Experimental study on wheel-soil interaction mechanics using in-wheel sensor and particle image velocimetry part II. Analysis and modeling of shear stress of lightweight wheeled vehicle

Wheeled vehicle mobility on loose sand is highly subject to shear deformation of sand around the wheel because the shear stress generates traction force of the wheel. The main contribution of this paper is to improve a shear stress model for a lightweight wheeled vehicle on dry sand. This work exploits two experimental approaches, an in-wheel sensor and a particle image velocimetry that precisely measure the shear stress and shear deformation generated at the interaction boundary. Further, the paper improves a shear stress model. The model proposed in this paper considers a force chain generated inside the granular media, boundary friction between the wheel surface and sand, and velocity dependency of the friction. The proposed model is experimentally validated, and its usefulness is confirmed through numerical simulation of the wheel traction force. The simulation result confirmed that the proposed model calculated the traction force with an accuracy about 70%, whereas the conventional one overestimated the force, and its accuracy was 13% at the best.     

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.     

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.     

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.     

Terrain classification using intelligent tire

A wheeled ground robot was designed and built for better understanding of the challenges involved in utilization of accelerometer-based intelligent tires for mobility improvements. Since robot traction forces depend on the surface type and the friction associated with the tire-road interaction, the measured acceleration signals were used for terrain classification and surface characterization. To accomplish this, the robot was instrumented with appropriate sensors (a tri-axial accelerometer attached to the tire innerliner, a single axis accelerometer attached to the robot chassis and wheel speed sensors) and a data acquisition system. Wheel slip was measured accurately using encoders attached to driven and non-driven wheels. A fuzzy logic algorithm was developed and used for terrain classification. This algorithm uses the power of the acceleration signal and wheel slip ratio as inputs and classifies all different surfaces into four main categories; asphalt, concrete, grass, and sand. The performance of the algorithm was evaluated using experimental data and good agreements were observed between the surface types and estimated ones.     

Trafficability analysis of lunar mare terrain by means of the discrete element method for wheeled rover locomotion

An irregularly shaped particulate system for simulation of lunar regolith is developed using discrete element modeling based on the fractal characteristics, particle shape, and size distribution of returned Apollo-14 samples. The model parameters are determined by dimensional analysis and biaxial test simulation with an improved boundary condition. Under terrestrial conditions, the trafficability of lunar mare terrain is estimated in terms of wheel-terrain interaction by experiment and simulation in order to validate the applicability of the wheel-terrain model employed here. The results show that the discrete element method combined with the wheel-terrain model is sufficiently accurate for mare terrain trafficability analysis without consideration of lunar environmental effects. To predict the trafficability of in situ lunar mare terrain, the non-contact forces attributed to the lunar surface environment are discussed and the initial mechanical model of discrete elements is modified by introduction of lunar gravitational force as well as electrostatic force. In the modified model, wheel-terrain interaction is analyzed under the same travel conditions as that of the experiment. The result shows the trafficability of the in situ lunar mare terrain is worse than that obtained by experiment and simulation with the initial model according to the value of horizontal force at any slip ratio. However, the wheel requires less drive torque on the moon than that on the earth. An explanation for these phenomena may be that lunar subsurface regolith particles are arranged in a looser manner under local environmental effects that effectively decrease the bearing and shearing strength of regolith.     

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.     

Torque distribution influence on tractive efficiency and mobility of off-road wheeled vehicles

Off-road vehicle performance is strongly influenced by the tire-terrain interaction mechanism. Soft soil reduces traction and significantly modifies vehicle handling; therefore tire dynamics plays a strong role in off-road mobility evaluation and needs to be addressed with ad-hoc models. Starting from a semi-empirical tire model based on Bekker–Wong theory, this paper, analyzes the performance of a large four wheeled vehicle driving on deformable terrain. A 14 degree of freedom vehicle model is implemented in order to investigate the influence of torque distribution on tractive efficiency through the simulation of front, rear, and all wheel drive configuration. Results show that optimal performance, regardless vertical load distribution, is achieved when torque is biased toward the rear axle. This suggests that it is possible to improve tractive efficiency without sacrificing traction and mobility. Vehicle motion is simulated over dry sand, moist loam, flat terrain and inclined terrain.     

