Influence of Tyre Inflation Pressure and Wheel Load on the Traction Performance of a 65 kW MFWD Tractor on a Cohesive Soil

The choice of tractor configuration is of primary importance in tillage operations for the optimisation of traction performance, i.e. for limiting slip which involves energy loss. To a great extent, this aspect affects the fuel consumption and the time required for soil tillage. Tyre inflation pressure and wheel load are both easily managed parameters which play a significant role in controlling the traction performance of a tractor. The present study aimed to investigate the influence of tyre inflation pressure and wheel load on the traction performance of a mechanical front wheel drive MFWD tractor (65 kW engine power) on an agricultural clay (C) Vertic Cambisol on the basis of results of traction tests and simulations with a semi-empirical soil-tyre interaction model adapted for MFWD vehicles. The traction tests were carried out using four tractor configurations with two tractor weights (40.8 kN and 50.2 kN) and two tyre inflation pressures (60 kPa and 160 kPa). Traction performance was considered in terms of drawbar pull, traction coefficient, tractive efficiency, power delivery efficiency and specific fuel consumption in relation to wheel slip. A decrease in tyre pressure and an increase in wheel load resulted in higher drawbar pull however, only the former produced improvements in terms of coefficient of traction, tractive efficiency, power delivery efficiency and specific fuel consumption, while the only significant benefit resulting from the latter was a reduction in specific fuel consumption at a tyre pressure of 160 kPa and a slip of under 15%.

