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.     

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.     

On the study of wheel-soil interaction

This paper presents a review of recent advancements in the study of wheel-soil interaction, based primarily on the papers submitted to the Eighth International Conference of ISTVS. Various methods of approach to the analysis of wheel-soil interaction are examined and their applications are discussed.     

Experimental study on wheel-soil interaction mechanics using in-wheel sensor and particle image velocimetry Part I: Analysis and modeling of normal stress of lightweight wheeled vehicles

This study aims to develop a wheel-soil interaction model for a lightweight wheeled vehicle by measuring the normal stress distribution beneath the wheel. The main contribution of this work is to clarify the wheel-soil interaction using a wheel testbed that equips multiple sensory systems. An in-wheel sensor accurately measures the normal stress distribution as well as the contact angles of the wheel. Particle image velocimetry with a standard off-the-shelf camera analyzes soil flow beneath the wheel. The proposed model for the normal stress distribution is formulated based on these experimental data and takes into account the following phenomena for the lightweight vehicles that have not been considered in the classical model: (1) the normal stress distribution takes the form of a Gaussian curve; (2) the normal stress distribution concentrates in the front region of the wheel contact patch; (3) the distribution is divided into two areas with the boundary determined by the maximum normal stress angle; and (4) the maximum normal stress exponentially decreases as the slip ratio increases. Then, the proposed model is experimentally validated. Furthermore, a simulation study for the wheel driving characteristics using the proposed model confirms the accuracy of the proposed model.     

Experimental study and analysis on driving wheels’ performance for planetary exploration rovers moving in deformable soil

Planetary rovers are different from conventional terrestrial vehicles in many respects, making it necessary to investigate the terramechanics with a particular focus on them, which is a hot research topic at the budding stage. Predicting the wheel-soil interaction performance from the knowledge of terramechanics is of great importance to the mechanical design/evaluation/optimization, dynamics simulation, soil parameter identification, and control of planetary rovers. In this study, experiments were performed using a single-wheel testbed for wheels with different radii (135 and 157.35 mm), widths (110 and 165 mm), lug heights (0, 5, 10, and 15 mm), numbers of lugs (30, 24, 15, and 8), and lug inclination angles (0°, 5°, 10°, and 20°) under different slip ratios (0, 0.1, 0.2, 0.3, 0.4, 0.6, etc.). The influences of the vertical load (30 N, 80 N, and 150 N), moving velocity (10, 25, 40, and 55 mm/s), and repetitive passing (four times) were also studied. Experimental results shown with figures and tables and are analyzed to evaluate the wheels’ driving performance in deformable soil and to draw conclusions. The driving performance of wheels is analyzed using absolute performance indices such as drawbar pull, driving torque, and wheel sinkage and also using relative indices such as the drawbar pull coefficient, tractive efficiency, and entrance angle. The experimental results and conclusions are useful for optimal wheel design and improvement/verification of wheel-soil interaction mechanics model. The analysis methods used in this paper, such as those considering the relationships among the relative indices, can be referred to for analyzing the performance of wheels of other vehicles.     

Prediction of wheel performance by analysis of normal and tengential stress distributions under the wheel-soil interface

Prediction of wheel performance by analysis of normal stress distribution under the wheel-soil interface was reported by one of our research members. In this study analysis of both normal and tangential stress distributions are included for the prediction of wheel performance. A visco-elastic soil model based on a three-element Maxwell model is used to evaluate normal stress distribution under a wheel running on soft ground. The values of the parameters characterizing the visco-elastic behavior of the soil can be derived from plate penetration tests. A rigid wheel-soil interface model is used to evaluate the tangential stress distribution under the wheel-soil interface. Shear deformation modulus, cohesion and angle of internal shearing resistance of the soil are derived from shear-displacement tests. Test results indicate that both maximum normal and shear stress occur in front of the wheel axle, and the location of peak normal stress shifts backwards towards the wheel axle while that of tangential stress shifts forwards when slippage is increased from a low value. Increasing slippage also causes a decrease in normal stress and an increase in tangential stress. Coefficients of traction and tractive efficiency are low at low slippage, increase with an increase in slippage, and level off at higher slippage.     