Design of manned lunar rover wheels and improvement in soil mechanics formulas for elastic wheels in consideration of deformation

Most of the current lunar rover vehicle wheels are inconvenient for changing broken wheels and have poor shock absorbing in driving, so they cannot be used to carry people on the moon. To meet the demands for manned lunar transportation, a new wheel possessing a woven metal wire mesh tire and using hub-rim combination slide mechanism is designed in this article. The characteristics of the new wheel is analyzed by comparing with the same-size conventional rover wheels after demonstrating the validity of FEM simulation. The new wheel possesses lighter structure and superior shock absorbing. It also provides stronger traction because the deformation of the designed wheel increases the contact area between the tire and lunar terrain. In order to establish an on-line soil parameter estimation algorithm for low cohesion soil, the stress distribution along a driven deformable wheel on off-road terrain is simplified. The basic mechanics equations of the interaction between the wheel and the lunar soil can be used for analytical analysis. Simulation results show that the soil estimation algorithm can accurately and efficiently identify key soil parameters for loose sand.     

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.     

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.     

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.     

Estimation of net traction for differential-steered wheeled robots

We present a method for estimating the net traction and resistive wheel torques for a suspensionless, differential-steered robot on rigid or deformable terrain. The method, based on extended Kalman-Bucy filtering (EKBF), determines time histories of net traction and resistive wheel torques and wheel slips during steady or transient maneuvers. This method assumes good knowledge of the vehicle dynamics and treats the unknown forces and moments due to terrain response as random variables to be estimated. A proprioceptive sensor suite renders a subset of the unknown forces and associated wheel slip and slip angles observable. This methodology decouples semi-empirical terramechanics models from the net effect of the vehicle-terrain interaction, namely the net traction developed by the vehicle on the terrain. By collecting sensor data and processing data off-line, force-slip characteristics are identified irrespective of the underlying terramechanics. These characteristics can in turn support development or validation of terramechanics models for the vehicle-terrain system. For autonomous robots, real-time estimates of force-slip characteristics can provide setpoints for traction and steering control, increasing vehicle performance, speed, and maneuverability. Finally, force-slip estimation is the first step in identifying terrain parameters during normal maneuvering. The methodology is demonstrated through both simulation and physical testing using a 13-kg robot.     

Improvement of traction performance and off-road mobility for a vehicle with four individual electric motors: Driving over icy road

To control speed and wheel slip for severe conditions of tire-surface interaction is a challenging task in the design of traction control system for electric vehicles with off-road capability. In this regard, the present paper focuses on a specific traction control for an electric vehicle with four individual in-wheel motors over icy road. The study demonstrates that a proper integration of the speed controller and wheel slip controller can essentially improve the mobility of the vehicle in the cases of acceleration and slope climbing. The paper discusses relevant case studies with particular attention given to the system architecture (sliding mode and PID control methods), extremum-seeking algorithm for maximum tire-road friction and corresponding slip value, and experimental validation of the tire model used in the controller with the help of the Terramechanics Rig in the Advanced Vehicle Dynamics Laboratory (AVDL) at Virginia Polytechnic Institute and State University.     

Analysis of a resistance force for the locked-wheel of push-pull locomotion rovers using large subsidence

This paper provides a quantitative analysis of the resistance force of the locked-wheel for push-pull locomotion rovers using intentional sinkage. Our previous study has confirmed that push-pull locomotion using intentional subsidence at an initial position can contribute to improving the traveling performance. The key factor of this scheme is the resistance force of the locked-wheel. However, the resistance force at different sinkage conditions and wheel sizes (e.g., mass, width, and diameter) remains unclear, especially for the individual locked-wheel. The detailed investigation of this interaction can contribute to the accurate estimation of rover mobility. This paper, therefore, investigates the locked-wheel and soil interaction at different sinkage conditions experimentally, especially focusing on the intentional sinkage condition. Additionally, the resistance force is considered theoretically through the knowledge based on the soil flow patterns beneath the locked-wheel. The experimental results confirmed that the resistance force of the locked-wheel rose as the initial sinkage, wheel size, and weight increases. Furthermore, the theoretical calculation suggested the resistance force increased with a similar tendency of the experimental data.     

