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.     

Some recent developments in vehicle—terrain interaction studies

This report presents a review of recent developments in the study of vehicle3-terrain interaction, based primarily on papers included in Session 2A of the 10th International Conference of ISTVS. Analytical studies of wheel-soil interaction using visco-elastic soil models and elasto-plastic and rigid-plastic finite element methods are reviewed. Results of experimental investigations of stress distributions on the wheel-soil interface as well as in the soil under various loading conditions are summarized. Various methods for predicting off-road vehicle performance are examined.     

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.     

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.     

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.     

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.     

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.     

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.     

Analysis and prediction of tyre-soil interaction and performance using finite elements

The finite element method [FEM] of analysis previously developed for prediction of rigid wheel-soil interaction is improved and extended to take into account (a) the effect of flexibility of tyre carcass where energy losses now occur in development of mobility, (b) a simpler requirement for specification of boundary condition using input loading, and (c) normal and tangential load stress from the tyre distributed across the tyre-soil interface and varying with slip. The comparisons of analytically computed (predicted) drawbar pull with actual experimentally obtained drawbar pull results for tests in three types of tyres show good correlations. The effect of inflation pressure on development of tyre deformation energy losses can be seen from the analytically computed values.     

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.     

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.     

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.     

Wheels' performance of Mars exploration rovers: Experimental study from the perspective of terramechanics and structural mechanics

The soft ground and stones on the surface of Mars may cause sinkage of and damage to the wheels of a Mars rover. Therefore, we analyzed the performance of a wheel-step Mars rover from the perspective of terramechanics and structural mechanics. Using China’s Mars rover wheel prototype and wheel-soil interaction testbed, we obtained the driving performance of the wheels of a Mars rover under various conditions, including full skidding conditions. The vertical load set in the tests was determined using the gravity of Mars and the mass of the wheel-step Mars rover. The results indicate that the driving torque, sinkage, and resistance coefficient have a linear relationship with the wheel vertical load. An analysis of the structural mechanical characteristics of the wheel of the Mars rover was conducted by testing the radial, axial, torsional, and deflection stiffness. We found that the wheel ribs can improve the stiffness of the wheel but may reduce its driving performance. The analysis methods and evaluation indices can be used to analyze the performance of the wheels of other Mars rovers. Furthermore, the findings of this study can be used to optimize wheel design and motion control of wheel-step Mars exploration rovers.     

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.     

Identification of the shear parameters for lunar regolith based on a GA-BP neural network

Identifying the mechanical parameters of lunar soil through the rover’s wheel can provide the basic data for path planning, risk avoidance, and traction control. In this paper, the shear parameters of lunar soil are identified by a Back Propagation neural network optimized by Genetic Algorithm (GA-BP) based on a simplified wheel-soil model. For the GA-BP identified model, the input data are driving torque (T), vertical load (W) and slip ratio (s) of the wheel. The output data are internal friction angle (φ) and shear deformation modulus (K). A total of 315 sets of data are used to train GA-BP and BP algorithms. Data from single-wheel soil bin test are put into the trained algorithms to identify φ and K of lunar soil simulant. The test results demonstrate that GA-BP algorithm is accurate and effect to identify shear parameters of regolith online. The comparison between identified results and test results shows that the GA-BP algorithm is better than the BP algorithm. The cohesion is set to 1.5 kPa and then the drawbar pull is predicted according to the identified φ and K of GA-BP. The test results show that the prediction of DP is reasonable.     

可压缩空间发展混合层亚谐扰动作用分析

基于线性稳定性理论,建立了可压缩空间发展混合层亚谐扰动作用的唯象分析图,用以分析并判定亚谐扰动相差对基频涡卷非线性演化类型的影响,据此导出了基频涡卷各类非线性演化的定量的相差唯象模型. 研究发现,当亚谐扰动波长较小时,对于单一亚谐扰动,基频涡卷的演化类型共4 类,分别是撕裂、中心对称群并、第1 类非对称群并和第2 类非对称群并现象. 撕裂与中心对称群并为特殊现象,对应特定的相差点;非对称群并为常见现象,对应除这些相差点之外的相差区间. 当亚谐扰动波长较大时,由于扰动幅值随空间指数增长,只存在非对称群并现象.      

可压缩空间发展混合层亚谐扰动作用分析简

基于线性稳定性理论,建立了可压缩空间发展混合层亚谐扰动作用的唯象分析图,用以分析并判定亚谐扰动相差对基频涡卷非线性演化类型的影响,据此导出了基频涡卷各类非线性演化的定量的相差唯象模型. 研究发现,当亚谐扰动波长较小时,对于单一亚谐扰动,基频涡卷的演化类型共4 类,分别是撕裂、中心对称群并、第1 类非对称群并和第2 类非对称群并现象. 撕裂与中心对称群并为特殊现象,对应特定的相差点;非对称群并为常见现象,对应除这些相差点之外的相差区间. 当亚谐扰动波长较大时,由于扰动幅值随空间指数增长,只存在非对称群并现象.     

The reinforcement and defect interaction of two-dimensional lattice materials with imperfections

The defect interaction and reinforcement of imperfect two-dimensional lattice materials are studied by theoretical investigations and finite element (FE) simulations. An analytical model is proposed to predict the interaction of two defects in lattice materials based on a single defect model. An interaction coefficient is introduced to characterize the degree of interaction. The effects of defect type and defect distance on interaction coefficients are studied. The critical interaction distance of defects, beyond which the interaction of two defects can be neglected, is derived. FE calculations are performed to validate the theoretical model. The simulated results indicate that increasing the number of defects can reduce the stress concentration rather than weakening the strength of the residual parts in certain circumstances. Subsequently, several reinforcement methods are proposed to reduce the stress concentration in the triangular and Kagome lattice for the single-bar-missing defect and single-joint-missing defect. An analytical model is developed for the reinforced lattices, and the predicted stress concentration factors are in good agreement with those of FE simulations. By theoretical studies and FE simulations, optimal reinforcement methods are derived for the triangular and Kagome lattice under planar loading conditions.     

Three reasons for freak wave generation in the non-uniform current

Three reasons for freak wave generation due to interaction of wave with spatially non-uniform current are considered in the paper. They are as follows: wave energy amplification due to wave-current interaction; wave height amplification around caustic due to refraction wave in non-uniform current; non-linear wave interaction in shallow water due to their intersection described by the Kadomtsev–Petviashvili equation. These mechanisms can generate a large wave amplification producing a dangerous natural phenomenon.     

Interaction of a streamwise vortex with the normal shock

Interaction of a supersonic streamwise vortex with the normal shock is considered. Two interaction modes (weak and strong interaction) are identified. It is demonstrated numerically that strong interaction can lead to vortex breakdown.