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.     

Measurement of soil parameters useful in predicting tractive ability of off-road vehicles using an instrumented portable device

An instrumented portable device that measures soil sinkage, shear, and frictional parameters in situ was developed to investigate the complexity of soil-traction device interaction process. The device was tested to determine its ability to measure soil frictional and shear characteristics. Extensive laboratory tests were conducted using dry and moist Capay clay and Yolo loam soils. In addition, field tests were also conducted in a Yolo loam field located at the UC Davis Agricultural Experiment Station. The Cohron sheargraph was also tested under the same laboratory experimental conditions to determine adhesion, soil-metal friction, cohesion, and angle of internal friction of soil. The analysis of experimental data indicated that soil adhesion and soil-metal friction were found to be functions of the intercept and slope values of cone torque versus cone index plot (r² = 0.94 and 0.95, respectively). Moreover, soil cohesion was found to be related to adhesion by the constrained adhesion relationship, and soil angle of internal friction was proportional to soil-metal friction as reported by Hettiaratchi [7] and [8]. These results imply that a simpler device consisting of a rotating cone can be developed to measure soil frictional and shear characteristics. Preliminary results showed that the soil parameters determined using this device predicted the maximum net traction developed by four different radial ply tires tested by Upadhyaya et al. [18] under similar soil conditions quite well. These results indicate that the parameters obtained from the device could be useful in obtaining traction related parameters of a soil-tractive device interaction process.     

A comparison of ground vehicle mobility analysis based on soil moisture time series datasets from WindSat,LIS, and in situ sensors

Soil moisture is a key terrain variable in ground vehicle off-road mobility. Historically, models of the land water balance have been used to estimate soil moisture. Recently, satellites have provided another source of soil moisture estimates that can be used to estimate soil-limited vehicle mobility. In this study, we compared the off-road vehicle mobility estimates based on three soil moisture sources: WindSat (a satellite source), LIS (a computer model source), and in situ ground sensors (to represent ground truth). Mobility of six vehicles, each with different ranges of sensitivity to soil moisture, was examined in three test sites. The results demonstrated that the effect of the soil moisture error on mobility predictions is complex and may produce very significant errors in off-road mobility analysis for certain combinations of vehicles, seasons, and climates. This is because soil moisture biases vary in both direction and magnitude with season and location. Furthermore, vehicles are sensitive to different ranges of soil moistures. Modeled vehicle speeds in the dry time periods were limited by the interaction between soil traction and the vehicles’ powertrain characteristics. In the wet season, differences in soil strength resulted in more significant differences in mobility predictions.     

天然盐渍土冻融循环时水盐迁移规律及强度变化试验研究

通过对新疆喀什地区12处天然盐渍土室内基本性质试验分析,选取典型天然盐渍土,在开放系统中进行反复冻融循环条件下的试验研究。研究了天然盐渍土在多次冻融循环时的水分和盐分迁移规律及强度变化特征。试验结果表明:经多次冻融循环,低液限粘土试样水分重分布与盐分重分布有很大的一致性,水分和盐分自下而上迁移;试样粘聚力自下而上线形减小,内摩擦角呈s形分布。含砂低液限粘土试样冻融循环过程中,易溶盐均随水分向冷端面迁移,离子剖面呈现中间大两端小的趋势;试样粘聚力呈反s形分布,内摩擦角均呈s形分布。     

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

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

Predicting mobility performance of a small,lightweight track system using the computer-aided method NTVPM

This paper describes the results of a study of applying the physics-based, computer-aided method – the Nepean Tracked Vehicle Performance Model (NTVPM), originally developed for evaluating the mobility of large, heavy tracked vehicles, to predicting the performance of a small, lightweight track system on sandy soil. The objective is to examine the applicability of NTVPM to predicting the cross-country performance of small, lightweight tracked vehicles on deformable terrain. The performance of the track system predicted by NTVPM is compared with experimental data obtained in a laboratory soil bin by the Robotic Mobility Group, Massachusetts Institute of Technology. It is shown that the correlation between the tractive performance predicted by NTVPM and that measured is reasonably close, as indicated by the values of the coefficient of correlation, coefficient of determination, root mean squared deviation, and coefficient of variation. The results of this study provide evidence for supporting the view that physics-based methods, such as NTVPM, that are developed on the understanding of the physical nature and detailed analysis of vehicle–terrain interaction, are applicable to large, heavy, as well as small, lightweight vehicles, provided that appropriate terrain data are used as input.     

