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.     

Overview of cold regions mobility modeling at CRREL

Over the last several decades, the Cold Regions Research and Engineering Laboratory (CRREL) has extensively tested and analyzed issues related to vehicle performance in winter. Using this knowledge and the experimental database, models were developed to capture the important elements for cold regions mobility performance. These models span a range of resolutions and fidelities and include three-dimensional finite element models of tire–terrain interaction, vehicle dynamics models of vehicles on winter surfaces, semi-empirical cold regions algorithms for winter performance within the NATO reference mobility model (NRMM), all-season vehicle performance in force-on-force war-gaming simulations, and vehicle–surface interaction for real-time vehicle simulators. Each of these types of models is presented along with examples of their application.     

An indoor traction measurement system for agricultural tires

To reliably study soil–wheel interactions, an indoor traction measurement system that allows creation of controlled soil conditions was developed. This system consisted of: (i) single wheel tester (SWT); (ii) mixing-and-compaction device (MCD) for soil preparation; (iii) soil bin; (iv) traction load device (TLD). The tire driving torque, drawbar pull, tire sinkage, position of tire lug, travel distance of the SWT and tire revolution angle were measured. It was observed that these measurements were highly reproducible under all experimental conditions. Also relationships of slip vs. sinkage and drawbar pull vs. slip showed high correlation. The tire driving torque was found to be directly influenced by the tire lug spacing. The effect of tire lug was also discussed in terms of tire slip.     

Numerical investigation of hydroplaning characteristics of three-dimensional patterned tire

Hydroplaning characteristics of patterned tire on wet road are investigated by making use of finite volume and finite element methods. A detailed 3-D patterned tire model is constructed by our in-house modeling program and the rainwater flow is considered as incompressible and inviscid. Meanwhile, the fluid–structure interaction between the highly complicated tire tread and the rainwater flow is effectively treated by the general coupling method. Through the numerical experiments, the rainwater flow drained through tire grooves, hydrodynamic pressure and contact force are investigated and compared with those of the three-grooved tire model.     

Effects of central tire inflation systems on ride quality of agricultural vehicles

Instrumentation to collect ISO2631 ride data was installed on a CaseIH 8950 tractor equipped with a central tire inflation system (CTIS). Data were collected at two speeds on three courses representing degraded secondary roads, moderately rough fields, and the toughest of farming conditions. Reductions in tire pressures available with central tire inflation resulted in greater tire deflections and, consequently, a smoother ride. The CTIS improved the ride of the vehicle by 99% over properly inflated tires on average, and by 177% when not in resonance.     

The effect of velocity on rigid wheel performance

A simulation model to predict the effect of velocity on rigid-wheel performance for off-road terrain was examined. The soil–wheel simulation model is based on determining the forces acting on a wheel in steady state conditions. The stress distribution at the interface was analyzed from the instantaneous equilibrium between wheel and soil elements. The soil was presented by its reaction to penetration and shear. The simulation model describes the effect of wheel velocity on the soil–wheel interaction performances such as: wheel sinkage, wheel slip, net tractive ratio, gross traction ratio, tractive efficiency and motion resistance ratio. Simulation results from several soil-wheel configurations corroborate that the effect of velocity should be considered. It was found that wheel performance such as net tractive ratio and tractive efficiency, increases with increasing velocity. Both, relative wheel sinkage and relative free rolling wheel force ratio, decrease as velocity increases. The suggested model improves the performance prediction of off-road operating vehicles and can be used for applications such as controlling and improving off-road vehicle performance.     

Tire tread pattern design trigger on the stress distribution over rigid surfaces and soil compaction

Studies comparing the structural differences of tires have not qualitatively or quantitatively considered the effects of tread geometry on tire behaviour or the interactions of the tire with the surface. Therefore, to determine the effects of different tire tread patterns on the stress distribution of the tire and soil compaction, we compared the structural behaviours of a high-flotation tractive-tread (TT) tire and a smooth-tread (ST) tire. The experiments were conducted over a rigid and over a deformable surface. The results from the rigid surface shows the influences of the tread pattern and sidewalls is dependent of the loads. Over the deformable surface, the contact area of the TT tire was larger than that of the ST tire. The inflation pressure (IP) was mainly responsible for the load support before the soil reached its maximum deformation. Next, the tread and sidewalls exhibited the same behaviour as observed on the rigid surface. In addition, we observed alterations in the balloon point with the tread geometry and the type of surface due to changes in the contact pressure. With carcass deformation, the volume of the tire was visibly reduced, which indicated that the IP could increase.     

