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.     

Mobility analysis of off-road vehicles: Benefits for development, procurement and operation

Nowadays the requirements on off-road vehicles are rising steadily. The ideal vehicle has to provide excellent off-road capability with low fuel consumption, offer a high customizability for each specific mission and, last but not least, it has to be easy to operate. To meet these demands, on the development side a lot of parameter studies have to be carried out. The customer has to compare offers from a multiplicity of suppliers to decide which vehicle fulfills the designated mission task best. And finally, the operator needs the best training on the vehicle to cope with all possible situations in off-road mobility. In response to these needs, the presented simulation program WinMaku was developed to offer a tool to facilitate development, procurement and operator training. Exemplary simulation results show, on the one hand, the influence of specific design parameters, e.g. tire size, engine power, torque characteristics, gear shifting, and engine working conditions, and on the other hand the (beneficial or adverse) effects of operational parameters like driving with maximum/partial engine load, gear selection, engine speed, tire inflation pressure or track tension, on mobility performance. Furthermore results of vehicle comparison analysis are presented. These types of analysis show comparisons of mobility performance of different vehicle types or vehicle concepts (e.g. wheel vs. track) in fulfilling a certain mission profile, characterized by passing a sequence of different soils with various inclines. Endowed with such capability, the presented simulation tool serves as a training tool for operators, provides a cost effective method to assess possible development steps, allows customers to run a pre-selection process prior to expensive and time-consuming field tests, and finally supports mission planning by providing data like expected fuel consumption or time needed to pass a certain mission profile.     

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.     

The ride comfort vs. handling compromise for off-road vehicles

When designing vehicle suspension systems, it is well-known that spring and damper characteristics required for good handling on a vehicle are not the same as those required for good ride comfort. Any choice of spring and damper characteristic is therefore necessarily a compromise between ride comfort and handling. The compromise is more pronounced on off-road vehicles, as they require good ride comfort over rough off-road terrain, as well as acceptable on-road handling. In this paper, the ride comfort vs. handling compromise for off-road vehicles is investigated by means of three case studies. All three case studies indicate that the spring and damper charcteristics required for ride comfort and handling lie on opposite extremes of the design space. Design criteria for a semi-active suspension system, that could significantly reduce, or even eliminate the ride comfort vs. handling compromise, are proposed. The system should be capable of switching safely and predictably between a stiff spring and high damping mode (for handling) as well as a soft spring and low damping mode (for ride comfort). A possible solution to the compromise, in the form of a four state, semi-active hydropneumatic spring-damper system, is proposed.     

Soft soil track interaction modeling in single rigid body tracked vehicle models

Single rigid body models are often used for fast simulation of tracked vehicle dynamics on soft soils. Modeling of soil-track interaction forces is the key modeling aspect here. Accuracy of the soil-track interaction model depends on calculation of soil deformation in track contact patch and modeling of soil resistive response to this deformation. An algorithmic method to calculate soft soil deformation at points in track contact patch, during spatial motion simulation using single body models of tracked vehicles, is discussed here. Improved calculations of shear displacement distribution in the track contact patch compared to existing methods, and realistically modeling plastically deformable nature of soil in the sinkage direction in single body modeling of tracked vehicle, are the novel contributions of this paper. Results of spatial motion simulation from a single body model using the proposed method and from a higher degree of freedom multibody model are compared for motion over flat and uneven terrains. Single body modeling of tracked vehicle using the proposed method affords quicker results with sufficient accuracy when compared to those obtained from the multibody model.     

