Estimation of a three-dimensional tyre footprint using dynamic soil–tyre contact pressures

A method for estimating the three-dimensional (3D) footprint of a 16.9R38 pneumatic tyre was developed. The method was based on measured values of contact pressure at the soil–tyre interface and wheel contact length determined from the contact pressures and the depths and widths of ruts formed in the soil. The 3D footprint was investigated in an area of the field where the pressure sensors of the tyre passed in a soft clay soil. The tyre was instrumented with six miniature pressure sensors, three on the lug face and the remaining three on the under-tread region between two lugs. The instrumented tyre was run at a constant forward speed of 0.27 m/s and 23% slip on a soft soil, 0.48 MPa cone index, 25.6% d.b. moisture content for four wheel load and tyre pressure combination treatments. The 3D footprint assessment derived from soil–tyre interface stress used in this research is a unique methodology, which could precisely relate the trend profile of the 3D footprint to the measured rut depth. The tyre–soil interface contact pressure distributions results showed that as inflation pressure increased the soil strength increased significantly near the centre of the tyre as a compaction increase sensed with the cone penetrometer.     

Modelling in FEM the soil pressures distribution caused by a tyre on a Rhodic Ferralsol soil

Tyre traffic over soil causes non-uniform ground pressures across the tyre width and along the soil–tyre contact area. The objective of this paper was to obtain in the topsoil the shape, magnitudes, distribution and transmission in depth of the ground pressures from a finite element model of soil compaction. The influence of tyre inflation pressure, tyre load and soil water content over the pressures propagation in the soil was analysed. The model shows how to low inflation pressure the tyre carcass supports most of the total load and the biggest peak pressures are distributed in the tyre axes when it traffics over firm soil. For high inflation pressure the incremented stiff causes that pressure is distributed with parabolic shape. In wet soil the inflation pressure does not influence on the ground pressure distribution, this depends only on the tyre load. The inflation pressure and tyre load changed the shape of the vertical pressures distribution on the surface of a hard dry soil, but these variables did not affect the distribution of vertical stresses in a soft wet soil or below a depth of 0.15 m.     

Tractive characteristics of radial ply and bias ply tyres in a California soil

Four tyres (18.4-38, 18.4R38, 14.9-28, 14.9R28) were tested using the UCD single wheel traction tester. Each tyre was tested at two different inflation pressures and three different vertical loads at each inflation pressure. All tests were conducted in a well tilled Yolo loam soil. A dimensional analysis procedure was used to design and analyse the experiment. Two models were considered: (A) using inflation pressure as a variable, and (B) using tyre deflection as a variable. The effect of tyre type, tyre size, tyre inflation pressure and dynamic load on (1) net traction ratio at 20% slip and (2) average tractive efficiency in the 0–30% slip range were investigated using an ANOVA technique. An estimate of the possible energy savings due to the use of radial ply tyres instead of bias ply tyres in California agriculture was made.     

The ability of agricultural tyres to distribute the wheel load at the soil-tyre interface

Bigger tyres with lower inflation pressure at equivalent wheel loads are expected to reduce the stresses transmitted to the soil. We measured the contact area and the vertical stress distribution near the soil-tyre interface for five agricultural implement tyres at 30 and 60 kN wheel load and rated inflation pressures. Seventeen stress transducers were installed at 0.1 m depth in a sandy soil at a water content slightly lower than field capacity and covered with loose soil. The recently developed model FRIDA was successfully fitted to the experimental stress data across the footprint. The contact area reflected the size of the tyres. The small tyres had identical contact area at the two loads, while it increased with load for the two biggest tyres. The small tyres presented uneven stress distributions with high peak stresses. Across the tests, the tyre inflation pressure described well the measured peak stress as well as the modelled maximum stress. The latter seems to be appropriate in evaluating vehicle trafficability. We found significant differences among tyres for the slope of a linear regression between the mean ground pressure and the inflation pressure, while the tyres displayed the same interception on the mean ground pressure axis. Our results therefore suggest that the slope of this relation is the most sensitive expression of tyres’ ability to deflect and transfer stresses to the soil. The two small tyres performed poorer in this respect than the larger tyres. Tests were limited to one soil strength, with future research directed toward a broader spectrum of soil strengths.     

