for legged vehicle locomotion, as well as the soil thrust available to the vehicle footprint. Empirical investigations were performed with a robotic arm in planetary soil simulants to validate a legged mobility model through determination of the draft force of a robotic leg pushing through soil at constant and varying sinkage levels. The resulting locomotion performance model will be used to predict the ability of the legged vehicle to traverse a specific soil. An introduction to the planetary soil simulants used in this study (SSC-1 quartz-based sand and SSC-2 garnet-based sand) and the process used to determine their mechanical properties is also briefly presented to provide a baseline for this research.     

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.     

Experimental validation of distinct element simulation for dynamic wheel–soil interaction

The deformation behaviour of the soil during dynamic wheel–soil interaction was studied by using the discontinuum modelling technique, distinct or discrete element method (DEM). The simulation model was developed using DEM for two types of soil, soil-A (coarse sand) and soil-B (medium sand). A transparent sided soil bin was used to observe the soil deformation. Three CCD video camera photographic images of the validation experiments were analyzed and compared with the simulation program results.This paper presents the simulation and validation results for two types of soil at three different vertical loadings of 4.9, 9.8 and 14.7 N. Wheel sinkage, vertical and horizontal draft force acting on the rigid wheel and the soil deformation images from the validation experiments were some of the data used to compare the simulation program results with the validation experiments. The simulation program was helpful to understand the complex deformation behaviour of the soils. The simulated results for the deformation behaviour of soil-B showed better correlation with the validation experiments than soil-A. The results obtained have also been compared with the previous work on DEM to explain phenomena such as the high simulated sinkage of the rigid wheel.     

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.     

Performance evaluation of a wire mesh wheel on deformable terrains

Because of the unique lunar environment, a suitable wheel for lunar rover decides the rover’s trafficability on deformable terrains. The wire mesh wheel (hereinafter referred to as WMW) has the advantages of light weight and superior stability, been widely adopted for lunar rovers. But a comprehensive research on performance of WMW on deformable terrains has not been conduct. This paper would provide particular study on a type WMW, including quasi-static pressure-sinkage test and driving performance. A novel pressure-sinkage model for the WMW on deformable soils was presented. In order to investigate the sinkage characteristics of the WMW, tests were performed using a single-wheel testbed for the WMW with different loads and velocities. The effects of load and velocity on sinkage were analyzed, and the relationship between real and apparent sinkage was presented. The research on traction performance of WMW under different slip ratios (0.1–0.6) was also conducted, contrast tests were proceed by using a normal cylindrical wheel (hereinafter referred to as CW). The traction performance of WMW is analyzed using performance indices including wheel sinkage, drawbar pull, driving torque, and tractive efficiency. The experimental results and conclusions are useful for optimal WMW design and improvement/verification of wheel–soil interaction mechanics model.     

Grousers improve drawbar pull by reducing resistance and generating thrust at the front of a wheel

Grousers are commonly used to increase wheel traction, though how grousers exactly influence wheel thrust and resistance, and thus drawbar pull, has continued to remain an open topic of research. This work explores rigid wheels with grousers traveling on homogeneous granular soil. Unique experiments that provide insights into what grousers are doing at various points on a wheel are presented. To perform these experiments, a novel wheel that enables grousers to extend and retract in various regions around the wheel is developed; specifically grousers can always be extended at the front of the wheel but retracted below the wheel, even as the wheel rotates. These experiments show that grousers are much more effective at increasing drawbar pull when they are interacting with soil ahead of the wheel, rather than below it. A wheel with grousers engaging soil only ahead of the wheel, and not below it, nonetheless achieves over 80% of the relative improvement in drawbar pull that a “full grouser” wheel achieves over a grouserless wheel. This reveals how thrust is generated primarily by the front-most grouser, and further suggests that the reduction of resistive forward soil flow also plays a key role in increasing drawbar pull.     

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.     

A novel rigid wheel for agricultural machinery applicable to paddy field with muddy soil

The working performance of agricultural machinery is largely determined by the walking performance of the wheel when driving in complex unstructured soil. However, the driving performance of existing wheels is not satisfactory for paddy field with muddy soil. The purpose of the current study is therefore to propose a novel rigid wheel for agricultural machinery which is applicable to paddy field with muddy soil. Firstly, a novel arc edge shaped wheel was designed based on the principles of mechanics on the ground. Then the driving performance of this arc edge shaped wheel was evaluated using FE modeling of interaction between rigid wheel and soil. Finally, the structure originally designed arc edge shaped wheel was improved according to FE modeling results, and this improved design was further evaluated by both FE simulation and prototype experiments. Both FE modeling and experimental results indicate that the improved arc edge shaped wheel proposed in this study has a good driving performance with regarding to wheel sinkage and soil reaction force. The proposed arc edge shaped wheel could be used as an effective component of rice harvester for paddy field with muddy soil.     

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.     

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.     

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.