Modelling tire-moist terrain interaction using advanced computational techniques

This paper focuses on predicting and analyzing the tire-moist terrain interaction. The moist terrain (sand) is modelled using Smoothed-Particle Hydrodynamics (SPH) technique. The SPH basic interpolation technique is described, and the necessary interpolation equations are implemented. The soil is modelled using the hydrodynamic elastic-plastic material, while the water is modelled using Murnaghan equation of state. The numerical interaction between both materials is defined using Darcy’s law. The soil moisturizing technique consists of layering water particles on top of sand particles and pressurizing the water into the sand. The moisturizing technique is examined using the direct shear-strength test, and validated against physical measurement carried out in a laboratory under similar soil conditions and bulk density. Finally, the results and the effect of moisture content on tire-moist terrain interaction are discussed and investigated using a previously modelled and validated off-road truck tire size 315/80R22.5.     

Rolling deformation of truck tires: Measurement and analysis using a tire sensing approach

Measurements on rolling tire deformation provide deep insights into the mechanism of generating tire forces and moments. For free rolling tires, substantial attention has been given to the rolling resistance because of its significant impact on the fuel consumption and CO₂ emissions. This paper attempts to investigate the rolling resistance force through measurements of the rolling deformation of truck tires using a tire sensing approach. An optical tire sensor system is used to measure rolling tire deformation, which includes the deformed inner profile, sidewall deformation, and tread deformation. Measurements were conducted on a test truck for both new and used tires. In addition, the influences from operational factors such as wheel load and inflation pressure on tread deformation were examined and analyzed.     

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.     

Three-dimensional dynamic model for off-road vehicles using discrete body dynamics

This paper presents a simple, reliable dynamics model of off-road vehicle operation in real-time (RT) on terrain with obstacles. The numerical model was formulated by a new method – DBD (Discrete Body Dynamics). The new method is based on a discrete-element method, where the equations of motion are linear and simple to solve.In this new method, the suspension systems are composed of soft and stiff springs and dampers (instead of suspension arms and joints constrains), to present the kinematics and dynamics of real suspension. Reduction of the number of bodies and avoidance of constraints significantly improves model efficiency and simplicity.The tires–soil interaction was modeled using Brixius prediction. Specific soil properties were obtained from the classification system for each tire–soil interaction, size, and geometric area. The tire–ground contact was determined by topographic surface and adjustment of the forces and direction acting on the tires.The proposed method allows quick and simple definition of a vehicle. The model is written as an independent software infrastructure, enabling easy integration with any other software component.Simulation results were compared with Siemens' VL commercial multibody dynamics program. The performance of the proposed method was very similar to the commercial program (R² > 0.9), with the significant advantage of much higher RT performance.     

Prediction of soil vertical stress under off-road tire using smoothed-particle hydrodynamics

Evaluation of vertical stress distribution in clay-loam soil using Smoothed-Particle Hydrodynamics-Finite Element Analysis (SPH-FEA) technique is presented in this research. The moist soil is modelled using the hydrodynamic elastic–plastic material and Murnaghan equation of state, while the tire is modelled using FEA in Visual Environment’s Pam-Crash software. Soil-tire interaction is performed using the node symmetric node to segment with edge treatment method. A single-wheel tester in a soil bin environment was utilized to provide experimental data. The objectives of the experimental test were to (1) calculate maximum subsoil stresses in the subsoil at 1 to 15 passes of a wheel with loads of 1, 2, 4, and 5 kN on soil with moisture levels of 0, 10, 17, and 24%.; (2) calibrate soil with different levels of moisture (3) compare predicted soil stresses with experiments. The maximum stress at 20 cm depth increased with increasing soil moisture and also with high levels of tire load. In contrast, successive traffic showed a decreasing effect on soil stress. The coefficient of determination 0.97 shows the predictions agreed very well with experiments. The moist soil-tire interaction model will be further used to analyze the soil stress in different soil depths and different forward velocity.     

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.     

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.     

