Research Paper: SW—Soil and WaterModelling effects of tyre inflation pressure on the stress distribution near the soil–tyre interface
Introduction
Agricultural vehicles impose mechanical stresses on soil, which may cause soil compaction. The loaded area and the magnitude and distribution of stresses at the soil surface are directly controlling the impact on topsoil horizons, and these factors are also decisive for the stresses reaching the subsoil. The optimisation of tyre characteristics for a uniform distribution is thus crucial for reducing topsoil as well as subsoil compaction. Keller (2005) and Keller et al. (2007) showed that the performance of soil compaction models is highly dependent on a correct upper model boundary, i.e., the contact area and the distribution of contact stresses. Therefore, knowledge on the shape and area of the tyre footprint, and the magnitude and distribution of contact stresses have direct, practical implications as well as the potential of improving our understanding of stress propagation to the subsoil.
Data on contact areas at the soil–tyre interface of modern agricultural tyres are scarce. Several researchers including Grečenko (1995) and Febo et al. (2000) have measured and tested empirical models of tyre footprint area on a rigid (hard) surface. However, contact area is a function of surface hardness (Diserens, 2002; Way & Kishimoto, 2004), and therefore, the contact area on a rigid surface may differ significantly from that on deformable soil. Diserens (2002) measured the contact area at the tyre–soil interface for a large number of different tyres and for different soil conditions in order to develop regression equations for estimation of the contact area. However, he did not analyse the shape of the tyre footprint.
Knowledge of the effects of tyre characteristics and soil conditions on distribution of vertical stresses at the tyre–soil interface is still limited. Several studies have shown that the distribution of vertical stresses at the tyre–soil interface may be highly non-uniform, that peak stresses may greatly exceed the tyre inflation pressure and that the stress distribution is affected by type of tyre, the loading characteristics and the soil conditions (Gysi et al., 2001; Way & Kishimoto, 2004; Jun et al., 2004; Keller, 2005). In spite of everything, simple approximations of the contact area and stress distribution (e.g. a uniform or parabolic stress distribution over a circular contact area) are often used in soil compaction modelling.
One major obstacle to a better understanding of factors affecting stress distribution beneath tyres seems to be the high variability of the soil material, which calls for detailed stress measurements in time and space. In this study, we have therefore aimed at quantifying the contact area as well as the stress distribution across the footprint in greater detail than seen previously. A main purpose was to improve our knowledge of the effect of tyre inflation pressure on stresses transferred to the soil. Keller (2005) suggested promising equations for the contact area and for the stress distribution in the driving direction as well as across the width of the wheel. Our study includes a refinement and combination of the Keller equations for description of stress in the contact area. We call the model “FRIDA” after the cooperation between FRench, SwIss, SweDish and DAnish researchers. We conducted empirical tests for two different tyres at three inflation pressures and used FRIDA to evaluate the impact on stresses transferred to the soil.
Section snippets
Description of the FRIDA model
The periphery of the contact area, when viewed from above, may be modelled by a super ellipse (Hallonborg, 1996; Febo et al., 2000; Keller, 2005), which, in an orthogonal coordinate system with centre at the origin, is given bywhere a and b are half the width of the minor and major axes in m, and n is the “squareness”. Let denote the boundary and interior of the super ellipse.
The distribution of the vertical stress in the contact area may be modelled by
Soil, tyres and test conditions
The experimental field was located at Research Centre Foulum, Denmark, (56°30′N, 09°34′E). The soil had been mouldboard ploughed to about 0.2 m depth in the autumn 2004 prior to the investigation in early summer 2005. A small grain cereal crop had been established in the spring but was cut and removed before the tests. The sandy Foulum soil is developed on Weichselian glacial till and is classified as a Mollic Luvisol according to the WRB (FAO) system (Krogh & Greve, 1999). Soil texture, density
Measurement of stress
The load predicted from the stress readings, Fapp, was on average approximately 26% higher than the real wheel load, Fwheel. This was probably due to interaction between the stress sensor and the compacting wheel as discussed by Kirby (1999). It is basically impossible to measure correct stresses with transducers exhibiting stiffness other than the surrounding medium (in this case soil). We corrected the stress readings to the level that should be expected from the weight of the wheel (Section
Conclusions
The proposed FRIDA model gave a good description of measured data: the tyre footprints were well described by a super ellipse, and the distribution of vertical stress by a combined exponential (perpendicular to the driving direction) and power-law (along the driving direction) function. The contact area doubled when reducing the inflation pressure from 240 to 50 kPa, while the recommended inflation pressure of 100 kPa displayed an intermediate value. The measured peak stress and the model-fitted
Acknowledgements
This study was conducted in cooperation with The Danish Agricultural Advisory Service and NDI Denmark (Nordisk Dæk Import A-S). We thank Jørgen Pedersen and Poul Otto M. Hansen for assistance in the selection of tyres and the inflation pressures used in the study. The tyres were kindly made available by NDI Denmark. We thank the staff at Foulumgaard Experimental Station for all their kind assistance during the experimental period. The technical assistance of Michael Koppelgaard and Stig T.
References (29)
Tyre footprint area on hard ground computed from catalogue values
Journal of Terramechanics
(1995)- et al.
Influence of single passes with high wheel load on a structured, unploughed sandy loam soil
Soil and Tillage Research
(1999) Super ellipse as tyre-ground contact area
Journal of Terramechanics
(1996)- et al.
Dynamic load and inflation pressure effects on contact pressures of a forestry forwarder tyre
Journal of Terramechanics
(2004) A model for the prediction of the contact area and the distribution of vertical stress below agricultural tyres from readily available tyre parameters
Biosystems Engineering
(2005)- et al.
Technical solutions to reduce the risk of subsoil compaction: effects of dual wheels, tandem wheels and tyre inflation pressure on stress propagation in soil
Soil & Tillage Research
(2004) - et al.
SoilFlex: A model for prediction of soil stresses and soil compaction due to agricultural field traffic including a synthesis of analytical approaches
Soil & Tillage Research
(2007) Soil stress measurement: I. Transducer in a uniform stress field
Journal of Agricultural Engineering Research
(1999)- et al.
The effects of reduced inflation pressure on soil–tyre interface stresses and soil strength
Journal of Terramechanics
(1995) SOCOMO: a soil compaction model to calculate soil stresses and the subsoil carrying capacity
Soil & Tillage Research
(2004)
Interface pressures of a tractor drive tyre on structured and loose soils
Biosystems Engineering
Influence of tyre inflation pressure on stress and displacement in the subsoil
Nonlinear Regression Analysis and Its Applications
Some comparisons of average to peak soil–tyre contact pressures
Transactions of the ASAE
Cited by (109)
Effect of contact length of bias ply tractor tire on its tractive performance
2024, Journal of TerramechanicsAn exhaustive investigation into power performance of an unmanned robotized vehicle for industrial transportations
2023, Measurement: Journal of the International Measurement ConfederationVertical and horizontal stresses from a lightweight autonomous field robot during repeated wheeling
2023, Soil and Tillage ResearchDiscrete element modelling of soil pressure under varying number of tire passes
2023, Journal of TerramechanicsAn empirical model for prediction of topsoil deformation in field traffic
2023, Soil and Tillage Research