The tractive performance of a wide, low-pressure tyre compared with conventional tractor drive tyres

The NIAE single-wheel test vehicle was used to compare the tractive performance of a 67 × 34.00-25 tyre at 0.34 bar inflation pressure with that of 20.8–38 radial tyre at 0.6 bar inflation pressure and a similar 18.4–34 tyre at 0.8 bar inflation pressure. All tyres had similar tread patterns and were tested at the same vertical load of 2250 kg. The best performance was achieved by the 20.8–38 tyre. There was little difference in performance between the other two tyres. When compared with empirical predictions of performance derived from previous work, the two narrower tyres were found to perform approximately as predicted, but the performance of the wide, low-pressure tyre was considerably worse than predicted. This was thought to be due to bulldozing, because of the great width and increased wheel-slip caused by deformation of the soft side-wall and also due to the relatively short ground contact area. It was concluded that wide, low-pressure tyres are only suitable for fitting to vehicles requiring a very low draught capability.     

Effects of tyre inflation pressure and forward speed on vibration of an unsuspended tractor

Relationships among intensity of vibrations, tractor speed, soil moisture content and tyre inflation pressure are important for the design of tractor suspension systems. This study was designed to evaluate the effect of tyre inflation pressure and forward speed on tractor vibration in the paddy fields of Southern China by using a two-wheel-drive unsuspended tractor with different combinations of forward speed, tyre inflation pressure and soil moisture content. During experiments, the vertical vibration accelerations in front and rear axles and triaxial vibration accelerations of the tractor body were measured using three accelerometers. Fourier analysis was applied to determine root mean square acceleration values in the low frequency range from 0.1 to 10 Hz. The results of the study indicate that tractor vibration is strongly affected by changing forward speed and tyre inflation pressure, and especially by changing forward speed and rear tyre inflation pressure. The research also shows the variation in the pattern of vibration intensity especially at the tractor’s front axle when field soil moisture content is changed.     

Determination of dynamic three-dimensional soil-tyre contact profile

A technique for measuring the dynamic three-dimensional contact profile between a tyre and deformable soil has been developed. The method involves measuring incremental lateral arc lengths of the profile at discrete locations along the contact length and fitting the coefficients of a model of soil deformation at the soil-tyre interface to the experimental data using a nonlinear constrained optimization algorithm (SUMT). Two representations of the measured contact area were compared: (i) the two-dimensional surface which is the union of all points on the original undeformed soil surface which undergo deformation by the tyre; (ii) the final three-dimensional deformed surface. Contact area measurements were made for two different sized tyres at two levels of inflation pressure, dynamic load and slip in two different soil conditions. The contact width, length and area predicted by the technique were compared with corresponding values for static contact between a tyre and a rigid surface.     

Tyre load capacity and energy loss with respect to varying soil support stiffness

An analytical model is developed to predict the tyre deformation and the resultant energy loss due to tyre flexibility relative to various soil stiffnesses ranging from rigid unyielding support to soft soil. The analysis allows for examination of a pneumatic tyre with respect to the wheel load to be carried, the supporting ground rigidity and the rigidity of the tyre casing. The important tyre characteristics in providing for wheel load capability under motion are demonstrated to be the tyre carcass construction, dimension, inflation pressure and the ability of the tyre casing to recover some of the resultant energy losses incurred by the tyre under motion.     

Static Tyre/Road Interaction Modelling

The understanding, modelling and predicting of tyre behaviouralcharacteristics, for both static and dynamic applications, requires theconsideration of many detailed aspects of this seemingly simple component.In order to investigate the problem more fully, computer analysis techniquesare becoming more common than the simplifications associated with analyticalmethods. The finite element method is one such technique that enablesengineers to examine tyre behaviour comprehensively and to predict tyreperformance at the design stage. In this paper, attention is drawn to theproblem of tyre/road interaction modelling. A purely theoretical approach ispresented which gives the analyst more flexibility in changing parameterssuch as inflation pressure, hub load, and material properties thanpreviously developed experimental/numerical techniques. A gap elementformulation is used to model the interaction so that contact patch area,shape and deflection are automatically accounted for under a given load andinflation pressure. Modelling and experimental results are also presented toillustrate the accuracy of the technique.     

