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.     

A modified pressure-sinkage model for small, rigid wheels on deformable terrains

Bekker’s semi-empirically derived equations allow the designers of off-road vehicles to understand and predict vehicle mobility performance over deformable terrains. However, there are several underlying assumptions that prevent Bekker theory from being successfully applied to small vehicles. Specifically, Bekker’s sinkage and compaction resistance equations are inaccurate for vehicles with wheel diameters less than approximately 50 cm and normal loading less than approximately 45 N. This paper presents a modified pressure-sinkage model that is shown to reduce sinkage and compaction resistance model errors significantly. The modification is validated with results from 160 experiments using five wheel diameters and three soil types.     

2D FE–DEM analysis of tractive performance of an elastic wheel for planetary rovers

We have been developing a simulation program for use with soil–wheel interaction problems by coupling Finite Element Method (FEM) and Discrete Element Method (DEM) for which a wheel is modeled by FEM and soil is expressed by DEM. Previous two-dimensional FE–DEM was updated to analyze the tractive performance of a flexible elastic wheel by introducing a new algorithm learned from the PID-controller model. In an elastic wheel model, four structural parts were defined using FEM: the wheel rim, intermediate part, surface layer, and wheel lugs. The wheel rigidity was controlled by varying the Young’s Modulus of the intermediate part. The tractive performance of two elastic wheels with lugs for planetary rovers of the European Space Agency was analyzed. Numerical results were compared with experimentally obtained results collected at DLR Bremen, Germany. The FE–DEM result was confirmed to depict similar behaviors of tractive performance such as gross tractive effort, net traction, running resistance, and wheel sinkage, as in the results of experiments. Moreover, the tractive performance of elastic wheels on Mars was predicted using FE–DEM. Results clarified that no significant difference of net traction exists between the two wheels.     

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.     

Performance evaluation of a wire mesh wheel on deformable terrains

Because of the unique lunar environment, a suitable wheel for lunar rover decides the rover’s trafficability on deformable terrains. The wire mesh wheel (hereinafter referred to as WMW) has the advantages of light weight and superior stability, been widely adopted for lunar rovers. But a comprehensive research on performance of WMW on deformable terrains has not been conduct. This paper would provide particular study on a type WMW, including quasi-static pressure-sinkage test and driving performance. A novel pressure-sinkage model for the WMW on deformable soils was presented. In order to investigate the sinkage characteristics of the WMW, tests were performed using a single-wheel testbed for the WMW with different loads and velocities. The effects of load and velocity on sinkage were analyzed, and the relationship between real and apparent sinkage was presented. The research on traction performance of WMW under different slip ratios (0.1–0.6) was also conducted, contrast tests were proceed by using a normal cylindrical wheel (hereinafter referred to as CW). The traction performance of WMW is analyzed using performance indices including wheel sinkage, drawbar pull, driving torque, and tractive efficiency. The experimental results and conclusions are useful for optimal WMW design and improvement/verification of wheel–soil interaction mechanics model.     

Longitudinal skid model for wheels of planetary rovers based on improved wheel sinkage considering soil bulldozing effect

To successfully deploy a wheeled mobile robot on deformable rough terrains, the wheel-terrain interaction mechanics should be considered. Skid terramechanics is an essential part of the wheel terramechanics and has been studied by the authors based on the wheel sinkage obtained using a linear displacement sensor that does not consider soil bulldozing effect. The sinkage measured by a newly developed wheel via detecting the entrance angle is about 2 times of that measured by the linear displacement sensor. On the basis of the wheel sinkage that takes the soil bulldozing effect into account, a linear function is proposed to the sinkage exponent. Soil flow in the rear region of wheel-soil interface is considered in the calculation of soil shear displacement, and its average velocity is assumed to be equal to the tangential velocity component of the transition point of shear stress. To compute the normal stress in the rear region directly, the connection of the entrance and leaving points is supposed as the reference of wheel sinkage. The wheel performance can be accurately estimated using the proposed model by comparing the simulation results against the experimental data obtained using two wheels and on two types of sands.     

Traction performance of a pushed/pulled drive wheel

A comprehensive method for prediction of off-road driven wheel performance is presented, assuming a parabolic wheel–soil contact surface. The traction performance of a driven wheel is predicted for both driving and braking modes. Simulations show significant non-symmetry of the traction performance of the driving and braking wheels. The braking force is significantly greater than the traction force reached in the driving mode. In order to apply the suggested model for prediction of the traction performance of a 4WD vehicle, the load transfer effect was considered. Simulated traction performances of front and rear driven wheels differ significantly, due to the load transfer. In the driving mode, the rear driven wheel develops a net traction force greater than that of the front wheel. On the other hand, in the braking mode the front driven wheel develops a braking force significantly greater than that of the rear driven wheel due to a pushed/pulled force affected by the load transfer. The suggested model was successfully verified by the data reported in literature and by full-scale field experiments with a special wheel-testing device. The developed approach may improve the prediction of off-road multi-drive vehicle traction performance.     

Improvement of a power tiller cage wheel for use in swampy peat soils

This study was aimed at investigating traction performance of a cage wheel for use in swampy peat soils in Indonesia. The tests were conducted in a soil bin filled with peat soil taken from the swampy areas. A set up was developed to measure tractive performance of a single cage wheel. Deep sinkage and high wheel slip were identified as the major problems of using the existing cage wheel design in swampy peat soils. The results revealed that increasing the lug angle from 15 to 35° and the length of lug improved the tractive performance of the cage wheel significantly, while increasing the number of lugs from 14 to 18 and width of lug did not improve the tractive performance significantly. A cage wheel with lug size 325×80 mm, 35° lug angle, 14 lugs (26° lug spacing), with 2 circumferential flat rings installed on the inner side of the lugs, out performed the other settings for use with power tillers in swampy peat soils.     

