Modeling wheel-induced rutting in soils: Rolling

Theoretical models for predicting penetration of non-driving (towed) rigid cylindrical wheels rolling on frictional/cohesive soils are presented. The models allow for investigating the influence of soil parameters and wheel geometry on the relationship between the inclined rolling force and wheel sinkage in the presence of permanently formed ruts. The rolling process is simulated numerically in three dimensions using the finite element code ABAQUS. The numerical simulations reveal that the advanced three-dimensional process of rutting can be regarded as steady, and an approximate analytic model for predicting sinkage under steady-state conditions, which accounts for three-dimensional effects, is also developed. The differences between wheel rolling and wheel indentation (considered in a separate paper) are discussed. Numerical and analytic results are compared with test results available in the literature and obtained from preliminary small-scale experiments, and general agreement is demonstrated.     

The effect of wheel width on the rolling resistance of rigid wheels in sand

The effect of width on the rolling resistance of rigid wheels in sand is shown to be very strong, coefficient of rolling resistance increasing rapidly with width at each of the sinkage levels used in the experiments. Wheel skid also increased rapidly as wheel width increased. Prediction of measured results on the narrow wheels using the modified Bekker analysis was quite good although this is shown to be partly fortuitous. Poor correlation was found between measured values of coefficient of rolling resistance and the Freitag sand number. Very good prediction of measured values of coefficient of rolling resistance was found using an expression comprising the square root of the sinkage/dia ratio multiplied by a factor correcting for width/dia ratio. The square root of the sinkage/dia ratio is shown to be the value of coefficient of rolling resistance of a narrow wheel at shallow sinkage predicted from the modified Bekker analysis. It is also shown to be identical to the inverse of the Freitag clay number, with soil cone index value replaced by mean soil radial stress.     

Rolling resistance and rut formation by implement tyres on tilled clay soil

The rolling resistance and rutting incurred by towed flotation implement tyres were investigated on an arable clay soil in three different soil strength conditions. Three radial (600/55R26.5) and two bias ply (600/55–26.5) tyres were compared. Experimental wheel loads were in the 35.4–36.4 kN range. Tyre inflation pressures, representing typical field operation, and road transport applications were in 100–150 kPa and 150–200 kPa, respectively. Soil strength was determined from mean soil penetration resistance (CI_0–15, in the layer 0–15 cm) and mean cohesion (C_0–10, 0–10 cm). Wheel rolling resistance evaluated by the coefficient of rolling resistance (CRR), rut depth (RD), driving speed, and field gradient were measured with the tyres mounted on a test trailer hitched to a tractor. CI_0–15 and C_0–10 values predicted the sinkage and the resistance to travel motion on clay soil reasonably well. When the CI_0–15 was less than 1 MPa and C_0–10 was below 100 kPa, CRR and RD increased rapidly. On average, CRR was 20% lower for the radials than the bias plies. In soft conditions (CI_0–15 ? 0.48 MPa), the radials produced 15% shallower ruts than bias plies, and the CRR was lower and RD shallower with field inflation pressures than with road pressures used. According to our results, flotation tyres can be recommended to agricultural machines when the implement or trailer is used in soft soil conditions.     

Rut depth, soil compaction and rolling resistance when using bogie tracks

There are few studies of rolling resistance for bogie tracks on forestry machines. The aim of this study was to compare the effects of wheels and two types of bogie tracks on rut formation, cone index, and vehicle rolling resistance on some typical forest soils in Sweden. In an experiment, two types of tracks were put on a trailer with a bogie with hydraulic extension on the pulling bar giving the trailer repeatable travelling speed. Loads of 0 and 9.9 Mg were used on the trailer. The main results of this study are: Compared to rather wide and soft tires, tracks on the bogie reduced rut depth by up to 40% and cone index in the ruts by about 10%, although the tracks increased the mass on the trailer by 10–12%. The relative rolling resistance coefficient was not higher for tracks than for wheels. Further studies should be conducted to show the effect of track tension on rolling resistance and flotation and of the effects of tracks on heavy vehicles on subsoil compaction.     

