Statistical modeling and comparison with experimental data of tire–soil interaction for combined longitudinal and lateral slip

The interaction of a tire with a soft terrain has multiple sources of uncertainties such as the mechanical properties of the terrain, and the interfacial properties between the tire and the terrain. These uncertainties are best characterized using statistical methods such as the development of stochastic models of tire–soil interaction. The quality of the models can be assessed via statistical validation measures or metrics. Although validation of stochastic tire–soil interaction models has recently been reported with good results, it involves longitudinal slip only without considering lateral slip which can occur simultaneously with longitudinal motion. This paper presents results of the validation of a simple stochastic tire–soil interaction model for the more complicated case of combined slip. The statistical methods used for validation include the development of a Gaussian process metamodel, the calibration of model parameters using the approach of the maximum likelihood estimate in conjunction with new test data. The validation of the calibrated model, when compared with test data, is obtained using four validation metrics with good results.     

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

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

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.     

Calibration of a simple cone-penetration model for snow

Numerical studies using the Material Point Method (MPM) have been conducted recently to model snow penetration tests for fine-grained and coarse-grained snows using small cones with diameters ranging from 2.5 mm to 4 mm, and cone half-angles between 15° and 45°. Although numerical studies have gained physical insight of these tests, due to the lengthy computation time needed for the MPM simulations, it is not feasible to use these simulations to develop a stochastic model to assess the large variations of the mechanical properties of snow typically shown in tests. In this paper, we present a simple and efficient physics-based analytical model based on equilibrium and a cavity expansion solution upon which a stochastic model is built to obtain calibrated material parameters for a Drucker–Prager (DP) model such that prediction of the model can be made. Sensitivity analysis of the analytical model indicates that cohesion and interfacial shear (friction) factor contribute significantly to the penetration hardness whereas the friction angle has little contribution. The calibrated material parameters are similar to those estimated via the MPM simulations. The quality of the stochastic model, when compared with test data, was assessed using four interval-based validation metrics with good results.     

Sensitivity analysis,calibration and validation of a snow indentation model

Quantification of the mechanical behavior of snow in response to loading is of importance in vehicle-terrain interaction studies. Snow, like other engineering materials, may be studied using indentation tests. However, unlike engineered materials with targeted and repeatable material properties, snow is a naturally-occurring, heterogeneous material whose mechanical properties display a statistical distribution. This study accounts for the statistical nature of snow behavior that is calculated from the pressure-sinkage curves from indentation tests. Recent developments in the field of statistics were used in conjunction with experimental results to calibrate, validate, and study the sensitivity of the plasticity-based snow indentation model. It was found that for material properties, in the semi-infinite zone of indentation, the cohesion has the largest influence on indentation pressure, followed by one of the the hardening coefficients. In the finite depth zone, the friction angle has the largest influence on the indentation pressure. A Bayesian metamodel was developed, and model parameters were calibrated by maximizing a Gaussian likelihood function. The calibrated model was validated using three local and global confidence-interval based metrics with good results.     

Development of high-mobility tracked vehicles for over snow operations

This paper describes a detailed investigation into the effects of some of the major design features on the mobility of tracked vehicles over snow. The investigation was carried out using the latest version of an advanced computer simulation model, known as NTVPM, developed under the auspices of Vehicle Systems Development Corporation (VSDC), Ottawa, Ontario, Canada. Results show that the road wheel system configuration, initial track tension (i.e., the tension in the track system when the vehicle is stationary on a level, hard ground) and track width have significant effects on vehicle mobility over snow. On deep snow where the vehicle belly (hull) contacts the snow surface, the location of the centre of gravity (C.G.) of the sprung weight in the longitudinal direction has a noticeable effect on vehicle mobility, as it affects the attitude of the belly and the belly–snow interaction. Based on the investigation, a conceptual high-mobility tracked vehicle for over snow operations is discussed. Results of this study will provide the vehicle designer with guiding principles for the development of high-mobility tracked vehicles. It also demonstrates that NTVPM is a useful and effective tool for design and performance evaluation of tracked vehicles from a traction perspective.     