Discrete element modelling for wheel-soil interaction and the analysis of the effect of gravity

The discrete element method (DEM) is widely seen as one of the more accurate, albeit more computationally demanding approaches for terramechanics modelling. Part of its appeal is its explicit consideration of gravity in the formulation, making it easily applicable to the study of soil in reduced gravity environments. The parallel particles (P²) approach to terramechanics modelling is an alternate approach to traditional DEM that is computationally more efficient at the cost of some assumptions. Thus far, this method has mostly been applied to soil excavation maneuvers. The goal of this work is to implement and validate the P² approach on a single wheel driving over soil in order to evaluate the applicability of the method to the study of wheel-soil interaction. In particular, the work studies how well the method captures the effect of gravity on wheel-soil behaviour. This was done by building a model and first tuning numerical simulation parameters to determine the critical simulation frequency required for stable simulation behaviour and then tuning the physical simulation parameters to obtain physically accurate results. The former were tuned via the convergence of particle settling energy plots for various frequencies. The latter were tuned via comparison to drawbar pull and wheel sinkage data collected from experiments carried out on a single wheel testbed with a martian soil simulant in a reduced gravity environment. Sensitivity of the simulation to model parameters was also analyzed. Simulations produced promising data when compared to experiments as far as predicting experimentally observable trends in drawbar pull and sinkage, but also showed limitations in predicting the exact numerical values of the measured forces.     

Linear normal stress under a wheel in skid for wheeled mobile robots running on sandy terrain

Wheeled mobile robots are often used on high risk rough terrain. Sandy terrains are widely distributed and tough to traverse. To successfully deploy a robot in sandy environment, wheel-terrain interaction mechanics in skid should be considered. The normal and shear stress is the basis of wheel-soil interaction modeling, but the normal stress in the rear region on the contact surface is computed through symmetry in classical terramechanics equations. To calculate that directly, a new reference of wheel sinkage is proposed. Based on the new reference, both the wheel sinakge and the normal stress can be given using a quadratic equation as the function of wheel-soil contact angle. Moreover, the normal stress can be expressed as a linear function of the wheel sinkage by introducing a constant coefficient named as sand stiffness in this paper. The linearity is demonstrated by the experimental data obtained using two wheels and on two types of sands. The sand stiffness can be estimated with high accuracy and it decreases with the increase of skid ratio due to the skid-sinkage phenomenon, but increases with the increase of vertical load. Furthermore, the sand stiffness can be utilized directly to compare the stiffness of various sandy terrains.     

Soft soil track interaction modeling in single rigid body tracked vehicle models

Single rigid body models are often used for fast simulation of tracked vehicle dynamics on soft soils. Modeling of soil-track interaction forces is the key modeling aspect here. Accuracy of the soil-track interaction model depends on calculation of soil deformation in track contact patch and modeling of soil resistive response to this deformation. An algorithmic method to calculate soft soil deformation at points in track contact patch, during spatial motion simulation using single body models of tracked vehicles, is discussed here. Improved calculations of shear displacement distribution in the track contact patch compared to existing methods, and realistically modeling plastically deformable nature of soil in the sinkage direction in single body modeling of tracked vehicle, are the novel contributions of this paper. Results of spatial motion simulation from a single body model using the proposed method and from a higher degree of freedom multibody model are compared for motion over flat and uneven terrains. Single body modeling of tracked vehicle using the proposed method affords quicker results with sufficient accuracy when compared to those obtained from the multibody model.     