Tire load rating to reduce soil compaction

Both experience and research warn that heavily loaded wheels of agricultural transport vehicles and heavy machinery may cause severe compaction damage to the farmland. A remedy consists of reducing both the wheel load and the contact pressure.Early in the 1990s, the author suggested an experimental examination of the problem of soil compaction under fully controlled conditions. The ensuing research program, which was sponsored by the Grant Agency of the Czech Republic, included a series of experiments with loaded wheels carried out in the experimental grounds of the Czech University of Agriculture and, subsequently, their physical modelling in the laboratory of the Department of Motor Vehicles, Technical faculty. This program has corroborated the idea that physical modelling under controlled conditions, complemented by an adequate evaluation procedure, has a promising potential to predict full-scale ground compaction and become a sound basis for practical measures. This paper describes the laboratory equipment, testing technique, and the way of evaluating the compaction potential of tires in terms of soil dry bulk density, leading to a Compaction Number (CN) rating of individual tires. Practically, the CN rating is supposed to be included in agricultural tire catalogues to complement the load capacity/inflation pressure values for hard ground (e.g., ETRTO specifications based on tire strength and wear).     

Tire inflation and its influence on drawbar characteristics and performance – Energetic indicators of a tractor set

This work deals with the influence of tire inflation on tractive characteristics and performance-energetic parameters of a ploughing set. The test was conducted using two tire sets with different tire pressures under field conditions. Measurements of tractive properties were performed by setting travel speeds to 5, 8, and 10 kph, respectively. The ploughing set was operated at 8 kph, according to the manufacturer’s recommendation. The measurement results were processed graphically and mathematically into the Vehicle Traction Ratio, drawbar power, and slip characteristics. The tire inflation, reduced from 180 to 65 kPa and/or 75 kPa, of tires with wide treads (low-profile) resulted in increase of the front tire footprint by 24.7% and rear tire footprint by 31.1%. This change had a positive impact on the specific tractive fuel consumption that decreased in the range from 3.4% to 16.0%, depending on the travel speed. The results of performed measurements revealed that reducing the tire inflation of appropriate tires can improve the drawbar characteristics and consequently the fuel consumption.     

Tire-ice model development for the simulation of rubber compounds effect on tire performance

The material properties of the rubber compounds, which are highly dependent on temperature, have a vital role in the tire behavior. A comprehensive study on the effect of the rubber properties on tire performance, for different temperatures, as well as different road conditions is required to adequately predict the performance of tires on ice.In this study, a theoretical model has been developed for the tire-ice interaction. The temperature changes obtained from the model are used to calculate the height of the water film created by the heat generated due to the friction force. Next, the viscous friction coefficient at the contact patch is obtained. By using the thermal balance equation at the contact patch, the dry friction is obtained. Knowing the friction coefficients for the dry and wet regions, the equivalent friction coefficient is calculated. The model has been validated using experimental results for three similar tires with different rubber compounds properties. The model developed can be used to predict the temperature changes at the contact patch, the tire friction force, the areas of wet and dry regions, the height of the water film for different ice temperatures, different normal load, etc.     

Thrust and slip of a low-pressure tire on compressible ground by the compression-sliding approach

Driving wheels with low-pressure lugged tires are standard propulsion components of wheeled off-road vehicles. Such wheels have been mostly treated in theory as shorter tracks or even as “black boxes”. These procedures, however, appear not to be necessary since an updated theory of thrust generation, based on experiments with double-plate meter, was presented at the 2008 ISTVS Turin conference. This theory is based on the compaction-sliding (CS) concept, which claims that the rearward displacement of soil, a reason for slip, starts as horizontal soil compression by lugs (C-stage at lower thrust), followed by the slide of sheared off soil blocks (S-stage at higher thrust). The thrust in terms of ISTVS Standards equals gross tractive effort minus internal rolling resistance of a tire. The resultant thrust of a tire equals the sum of component thrusts of individual soil segments. The respective technique provides thrust-slip curves, which reflect tire size, loading, inflation pressure and tread pattern design, e.g. tread density, lug angle, pitch, height and tire casing lay-out and thus can be useful notably in assessing the traction properties of new tire designs. Concerning the evaluation of tire traction tests or similar applications, the CS approach offers a simplified version of thrust-slip formula (G-function), which complies with the CS concept and is easy to use.     

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.     