Dual-indentation technique for the assessment of strength properties of cohesive-frictional materials

We propose a dual indentation technique for the assessment of the cohesion and friction angle of cohesive-frictional materials of the Mohr–Coulomb type. The technique is based on a computational implementation of the yield design theorems applied to conical indentation tests with different apex angles. The upper bound solutions are found to be very close to flat indentation solutions available for cohesive-frictional materials. On this basis we derive fundamental hardness-to-cohesion solutions in function of the friction angle and the apex angle. By studying the property of these dimensionless relations, we show that the ratio of two hardness measurements obtained from indentation tests with different apex angles, allows one to determine the friction angle. This dual indentation method is applied to Berkovich and Corner Cube indenter assimilated to equivalent cones of different apex angle. The method is validated for a ‘model’ material, metallic glass, which has recently been identified as a cohesive-frictional materials. The only input to the method are two hardness values which we obtain by microindentation on metallic glass. The outcome are values of the cohesion and friction angle, which are found to be in excellent agreement with reported cohesion and friction angle values of metallic glass obtained by macroscopic triaxial testing and comprehensive finite-element backanalysis of indentation curves.     

The air cushion vehicle as a load-spreading transport device

The most effective fields of operation of the ACV are discussed, and it is shown that the vehicle effectively fills the role of a heavy transporter over weak terrain. A speculative discussion of the interaction between ACV skirts and various terrain is given in some detail. In conclusion short notes are given on some current experimental programmes, and on the work of some actual vehicles in the field.     

A mathematical model for spatial motion of tracked vehicles on soft ground

A mathematical model which predicts spatial motion of tracked vehicles on non-level terrain has been developed. The motion of the vehicle is represented by three translational and three rotational degrees of freedom. In order to incorporate the inelastic deformation of soil, a soil-track interaction model is introduced; this constitutive model relates the traction exerted on the track by soil to the slip velocity and sinkage of the track. The model is based upon available soil plasticity theories and furnishes mechanics-based interpretation of Bekker's empirical relations. For planar motion the proposed model reduces to the existing equations of motion by introducing kinematic constraints on the vertical translation, pitching and rolling degrees-of-freedom.     

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.     

Cone penetration resistance equation as a function of the clay ratio, soil moisture content and specific weight

The cone penetrometer is a simple versatile device which is widely used to monitor the strength of a soil in terms of its resistance to the penetration of a standard cone. The soil penetration resistance is a function of soil moisture content, soil specific weight and soil type. The soil type is characterised by means of a clay ratio which is the ratio of the clay content of the soil to the content of silt and sand.Based on the classical bearing capacity theories for strip foundations, a general cone penetration resistance equation is developed to represent the variability of cohesion and friction angle by means of soil type and moisture content. The empirical relationship is shown to give an accurate prediction of the cone penetration resistance for a wide range of soils from a loamy sand to a heavy clay (clay ratios 0.10–1.60) and over a wide spectrum of soil moisture contents from 10 to 65% w/w.     

A coupled sliding and rolling friction model for DEM calibration

The accuracy of dense Discrete Element Method (DEM) simulations is sensitive to initial density, contact orientation, particle size and shape, and interparticle interaction parameters including contact stiffness, cohesion, coefficients of friction, and coefficients of restitution. Although studies have characterized the effects of individual particle interaction parameters on mechanical responses of loaded granular material, research combining DEM parameters for calibration is scarce. Robust DEM calibration methodology combining sliding and rolling friction coefficients was developed and validated to predict bulk residual soil strength of initially dense DEM particle assemblies.     

