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.     

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.     

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.     

“Wheels vs. tracks” – A fundamental evaluation from the traction perspective

The issue of wheeled vehicles vs. tracked vehicles for off-road operations has been a subject of debate for a long period of time. Recent interest in the development of vehicles for the rapid deployment of armed forces has given a new impetus to this debate. While a number of experimental studies in comparing the performances of specific wheeled vehicles with those of tracked vehicles under selected operating environments have been performed, it appears that relatively little fundamental analysis on this subject has been published in the open literature, including the Journal of Terramechanics. This paper is aimed at evaluating the tractive performance of wheeled and tracked vehicles from the standpoint of the mechanics of vehicle–terrain interaction. The differences between a tire and a track in generating thrust are elucidated. The basic factors that affect the gross traction of wheeled and tracked vehicles are identified. A general comparison of the thrust developed by a multi-axle wheeled vehicle with that of a tracked vehicle is made, based on certain simplifying assumptions. As the interaction between an off-road vehicle and unprepared terrain is very complex, to compare the performance of a wheeled vehicle with that of a tracked vehicle realistically, comprehensive computer simulation models are required. Two computer simulation models, one for wheeled vehicles, known as NWVPM, and the other for tracked vehicles, known as NTVPM, are described. As an example of the applications of these two computer simulation models, the mobility of an 8 × 8 wheeled vehicle, similar to a light armoured vehicle (LAV), is compared with that of a tracked vehicle, similar to an armoured personnel carrier (APC). It is hoped that this study will illustrate the fundamental factors that limit the traction of wheeled vehicles in comparison with that of tracked vehicles, hence contributing to a better understanding of the issue of wheels vs. tracks.     

Stochastic modeling of tire–snow interaction using a polynomial chaos approach

Developing accurate models to simulate the interaction between pneumatic tires and unprepared terrain is a demanding task. Such tire–terrain contact models are often used to analyze the mobility of a wheeled vehicle on a given type of soil, or to predict the vehicle performance under specified operational conditions (as related to the vehicle and tires, as well as to the running support). Due to the complex nature of the interaction between a tire and off-road environment, one usually needs to make simplifying assumptions when modeling such an interaction. It is often assumed that the tire–terrain interaction can be captured using a deterministic approach, which means that one assumes fixed values for several vehicle or tire parameters, and expects exact responses from the system. While this is rarely the case in real life, it is nevertheless a necessary step in the modeling process of a deterministic framework. In reality, the external excitations affecting the system, as well as the values of the vehicle and terrain parameters, do not have fixed values, but vary in time or space. Thus, although a deterministic model may capture the response of the system given one set of deterministic values for the system parameters, inputs, etc., this is in fact only one possible realization of the multitude of responses that could occur in reality. The goal of our study is to develop a mathematically sound methodology to improve the prediction of the tire–snow interaction by considering the variability of snow depth and snow density, which will lead to a significantly better understanding and a more realistic representation of tire–snow interaction. We constructed stochastic snow models using a polynomial chaos approach developed at Virginia Tech, to account for the variability of snow depth and of snow density. The stochastic tire–snow models developed are based on the extension of two representative deterministic tire–snow interaction models developed at the University of Alaska, including the pressure–stress deterministic model and the hybrid (on-road extended for off-road) deterministic model. Case studies of a select combination of uncertainties were conducted to quantify the uncertainties of the interfacial forces, sinkage, entry angle, and the friction ellipses as a function of wheel load, longitudinal slip, and slip angle. The simulation results of the stochastic pressure–stress model and the stochastic hybrid model are compared and analyzed to identify the most convenient tire design stage for which they are more suitable. The computational efficiency of the two models is also discussed.     