Other important parameters involving the energy aspects of traction performance are tractive efficiency η tr and power delivery efficiency η PD .The tractive efficiency of a drive wheel is defined as: which expresses the ratio of output power to input power of the wheel, NT being the net traction force, V a the actual forward velocity of the wheel, T the total driving torque on the wheel, and ω the angular velocity of the wheel.The same tractive efficiency can be defined for the tractor as: and represents the fraction of power delivered to the tractor wheels that is available as drawbar power.Servadio (2010) considered both the traction coefficient and the tractive efficiency to characterise field performance of several wheeled and tracked vehicles in central Italy.
Power delivery efficiency is defined as the ratio of delivered tractive power (drawbar power) to tractor input power from the engine, and represents the fraction of power produced by the engine of a tractor that is available as tractive power (Shell, Zoz, & Turner, 1997;Turner, Shell, & Zoz, 1997).In order to consider the engine power input, the equivalent PTO (power-take-off) power can be used (Zoz, Turner, & Shell, 2002), in which case the power delivery efficiency can be defined as: In terms of fuel consumption, a parameter related to the traction performance of the tractor is the specific fuel consumption SFC, defined as the ratio of the fuel consumption expressed in kg h -1 (gravimetric) or l h -1 (volumetric) to the engine power input, or alternatively to the drawbar power.
The traction performance of a wheeled tractor is the result of a stress-strain interaction between the tractor wheels and the topsoil.This interaction is affected by several factors, including the mechanical behaviour of the topsoil, power and geometry (wheelbase and drawbar height) of the tractor, number of drive wheels, wheel load, wheel slip, tyre dimensions (width and diameter), tyre inflation pressure and stiffness, all of which exert a significant influence.While most of the above factors are more or less constrained, wheel load and tyre inflation pressure can be varied within wide ranges, allowing easy management of the traction performance of the tractor.Consequently, these factors are highly advantageous for practical applications.The influence of wheel load and tyre inflation pressure on tractor traction performance has been investigated using both a theoretical and an experimental approach.
With regard to the former approach, the semi-empirical models of interaction between soil and a pneumatic wheel based on Bekker's theory (Bekker, 1960) offer a valid framework for the better understanding and simulation of the effects of both tyre inflation pressure and wheel load on the traction performance of the tractor-soil system.In this context several approaches have been presented assuming the contact surface between soil and tyre to be a combination of a flattened portion and the unloaded contour (Bekker, 1960;Wong, 1989), or as an arc of an equivalent rigid wheel of larger diameter (Fujimoto, 1977), or also described as a parabolic configuration with its apex at the front point of contact (Schmid, 1995).More recently, Shmulevich and Osetinsky proposed a model based on a parabolic soil-tyre contact surface with its apex at the rear point of contact (Shmulevich & Osetinsky, 2003;Osetinsky & Shmulevich, 2004), which presents a simple mathematical treatment and allows a reliable simulation of traction performance.
With regard to the latter approach, many authors have reported experimental results showing some benefits of reduced tyre inflation pressure for tractor traction performance (Zombori, 1967;Gee-Clough, McAllister, & Evernden, 1977;Burt & Bailey, 1982;Turner, 1993;Zoz & Grisso, 2003).Whilst evident for radial-ply tyres, these benefits in some cases turned out to be less or not at all significant for bias-ply tyres (Lee & Kim, 1997).Serrano, Peça, Silva, and Márquez (2009) studied the performance of a tractor (59 kW engine power) with two static ballasts, with and without liquid tyre ballast, and at three different inflation pressures.The use of liquid ballast in the tyres turned out not to improve work-rate and besides to increase fuel consumption per hectare of 5-10%.The use of higher tyre inflation pressures produced a slight reduction in work-rate (3-5%) with a large increase in fuel consumption per hectare (10-25%).Burt, Balley, Patterson, & Taylor (1979) investigated the influence of dynamic wheel load on tractive efficiency on both a compacted and an uncompacted soil, observing that, with constant travel reduction (slip), an increase in dynamic load produced in the former case an increase and in the latter case a decrease in tractive efficiency.Charles (1984) carried out tractor-traction tests on a low-plasticity silt soil in both a tilled (soft) and firm condition at different static loads and tyre inflation pressures.His findings show that both an increase in static load and a decrease in tyre pressure resulted in higher traction performance in terms of drawbar pull and tractive efficiency for both of the soil conditions considered.Lyne, Burt, and Meiring (1984) reported results of traction tests with a 4WD tractor on a Westleigh clay in two soil conditions and with several combinations of static load and tyre pressure, showing that as static load increased at each inflation pressure, so did drawbar pull, drawbar power and power demand on the engine, with a corresponding decrease in specific fuel consumption (drawbar power basis).According to results reported by Turner (1993) and Zoz and Grisso (2003), an increase in tractor weight (wheel load), obtained with ballasts and tyre inflation pressure adapted to the weight, makes for higher drawbar pull, although it does not seem to result in a significant variation in terms of traction coefficient or power delivery efficiency.Results of traction tests reported by Zoz and Grisso (2003) for a single 520/85R46 radial tyre with inflation pressure adapted for different wheel loads showed a negligible influence on maximum tractive efficiency.Burt, Lyne, Meiring, and Keen (1983) and Burt and Bailey (1982) showed how, for a given drawbar pull, the tractive efficiency of both radial-ply and bias-ply tyres can be maximised by selecting proper levels of dynamic load and inflation pressure.Lyne et al. (1984) also pointed out the importance of an appropriate choice of both dynamic load and tyre inflation pressure in order to optimise the tractive efficiency of a tractor.Moreover, it was observed that operating at optimum tractive efficiency allows minimum specific fuel consumption (Lyne et al., 1984;Jenane, Bashford, & Monroe, 1996).Gee-Clough, Pearson, and McAllister (1982) demonstrated the key role of a wheel load properly matched to tractor power, speed, and drawbar pull at low tyre inflation pressure (110 kPa or less), in the optimisation of the power output of wheeled tractors in frictional-cohesive soils.This variety of studies has produced results which in some cases appear to contradict one another.It should be pointed out, however, that the widely differing experimental conditions considered (soil and tyre types, wheel load range, tyre pressure range) make it difficult to draw proper comparisons, as do the different layouts and methodologies used for the traction tests.
In this context, the issue of improving traction performance of a tractor by ballasting or by reducing the inflation pressure of the tyres is thought to require further and deeper understanding in order to better define clear indications for a correct choice of the tractor configuration, this latter considerably contributing in more appropriate tillage management.Furthermore, some of the studies presented either dealt with big tractors (Turner, 1993;Zoz & Grisso, 2003) or the single wheel testers (Burt et al., 1979;Burt & Bailey, 1982;Gee-Clough et al., 1977), whilst the performance of medium powered tractors, which are reasonably widespread in Central Europe, has received less attention.
In this paper, the influence of tyre inflation pressure and wheel load on the traction performance of a MFWD tractor (65 kW engine power) on an agricultural clay (C) Vertic Cambisol is compared and discussed on the basis of results of field traction tests as well as simulations with a semi-empirical soil-tyre interaction model adapted for MFWD vehicles, with a mechanistic interpretation of results.In addition, two equations describing the relationships power delivery efficiency-wheel slip and specific fuel consumption-wheel slip are presented.