Experimental and DEM analyses on wheel-soil interaction

In this paper, the wheel-soil interaction for a future lunar exploration mission is investigated by physical model tests and numerical simulations. Firstly, a series of physical model tests was conducted using the TJ-1 lunar soil simulant with various driving conditions, wheel configurations and ground void ratios. Then the corresponding numerical simulations were performed in a terrestrial environment using the Distinct Element Method (DEM) with a new contact model for lunar soil, where the rolling resistance and van der Waals force were implemented. In addition, DEM simulations in an extraterrestrial (lunar) environment were performed. The results indicate that tractive efficiency does not depend on wheel rotational velocity, but decreases with increasing extra vertical load on the wheel and ground void ratio. Rover performance improves when wheels are equipped with lugs. The DEM simulations in terrestrial environment can qualitatively reproduce the soil deformation pattern as observed in the physical model tests. The variations of traction efficiency against the driving condition, wheel configuration and ground void ratio attained in the DEM simulations match the experimental observations qualitatively. Moreover, the wheel track is found to be less evident and the tractive efficiency is higher in the extraterrestrial environment compared to the performance on Earth.     

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.     

Effect of wheel loads on the elevated roads between retaining structures

Deformations and stresses in a saturated soil between two retaining structures under wheel loads are analyzed. The problem has a practical importance especially in case of elevated roads. Expressions are given in graphical forms for one, two and four point loads which are representation of one and two vehicles with different axle lengths. Results provide information of predict contacting stresses at the wheel-soil interface and lateral pressures for design of retaining walls.     

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.     

Finite element modeling of tire/terrain interaction: Application to predicting soil compaction and tire mobility

Tire/terrain interaction has been an important research topic in terramechanics. For off-road vehicle design, good tire mobility and little compaction on terrain are always strongly desired. These two issues were always investigated based on empirical approaches or testing methods. Finite element modeling of tire/terrain interaction seems a good approach, but the capability of the finite element has not well demonstrated. In this paper, the fundamental formulations on modeling soil compaction and tire mobility issues are further introduced. The Drucker-Prager/Cap model implemented in ABAQUS is used to model the soil compaction. A user subroutine for finite strain hyperelasticity model is developed to model nearly incompressible rubber material for tire. In order to predict transient spatial density, large deformation finite element formulation is used to capture the configuration change, which combines with soil elastoplastic model to calculate the transient spatial density due to tire compaction on terrain. Representative simulations are provided to demonstrate how the tire/terrain interaction model can be used to predict soil compaction and tire mobility in the field of terramechanics.     

The influence of the soil stratification on free field traffic-induced vibrations

Summary  This paper deals with the influence of the soil stratification on the free field vibrations generated by the passage of a vehicle on an uneven road. A two-stage solution procedure is applied for the numerical prediction of the free field traffic-induced vibrations. First, a 2D vehicle model is used for the calculation of the axle loads from the longitudinal road profile. Next, the free field response is calculated with the dynamic Betti-Rayleigh reciprocity theorem, using a transfer function between the road and the receiver. The dynamic road-soil interaction problem is solved with a substructure method. The road is modelled as a beam of infinite length, while the boundary element method, based on the Green's functions for a horizontally layered linear elastic halfspace is used for the soil. The influence of the soil stratification is demonstrated by a numerical example where the free field vibrations during the passage of a vehicle on a traffic plateau are calculated. Three different cases are considered for the layering of the soil: a homogeneous halfspace, a layer built in at its base and a layer on a halfspace. Special emphasis goes to the dynamic interaction between the road and the soil. It is demonstrated that the stratification of the soil has a considerable influence on both the peak particle velocity and the frequency content of the free field vibrations. Received 28 November 2000; accepted 24 April 2001     

Terrain-vehicle systems modelling using a multi-body dynamics program

A general purpose vehicle dynamics modelling capability is described. The development of suspension system superelements as standard elements in a general multi-body dynamics program is discussed. Terrain interaction models for wheeled vehicles with deformable tires operating on rigid pavement are described. A track vehicle suspension superelement is also described that includes a loop force element model of tracks and the use of terramechanical relations to describe soil compliance.     