Prediction of impacts of wheeled vehicles on terrain

Traffic of off-road vehicles can disturb soil, decrease vegetation development, and increase soil erosion. Terrain impacts caused by wheeled off-road vehicles were studied in this paper. Models were developed to predict terrain impacts caused by wheeled vehicles in terms of disturbed width and impact severity. Disturbed width and impact severity are not only controlled by vehicle types and vehicle dimensions, but also influenced by soil conditions and vehicle dynamic properties (turning radius, velocity). Field tests of an eight-wheeled vehicle and a four-wheeled vehicle were conducted to test these models. Field data of terrain–vehicle interactions in different vehicle dynamic conditions were collected. Vehicle dynamic properties were derived from a global position system (GPS) based tracking system. The average prediction percentage error of the theoretical disturbed width model is less than 20%. The average absolute error between the predicted impact severity and the measured value is less than an impact severity value of 12%. These models can be used to predict terrain impacts caused by off-road wheeled vehicles.     

Off-road tire modeling and the multi-pass effect for vehicle dynamics simulation

Off-road operations are critical in many fields and the complexity of the tire-terrain interaction deeply affects vehicle performance. In this paper, a semi-empirical off-road tire model is discussed. The efforts of several researchers are brought together into a single model able to predict the main features of a tire operating in off-road scenarios by computing drawbar pull, driving torque, lateral force, slip-sinkage phenomenon and the multi-pass behavior. The approach is principally based on works by Wong, Reece, Chan, and Sandu and it is extended in order to catch into a single model the fundamental features of a tire running on soft soil. A thorough discussion of the methodology is conducted in order to highlight strengths and weakness of different implementations. The study considers rigid wheels and flexible tires and analyzes the longitudinal and the lateral dynamics. Being computationally inexpensive a semi-empirical model is attractive for real time vehicle dynamics simulations. To the best knowledge of the authors, current vehicle dynamics codes poorly account for off-road operations where tire-terrain interaction dominates vehicle performance. In this paper two soils are considered: a loose sandy terrain and a firmer loam. Results show that the model realistically predicts longitudinal and lateral forces providing at the same time good estimates of the slip-sinkage behavior and tire parameters sensitivity.     

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.     

Agile tire slippage dynamics for radical enhancement of vehicle mobility

There is a need to radically increase mobility of terrain vehicles through new modalities of vehicle locomotion, i.e., by establishing a new technological paradigm in vehicle dynamics and mobility. The new paradigm greatly applies to military vehicles for the radical improvement of tactical and operational mobility. This article presents a new technological paradigm of agile tire slippage dynamics that is studied as an extremely fast and exact response of the tire–soil couple to (i) the tire dynamic loading, (ii) transient changes of gripping and rolling resistance conditions on uniform stochastic terrains and (iii) rapid transient changes from one uniform terrain to a different uniform terrain. Tire longitudinal relaxation lengths are analyzed to characterize the longitudinal relaxation time constants. A set of agile characteristics is also considered to analyze agile tire slippage dynamics within a time interval that is close to the tire longitudinal relaxation time constants. The presented paradigm of agile tire slippage dynamics lays out a foundation to radically enhance vehicle terrain mobility by controlling the tire slippage in its transient phases to prevent the immobilization of a vehicle. Control development basis and requirements for implementing an agile tire slippage control are also analyzed and considered.     

Experimental validation of a differential variational inequality-based approach for handling friction and contact in vehicle/granular-terrain interaction

The observation motivating this contribution was a perceived lack of expeditious deformable terrain models that can match in mobility analysis studies the level of fidelity delivered by today’s vehicle models. Typically, the deformable terrain-tire interaction has been modeled using Finite Element Method (FEM), which continues to require prohibitively long analysis times owing to the complexity of soil behavior. Recent attempts to model deformable terrain have resorted to the use of the Discrete Element Method (DEM) to capture the soil’s complex interaction with a wheeled vehicle. We assess herein a DEM approach that employs a complementarity condition to enforce non-penetration between colliding rigid bodies that make up the deformable terrain. To this end, we consider three standard terramechanics experiments: direct shear, pressure-sinkage, and single-wheel tests. We report on the validation of the complementarity form of contact dynamics with friction, assess the potential of the DEM-based exploration of fundamental phenomena in terramechanics, and identify numerical solution challenges associated with solving large-scale, quadratic optimization problems with conic constraints.     