THREE DIMENSIONAL MODELING AND DYNAMIC ANALYSIS OF FOUR—WHEEL—STEERING VEHICLES

The paper presents a nonlinear dynamic model of 9 degrees of freedom for four-wheel-steering vehicles. Compared with those in previous studies, this model includes the pitch and roll of the vehicle body, the motion of 4 wheels in the accelerating or braking process, the nonlinear coupling of vehicle body and unsprung part, as well as the air drag and wind effect. As a result, the model can be used for the analysis of various maneuvers of the four-wheel-steering vehicles. In addition, the previous models can be considered as a special case of this model. The paper gives some case studies for the dynamic performance of a four-wheel-steering vehicle under step input and saw-tooth input of steering angle applied on the front wheels, respectively. The project supported by the National Natural Science Foundation of China (59625511)     

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.     

The applicability of ride comfort standards to off-road vehicles

The correlation between objective methods for determining ride comfort and subjective comments from crew driving in vehicles were investigated. For objective measurements, the ISO 2631, BS 6841, Average Absorbed Power and VDI 2057 methods were used. The emphasis was on the ride comfort of military vehicles operated under off-road conditions over typical terrains. An experiment was devised and executed in order to obtain both objective and subjective ride comfort values. The correlation between the different methods, measuring positions, measurement directions and calculation methods was determined. It is concluded that all the methods can be used to specify and evaluate ride comfort, but that acceptable ride comfort limits vary. The vertical measurement direction was dominant. Due to the frequency content of the measured acceleration, the specific weighing curve is not very important for the type of vehicle considered.     

An instrumented vehicle for offroad dynamics testing

The paper presents an instrumented vehicle that was equipped with measuring systems to perform complete dynamics tests, especially in off-road conditions. The equipment consists of four wheel dynamometers, a steering robot, and a differential GPS system together with an inertial platform, a non-contact vehicle speed sensor, and an on-board computer with software to control the devices and collect experimental data. The four wheel dynamometers measure six elements; based on strain gage force transducers, it measures three orthogonal forces and three moments. The steering robot can control the steering wheel of the vehicle at a variety of excitation modes; it can carry out typical vehicle dynamics tests (ISO 7401, ISO 4138, ISO/TR3888, etc.) as well as custom engineered tests at a wide range of setting parameters (steer angle rate up to 1600 deg/s). The differential GPS system gives true time vehicle kinematics data (velocities, accelerations, angles, etc.) at 10-ns sample rate and 20-mm accuracy. The base vehicle, a Suzuki Vitara 4 × 4, required no special modifications or changes to install the measuring equipment. The paper also describes typical tests performed with the use of the instrumented vehicle together with sample results.     

Investigation of the soil thrust interference effect for tracked unmanned ground vehicles (UGVs) using model track tests

The traction force of a tracked unmanned ground vehicle (UGV) depends on the soil thrust generated by the shearing action on the soil-track interface. In the development of soil thrust, because the continuous-track system consists of a number of single-track systems connected to each other, interference occurs between the adjacent single-track systems through the surrounding soil. Thus, the total soil thrust of the continuous-track system is not equal to the sum of the soil thrust of each single-track system, and the interference effect needs to be carefully considered. In this study, model track tests were conducted on model single-, double-, and triple-track systems according to relative density of soil and shape ratio (i.e., the length of the track plate to grouser depth). The test results indicated that the interference effect reduced soil thrust due to the overlapping shear zones between adjoining single-track systems. The loss of soil thrust increased as the relative density of the soil increased and the shape ratio decreased. Based on these findings, a soil thrust multiplier that can be utilized to assess the soil thrust of a continuous-track system was developed.     

Modelling of off-road wheeled vehicles for real-time dynamic simulation

Simulation of wheel-ground and vehicle-ground interactions is very important in many applications. Achieving accuracy and efficiency is challenging for both soft and hard terrains. This is not only because of the simulation and numerical challenges, but also due to the questionable nature of the existing terrain models. For example, the most widely used terramechanics model is not a representative constitutive relation for a full range of dynamic conditions and applications, but rather a parametrization of steady state conditions. In general, the selection and development of the proper constitutive model and the parametrization of the ground properties are very challenging. Here, we present a unified framework for general wheel-ground interaction which can be used with different terramechanics models. The framework is based on a complementarity formulation and also uses the concept of kinematic constitutive relations, beside the other known concepts for modelling and parametrizing the soil properties. The framework makes it possible to consider the appropriate modelling of the terrain for a broad range of dynamic behaviours and simulation conditions. We will illustrate the material with several examples for off-road conditions.     

