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.     

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.     

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.     

Influence of soil deformation on off-road heavy vehicle suspension vibration

Analyses of the dynamic behaviour of a heavy vehicle during off-road operation are conducted under steady state condition. Three different numerical quarter-vehicle models (single point contact model, rigid wheel contact model and deformable wheel contact model) are introduced, and the simulation results are compared in order to find the most appropriate vehicle model. During the longitudinal travel of the vehicle, arbitrary ground profile is an input of vertical excitation to the vehicle. When ground deformation is included in the numerical model, the deformation filters the vertical excitation to the vehicle while the level of excitation varies depending on the soil deformability. Bekker's non-linear pressure/sinkage relationship is applied in modelling the ground behaviour. The simulations are conducted in the time domain and various surface roughness and ground deformability are applied in the ground/vehicle interaction during a parameter study. The ground deformation under the wheel acts like a non-linear spring during the vehicle movement and influences the vehicle vibration. If a vehicle mainly operates on off-road condition with high ground deformability lower value of damping is required in order to minimise the vertical body acceleration.     

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.     

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.     

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.     

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.     

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.     

Finite element analysis of tire traveling performance using anisotropic frictional interaction model

The traveling performance of off-the-road vehicles, such as construction machinery and exploration rovers, significantly depends on the interaction between the ground and the traveling mechanism, since inelastic ground deformation and frictional sliding phenomena are induced by the vehicle’s movement. In general, a tread surface causes anisotropic frictional interaction behavior on a macroscopic scale. In this study, an acceptable frictional interaction model was implemented to finite element method to rationally examine the anisotropic frictional interaction behavior between the tire and the ground. Finite element analysis of the single tire traveling performance, including certain slippage and side slip (skid), was then carried out to examine the effect of the anisotropic frictional interaction on the numerical results for the drawbar-pull and side force.     

A roll stability performance measure for off-road vehicles

The roll stability is significant for both road and off-road commercial vehicles, while the majority of reported studies focus on road vehicles neglecting the contributions of uneven off-road terrains. The limited studies on roll stability of off-road vehicles have assessed the stability limits using performance measures derived for road vehicles. This study proposes an alternative performance measure for assessing roll stability limits of off-road vehicles. The roll dynamics of an off-road mining vehicle operating on random rough terrains are investigated, where the two terrain-track profiles are synthesized considering coherency between them. It is shown that a measure based on steady-turning root-mean-square lateral acceleration corresponding to the sustained period of unity lateral-load-transfer-ratio prior to the absolute-rollover, could serve as a reliable measure of roll stability of the vehicle operating on random rough terrains. The robustness of proposed performance measure is demonstrated considering sprung mass center height variations and different terrain excitations. The simulation results revealed adverse effects of terrain elevation magnitude on the roll stability, while a relatively higher coherency resulted in lower terrain roll-excitation and thereby enhanced vehicle roll stability. Terrains with relatively higher waviness increased the magnitude of lower spatial frequency components, which resulted in reduced roll stability limits.     

Longitudinal vehicle dynamics control for improved vehicle safety

The aim is to investigate the improvements in vehicle safety that can be achieved by limiting the vehicle speed based on GPS path information. The control strategy is aimed at reducing vehicle speed before a potentially dangerous situation is reached, in contrast with widely used stability control systems that only react once loss of control by the driver is imminent. An MSC.ADAMS/View simulation model of an off-road test vehicle was developed and validated experimentally. A longitudinal speed control system was developed by generating a reference speed based on the path information. This reference speed was formulated by taking into account the vehicle’s limits due to lateral acceleration, combined lateral and longitudinal acceleration and the vehicle’s performance capabilities. The model was used to evaluate the performance of the control system on various tracks. The control system was implemented on the test vehicle and the performance was evaluated by conducting field tests. Results of the field tests indicated that the control system limited the acceleration vector of the vehicle’s centre of gravity to prescribed limits, as predicted by the simulations, thereby decreasing the possibility of accidents caused by rollover or loss of directional control due to entering curves at inappropriately high speeds.     

Hybrid soft soil tire model (HSSTM). Part III: Model parameterization and validation

Part I describes the tire structure model; part II the contact detection and contact interface models for rigid and deformable terrains; part III the model parameterization and validation. Model parameters are estimated using non-linear least-square optimization to minimize the error between the Hybrid Soft Soil Tire Model (HSSTM) predictions and experimental data. The parameterization routines’ initial conditions are estimated from modal analysis in radial and circumferential directions. The preliminary parameterized model is incorporated in the optimization routine to find tire sidewall and belt parameters in the radial direction using quasi-static cleat loading test data. The vertical force at the spindle and tire contact patch are used to study the model accuracy in the radial direction. FlatTrac tire longitudinal and lateral force test data are employed to estimate the parameters in these directions. The tire shear force and moment at the spindle are validated against experimental data for lateral dynamics performance.     

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.     

“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.     

基于轮胎非线性特性的汽车动力学问题

长期以来,人们对轮胎的非线性进行了大量的理论与试验研究,总结出各种理论模型与经验模型。利用这些非线性轮胎模型建立汽车动力学的非线性常微分方程组,通过数值积分,可以获得汽车在各种工况条件下的稳态与瞬态转向特性。但这些模型的普遍缺点是不能用于对汽车行驶的稳定性作定性分析。本文提出了一种轮胎非线性侧特性的摄动模型,利用近似解析方法,讨论了轮胎非线性特性对汽车的转向特性、动态响应和汽车行驶稳定性的影响,导     

Identification of tire forces using Dual Unscented Kalman Filter algorithm

Nowadays, application of active control systems in vehicles has been developed in order to increase safety and steerability. In these systems, using an appropriate dynamic model can be very effective in increasing the accuracy of simulations and analysis. Tire-road forces are crucial in vehicle dynamics and control since they are the only forces that a vehicle experiences from the ground and have maximum uncertainty on vehicle dynamic model. In order to simulate the non-linear regimes of vehicle motion, the ‘Pacejka’ tire model is being utilized. In this paper, a dynamic model with Dual Unscented Kalman Filter algorithm has been utilized to identify the lateral forces, side slip angle, and normal forces of tires. In order to solve the non-linear least squares problem, these parameters were given as input to the hybrid Levenberg–Marquardt and quasi Newton algorithm to find the Pacejka tire model coefficients in the offline mode. Four degrees of freedom vehicle model combined with Pacejka tire model are used for simulation in various maneuvers. Results show appropriate compatibility with CarSim software.     

Design and testing of lateral seat suspension for off-road vehicles

Operators of off-road vehicles such as construction, forestry, agricultural vehicles and mining vehicles are exposed to excessively high levels of vertical and lateral vibrations which can pose health risks to the drivers. Ride improvement through seat suspensions has been successful in the vertical mode, however, seat suspensions have been virtually ineffective in the lateral mode. Computer simulation studies have shown that a seat suspension with a dynamic absorber can significantly improve lateral ride. In this investigation, the lateral ride performance of an off-road vehicle with a seat suspension having a dynamic vibration absorber is studied. Based on parametric sensitivity and optimization analyses in establishing optimal parameters, a prototype suspension is designed and fabricated, and then tested in the laboratory as well as on the field. Analytical results are compared to those derived from the test data in order to illustrate the validity of the computer model. The investigations through laboratory and field testing of the lateral seat suspension system have demonstrated potential in improving ride.