Soil-Tyre Interaction Modelling
Forces acting on the driven pneumatic wheel with a detail of the elementary forces acting at soil-tyre contact according to Shmulevich and Osetinsky (2003) are shown in Figure 1.
The following assumptions are considered: the soil behaves as a plastic non-linear medium, the wheel rolls in steady-state motion at a low velocity, tyre deformations are linear elastic, the wheel-soil interaction is two dimensional (plane-strain approach).This latter assumption implies that the rut depth is the same across the width, and the width is the same along the contact surface, moreover all values are referred to the unit width of the wheel.
According to Bekker's theory, the vertical soil pressure along the soil-tyre contact surface is assumed to be equal to the soil pressure beneath the compression plate of a bevameter at the same depth: wherein p s is the vertical soil pressure under the plate, z is the soil sinkage, n is the exponent of deformation, and b is the smaller dimension of the contact patch (width of the tyre), whilst K c and K φ are the cohesive and frictional modulus of soil deformation, respectively.
The vertical component of the total soil reaction must balance out the wheel load W, this condition is expressed as follows: The equation of the parabolic contact surface (Osetinsky & Shmulevich, 2004) expresses the sinkage z as a function of the horizontal coordinate x: z 0 being the rut depth and a being the parameter of the parabolic equation.
Integral 6 is solved by means of a series expansion of function 7 limited to the second term, similarly to the approach reported by Wong (2008).This results in: Tyre stiffness is defined according to Lines and Murphy (1991) as the sum of two components, the carcass stiffness K carc and the product ΔK p P in , where ΔK p is the inflation pressure dependence of the tyre and P in is the inflation pressure.Consequently, the stiffness has both a constant component and a component which varies with the inflation pressure.
The same equilibrium condition in equation 6 can be expressed in terms of the tyre stress state according to its stress-deflection relationship: ( ) where e 0 is the eccentricity of the centre of the wheel relative to the rear point of the contact surface (Figure 1), R is the unloaded radius of the wheel, and K v is the coefficient of vertical stiffness of the tyre for unit length of contact surface, which can be expressed as a function of K carc and the product ΔK p P in : A detailed derivation of equation 9 is described in Osetinsky and Shmulevich (2004).
Rut depth z 0 and the parameter a which define the soil-tyre contact surface are determined by simultaneously solving equations 8 and 9.
The horizontal component of the elementary force p h and the vertical component of the elementary force p v acting at soil-tyre contact are given by: where ds is the infinitesimal area of the contact surface and α is the angle between the tangent to the infinitesimal area of the soil-tyre contact surface and the x-axis (Figure 1), whilst σ and τ are the normal stress and the tangential stress at the soil-tyre contact surface, respectively.Moreover, it turns out that (Figure 1): The shear stress τ at each point of the contact surface depends on the normal stress σ, the soil cohesion c, the angle of soil shear resistance φ, the soil shear deformation modulus k, and the soil shear displacement j along the contact surface.This dependence is described by the well known equation proposed by Janosi and Hanamoto (1961): The soil shear displacement at each point of the contact surface is calculated by integrating the component of the absolute velocity tangent to the surface (slip velocity) over time, similarly to the approach described by Wong and Reece (1967) for a rigid wheel.The calculation of the soil shear displacement is described in detail in Osetinsky and Shmulevich (2004) and yields the following integral to be solved by a numerical approach: In integral 16, V a is the actual forward velocity of the wheel, whilst ω is the angular velocity of the wheel.The wheel slip i relates the actual forward velocity and the angular velocity of the wheel: where R r is the rolling radius of the wheel.
The normal stress at each point of the contact surface is given by: )ax where δ is the vertical tyre deflection at each point of the contact surface (Figure 1) which can be defined on the basis of the geometry of the contact surface as: ( ) The gross traction GT is obtained by using a numerical approach to integrate the horizontal components p h of the elementary force over the contact surface.According to equations 11, 13, 14, 15 and 18 this condition is defined as: The main resisting forces acting on a tractor moving on a flat terrain are represented by the internal resistance of the running gear and the resistance due to the interaction with the terrain.Since the latter factor is, to a great extent, the most significant (Bekker, 1960;Wong, 2008), the internal resistance can be neglected, at least in the first approximation.The resistance due to interaction with the terrain, according to Figure 1, corresponds to the soil compaction resistance R c .Additional soil bulldozing resistance must be taken into account in soft soils where wheel sinkage is significant.In the cases considered here, the bulldozing effect may be reliably expected not to occur because of the limited wheel sinkage values.The soil compaction resistance is calculated as the vertical work performed in making a rut of a depth z 0 (Bekker, 1960): ( ) The net traction NT is finally calculated as: According to Figure 1, the total driving torque T on the wheel is calculated as: www.ccsen The term M where R GT calculated The term M centre on w The eccent moving wh