ANALYSIS OF GROUNDING CHARACTERISTICS AND STRAIN ENERGY OF RADIAL TIRES WITH RADIAL STIFFNESS1)

利用轮胎综合试验机对径向刚度下子午线轮胎进行性能试验,采用正交试验法针对不同胎压、垂向载荷下轮胎的接地特性进行分析,结合仿真软件ABAQUS与试验进行对比。结果表明,橡胶材料Mooney-Rivli模型也具有一定的适用性,胎压增大时径向刚度发生线性变化,胎面印痕由椭圆形转变成近似矩形,印痕面积略微增大;随着胎压的不断增大,胎面印痕的面积显著减小,接触面的压力主要集中在胎肩,胎冠处也有所增加;胎压一定时,垂向载荷逐渐增大时,整个印痕面的应力呈对称分布,印痕面应力由内高外低逐渐向外高内低变化。建立数学模型与有限元软件同时对轮胎进行应变能分析,发现在低胎压150 kPa下受载荷时轮胎容易发生微小侧向位移同时发生变形,此时极易引起迟滞损失并造成应变能急剧增加。     

Rolling deformation of truck tires: Measurement and analysis using a tire sensing approach

Measurements on rolling tire deformation provide deep insights into the mechanism of generating tire forces and moments. For free rolling tires, substantial attention has been given to the rolling resistance because of its significant impact on the fuel consumption and CO₂ emissions. This paper attempts to investigate the rolling resistance force through measurements of the rolling deformation of truck tires using a tire sensing approach. An optical tire sensor system is used to measure rolling tire deformation, which includes the deformed inner profile, sidewall deformation, and tread deformation. Measurements were conducted on a test truck for both new and used tires. In addition, the influences from operational factors such as wheel load and inflation pressure on tread deformation were examined and analyzed.     

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.     

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.     

A tire–ice model (TIM) for traction estimation

Increased traffic safety levels are of highest importance, especially when driving on icy roads. Experimental investigations for a detailed understanding of pneumatic tire performance on ice are expensive and time consuming. The changing ambient and ice conditions make it challenging to maintain repeatable test conditions during a test program. This paper presents a tire–ice contact model (TIM) to simulate the friction levels between the tire and the ice surface. The main goal of this model is to predict the tire–ice friction based on the temperature rise in the contact patch. The temperature rise prediction in the contact patch is based on the pressure distribution in the contact patch and on the thermal properties of the tread compound and of the ice surface. The contact patch is next classified into wet and dry regions based on the ice surface temperature and temperature rise simulations. The principle of thermal balance is then applied to compute the friction level in the contact patch. The tire–ice contact model is validated by comparing friction levels from simulations and experimental findings. Friction levels at different conditions of load, inflation pressure, and ice temperatures have been simulated using the tire–ice contact model and compared to experimental findings.     

Erratum to “Bistable Waves in an Epidemic Model” [<Emphasis Type="Italic">J. Dynam. Diff. Eq.</Emphasis> 16, 679--707 (2004)]

The existence, uniqueness up to translation and global exponential stability with phase shift of bistable travelling waves are established for a quasi- monotone reaction–diffusion system modelling man–environment–man epidemics. The methods involve phase space investigation, monotone semiflows approach and spectrum analysis.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday; Supported in part by the NSERC of Canada.     