Steering forces on undriven tractor wheel

The steering forces on an undriven, angled wheel mounting a 6-16 8PR tire were measured on a wheel test carriage at zero camber angle and at 1.5 km/h forward speed in a soil bin with sandy clay loam soil. The lateral force developed was found to be a function of slip angle, normal load, and inflation pressure for a particular soil condition. An exponential relationship could estimate the coefficient of lateral force of the 6-16 tire. The coefficients of this equation were found to be linearly related to inflation pressure. Rolling resistance of the wheel tested was found to be a function of slip angle, normal load, and inflation pressure for the soil condition tested. A linear relationship existed between the rolling resistance and slip angle, where the coefficients were found to be a function of inflation pressure and normal load. The generalized equations developed in the present study for estimating coefficients of lateral force and rolling resistance by taking both the tire and operating parameters into account, were found to be reasonably good by looking at the high coefficient of determination between experimental and estimated values.     

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.     

Performance prediction of animal drawn vehicle tyres in sand

Four animal drawn vehicle (ADV) tyres of 5.00–19, 6.00–19, 7.00–19 and 8.00–19 sizes were tested in sand under various but controlled conditions in an indoor soil bin. A tyre test carriage with four-bar parallel linkage was developed for accommodating a single wheel of different sizes. Performance tests were conducted at five levels of inflation pressure and load. The sand compaction level was varied in the range of 3.4–4.5 MPa/m and forward speed of the test carriage was maintained at 3.1 km/h. Performance of the tyres 7.00–19 and 8.00–19 was identical and offered less rolling resistance as compared to other tyres. However, their use in camel carts may not be recommended beyond the payload of 6 kN on single wheel with inflation pressure and sand compaction range of 172–379 kPa and 3.4 –4.5 MPa/m, respectively. Based on the experimental results, empirical models were developed to predict the performance of tyres. The accuracy of prediction of the developed empirical models was compared with that of existing semi-empirical approaches. Model with sand mobility number considered relatively simple and convenient to use in the field and yields reasonably good prediction for rolling resistance and sinkage.     

Experimental and DEM analyses on wheel-soil interaction

In this paper, the wheel-soil interaction for a future lunar exploration mission is investigated by physical model tests and numerical simulations. Firstly, a series of physical model tests was conducted using the TJ-1 lunar soil simulant with various driving conditions, wheel configurations and ground void ratios. Then the corresponding numerical simulations were performed in a terrestrial environment using the Distinct Element Method (DEM) with a new contact model for lunar soil, where the rolling resistance and van der Waals force were implemented. In addition, DEM simulations in an extraterrestrial (lunar) environment were performed. The results indicate that tractive efficiency does not depend on wheel rotational velocity, but decreases with increasing extra vertical load on the wheel and ground void ratio. Rover performance improves when wheels are equipped with lugs. The DEM simulations in terrestrial environment can qualitatively reproduce the soil deformation pattern as observed in the physical model tests. The variations of traction efficiency against the driving condition, wheel configuration and ground void ratio attained in the DEM simulations match the experimental observations qualitatively. Moreover, the wheel track is found to be less evident and the tractive efficiency is higher in the extraterrestrial environment compared to the performance on Earth.     

Dynamic behaviour of an open lugged wheel under paddy soil conditions

Many experimental studies of open lugged wheel-soil interaction have been conducted, mainly based on the condition of constant slip and sinkage. As a result the reaction force to lugs seemed to be equal to the soil cutting resistance to a metal surface. However, analyses based on such methods do not appear to represent the actual behaviour of lugged wheel-soil interaction, especially when the lugs are spaced widely. The actual motion the wheel axle. In this study, an experimental device for a model lugged wheel was constructed to investigate the characteristics of the interaction between a lugged wheel and soil. Experiments were conducted under several test conditions of soil including paddy soil with a hard pan. The result of both theoretical and experimental data indicated that slip and sinkage of a lugged wheel showed a fluctuation with rotation angle of which the period is equal to the angular lug spacing. In each test soil condition used, the motion of the lugged wheel and the reaction forces acting on each lug from the soil for a free sinking wheel were different from that of the condition of constant slip and sinkage. It was found that the results obtained from this study could clarify the actual behaviour of lugged wheel-soil interaction.     