Design and development of a new transformable wheel used in amphibious all-terrain vehicles (A-ATV)

Conventional ground-wheeled vehicles usually have poor trafficability, low efficiency, a large amount of energy consumption and possible failure when driving on soft terrain. To solve this problem, this paper presents a new design of transformable wheels for use in an amphibious all-terrain vehicle. The wheel has two extreme working statuses: unfolded walking-wheel and folded rigid wheel. Furthermore, the kinematic characteristics of the transformable wheel were studied using a kinematic method. When the wheel is unfolded at walking-wheel status, the displacement, velocity and acceleration of the wheel with different slip rates were analyzed. The stress condition is studied by using a classic soil mechanics method when the transformable wheel is driven on soft terrain. The relationship among wheel traction, wheel parameters and soil deformation under the stress were obtained. The results show that both the wheel traction and trafficability can be improved by using the proposed transformable wheel. Finally, a finite element model is established based on the vehicle terramechanics, and the interaction result between the transformable wheel and elastic–plastic soil is simulated when the transformable wheel is driven at different unfold angles. The simulation results are consistent with the theoretical analysis, which verifies the applicability and effectiveness of the transformable wheel developed in this paper.     

Measurement and modeling for two-dimensional normal stress distribution of wheel on loose soil

On the Moon or Mars, typical target environments for exploration rovers are covered with fine sand, so their wheels easily slip on such weak ground. When wheel slippage occurs, it is hard for the rover to follow its desired route. In the worst case, the rover gets stuck in loose soil and cannot move anymore. To reduce the risk of the rover getting stuck, analysis of the contact mechanics between the soil and wheel is important. Various normal stress distribution models for under the wheel surface have been proposed so far. However, classical models assume a uniform stress distribution in the wheel’s width direction. In this study, we measured the two-dimensional normal stress distribution of a wheel in experiments. The results clarified that the stress distribution in the wheel’s width direction is a mountain-shape curve with a peak located at the center of the wheel. Based on the results, we constructed a stress distribution model for the wheel’s width direction. In this paper, we report our measurements for the two-dimensional stress distribution of a wheel on loose soil and introduce our stress distribution model for the wheel’s width direction based on our experimental results.     

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.     

On the impact of cargo weight, vehicle parameters, and terrain characteristics on the prediction of traction for off-road vehicles

A realistic prediction of the traction capacity of vehicles operating in off-road conditions must account for stochastic variations in the system itself, as well as in the operational environment. Moreover, for mobility studies of wheeled vehicles on deformable soil, the selection of the tire model used in the simulation influences the degree of confidence in the output. Since the same vehicle may carry various loads at different times, it is also of interest to analyze the impact of cargo weight on the vehicle’s traction.This study focuses on the development of an algorithm to calculate the tractive capacity of an off-road vehicle with stochastic vehicle parameters (such as suspension stiffness, suspension damping coefficient, tire stiffness, and tire inflation pressure), operating on soft soil with an uncertain level of moisture, and on a terrain topology that induces rapidly changing external excitations on the vehicle. The analysis of the vehicle–soil dynamics is performed for light cargo and heavy cargo scenarios. The algorithm relies on the comparison of the ground pressure and the calculated critical pressure to decide if the tire can be approximated as a rigid wheel or if it should be modeled as a flexible wheel. It also involves using previously-developed vehicle and stochastic terrain models, and computing the vehicle sinkage, resistance force, tractive force, drawbar pull, and tractive torque.The vehicle model used as a case study has seven degrees of freedom. Each of the four suspension systems is comprised of a nonlinear spring and a viscous (linear or magneto-rheological) damper. An off-road terrain profile is simulated as a 2-D random process using a polynomial chaos approach [Sandu C, Sandu A, Li L. Stochastic modeling of terrain profiles and soil parameters. SAE 2005 transactions. J Commer Vehicles 2005-01-3559]. The soil modeling is concerned with the efficient treatment of the impact of the moisture content on relationships critical in defining the mobility of an off-road vehicle (such as the pressure–sinkage [Sandu C et al., 2005-01-3559] and the shear stress–shear displacement relations). The uncertainties in vehicle parameters and in the terrain profile are propagated through the vehicle model, and the uncertainty in the output of the vehicle model is analyzed [Sandu A, Sandu C, Ahmadian M. Modeling multibody dynamic systems with uncertainties. Part I: theoretical and computational aspects, Multibody system dynamics. Publisher: Springer Netherlands; June 29, 2006. p. 1–23 (23), ISSN: 1384-5640 (Paper) 1573-272X (Online). doi:10.1007/s11044-006-9007-5; Sandu C, Sandu A, Ahmadian M. Modeling multibody dynamic systems with uncertainties. Part II: numerical applications. Multibody system dynamics, vol. 15, No. 3. Publisher: Springer Netherlands; 2006. p. 241–62 (22). ISSN: 1384-5640 (Paper) 1573-272X (Online). doi:10.1007/s11044-006-9008-4]. Such simulations can provide the basis for the study of ride performance, handling, and mobility of the vehicle in rough off-road conditions.