Numerical investigation of snow traction characteristics of 3-D patterned tire

Traction and braking performances of automobile tire on the snow road are quite distinct from those on the dry or wet road, because of the complicated snow deformation caused by the complex tread blocks. In fact, the mathematical formulation of the snow deformation is extremely difficult, because not only it depends on the loading condition but its material properties are significantly dependent on the icing state (i.e. the snow density). The purpose of the current study is to introduce a numerical simulation of the snow–tire interaction by making use of Lagrangian finite element method and Eulerian finite volume method. The interaction between the tire tread blocks and the snow deformation is implemented by the explicit Euler–Lagrangian coupling scheme. The multi-surface yield model is adopted to describe both the softening and yielding of snow, and the associated material properties are chosen based upon the existing data in literature and the preliminary verification simulation. The numerical experiments are carried out by MSC/Dytran to investigate the parametric characteristics of the snow traction to the snow hardness, the block depth and the tread pattern.     

结构动力学有限元模型确认方法研究

随着结构动力学求解问题的复杂化，有限元分析方法越来越起着关键作用。由于许多结构系统本身存在不确定性因素，试验数据存在随机误差，而计算的三类误差也会包含着不确定性误差，如何用有限的试验来修正和检验计算模型，最后得到具有一定置信度的有限元模型，即模型确认，在工程领域越来越得到关注。在与模型修正比较的基础上，详细讨论了模型确认的主要研究内容，并结合两个应用实例，讨论模型确认的总体思路与实现方法。     

Cross-country mobility on various snow conditions for validation of a virtual terrain

Realistic simulation of on- and off-road vehicle performance in all weather conditions is needed by the U.S. Army for virtual training of personnel on existing vehicles, and for new vehicle design. The virtual test site is a computer simulation representing an actual terrain defined as having spatially distributed terramechanics properties and terrain interaction with vehicles. We developed a virtual test site for Ethan Allen Firing Range (EAFR) in northern Vermont. The virtual test site for EAFR is composed of terramechanics properties including spatially distributed snow depth and density, soil type, drainage class, slope, and vegetation type. Snow depth and density were spatially distributed with regard to elevation, slope, and aspect using a surface energy balance approach. This paper evaluates whether the terramechanics representation of a virtual test site is improved by adding spatially distributed snow and soil properties, rather than using uniform properties. The evaluation was accomplished by conducting a cross-country vehicle performance analysis using the North Atlantic Treaty Organization (NATO) Reference Mobility Model (NRMM) to validate the new algorithms for realistic spatial distribution of snow properties. The results showed that the percentage of No-Go areas for uniform snow is lower than the distributed snow by 4% for the CIV (CRREL Instrumented Vehicle), 8% for the HMMWV (High Mobility Multipurpose Wheeled Vehicle), and 5% for the Stryker vehicle. For both light vehicles, approximately 12% of the No-Go areas are classified as such because of slopes 29%. These results imply that spatial distribution of snow properties provides realistic vehicle response as opposed to having the snow properties distributed uniformly throughout the entire terrain. This represents an improvement over previous versions of the terramechanics properties.     

风吹雪廓线的风洞实验研究

利用颗粒图像测速仪对新雪形成的风吹雪进行风洞实验研究, 给出了不同高度处雪粒粒径分布函数以及平均粒径廓线、雪粒数通量廓线的分布规律. 发现当摩阻风速大于0.5 m/s 时单宽输雪率与摩阻风速满足指数函数的关系, 小于0.5 m/s 时两者满足幂函数的关系, 总体而言, 单宽输雪率与摩阻风速呈线性关系.     

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.     

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

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

Continuum slip viscoplasticity with the Haasen constitutive model: Application to CdTe single crystal inelasticity

Small strain constitutive equations are developed for the thermomechanical behavior of semiconductor single crystals, including dislocation density as an evolving parameter. The model of Haasen, Alexander and coworkers is modified (extended) to include evolution of coefficients in the definition of internal stress. These account for an evolving dislocation substructure. The resulting model is applied in a continuum slip framework to allow multiple slip orientations. Slip system interaction rules are adapted to include slip system interaction for multiple slip conditions and to suppress secondary slip and dislocation density generation for single slip orientations. The approach is discussed relative to other models for viscoplasticity of single crystals and is examined in the context of thermodynamics with internal state variables. The framework is used to correlate experimental data from compression tests of single crystals of the compound semiconductor CdTe from room temperature to near the melting point. Sensitivity of the model to uncertainties such as initial dislocation density is explored.     