Bistable Waves in an Epidemic Model

The existence, uniqueness up to translation and global exponential stability with phase shift of bistable travelling waves are established for a quasimonotone reaction–diffusion system modelling man–environment–man epidemics. The methods involve phase space investigation, monotone semiflows approach and spectrum analysis.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.Supported in part by the NSERC of Canada     

Real-time side-slip angle measurements using digital image correlation

In vehicle dynamics there are many parameters that are desired for vehicle control and modelling. One of the most important parameters for handling and stability is the vehicle side-slip angle. The ability to directly measure the vehicle side-slip in real-time will aid and improve many driver assist systems such as stability control schemes and roll-over mitigation, especially over rough terrain.Commercial side-slip angle solutions are available but they are prohibitively expensive and are only suitable for use during vehicle development and performance evaluation. They are also restricted to small side-slip angles and give unsatisfactory results at low speeds and over uneven terrain. Previous research has proven that digital image correlation can be used to accurately measure vehicle side-slip angle over rough off-road terrain using inexpensive, off-the-shelf cameras. However, side-slip angle calculations were performed in post processing from pre-recorded footage and not implemented in real time due to the large computational times of the novel algorithms developed.This paper describes the improvements made to the algorithms that enable real-time implementation. The side-slip angle is measured using a single camera pointing downwards to the terrain and digital image correlation. The sensor is tested on a flat surface using a rig that allows for validation. The maximum sampling frequency and accuracy are investigated. The system is shown to measure accurately and in real-time up to 100 km/h speeds.     

Estimation of wear life of wheel loader tyre

The purpose of this paper is to analyse the several factors affecting the critical wear life of off-road tyres of wheel loaders, and to estimate the wear life of the tyre. Here, the variation of tread wear depth with service meter hour was measured for two kinds of OR tyre, 37.25-35-30/36PR and 45/65-45-50PR which were used for bucket capacity 7.7 and 9.1–12.0 m³ of wheel loader, respectively. As a result, the critical wear life could be expressed by the initial tread depth, the tyre diameter, the real contact pressure, the roughness of terrain surface, the loading cycle and the amount of slippage. To elongate the wear life, the terrain surface should be controlled to be as smooth as possible and the amount of tyre slippage should be decreased by means of increasing the rear axle load.     

On the effect of pulsating flow on surge margin of small centrifugal compressors for automotive engines

Surge is becoming a limiting factor in the design of boosting systems of downsized diesel engines. Although standard compressor flowcharts are used for the selection of those machines for a given application, on-engine conditions widely differ from steady flow conditions, thus affecting compressor behaviour and consequently surge phenomenon. In this paper the effect of pulsating flow is investigated by means of a steady gas-stand that has been modified to produce engine-like pulsating flow. The effect of pressure pulses’ amplitude and frequency on the compressor surge line location has been checked. Results show that pulsating flow in the 40–67 Hz range (corresponding to characteristic pulsation when boosting an internal combustion engine) increases surge margin. This increased margin is similar for all the tested frequencies but depends on pulsation amplitude. In a further step, a non-steady compressor model is used for modelling the tests, thus allowing a deeper analysis of the involved phenomena. Model results widely agree with experimental results.     

A modified point contact tire model for the simulation of vehicle ride quality

The vertical response characteristics of several tire models were mathematically analysed by computer program. The results from the computation were compared with those from experiments. The tire models mentioned in this paper are evaluated. Finally, a modified point contact tire model has been proposed. The validity of it was then examined by experiment with tires 6.50–16 and 6.50R16.     

Thrust and slip of a low-pressure tire on compressible ground by the compression-sliding approach

Driving wheels with low-pressure lugged tires are standard propulsion components of wheeled off-road vehicles. Such wheels have been mostly treated in theory as shorter tracks or even as “black boxes”. These procedures, however, appear not to be necessary since an updated theory of thrust generation, based on experiments with double-plate meter, was presented at the 2008 ISTVS Turin conference. This theory is based on the compaction-sliding (CS) concept, which claims that the rearward displacement of soil, a reason for slip, starts as horizontal soil compression by lugs (C-stage at lower thrust), followed by the slide of sheared off soil blocks (S-stage at higher thrust). The thrust in terms of ISTVS Standards equals gross tractive effort minus internal rolling resistance of a tire. The resultant thrust of a tire equals the sum of component thrusts of individual soil segments. The respective technique provides thrust-slip curves, which reflect tire size, loading, inflation pressure and tread pattern design, e.g. tread density, lug angle, pitch, height and tire casing lay-out and thus can be useful notably in assessing the traction properties of new tire designs. Concerning the evaluation of tire traction tests or similar applications, the CS approach offers a simplified version of thrust-slip formula (G-function), which complies with the CS concept and is easy to use.