Experimental validation of distinct element simulation for dynamic wheel–soil interaction

The deformation behaviour of the soil during dynamic wheel–soil interaction was studied by using the discontinuum modelling technique, distinct or discrete element method (DEM). The simulation model was developed using DEM for two types of soil, soil-A (coarse sand) and soil-B (medium sand). A transparent sided soil bin was used to observe the soil deformation. Three CCD video camera photographic images of the validation experiments were analyzed and compared with the simulation program results.This paper presents the simulation and validation results for two types of soil at three different vertical loadings of 4.9, 9.8 and 14.7 N. Wheel sinkage, vertical and horizontal draft force acting on the rigid wheel and the soil deformation images from the validation experiments were some of the data used to compare the simulation program results with the validation experiments. The simulation program was helpful to understand the complex deformation behaviour of the soils. The simulated results for the deformation behaviour of soil-B showed better correlation with the validation experiments than soil-A. The results obtained have also been compared with the previous work on DEM to explain phenomena such as the high simulated sinkage of the rigid wheel.     

Automatic control system of a rear-wheel drive vehicle moving on a sloped weak sandy terrain

The general mechanism of tractive performance of a four-wheel vehicle with rear-wheel drive moving up and down a sloped sandy soil has been considered theoretically. For the given vehicle dimensions and terrain-wheel system constants, the relationships among the effective tractive or braking effort of the vehicle, the amount of sinkage of the front and rear wheels, and the slip ratio were analysed by simulation. The optimum eccentricity of the vehicle’s center of gravity and the optimum application height of the drawbar-pull for obtaining the largest value of maximum effective tractive or braking effort could be calculated by means of the analytical simulation program. For a 5.88 kN weight vehicle, it was found that the optimum eccentricity of the center of gravity e_opt was 1/6 for the range of slope angle—0βπ/24 rad during driving action of the rear wheel and e_opt was also 1/6 for the range of slope angle—π/24β0 rad during braking action of the rear wheel. The optimum application height H_opt was found to be 35 cm for the range of slope angle 0βπ/24 rad during driving action of the rear wheel and H_opt was 0 cm for the range of slope angle—π/24β0 rad during braking action of the rear wheel.     

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.     

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.     

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.     

Experimental and DEM analyses on wheel-soil interaction

In this paper, the wheel-soil interaction for a future lunar exploration mission is investigated by physical model tests and numerical simulations. Firstly, a series of physical model tests was conducted using the TJ-1 lunar soil simulant with various driving conditions, wheel configurations and ground void ratios. Then the corresponding numerical simulations were performed in a terrestrial environment using the Distinct Element Method (DEM) with a new contact model for lunar soil, where the rolling resistance and van der Waals force were implemented. In addition, DEM simulations in an extraterrestrial (lunar) environment were performed. The results indicate that tractive efficiency does not depend on wheel rotational velocity, but decreases with increasing extra vertical load on the wheel and ground void ratio. Rover performance improves when wheels are equipped with lugs. The DEM simulations in terrestrial environment can qualitatively reproduce the soil deformation pattern as observed in the physical model tests. The variations of traction efficiency against the driving condition, wheel configuration and ground void ratio attained in the DEM simulations match the experimental observations qualitatively. Moreover, the wheel track is found to be less evident and the tractive efficiency is higher in the extraterrestrial environment compared to the performance on Earth.     

Improved sinkage algorithms for powered and unpowered wheeled vehicles operating on sand

Modeling and simulation of vehicles in sand is critical for characterizing off-road mobility in arid and coastal regions. This paper presents improved algorithms for calculating sinkage (z) of wheeled vehicles operating on loose dry sand. The algorithms are developed based on 2737 tests conducted on sand with 23 different wheel configurations. The test results were collected from Database Records for Off-road Vehicle Environments (DROVE), a recently developed database of tests conducted with wheeled vehicles operating in loose dry sand. The study considers tire diameters from 36 to 124 cm with wheel loads of 0.19–36.12 kN. The proposed algorithms present a simple form of sinkage relationships, which only require the ratio of the wheel ground contact pressure and soil strength represented by cone index. The proposed models are compared against existing closed form solutions defined in the Vehicle Terrain Interface (VTI) model. Comparisons suggest that incorporating the proposed models into the VTI model can provide comparable predictive accuracy with simpler algorithms. In addition to simplicity, it is believed that the relationship between cone index (representing soil shear strength) and the contact pressure (representing the applied pressure to tire-soil interface) can better capture the physics of the problem being evaluated.     

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.     

Tractive performance of a bulldozer running on weak ground

To determine the tractive performance of a bulldozer running on weak ground in the driven state, the relations between driving force, drawbar pull, sinkage, eccentricity and slip ratio have been analysed together with each energy balance; effective input energy, sinkage deformation energy, slippage energy and drawbar pull energy. It is considered that the thrust is developed not only on the main straight part of the bottom track belt but also on parts of the front idler and rear sprocket, and the compaction resistance is calculated from the amount of slip sinkage. For a given vehicle and soil properties, it is determined that the drawbar pull increases directly with the slip ratio and reaches about 70% of the maximum driving force. The compaction resistance reaches about 13% of the maximum driving force. The sinkage of the rear sprocket, the eccentricity, and the trim angle increase with the increment of slip ratio due to the slip sinkage. These analytical results have been verified experimentally. After determining the optimum slip ratio to obtain a maximum effective tractive power, it is found that a larger optimum drawbar pull at optimum contact pressure could be obtained for a smaller eccentricity of vehicle center of gravity and a larger track length-width ratio under the same contact area.     

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.     

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.