A methodology for quantitatively assessing vehicular rutting on terrains

This paper presents a quantitative method for assessing the environmental impact of terrain/vehicle interactions during tactical missions. Area wide mobility analyses were conducted using three standard US military tracked and wheeled vehicles over terrain regions representing both fine-grained and course-grained soils. The NATO reference mobility model, Version 2, was used to perform the on- and off-road mobility analysis. Vehicle and terrain characterizations along with different climate scenarios were used as input parameters to predict vehicle rut depth performance for the different vehicles and terrain conditions. The vehicles’ performance was statistically mapped over these terrain regions for percent area traveled and the resulting rut depth created by each vehicle. A selection of tactical scenarios for each vehicle was used to determine rut depth for a range of vehicle missions. A vehicle mission severity rating method, developed at the US Army Engineer Research and Development Center, was used to rate the selected missions and resulting rut depths.     

Efficient generation of accurate mobility maps using machine learning algorithms

U.S Army’s mission is to develop, integrate, and sustain the right technology solutions for all manned and unmanned ground vehicles, and mobility is a key requirement for all ground vehicles. Mobility focuses on ground vehicles’ capabilities that enable them to be deployable worldwide, operationally mobile in all environments, and protected from symmetrical and asymmetrical threats. In order for military ground vehicles to operate in any combat zone, the planners require a mobility map that gives the maximum predicted speeds on these off-road terrains. In the past, empirical and semi-empirical techniques (Ahlvin and Haley, 1992; Haley et al., 1979) were used to predict vehicle mobility on off-road terrains such as the NATO Reference Mobility Model (NRMM). Because of its empirical nature, the NRMM method cannot be extrapolated to new vehicle designs containing advanced technologies, nor can it be applied to lightweight robotic vehicles.The mobility map is a function of different parameters such as terrain topology and profile, soil type (mud, snow, sand, etc.), vegetation, obstacles, weather conditions, and vehicle type and characteristics.A physics-based method such as the discrete element method (DEM) (Dasch et al., 2016) was identified by the NATO Next Generation NRMM Team as a potential high fidelity method to model the soil. This method allows the capture of the soil deformation as well as its non-linear behavior. Hence it allows the simulation of the vehicle on any off-road terrain and have an accurate mobility map generated. The drawback of the DEM method is the required simulation time. It takes several weeks to generate the mobility map because of the large number of soil particles (millions) even while utilizing high performance computing.One approach to reduce the computational time is to use machine learning algorithms to predict the mobility map. Machine learning (Boutell et al., 2004; Burges, 1998; Barber et al., 1997) can lead to very accurate mobility predictions over a wide range of terrains. Machine learning is divided into two categories: the supervised and the unsupervised learning. Supervised learning requires the training data to be labeled into predetermined classes, while the unsupervised learning does not require the training data to be labeled. Machine learning can help generate mobility maps using trained models created from a minimum number of simulation runs. In this study different supervised machine learning algorithms such as the support vector machine (SVM), the nearest neighbor classifier (k-NN), decision trees, and boosting methods were used to create trained models labeled as 2 classes for the ‘go/no-go’ map, 5 classes for the 5-speed map, and 7 classes for the 7-speed map. The trained models were created from the physics-based simulation runs of a nominal wheeled vehicle traversing on a cohesive soil.     

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.     

地面力学及其在行星探测研究中的应用

地面力学是研究越野行驶中机器与地面相互作用的一门力学学科,包括对机器通过性的预测和评价,行走机构的优化设计以及对地面可行驶性的预测判断等几个方面.首先简介地面力学的研究方法、试验仪器和设备以及主要的成果和结论,其中包括在这些方面的最新研究进展情况.之后重点介绍行星探测领域中所开展的地面力学研究,主要从行星探测器设计阶段对地面力学理论和方法的应用、行星模拟土壤研制和力学特性研究、行星就位土壤力学参数测量等几个方面进行了综述.最后对这一领域今后的研究方向进行了探讨.      

