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.     

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.     

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.     

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.     

An overview of methods to convert cone index to bevameter parameters

This paper reviews experimental methods for the conversion of cone index measurements to bevameter parameters in support of vehicle soil/tire/track interactions for two general soil types, sand and lean clay. The accurate prediction of traction, motion resistance, and sinkage of tire/tracks off-road requires estimates of soil strength. Equipment used in the measurement of soil strength to support predictions of off-road mobility include the bevameter and the cone penetrometer. The portability of the cone penetrometer and rapid estimates of spatial/temporal variability in all terrain conditions make it an invaluable tool. The bevameter, a less portable tool, is used for the mechanical analysis of soils. The bevameter measures parameters defining soil strength in terms of cohesive modulus of soil deformation (k_c), frictional modulus of soil deformation (k_φ), exponent of soil sinkage (n), cohesion (c), angle of internal friction (φ), and the plate pressure at 1 in. (2.54 cm) of penetration (K) (Bekker, 1969). The field of terramechanics would greatly benefit from having the ability to convert cone penetrometer data in areas where bevameter parameters are difficult to collect. That ability to convert from cone index to bevameter parameters could be used for the large sets of existing cone index data to support determination of traction and motion resistance. This paper examines those methods for converting cone index to bevameter plate penetration parameters k_c, k_φ, and n.     

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.     

“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.     

An empirical model for tractive performance of rubber-tracks in agricultural soils

Mathematical models capable of describing the interaction between traction devices and soils have been effective in predicting the performance of off-road vehicles. Such a model capable of predicting the performance of bias-ply tires in agricultural soils was first developed by Brixius [Brixius WW. Traction prediction equations for bias-ply tires. ASAE Paper No. 871622. St. Joseph, MI: ASAE; 1987]. When the soil and vehicle parameters are known, this model uses an iterative procedure to predict the tractive performance of a vehicle including pull, tractive efficiency, and motion resistance. Al-Hamad et al. [Al-Hamad SA, Grisso RD, Zoz FM, Von Bargen K. Tractor performance spreadsheet for radial tires. Comput Electron Agr 1994:10(1):45–62] modified the Brixius equations to predict the performance of radial tires. Zoz and Grisso [Zoz, FM, Grisso RD. Traction and tractor performance. ASAE Distinguished Lecture Series #27. St. Joseph, MI: ASAE; 2003] have demonstrated that the use of spreadsheet templates is more efficient than the original iterative procedure used to predict the performance of 2WD and 4WD/MFWD tractors. As tractors equipped with rubber-tracks are becoming popular, it is important that we have the capability to predict the performance for off-road vehicles equipped with rubber-tracks during agricultural operations. This paper discusses the development of an empirical model to accomplish this goal and its validity by comparing the predicted results with published experimental results.     

An indoor traction measurement system for agricultural tires

To reliably study soil–wheel interactions, an indoor traction measurement system that allows creation of controlled soil conditions was developed. This system consisted of: (i) single wheel tester (SWT); (ii) mixing-and-compaction device (MCD) for soil preparation; (iii) soil bin; (iv) traction load device (TLD). The tire driving torque, drawbar pull, tire sinkage, position of tire lug, travel distance of the SWT and tire revolution angle were measured. It was observed that these measurements were highly reproducible under all experimental conditions. Also relationships of slip vs. sinkage and drawbar pull vs. slip showed high correlation. The tire driving torque was found to be directly influenced by the tire lug spacing. The effect of tire lug was also discussed in terms of tire slip.     

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.     

Comparison of the traffic performance of a two-axle four wheel drive (4WD), rear wheel drive (RWD), and front wheel drive (FWD) vehicle on loose sandy sloped terrain

The traffic performances during driving and braking of a 5.88 kN weight wheeled vehicle with two-axle four wheel drive, rear wheel drive, and front wheel drive running up and down a loose sandy sloped terrain were compared by means of a simulation. For the given dimensions of the vehicle and the given terrain-wheel system constants, the relationship between the effective tractive and braking effort of the vehicle, the amount of sinkage of the front and rear wheels, the total amount of sinkage of the vehicle, and the slip ratio were calculated to estimate the optimum height of force of application and the optimum eccentricity of the center of gravity of the vehicle. It was observed that, during driving action, the maximum effective tractive effort of the four wheel drive vehicle (4WD) was larger than that of the rear wheel drive vehicle (RWD), which in turn was greater than that of the front wheel drive vehicle (FWD). During the braking action, the effective braking effort at skid -20% of the four wheel vehicle (4WB) was larger than that of the front wheel brake vehicle (FWB), in turn greater than that of the rear wheel brake vehicle (RWB), when the two-axle four wheel vehicle is moving up or down the loose sandy sloped terrain. The maximum terrain slope angle up which the two-axle wheeled vehicle is able to move during driving action was found to be about 0.067π rad for the 4WD vehicle, about 0.031π rad for the RWD vehicle, and about 0.017π rad for the FWD vehicle. The effective braking effort at skid-20% of 4WB, FWB and RWB was found to decrease with slope angle.     