基于离散元法的干湿颗粒系统仿真

介绍了基于离散元法的干湿颗粒系统仿真软件DEMSIM。对于干颗粒系统,DEMSIM可以分析二维和三维颗粒系统的弹性和塑性接触碰撞过程;对于湿颗粒系统,DEMSIM采用传统的液桥模型;对于颗粒-流体系统,DEMSIM采用CFD-DEM细观耦合模型模拟。一系列典型算例的模拟分析,验证了干湿颗粒系统仿真软件DEMSIM的精度和有效性。     

The influence of strong crosswinds on safety of different types of road vehicles

Strong crosswinds have a great influence on the safety of road vehicles. Different vehicle types may have different behavior under strong crosswinds, thereby leading to different dominant accident modes and accident risks. In order to compare the crosswind stability of road vehicles, a probabilistic method based on reliability analysis has been applied in this paper. The crosswind is simulated as a stochastic gust model with nonstationary wind turbulence. The vehicles are classified into several categories. For each vehicle type, a worst case vehicle model and the corresponding aerodynamic coefficients have been identified. Dominant accident modes and failure probabilities have been computed and are compared. The influence of road conditions (dry/wet) and wind directions on the crosswind stability has been taken investigated. The proposed model makes it possible to compare the effect of crosswind on different vehicle types based on a risk analysis.

     

A Bayesian Calibration–Prediction Method for Reducing Model-Form Uncertainties with Application in RANS Simulations

Model-form uncertainties in complex mechanics systems are a major obstacle for predictive simulations. Reducing these uncertainties is critical for stake-holders to make risk-informed decisions based on numerical simulations. For example, Reynolds-Averaged Navier-Stokes (RANS) simulations are increasingly used in the design, analysis, and safety assessment of mission-critical systems involving turbulent flows. However, for many practical flows the RANS predictions have large model-form uncertainties originating from the uncertainty in the modeled Reynolds stresses. Recently, a physics-informed Bayesian framework has been proposed to quantify and reduce model-form uncertainties in RANS simulations for flows by utilizing sparse observation data. However, in the design stage of engineering systems, when the system or device has not been built yet, measurement data are usually not available. In the present work we extend the original framework to scenarios where there are no available data on the flow to be predicted. In the proposed method, we first calibrate the model discrepancy on a related flow with available data, leading to a statistical model for the uncertainty distribution of the Reynolds stress discrepancy. The obtained distribution is then sampled to correct the RANS-modeled Reynolds stresses for the flow to be predicted. The extended framework is a Bayesian calibration–prediction method for reducing model-form uncertainties. The merits of the proposed method are demonstrated on two flows that are challenging to standard RANS models. By not requiring observation data on the flow to be predicted, the present calibration–prediction method will gain wider acceptance in practical engineering design and analysis compared to the original framework. While RANS modeling is chosen to demonstrate the merits of the proposed framework, the methodology is generally applicable to other complex mechanics models involving solids, fluids flows, or the coupling between the two (e.g., mechanics models for the cardiovascular systems), where model-form uncertainties are present in the constitutive relations.     

Upwinded finite difference schemes for dense snow avalanche modeling

Avalanche dynamics models are used by engineers and land‐use planners to predict the reach and destructive force of snow avalanches. These models compute the motion of the flowing granular core of dense snow avalanches from initiation to runout. The governing differential equations for the flow height and velocity can be approximated by a hyperbolic system of equations of first‐order with respect to time, formally equivalent to the Euler equations of a one‐dimensional isentropic gas. In avalanche practice these equations are presently solved analytically by making restrictive assumptions regarding mountain topography and avalanche flow behaviour. In this article the one‐dimensional dense snow avalanche equations are numerically solved using the conservative variables and stable upwinded and total variation diminishing finite difference schemes. The numerical model is applied to simulate avalanche motion in general terrain. The proposed discretization schemes do not use artificial damping, an important requirement for the application of numerical models in practice. In addition, non‐physical M‐wave solutions are not encountered as in previous attempts to solve this problem using Eulerian finite difference methods and non‐conservative variables. The simulation of both laboratory experiments and a field case study are presented to demonstrate the newly developed discretization schemes. Copyright © 2000 John Wiley & Sons, Ltd.     