Development and validation of off-road tire-gravelly soil interaction using advanced computational techniques

This paper presents a novel modelling technique to compute the interaction between an 8x4 off-road truck and gravelly soil (sand with gravel soil). The off-road truck tire size 315/80R22.5 is modelled using the Finite Element Analysis (FEA) technique and validated using manufacturer-provided data in static and dynamic responses. The gravelly soil is modelled using Smoothed-Particle Hydrodynamics (SPH) technique and calibrated against physical measurements using pressure-sinkage and direct shear-strength tests. The tire-gravelly soil interaction is captured using the node symmetric node to segment with edge treatment algorithm deployed for interaction between FEA and SPH elements. The model setup consists of four tires presenting the four axles of the truck, the first tire is a free-rolling steering tire, the second and third tires are driven tires and the fourth tire is a free-rolling push tire. The truck tires-gravelly soil interaction is computed and validated against physical measurements performed in Göteborg, Sweden. The effect of gravelly soil compaction and truck loading on the tire performance is discussed and investigated.     

An approach to computer control for legged vehicles

Observation of the locomotion of animals and human beings in difficult terrain makes it quite obvious that legged locomotion offers substantial mobility advantages over conventional wheeled or tracked systems. However, effective adaptation of legged locomotion principles to off-road vehicles has to date been frustrated by the complexity of the joint coordination control problem and by the lack of suitable sources of power for individual leg joints. This paper is addressed to the first problem and is intended to show that some of the techniques used in aircraft autopilots can be adapted to legged vehicle control. The main results presented are derived from a computer simulation study of a system in which vehicle speed and direction are determined by a human operator while individual joint commands are generated automatically by a digital computer. Present indications are that such a vehicle might be as easy to control as a conventional wheeled or tracked automotive system.     

Laboratory experimental study of tire tractive performance on soft soil: Towing mode,traction mode,and multi-pass effect

Tire tractive performance, soil behavior under the traffic, and multi-pass effect are among the key topics in the research of vehicle off-road dynamics. As an extension of the study (He et al., 2019a), this paper documents the testing of a tire moving on soft soil in the traction mode or towing mode, with a single pass or multiple passes, and presents the testing results mainly from the aspects of tire tractive performance parameters, soil behavior parameters, and multi-pass effect on these parameters. The influence of tire inflation pressure, initial soil compaction, tire normal load, or the number of passes on the test data has been analyzed; for some of the tests, the analysis was completed statistically. A multi-pass effect phenomenon, different from any phenomenon recorded in the available existing literature, was discovered and related to the ripple formation and soil failure. The research results of this paper can be considered groundwork for tire off-road dynamics and the development of traction controllers for vehicles on soft soil.     

Terrain classification using ToF sensors for the enhancement of agricultural machinery traversability

Ground properties influence various aspects of mobile machinery navigation including localization, mobility status or task execution. Excessive slipping, skidding or trapping situations can compromise the vehicle itself or other elements in the workspace. Thus, detecting the soil surface characteristics is an important issue for performing different activities in an efficient, safe and satisfactory manner. In agricultural applications, this point is specially important since activities such as seeding, fertilizing, or ploughing are carried on within off-road landscapes which contain a diversity of terrains that modify the navigation behaviour of the vehicle. Thus, the machinery requires a cognitive capability to understand the surrounding terrain type or its characteristics in order to take the proper guidance or control actions. This work is focused on the soil surface classification by implementing a visual system capable to distinguish between five usual types of off-road terrains. Computer vision and machine learning techniques are applied to characterize the texture and color of images acquired with a Microsoft Kinect V2 sensor. In a first stage, development tests showed that only infra-red and RGB streams are useful to obtain satisfactory accuracy rates (above 90%). The second stage included field trials with the sensor mounted on a mobile robot driving through various agricultural landscapes. These scenarios did not present illumination restrictions nor ideal driving roads; hence, conditions can resemble real agricultural operations. In such circumstances, the proposed approach showed robustness and reliability, obtaining an average of 85.20% of successful classifications when tested along 17 trials within agricultural landscapes.