Experimental analysis of soil reaction on a lug of a movable lug wheel

A movable lug wheel was tested in a soil bin test apparatus to determine its traction performance and to measure the soil reaction forces on its lugs. Similar tests were also conducted using a fixed lug wheel. The effects of the lug motion pattern, lug spacing and horizontal load on pull and lift forces were studied. From the experiments it is confirmed that the movable action of the lug plate could generate superior pull and lift forces in comparison with the fixed lug wheel. Among the test wheels, lug motion pattern-2 generated the highest pull and lift forces. Within the range of the test conditions, there was no significant difference in pull and lift forces of the lug plate between the test lug wheels with 12 lugs and 15 lugs at the same level of horizontal and vertical loads. The increase of horizontal load up to 200 N generally increased the pull force and generated smaller rolling resistance before the lug left the soil, but did not increase the lift force significantly. The patterns of pull force, lift force and drawbar pull generated under a constant slip were slightly different from those under a constant horizontal load. Finally, the results were also elucidated by their actual lug trajectories in soil.     

Modeling motion resistance of rigid wheels

A mathematical model was developed to describe the motion resistance of rigid wheels under self-propelled conditions where no drawbar pull is developed. The modeling was based on the concept that the work required to overcome the motion resistance is equal to the energy dissipated in compacting the soil beneath the wheel. Slippage of the wheel was also considered in the modeling. Finally the validity of the proposed model was discussed.     

Soil compaction and over-winter changes to tracked-vehicle ruts, Yakima Training Center, Washington

We monitored two experimental areas at the Yakima Training Center (YTC) in central Washington to measure changes to M1A2 Abrams (M1) tank-rut surface geometry and in- and out-of-rut saturated hydraulic conductivity (K_fs), soil penetration resistance (SPR) and soil bulk density (BD). Profile-meter data show that rut cross-sectional profiles smoothed significantly and that turning ruts did so more than straight ruts. Rut edges were zones of erosion and sidewall bases were zones of deposition. K_fs values were similar in and out of ruts formed on soil with 0–5% moisture by volume, but were lower in ruts formed on soil with about 15% water. Mean SPR was similar in and out of ruts from 0- to 5-cm depth, increased to 2 MPa outside ruts and 4 MPa inside ruts at 10- to 15-cm depth, and decreased by 10–38% outside ruts and by 39–48% inside ruts at the 30-cm depth. Soil BD was similar in and out of ruts from 0- to 2.5-cm depth, and below 2.5 cm, it was generally higher in ruts formed on moist soil with highest values between 10- and 20-cm depth. Conversely, BD in ruts formed on dry soil was similar to out-of-rut BD at all depths. This information is important for determining impacts of tank ruts on water infiltration and soil erosion and for modifying the Revised Universal Soil Loss Equation (RUSLE) and the Water Erosion Prediction Project (WEPP) models to more accurately predict soil losses on army training lands.     

The rolling resistance of towed, rigid wheels in sand

A simple relationship is developed which expresses the rolling resistance of a wheel in terms of its geometry, load and accepted soil constants. Experimental results are given which support the validity of the expression.     

Improvement of a power tiller cage wheel for use in swampy peat soils

This study was aimed at investigating traction performance of a cage wheel for use in swampy peat soils in Indonesia. The tests were conducted in a soil bin filled with peat soil taken from the swampy areas. A set up was developed to measure tractive performance of a single cage wheel. Deep sinkage and high wheel slip were identified as the major problems of using the existing cage wheel design in swampy peat soils. The results revealed that increasing the lug angle from 15 to 35° and the length of lug improved the tractive performance of the cage wheel significantly, while increasing the number of lugs from 14 to 18 and width of lug did not improve the tractive performance significantly. A cage wheel with lug size 325×80 mm, 35° lug angle, 14 lugs (26° lug spacing), with 2 circumferential flat rings installed on the inner side of the lugs, out performed the other settings for use with power tillers in swampy peat soils.     