Travelling performance of a wheel on a finite thickness ground

Off-road terrain can often be regarded as a finite thickness ground consisting of a soft soil layer on a rigid base. Experiments for the traveling performance of a wheel in a dense sand layer on a rigid base revealed that as the soil layer thickness decreases under the condition of high constant slip, the drawbar pull does not increase monotonically but increases gradually to a maximal value, then decreases to a minimal value, and thereafter again increases rapidly to the highest value at zero soil layer thickness. The mechanical interpretation of the relationship between the drawbar pull and the soil layer thickness is given qualitatively from the aspects of the shear characteristics of dense sand and the rigid-body friction between the wheel and the rigid base of the soil layer. It is indicated that the relationship takes the same form as van der Waals' state equation for the pressure and the volume of an imperfect gas with a phase transition between gas and liquid. The equation representing the relationship of the drawbar pull to the soil layer thickness is proposed in accordance with van der Waals' equation.     

Tyre rubber friction on a rough road

One of the most challenging aspects of vehicle dynamics is accurate modelling of the tyre-road interface. Forces between the tyre and road need to be accurately represented in simulation. This is challenging over rough roads since the friction changes along the road due to large surface asperities.The Heinrich/Klüppel friction coefficient estimation model has been implemented on smooth roads in the past. However, this study investigates the applicability of using this model over a rough but hard terrain, such as Belgian paving or cobblestones. The model is based on physical properties that can be determined mathematically or experimentally. The study includes detailed terrain topography and the difference between the top and bottom topography is used to determine the radially averaged PSD. Emphasis is placed on finding and implementing the flash temperature in a practical manner that could also be used in further studies.An experimental setup is built to validate the model. The experimental friction coefficient is compared to the friction coefficient calculated using the Heinrich/Klüppel model. The relative percentage error difference between experimental and friction model results is found to be less than 10% on a smooth concrete road and 20% on a rough road (concrete Belgian paving).     

Vehicle mobility on highly organic soils

Current political climates have generated a renewed interest in the northern regions of the world. These areas are known to have soft marshy peat, highly organic soils, and harsh winter climates. Current capabilities for vehicle mobility modeling on this terrain is limited and existing studies do not include contemporary military vehicles. This work presents mobility experiments of modern military vehicles at multiple field sites containing peat or highly organic soils that can be used to improve mobility modeling on these soils. Field experiments are being conducted during multiple seasons, including winter, spring, and summer. The vehicle traction, motion resistance, and hard surface rolling resistance of an instrumented High Mobility Multipurpose Wheeled Vehicle (HMMWV) and a Small Unit Support Vehicle (SUSV) were examined. The first is a common multi-purpose vehicle and the second is a vehicle designed to operate in these types of environments. This data set will provide the basis for model development and validation for vehicle mobility in highly organic soils.     

A methodology for quantitatively assessing vehicular rutting on terrains

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

Parameterization and modelling of large off-road tyres for ride analyses: Part 2 – Parameterization and validation of tyre models

Every mathematical model used in a simulation is an idealization and simplification of reality. Vehicle dynamic simulations that go beyond the fundamental investigations require complex multi-body simulation models. The tyre–road interaction presents one of the biggest challenges in creating an accurate vehicle model. Many tyre models have been proposed and developed but proper validation studies are less accessible. These models were mostly developed and validated for passenger car tyres for application on relatively smooth roads. The improvement of ride comfort, safety and structural integrity of large off-road vehicles, over rough terrain, has become more significant in the development process of heavy vehicles. This paper investigates whether existing tyre models can be used to accurately describe the vertical behaviour of large off road tyres while driving over uneven terrain. [1] Presented an extensive set of experimentally determined parameterization and validation data for a large off-road tyre. Both laboratory and field test are performed for various loads, inflation pressures and terrain inputs. The parameterization process of four tyre models or contact models are discussed in detail. The parameterized models are then validated against test results on various hard but rough off-road terrain and the results are discussed.     