攒尖四坡屋面风致雪漂移的数值模拟

为获得攒尖四坡屋面的风致雪漂移规律,基于欧拉-欧拉方法和风雪单向耦合假定,运用计算流体动力学软件,选取Mixture模型分别对立方体周边和高低屋面上的风致雪漂移运动进行数值模拟,将模拟结果与两者的实地观测数据对比,探讨分析数值风洞的关键技术和参数设置,验证数值模拟方法的合理性与可靠性。依据攒尖四坡房屋的使用功能要求,设计分析模型与分析工况,在试算的基础上对屋面进行分区。以风速5 m/s,7 m/s,9 m/s,11 m/s,13 m/s和15 m/s,风向角0°,15°,30°和45°以及屋面坡度25°,30°,34°,40°和45°为分析参数,对攒尖四坡房屋的120种工况进行数值模拟,得到屋面各分区侵蚀沉积的基本规律,提出可用于抗雪设计的屋面积雪分布系数。研究表明,风向角的改变会使屋面积雪分布状态发生较大程度的变化,风速和屋面坡度的变化对屋面整体积雪量有较大影响。     

A new indentation model for snow

Plate indentation tests have been used widely to characterize the properties of terrains. In particular, pressure-sinkage curves obtained from these tests have been used for vehicle-terrain interaction predictions. However, there is a lack of physical basis to properly interpret the meaning of these empirical curves such that they cannot be related to fundamental material properties. Also, the relation between the plate indentation tests and static (non-rolling) pneumatic tire indentation is not clear. In this paper, we conducted finite element analysis of circular plate indentation and static tire indentation simulations for fresh snow of different depths. The results indicate that the pressure-sinkage relationship for the plate indentation test is qualitatively similar to that for static tire indentation. Three deformation zones have been identified for these tests using pressure-sinkage and density-sinkage data: a small elastic zone (Zone I), a propagating hardening plastic zone (Zone II) and a densification (finite depth) zone (Zone III). The onset of a finite-depth zone was identified where the pressure bulb beneath the plate/tire has reached the bottom of snow. It is shown that Zone I and Zone II correspond to a semi-infinite terrain typical of vehicle-soil interaction, whereas Zone III corresponds to a finite-depth domain for snow and other multilayered media. The plastic constraint underneath the indenters suggests a quasi-uniaxial stress state such that a simple 1-D indentation model was proposed for Zone I, a spherical cavity expansion solution was adapted for Zone II, and an upper bound solution was adapted for Zone III. The results of the prediction of the transition between Zone II and Zone III as well as the pressure-sinkage relationships compared well with finite element solutions of plate indentation and static tire indentation tests, and with field data.     

Modeling track-terrain interaction for transient robotic vehicle maneuvers

This article describes integration of a realistic and efficient track-terrain interaction model with a multibody dynamics model of a robotic tracked vehicle. The track-terrain interface continuum is approximated by discretized and parameterizable force elements. Of particular note is a kinematic model used to estimate dynamic shear displacement, taking the form of a partial differential equation. This equation is approximated by a series of ordinary differential equations, making it compatible with multibody dynamics model formulations. Comparisons between simulated results and those obtained from field testing with a remotely-operated unmanned tracked vehicle are made to evaluate the effectiveness of this approach and to validate the use of nominal parameter data from the literature. The test vehicle was subjected to four different types of maneuvers (go-and-stop, j-turn, double lane change, and zero radius turn) on asphalt and dry sand. Simulated results using both the dynamic and steady-state track-terrain interaction models match very well with those obtained from the tests, except for the zero radius turning maneuver in sand. In this case, bulldozing effects must be incorporated to improve prediction of lateral forces.