Measurement of contact area, contact pressure and compaction under tires in soft soil

This paper reports about measurements of the contact area of agricultuural tires in a soil bin. Four tires of the dimensions 12.5/80-18, 13.6–28, 16.9–34 and 16.9–26 were tested on a soft sandy loam. Because the existing models for predicting the footprint are complicated, a simplified model has been established, yielding good results. Measured different contact areas of all four tires are nearly constant related to wheel load except for a small increase at higher loads. Using rated loads and applying the appropriate inflation pressure, the ground pressure of a group of similar tires in loose sandy loam is independent of the tire dimensions. Measured soil compaction under at tire a various wheel loads is compared with results obtained by a mathematical model.     

Tire compaction capacity rating on non-standard soil

Tire Compaction Capacity rating system with its CC index was evolved to support the choice of proper tires for off-road vehicles or machines operating on crop producing land with aim to prevent harmful compaction of the ground. This system, fundamentally presented in the Journal of Terramechanics, Vol. 52/2014, is based on a great number of laboratory compaction tests in common clay–loam soil (here marked as standard soil). The presented article deals especially with more accurate application of numerical rating to sandy and clay soils (very different grain size) under the designation equivalent Compaction Capacity (eCC) index, however, is applicable to an arbitrary soil type. The features and practical use of eCC rating are explained and discussed in this technical note.     

Finite element modeling of interfacial forces and contact stresses of pneumatic tire on fresh snow for combined longitudinal and lateral slips

Significant challenges exist in the prediction of interaction forces generated from the interface between pneumatic tires and snow-covered terrains due to the highly non-linear nature of the properties of flexible tires, deformable snow cover and the contact mechanics at the interface of tire and snow. Operational conditions of tire-snow interaction are affected by many factors, especially interfacial slips, including longitudinal slip during braking or driving, lateral slip (slip angle) due to turning, and combined slip (longitudinal and lateral slips) due to brake-and-turn and drive-and-turn maneuvers, normal load applied on the wheel, friction coefficient at the interface and snow depth. This paper presents comprehensive three-dimensional finite element simulations of tire-snow interaction for low-strength snow under the full-range of controlled longitudinal and lateral slips for three vertical loads to gain significant mechanistic insight. The pneumatic tire was modeled using elastic, viscoelastic and hyperelastic material models; the snow was modeled using the modified Drucker-Prager Cap material model (MDPC). The traction, motion resistance, drawbar pull, tire sinkage, tire deflection, snow density, contact pressure and contact shear stresses were obtained as a function of longitudinal slip and lateral slip. Wheel states - braked, towed, driven, self-propelled, and driving - have been identified and serve as key classifiers of discernable patterns in tire-snow interaction such as zones of contact shear stresses. The predicted results can be applied to analytical deterministic and stochastic modeling of tire-snow interaction.     

Tire tread pattern design trigger on the stress distribution over rigid surfaces and soil compaction

Studies comparing the structural differences of tires have not qualitatively or quantitatively considered the effects of tread geometry on tire behaviour or the interactions of the tire with the surface. Therefore, to determine the effects of different tire tread patterns on the stress distribution of the tire and soil compaction, we compared the structural behaviours of a high-flotation tractive-tread (TT) tire and a smooth-tread (ST) tire. The experiments were conducted over a rigid and over a deformable surface. The results from the rigid surface shows the influences of the tread pattern and sidewalls is dependent of the loads. Over the deformable surface, the contact area of the TT tire was larger than that of the ST tire. The inflation pressure (IP) was mainly responsible for the load support before the soil reached its maximum deformation. Next, the tread and sidewalls exhibited the same behaviour as observed on the rigid surface. In addition, we observed alterations in the balloon point with the tread geometry and the type of surface due to changes in the contact pressure. With carcass deformation, the volume of the tire was visibly reduced, which indicated that the IP could increase.     

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.     

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.     

Creating 3D models of tractor tire footprints using close-range digital photogrammetry

Close-range digital photogrammetry is utilized to construct the 3D models of an agricultural tire footprint. These models were then analyzed to obtain the tire footprint depth, area and volume. The procedure of using the photogrammetry technique for developing 3D models of a tire footprint on soil as well as an assessment of the accuracy of the 3D models are discussed in this paper. Testing was conducted using a tractor tire in a large soil bin in a lab to generate a single tire footprint along with a rolling tire test to simulate a longer tire rut. Our experiments showed that the close-range digital photogrammetry provides an efficient and accurate method to assess the depth and volume of the tire footprint in soil.