Design and development of a new transformable wheel used in amphibious all-terrain vehicles (A-ATV)

Conventional ground-wheeled vehicles usually have poor trafficability, low efficiency, a large amount of energy consumption and possible failure when driving on soft terrain. To solve this problem, this paper presents a new design of transformable wheels for use in an amphibious all-terrain vehicle. The wheel has two extreme working statuses: unfolded walking-wheel and folded rigid wheel. Furthermore, the kinematic characteristics of the transformable wheel were studied using a kinematic method. When the wheel is unfolded at walking-wheel status, the displacement, velocity and acceleration of the wheel with different slip rates were analyzed. The stress condition is studied by using a classic soil mechanics method when the transformable wheel is driven on soft terrain. The relationship among wheel traction, wheel parameters and soil deformation under the stress were obtained. The results show that both the wheel traction and trafficability can be improved by using the proposed transformable wheel. Finally, a finite element model is established based on the vehicle terramechanics, and the interaction result between the transformable wheel and elastic–plastic soil is simulated when the transformable wheel is driven at different unfold angles. The simulation results are consistent with the theoretical analysis, which verifies the applicability and effectiveness of the transformable wheel developed in this paper.     

Vehicle vibrating on a soft compacting soil half-space: Ground vibrations, terrain damage, and vehicle vibrations

The point of departure of the present work may be either an interest in vehicle vibrations themselves, or in ground vibrations and terrain damage due to vehicles traveling off-road. The vibrations of a vehicle traversing dry, soft terrain, which is either rough or undulating, may be significantly modified by the dynamic interaction of the vehicle with the soil, particularly due to losses of energy by soil compaction and as elastic waves. The present work provides a prediction methodology for both vehicle and soil vibrations, accounting for the effects mentioned above. An expedient linear method is compared to a rheologically-based non-linear method. In the linear method, the soil compaction is incorporated as a loss factor in the dynamic stiffness of the otherwise elastic half-space; the imaginary part of that dynamic stiffness already includes the effects of wave damping. The non-linear model treats the compaction using a general rheological model for soils exhibiting both viscous and thixotropic effects, and requires iterative solution. A key feature of the latter model is the hypothesis that the stress distribution may be approximately regarded as quasi-static when calculating compaction losses; that approximation is expected to hold at low frequencies, since the P-wavelength in the soil is then much greater than the dimensions of the zone in which most compaction occurs. The methods predict that the soil compaction and excited ground vibrations have maxima at the vehicle bounce and hop resonances, and at high frequencies at which the Rayleigh wavelength approaches the order of the contact patch diameter. Moreover, sufficiently soft, compactable soils, but fully realizable in nature, control the vehicle response at the hop resonance, and possibly also at the bounce resonance.     

Design of manned lunar rover wheels and improvement in soil mechanics formulas for elastic wheels in consideration of deformation

Most of the current lunar rover vehicle wheels are inconvenient for changing broken wheels and have poor shock absorbing in driving, so they cannot be used to carry people on the moon. To meet the demands for manned lunar transportation, a new wheel possessing a woven metal wire mesh tire and using hub-rim combination slide mechanism is designed in this article. The characteristics of the new wheel is analyzed by comparing with the same-size conventional rover wheels after demonstrating the validity of FEM simulation. The new wheel possesses lighter structure and superior shock absorbing. It also provides stronger traction because the deformation of the designed wheel increases the contact area between the tire and lunar terrain. In order to establish an on-line soil parameter estimation algorithm for low cohesion soil, the stress distribution along a driven deformable wheel on off-road terrain is simplified. The basic mechanics equations of the interaction between the wheel and the lunar soil can be used for analytical analysis. Simulation results show that the soil estimation algorithm can accurately and efficiently identify key soil parameters for loose sand.