Terrain-vehicle systems modelling using a multi-body dynamics program

A general purpose vehicle dynamics modelling capability is described. The development of suspension system superelements as standard elements in a general multi-body dynamics program is discussed. Terrain interaction models for wheeled vehicles with deformable tires operating on rigid pavement are described. A track vehicle suspension superelement is also described that includes a loop force element model of tracks and the use of terramechanical relations to describe soil compliance.     

Fast dynamic modeling for off-road track vehicles

The paper presents a simple, fast, and reliable dynamic model for an off-road track vehicle operating on terrain with obstacles. The method has been proven previously for wheeled-vehicle formulation. The model is based on a discrete body dynamics (DBD) method, which leads to simplistic linear decoupled motion equations. In this method, joints and bodies with relatively small mass are replaced with stiff springs and dampers, eliminating the system’s constraints and reducing the number of system bodies; this is important for accelerating the simulation runtime of the track vehicle model. The track in this approach is based on modeling each link as a point-mass. Two consecutive links are connected by stiff springs and dampers. This approach reduces the calculation time and increases system stability. The track–soil interaction was modeled using Bekker’s and Janosi’s formulation (Bekker, 1956; Hanamoto and Janosi, 1961). Specific soil properties were obtained for each link–soil interaction from soil classification and GIS. The link–ground contact was determined from topographic surface and adjustment of the force and direction acting on the track. The results of the simulation using the DBD method were compared with Siemens' VL commercial multibody dynamics program and with experiments reported in the literature. Results using the proposed method were found to be similar to the commercial program based on published experiments. The solution runtimes obtained for unpaved soil were two orders faster with the DBD method compared with the Siemens' VL program. The model was written as an independent software infrastructure, enabling easy integration with any other software component, such as a control system. The algorithm is in a suitable form for parallel processing calculation to speed up the runtime simulation close to real-time.     

基于LS -DYNA公路桥车桥耦合的车辆模型研究

研究公路桥梁在移动车辆荷载作用下的动力响应,建立合理的车辆模型非常重要。为更真实地体现桥梁在车载作用下的动力响应,基于LS-DYNA程序,结合常用重型车辆的结构特性及参数,对车辆的橡胶轮胎、轮胎内气体压力、车轮转动和车辆悬架系统进行模拟,使车辆模型更接近实际车辆。通过车辆轴重和动力特性初步验证车辆有限元模型的有效性;同时,以一座混凝土简支空心板梁桥为算例,验证车轮转动和车桥相互接触力,并将LS-DYNA计算结果与桥梁实测结果进行对比,进一步验证车辆有限元模型的有效性。研究结果表明,基于LS-DYNA建立的三维车辆有限元模型是可行的,可以用于研究车桥相互作用。     

Off-road tire modeling and the multi-pass effect for vehicle dynamics simulation

Off-road operations are critical in many fields and the complexity of the tire-terrain interaction deeply affects vehicle performance. In this paper, a semi-empirical off-road tire model is discussed. The efforts of several researchers are brought together into a single model able to predict the main features of a tire operating in off-road scenarios by computing drawbar pull, driving torque, lateral force, slip-sinkage phenomenon and the multi-pass behavior. The approach is principally based on works by Wong, Reece, Chan, and Sandu and it is extended in order to catch into a single model the fundamental features of a tire running on soft soil. A thorough discussion of the methodology is conducted in order to highlight strengths and weakness of different implementations. The study considers rigid wheels and flexible tires and analyzes the longitudinal and the lateral dynamics. Being computationally inexpensive a semi-empirical model is attractive for real time vehicle dynamics simulations. To the best knowledge of the authors, current vehicle dynamics codes poorly account for off-road operations where tire-terrain interaction dominates vehicle performance. In this paper two soils are considered: a loose sandy terrain and a firmer loam. Results show that the model realistically predicts longitudinal and lateral forces providing at the same time good estimates of the slip-sinkage behavior and tire parameters sensitivity.     

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.     

Experimental analysis of vertical soil reaction and soil stress distribution under off-road tires

In this study, the vertical soil reaction acting on a driven wheel was measured by strain gages bonded to the left rear axle of a 2WD tractor driven under steady-state condition on different soil surfaces, tractor operations, and combinations of static wheel load and tire inflation pressure. In addition, the measurements of radial and tangential stresses on the soil–tire interface were made simultaneously at lug’s face and leading side near the centerline of the left rear tire using spot pressure sensors. The experimental results indicate that the proposed method of vertical soil reaction measurement is capable of monitoring the real-time vertical wheel load of a moving vehicle and provides a tool for further studies on vehicle dynamics and dynamic wheel–soil interaction. Furthermore, the measured distributions of soil stresses under tractor tire could provide more real insight into the soil–wheel interactions.     

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.     

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.     

Soil compaction and tires for harvesting and transporting sugarcane

Four tire types (A, block-shape tread; B, rib-shape tread; C, low-lug tread; D, high-lug tread) used to harvest and transport sugarcane were compared regarding the compaction induced to the soil. Tires were tested at three inflation pressures (207, 276, 345 kPa) and six loads ranging from 20 to 60 kN/tire. Track impressions were traced, and 576 areas were measured to find equations relating inflation pressure, load, contact surface and pressure. Contact surface increased with increasing load and decreasing inflation pressure; however, the contact pressure presented no defined pattern of variation, with tire types A and B generating lower contact pressure. The vertical stresses under the tires were measured and simulated with sensors and software developed at the Colombian Sugarcane Research Center (Cenicaña). Sensors were placed at 10, 30, 50 and 70 cm depth. Tire types A and B registered vertical stresses below 250 kPa at the surface. These two tires were better options to reduce soil compaction. The equations characterizing the tires were introduced into a program to simulate the vertical stress. Simulated and measured stresses were adjusted in an 87–92% range. Results indicate a good correlation between the tire equations, the vertical stress simulation and the vertical stress measurement.     