Suspension settings for optimal ride comfort of off-road vehicles travelling on roads with different roughness and speeds

This paper reports on an investigation to determine the spring and damper settings that will ensure optimal ride comfort of an off-road vehicle, on different road profiles and at different speeds. These settings are required for the design of a four stage semi-active hydro-pneumatic spring damper suspension system (4S₄). Spring and damper settings in the 4S₄ can be set either to the ride mode or the handling mode and therefore a compromise ride-handling suspension is avoided. The extent to which the ride comfort optimal suspension settings vary for roads of different roughness and varying speeds and the levels of ride comfort that can be achieved, are addressed. The issues of the best objective function to be used when optimising and if a single road profile and speed can be used as representative conditions for ride comfort optimisation of semi-active suspensions, are dealt with. Optimisation is performed with the Dynamic-Q algorithm on a Land Rover Defender 110 modelled in MSC.ADAMS software for speeds ranging from 10 to 50 km/h. It is found that optimising for a combined driver plus rear passenger seat weighted root mean square vertical acceleration rather than using driver or passenger values only, returns the best results. Results indicate that optimisation of suspension settings using one road and speed will improve ride comfort on the same road at different speeds. These settings will also improve ride comfort for other roads at the optimisation speed and other speeds, although not as much as when optimisation has been done for the particular road. For improved ride comfort damping generally has to be lower than the standard (compromised) setting, the rear spring as soft as possible and the front spring ranging from as soft as possible to stiffer depending on road and speed conditions. Ride comfort is most sensitive to a change in rear spring stiffness.     

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

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

Bayesian calibration of Vehicle-Terrain Interface algorithms for wheeled vehicles on loose sands

The Vehicle-Terrain Interface (VTI) model is commonly used to predict off-road mobility to support virtual prototyping. The Database Records for Off-road Vehicle Environments (DROVE), a recently developed database of tests conducted with wheeled vehicles operating on loose, dry sand, is used to calibrate three equations used within the VTI model: drawbar pull, traction, and motion resistance. A two-stage Bayesian calibration process using the Metropolis algorithm is implemented to improve the performance of the three equations through updating of their coefficients. Convergence of the Bayesian calibration process to a calibrated model is established through evaluation of two indicators of convergence. Improvements in root-mean square error (RMSE) are shown for all three equations: 17.7% for drawbar pull, 5.5% for traction, and 23.1% for motion resistance. Improvements are also seen in the coefficient of determination (R²) performance of the equations for drawbar pull, 2.8%, and motion resistance, 2.5%. Improvements are also demonstrated in the coefficient of determination for drawbar pull, 2.8%, and motion resistance, 2.5%, equations, while the calibrated traction equation performs similar to the VTI equation. A randomly selected test dataset of about 10% of the relevant observations from DROVE is used to validate the performance of each calibrated equation.     

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.     

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.     

Modeling of terrain impact caused by tracked vehicles

Analytical models that can predict the terrain impact caused by tracked vehicles on a horizontal plane were developed and tested. The models included a disturbed width model and an impact severity model. Inputs of the terrain impact models included vehicle static properties, vehicle dynamic properties, and terrain properties. The tested vehicles included an M1A1 tank, an M577 Armored Personal Carrier (APC), and an M548 cargo carrier. The models were verified with field tests conducted in Yakima Training Center in Yakima, WA, Fort Riley, KS, and Camp Atterbury, Indiana. The average percentage errors of the disturbed width model for the M1A1, M577, and the M548 were 10.0%, 27.3%, and 8.5%, respectively. The average percentage errors of the impact severity model of the M1A1 and M577 were 25.0% and 21.4%, respectively.