Soil stress and compaction effects for four tractor tyres

Compaction effects and soil stresses were examined for four tractor tyres under three inflation pressures: 67, 100 and 150% of the recommended pressure. The four tyres were 18.4 R 38, 520/70 R 38, 600/65 R 38 and 650/60-38 and they carried a wheel load of 2590 kg. The 650/60-38 was a bias-ply tyre while the other three were radial tyres. Increased inflation pressure significantly increased all measured parameters: rut depth, penetration resistance and soil stress at 20 and 40 cm depth. The 18.4 R 38 caused a greater rut depth and penetration resistance than the other tyres, which did not differ significantly from each other. The soil stress was highest for the 18.4 R 38, followed by the 650/60-38. The low-profile tyres decreased compaction compared with the 18.4–38 tyre, mainly by allowing a lower inflation pressure. The use of low-profile tyres did not reduce compaction if not used at a lower inflation pressure. The bias-ply tyre caused a higher stress in the soil than the radial tyres when used with the same inflation pressure, but the compaction effects in terms of rut depth and penetration resistance were not greater for this tyre than for the radial low-profile tyres.     

Effect of inflation pressure on motion resistance ratio of a high-lug agricultural tyre

A single wheel tyre facility at University Putra Malaysia (UPM) was used to check the validity of Wismer–Luth and Brixius equations in predicting the motion resistance ratio of a high-lug agricultural tyre and to investigate the effect of inflation pressure. A Bridgestone 5-12, 4 ply, lug M was tested on sandy-clay-loam soil. The experiments were conducted by running the tyre in towing mode. Three inflation pressures (i.e., 166, 193 and 221 kPa) were investigated and wheel numerics ranging between 0 and 70. The analysis of covariance (ANCOVA) revealed that both inflation pressure and wheel numeric have significant effects on tyre motion resistance ratio. Regression analysis was also conducted to determine the closeness of fit for Wismer–Luth’s and Brixius’ equations in predicting the motion resistance ratio of the tested tyre. Finally, three new logarithmic models for tyre motion resistance were formulated. The advantage of reducing tyre inflation pressure from 221 (nominal pressure) to 193 kPa on the motion resistance ratio of the high-lug agricultural tyre was pronounced. However, the tyre’s motion resistance ratio deteriorated with further reduction in tyre inflation pressure from 221 (nominal pressure) to 166 kPa.     

Measurement of contact area, contact pressure and compaction under tires in soft soil

This paper reports about measurements of the contact area of agricultuural tires in a soil bin. Four tires of the dimensions 12.5/80-18, 13.6–28, 16.9–34 and 16.9–26 were tested on a soft sandy loam. Because the existing models for predicting the footprint are complicated, a simplified model has been established, yielding good results. Measured different contact areas of all four tires are nearly constant related to wheel load except for a small increase at higher loads. Using rated loads and applying the appropriate inflation pressure, the ground pressure of a group of similar tires in loose sandy loam is independent of the tire dimensions. Measured soil compaction under at tire a various wheel loads is compared with results obtained by a mathematical model.     

Analysis and prediction of tyre-soil interaction and performance using finite elements

The finite element method [FEM] of analysis previously developed for prediction of rigid wheel-soil interaction is improved and extended to take into account (a) the effect of flexibility of tyre carcass where energy losses now occur in development of mobility, (b) a simpler requirement for specification of boundary condition using input loading, and (c) normal and tangential load stress from the tyre distributed across the tyre-soil interface and varying with slip. The comparisons of analytically computed (predicted) drawbar pull with actual experimentally obtained drawbar pull results for tests in three types of tyres show good correlations. The effect of inflation pressure on development of tyre deformation energy losses can be seen from the analytically computed values.     

Net traction ratio prediction for high-lug agricultural tyre

A study was conducted to determine the accuracy of Wismer-Luth and Brixius equations in predicting net traction ratio of a high-lug agricultural tyre. The tyre was tested on a sandy clay loam soil in an indoor University Putra Malaysia (UPM) tyre traction testing facility. The experiment was conducted by running the tyre in driving mode. A total of 126 test runs were conducted in a combination consisting of three selected inflation pressures (i.e., 166, 193 and 221 kPa) and two wheel numerics (i.e., 19 and 29) representing two extreme types of soil strength under different levels of travel reduction ranging between 0% and 40%. Regression analysis was conducted to determine the prediction equation describing the tyre torque ratio. Marqurdt’s method used by Wismer-Luth for predicting non-linear equation was not found suitable in predicting the torque ratio of the test tyre awing its low coefficient of determination and inadequacy. The logarithmic model was found suitable in torque ration prediction. From analysis of covariance (ANCOVA) the mean effect of travel speed, tyre inflation pressure and wheel numeric on tyre net traction ratio were found to be highly significant, while the interaction of inflation pressure and wheel numeric was not significant. The 193 kPa inflation pressure was found the best, among the three inflation pressures used, in getting higher net traction ratio and higher maximum efficiency. Finally, two models were formulated for tyre net traction ratio; one in terms of wheel numeric and travel speed reduction and the other in terms of mobility number and travel reduction, to describe the tested tyre performance at different soil strengths.     