Effect of variations in front wheels driving lead on performance of a farm tractor with mechanical front-wheel-drive

Most previous researches indicate that about 20–55% of available tractor power is lost in the process of interaction between tires and soil surface. Vertical wheel loads and tire performance are parameters that play a significant role in controlling slip and fuel consumption of a tractor. Tractor’s slip is adjusted by attaching additional weights and/or reducing tire pressures, and this may have an impact on driving lead of front wheels. Mechanical Front-Wheel-Drive (MFWD) tractors work efficiently when driving lead of front wheels is 3–4% in soft soil and 1–2% in hard soil. This research was aimed to experimentally determine such tire pressures that allow adjusting tractor’s slip without deviating from set value of driving lead of front wheels. The research was also aimed to determine the effect of driving lead of front wheels on MFWD tractor’s slip and fuel consumption. Experimental results showed that front/rear tire pressure combinations that generate a well-targeted driving lead of front wheels have no effect on slip on hard soil; however, it significantly affect fuel consumption. Results show that when air pressures in front/rear tires varied within 80–220 kPa, driving lead of front wheels varied in the range from +7.25% to −0.5%.     

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     

考虑胎路多点接触的电动汽车?路面耦合系统振动分析

轮毂电机驱动电动汽车的簧下质量大, 使得轮胎动载荷增加, 且电机激励进一步加剧车轮振动. 同时, 轮胎与路面单点接触的简化模型, 其动力学计算结果与实际存在差别. 鉴于此, 考虑电机的电磁激励、胎路多点接触和非线性地基, 建立了电动汽车?路面系统机电耦合动力学模型, 通过Galerkin法推导了非线性地基梁的垂向振动, 利用积化和公式推导了非线性地基梁中非线性项积分的精确表达式, 提出了路面截断阶数选取的简易方法, 并通过路面位移响应的收敛性进行了验证. 在此基础上, 研究了胎路多点接触、非线性地基、电机激励、车速、路面不平顺幅值等对路面及车辆响应的影响. 结果表明, 非线性地基及多点接触对车辆响应的影响中, 轮胎动载荷的影响最大, 车身加速度和悬架动挠度的影响较小, 且考虑电机激励时, 二者对车辆响应的影响显著增大. 从对路面响应的影响看, 电机激励的影响最大, 非线性地基的影响次之, 多点接触的影响较小. 所建模型及研究方法可为电动汽车的垂向动力学分析提供一种新思路.      

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.     

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.     

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.     

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.     

Algorithm and implementation of soil–tire contact analysis code based on dynamic FE–DE method

One of the fundamental problems in terramechanics is soil–tire system. Past achievements on this topic can be observed in various literatures. Fast development on CPU power of PC system enables us to apply numerical methods to this basic subject. Among others, finite element method (FEM) has been applied to simple problems of soil–tire system not only in 2D but also in 3D approach. However, it is noted that the current FEM technology cannot handle “singular” boundary conditions with sufficient accuracy of analysis. Typical example of this limitation can be seen in an application to traction tire–soil contact problems, where the contact point of tire lug tip behaves as the singular point of stress field. On the other hand, distinct or discrete element method (DEM) has in essence the capability of analyze microscopic deformation (or flow) of soil as many researchers have already been demonstrated. It is noted that DEM suffers large calculation time that is consumed not only at contact check between particulate elements but also at incremental time step. In our present study, we try to combine both merit of FEM and DEM together in order to analyze the soil–tire system interaction, where, for example, a tire and deep soil layer are modeled as FEM and soil surface layer as DEM. We propose simple algorithm of this FE–DE coupled method and sample program is developed that can solve some basic terramechanics problems in order to verify our idea. The obtained result shows qualitatively sufficient accuracy.     

Next-generation NATO reference mobility model complex terramechanics – Part 1: Definition and literature review

The US army along with NATO member and partner nations’ militaries need an accurate software tool for predicting ground vehicle mobility (such as speed-made-good and fuel-consumption) on world-wide terrains where military vehicles may be required to operate. Currently, the NATO Reference Mobility Model (NRMM) is the only NATO recognized tool for assessing ground vehicle mobility. NRMM was developed from the 1960s to the 1980s and relies on steady-state empirical formulas which may not be accurate for new military ground vehicles. A NATO research task group (RTG-248) was established from 2016 to 2018 to develop the NG-NRMM (next-generation NRMM) software tool requirements and an NG-NRMM prototype which uses high-fidelity “simple” or “complex” terramechanics models for the terrain/soil along with modern 3D multibody dynamics software tools for modeling the vehicle. NG-NRMM Complex Terramechanics (CT) models are those that utilize full 3D soil models capable of predicting the 3D soil reaction forces on the vehicle surfaces (including tires, tracks, legs, and under body) and the 3D flow and deformation of the soil including both elastic and plastic deformation under any 3D loading condition. In Part 1 of this paper, an overview of the full spectrum of terramechanics models from the highest fidelity to the lowest fidelity is presented along with a literature review of CT ground vehicle mobility models.