Multi-pass effect on off-road vehicle tractive performance

The paper presents an analysis and qualitative and quantitative evaluation of the multi-pass effect on off-road vehicle tractive performance in different soils. A literature review and the results of this study indicated that to accurately predict a vehicle’s tractive performance, the multi-pass effect should be taken into account. A new method has been developed on how to calculate the effect in given soil and operating conditions. The method includes consecutive calculation of the tractive performance: (a) for the first vehicle pass using an analytical model with soil input including an initial soil parameters set, (b) for the following vehicle passes using the same analytical model with corresponding soil input for each pass which can be obtained using the new procedure.     

How to calculate the effect of soil conditions on tractive performance

The paper presents an analysis and quantitative evaluation of the effect of soil conditions on tractive performance of off-road wheeled and tracked vehicles. The results of this study indicated that to accurately calculate the tractive performance of a vehicle in a given soil condition, soil properties and parameters and their changes as functions of soil moisture content and density should be taken into account. An effective Tractive Performance Analytical (TPA) model which takes into consideration the effect of soil conditions on tractive performance of the vehicles is developed. The TPA model uses invariant soil parameters that can be given or measured before the calculations by routine methods of classical soil mechanics. Soil parameters can also be obtained by recommended empirical equations using four physical soil parameters measured in the field with hand held instruments without time consuming and costly plate or vehicle tests. The model was validated in different soil conditions and compared with other models used in terramechanics for tractive performance predictions. The paper includes also an analysis of capabilities and limitations of the observed models.     

Tractive performance and compaction effect of a road roller running on a weak sandy soil

This study aims to investigate the tractive performance of a two-axle, two-wheel vehicle with rear-wheel drive or brake and the compaction of a decomposed granite soil. The effects of traction or braking, the change of sinkage, the slip ratio of the front and rear roller, and the number of passes of the road roller were studied. A number of tests were conducted and the experimental data were compared with the theoretical analysis results. It was observed that the amount of sinkage on the front and rear roller took the minimum value when the front roller was in the unpowered rolling state and the slip ratio of the rear roller was almost zero. When the absolute value of the slip ratio of rear roller increased, the amount of sinkage on the front and rear rollers, the absolute value of the driven or braking force of the rear roller and the absolute value of effective tractive or braking effort of the road roller increased. When the front roller was in the unpowered rolling state and the rear roller was in the braking state at −5% skid, the compaction density of the soil was at a maximum.     

Evaluation of an empirical traction equation for forestry tires

Variable load test data were used to evaluate the applicability of an existing forestry tire traction model for a new forestry tire and a worn tire of the same size with and without tire chains in a range of soil conditions. The clay and sandy soils ranged in moisture content from 17 to 28%. Soil bulk density varied between 1.1 and 1.4g cm⁻³ with cone index values between 297 and 1418 kPa for a depth of 140 mm. Two of the clay soils had surface cover or vegetation, the other clay soil and the sandy soil had no surface cover. Tractive performance data were collected in soil bins using a single tire test vehicle with the tire running at 20% slip. A non-linear curve fitting technique was used to optimize the model by fitting it to collected input torque data by modifying the coefficients of the traction model equations. Generally, this procedure resulted in improved prediction of input torque, gross traction ratio and net traction ratio. The predicted tractive performance using the optimized coefficients showed that the model worked reasonably well on bare, uniform soils with the new tire. The model was flexible and could be modified to predict tractive performance of the worn tire with and without chains on the bare homogeneous soils. The model was not adequate for predicting tractive performance on less uniform soils with a surface cover for any of the tire treatments.     

Slip sinkage effect in soil-vehicle mechanics

The paper presents an analysis and quantitative evaluation of the slip sinkage and its effect on the tractive performance of wheeled and tracked vehicles in different soils. The results of this study indicated that to accurately predict the sinkage and motion resistance of a vehicle in a given soil and operating conditions, the slip sinkage effect should be taken into account. An effective analytical formula that takes into consideration the slip sinkage effect on sinkage of plates and vehicles is developed. The formula was validated in different soil conditions and compared with other formulae used in terramechanics for slip sinkage effect predictions.     

Off-road tyre modelling II: effect of camber on tyre performance

The problem of off-road vehicle tyre-terrain interaction is that it is difficult to model accurately. For an off-road vehicle over medium to firm terrain, the tyre load may be entirely supported by the tips of the lugs, or with a minimum carcass contact with the terrain. In this case, the effect of the lugs should be taken into consideration. The forces at the interface between lugged tyre and the soil, including normal and shear stresses, are discussed in this paper. The multi-spoke tyre model was developed to study the effect of tyre lugs on the forces between tyre and terrain and it has been extended to predict the tyre forces and moments in the case of combined lateral and longitudinal slip for a cambered tyre. The influence of slip angle, camber angle and soil hardness on off-road tyre performance has been investigated. A computer program was developed using MATLAB software. The results were derived as tyre forces and moments in the three directions along the tyre contact length. A comparison between the results of the multi-spoke tyre model of a smooth off-road tyre and an off-road tyre with straight lugs, in the cambered case, has been made. The results indicated that slip angle, camber angle and soil characteristics have a strong effect on off-road tyre performance. The modified mathematical model results help the off-road tyre engineering designers to predict accurate values of tyre forces and moments in this complex case.