Tire footprint characteristics as a function of soil properties and tire operations

The main objective of the following presentation is to examine the possibility of predicting agricultural tire footprint parameters under different operational conditions. The experimental part of the research involved the operation of two agricultural transport tires on two soils, under variations of tire load, inflation pressures and soil moisture contents. Results obtained show that tire footprint parameters, such as contact area, length, width and sinkage, can be reliably predicted using multifactorial linear and total regressions, within the range of recommended tire loads, inflation pressures and soil moisture contents around the plastic limit.     

Prediction of traction and soil compaction using three-dimensional soil-tyre contact profile

Prediction of traction and compaction in the soil profile based upon two-dimensional (2D) and three-dimensional (3D) representations of the dynamic soil-tyre contact area and an assumed pressure distribution over the profile are presented for two tyre sizes at two inflation pressures, two levels of dynamic load and two slip levels in a tilled Yolo Loam soil condition. A soil model based upon a semi-logarithmic porosity-stress relationship was used to obtain the pressure distribution. Traction predictions based upon the 3D surface were significantly better than those based upon the 2D surface. Compaction predictions were similar for both surfaces except for immediately below the soil surface.     

The radial damping of agricultural tractor tyres

The damping coefficients of rolling agricultural tractor tyres in the radial (or vertical) direction have been measured. Six different tyres ranging in age from 1 to 16 years have been measured. Factors which most affect the apparent radial damping of the tyre are the inflation pressure, the tyre age, and the surface over which it rolls. The effects of rolling speed, load, torque, amplitude, frequency, ply rating and lug length are also discussed.     

Sources of variability in traction data

A 18.4R38 tyre was tested at 124 kPa inflation pressure, approximately 24 kN axle load in a firm and in a tilled Yolo-loam soil using (i) constant slip, (ii) constant draught, (iii) varying slip and (iv) varying draught tyre testing procedures. The results indicated that the constant slip test procedure leads to repeatable and consistent results whereas a variable slip test procedure leads to considerable scatter in the data. The constant draught test procedure yielded acceptable results. Varying slip appeared to influence the system dynamics much more than varying draught during tyre testing. An accurate method of predicting “true rolling radius” and “true slip” for an assumed zero condition is presented. The concept of motion resistance, its variability due to assumed zero conditions, and possible interpretations are discussed. The traction test data indicates that the motion resistance is not constant but varies with slip.     

Steering forces on undriven, angled wheels

The steering forces at low speed and zero camber angle were measured on undriven, angled wheels using tyres with no tread. The forces were measured in a soil bin using a moist loam soil at different levels of compaction. It was found that the coefficient of side force relative to the wheel was related to slip angle by an exponential relationship. Coefficient of rolling resistance relative to the wheel was a linear function of slip angle in the region zero to 20° but was an irregular function of slip angle at higher angles. The effects of tyre size, load, inflation pressure and soil condition were modelled well using different versions of the tyre mobility number. The most successful version of mobility number was one which incorporated both soil cohesion and internal friction angle. The coefficients of the exponential and linear relationships mentioned above were predicted with varying degrees of success using mobility number.     

Tyre flexibility and mobility on soft soils

Five model tyres were tested in the soil bin to investigate the effects of wheel flexibility on the tyre-soil performances. Two different soil types were used together with various inflation pressures which governed the tyre flexibility. The results confirm that tyre flexibility contributes significantly to the development of all the energy components [equation (1)] in the tyre-soil system. As can be seen from the contrasting performances shown, increasing the inflation pressure may allow for a favourable increase in the drawbar pull in one soil (frictional soil) so long as the input energy available can be increased, whilst the reverse may be true in the case of the other (clay) soil. The finite element model used satisfactorily confirms the measered values obtained and is seen to be able to account for tyre flexibility as shown in Figs. 11–14.