A device to measure wheel slip to improve the fuel efficiency of off road vehicles

A hall sensor based simple technique was introduced to measure wheel slip and a microcontroller based embedded digital system was developed to display wheel slip data and warn the operator with audible and visible warnings if the optimum range is exceeds. Hall sensor slip measurement system was validated in controlled soil bin condition, tar macadam surface and actual field condition and compared with the commercial radar sensor. The developed system is simple in construction and can be mounted to any make and model of agricultural tractors by entering the appropriate rolling radius via the computer interface. Field trials were conducted to measure wheel slip and fuel consumption on farm use with and without activation of slip indicator; it was observed that, the amount of fuel saving during various agricultural operation was up 1.3 l/h.     

车轮钢滚动剥离摩擦磨损特性研究

在NENE-2型摩擦磨损试验机上利用往复滚动试验装置研究了不同滚滑状态下车轮钢的剥离摩擦磨损特性和碳含量对车轮钢滚动剥离磨损性能的影响.结果表明:在不同滚滑状态下摩擦副之间的摩擦力不同,平面试样的表面磨痕形貌随着不同的切向摩擦力而明显不同,随着切向摩擦力的增大滚动磨损机制亦发生改变,剥离磨损加剧且磨损深度变大,当相对滑动量增大到一定程度后,磨损表现为明显的剥层机制;碳含量对车轮钢的滚动磨损表面磨痕形貌影响显著,碳含量低时磨痕以犁沟为主,碳含量高时剥离磨损发生的概率增加.     

Prediction of sinkage and rolling resistance for off-the-road vehicles considering penetration velocity

The use of plate pressure tests is common for the prediction of sinkage and rolling resistance for off-the-road vehicles. Most of these penetration tests are carried out with small penetration bodies in a quasi-static way. However, when vehicles are rolling on soft soil, the soil is charged dynamically. Consequently, this dynamic effect should be considered by the prediction of sinkage and rolling resistance. At the Institute of Automotive Engineering at Hamburg, tests were carried out with penetration bodies in sizes up to 900 cm², which is comparable to the contact area of wheels. The results confirm the influence of the penetration velocity. With a constant load, the body sinkage is smaller at a higher penetration velocity. Also shear tests with shear rings of different sizes have been carried out and an exponential equation for the shear strength, not depending on the shear ring size, was found. A dynamic pressure-sinkage relationship depending on the penetration velocity or driving speed was derived and transferred to the sinkage and rolling resistance of a rigid wheel.     

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.     

An evaluation of the concept of rolling resistance

Certain fundamental equations are part of every scientific discipline. These can form the starting point of relevant research. Later on, however, these equations themselves should be further developed. The fundamental equations in terrain-vehicle mechanics are those which deal with the peripheral force and rolling resistance. Both have formed the subject of numerous investigations, yet many open questions remain. An example is the interpretation of the properties of rolling resistance. According to the present study the mechanical conditions are identical for both towed and driving wheels. Rolling resistance is essentially a moment, but an active force is needed to move the wheel forward. This force acts in the travel direction at the axle of a towed wheel and at the perimeter of a driving wheel.     

Analysis of a resistance force for the locked-wheel of push-pull locomotion rovers using large subsidence

This paper provides a quantitative analysis of the resistance force of the locked-wheel for push-pull locomotion rovers using intentional sinkage. Our previous study has confirmed that push-pull locomotion using intentional subsidence at an initial position can contribute to improving the traveling performance. The key factor of this scheme is the resistance force of the locked-wheel. However, the resistance force at different sinkage conditions and wheel sizes (e.g., mass, width, and diameter) remains unclear, especially for the individual locked-wheel. The detailed investigation of this interaction can contribute to the accurate estimation of rover mobility. This paper, therefore, investigates the locked-wheel and soil interaction at different sinkage conditions experimentally, especially focusing on the intentional sinkage condition. Additionally, the resistance force is considered theoretically through the knowledge based on the soil flow patterns beneath the locked-wheel. The experimental results confirmed that the resistance force of the locked-wheel rose as the initial sinkage, wheel size, and weight increases. Furthermore, the theoretical calculation suggested the resistance force increased with a similar tendency of the experimental data.