Vehicle vibrating on a soft compacting soil half-space: Ground vibrations, terrain damage, and vehicle vibrations

The point of departure of the present work may be either an interest in vehicle vibrations themselves, or in ground vibrations and terrain damage due to vehicles traveling off-road. The vibrations of a vehicle traversing dry, soft terrain, which is either rough or undulating, may be significantly modified by the dynamic interaction of the vehicle with the soil, particularly due to losses of energy by soil compaction and as elastic waves. The present work provides a prediction methodology for both vehicle and soil vibrations, accounting for the effects mentioned above. An expedient linear method is compared to a rheologically-based non-linear method. In the linear method, the soil compaction is incorporated as a loss factor in the dynamic stiffness of the otherwise elastic half-space; the imaginary part of that dynamic stiffness already includes the effects of wave damping. The non-linear model treats the compaction using a general rheological model for soils exhibiting both viscous and thixotropic effects, and requires iterative solution. A key feature of the latter model is the hypothesis that the stress distribution may be approximately regarded as quasi-static when calculating compaction losses; that approximation is expected to hold at low frequencies, since the P-wavelength in the soil is then much greater than the dimensions of the zone in which most compaction occurs. The methods predict that the soil compaction and excited ground vibrations have maxima at the vehicle bounce and hop resonances, and at high frequencies at which the Rayleigh wavelength approaches the order of the contact patch diameter. Moreover, sufficiently soft, compactable soils, but fully realizable in nature, control the vehicle response at the hop resonance, and possibly also at the bounce resonance.     

A comparison of ground vehicle mobility analysis based on soil moisture time series datasets from WindSat,LIS, and in situ sensors

Soil moisture is a key terrain variable in ground vehicle off-road mobility. Historically, models of the land water balance have been used to estimate soil moisture. Recently, satellites have provided another source of soil moisture estimates that can be used to estimate soil-limited vehicle mobility. In this study, we compared the off-road vehicle mobility estimates based on three soil moisture sources: WindSat (a satellite source), LIS (a computer model source), and in situ ground sensors (to represent ground truth). Mobility of six vehicles, each with different ranges of sensitivity to soil moisture, was examined in three test sites. The results demonstrated that the effect of the soil moisture error on mobility predictions is complex and may produce very significant errors in off-road mobility analysis for certain combinations of vehicles, seasons, and climates. This is because soil moisture biases vary in both direction and magnitude with season and location. Furthermore, vehicles are sensitive to different ranges of soil moistures. Modeled vehicle speeds in the dry time periods were limited by the interaction between soil traction and the vehicles’ powertrain characteristics. In the wet season, differences in soil strength resulted in more significant differences in mobility predictions.     

A high-fidelity approach for vehicle mobility simulation: Nonlinear finite element tires operating on granular material

Assessing the mobility of off-road vehicles is a complex task that most often falls back on semi-empirical approaches to quantifying the vehicle–terrain interaction. Herein, we concentrate on physics-based methodologies for wheeled vehicle mobility that factor in both tire flexibility and terrain deformation within a fully three-dimensional multibody system approach. We represent the tire based on the absolute nodal coordinate formulation (ANCF), a nonlinear finite element approach that captures multi-layered, orthotropic shell elements constrained to the wheel rim. The soil is modeled as a collection of discrete elements that interact through contact, friction, and cohesive forces. The resulting vehicle/tire/terrain interaction problem has several millions of degrees of freedom and is solved in an explicit co-simulation framework, built upon and now available in the open-source multi-physics package Chrono. The co-simulation infrastructure is developed using a Message Passing Interface (MPI) layer for inter-system communication and synchronization, with additional parallelism leveraged through a shared-memory paradigm. The formulation and software framework presented in this investigation are proposed for the analysis of the dynamics of off-road wheeled vehicle mobility. Its application is demonstrated by numerical sensitivity studies on available drawbar pull, terrain resistance, and sinkage with respect to parameters such as tire inflation pressure and soil cohesion. The influence of a rigid tire assumption on mobility is also discussed.