Tractio
The soil-ty wheel load slip of the between th The multip with the f passage as

Characteristics of the Topsoil
Some physical parameters of the agricultural clay (C) Vertic Cambisol are listed in Table 2, along with the mechanical parameters for the soil-tyre interaction model.
Soil texture was characterised according to the United States Department of Agriculture (USDA) classification system, moreover, soil type was classified according to the Food and Agriculture Organization of the United Nations (FAO) system (2006).Bulk density was measured on undisturbed soil samples according to Blake and Hartge (1986).Volumetric water content was measured via a time domain reflectometry (TDR) device (E.S.I.Environmental sensors MP-917, Sidney, Canada) with two-rod single diode probes.
Topsoil mechanical parameters for the soil-tyre interaction model were derived via vertical plate penetration tests and horizontal plate shear deformation tests with a tractor-mounted bevameter (Bekker, 1960).An exhaustive description of the bevameter used was given by Diserens and Steinmann (2003).
Vertical plate penetration tests were carried out with two circular plates of 20 cm and 30 cm diameter at a penetration rate of around 0.02 m s -1 .The cohesive and frictional moduli of deformation K c and K φ as well as the exponent of deformation n were determined according to Wong (1980).The horizontal plate shear deformation tests were performed by an annular plate with an outer diameter of 30 cm and an inner diameter of 20 cm at different vertical pressures ranging between 25 and 215 kPa.Measured shear stress-displacement curves were fitted with equation 15, and values of c, φ and k were determined according to the procedure described by Wong (1980).
In order to consider the multipass effect, i.e. the different behaviour of soil interacting with the front and rear wheel, the vertical plate penetration tests and the horizontal plate shear deformation tests were performed before the passage of the tractor, as well as on the rut left by the passage of the front wheel.Because the parameters K c , K φ and n calculated before and after the passage of the front wheel changed significantly, they were differentiated for soil interacting with the front wheel (K c,f , K φ,f , n f ) and soil interacting with the rear wheel (K c,r , K φ,r , n r ), as reported in Table 2.A unique characterization was adopted for shear parameters c, φ and k, as they did not change significantly before and after the passage of the front wheel (Table 2).

Simulation of Contact Surface and Contact Stresses
The reliability of the soil-tyre interaction model for simulating both wheel sinkage (rut depth) and traction performance was pointed out by Osetinsky and Shmulevich (2004).
The simulation of the soil-tyre contact surface and the contact stresses (normal σ and shear τ) together with the soil www.ccsen strength τ m is given by the latter c under a giv The geom system in x-axis and The geome increase in contact sur

Measu
The measu function o

Lowering without ba
The increa although it     partly due to a higher total contribution of the frictional component of the soil strength and partly due to a higher total contribution of the cohesive component of the soil strength along the contact surface.In spite of the higher drawbar pull, this way of using the soil strength did not result in any improvement in terms of traction coefficient (Figures 8 and 9), simulated tractive efficiency (Figure 10), or power delivery efficiency (Figure 11).At a slip of under 15%, only the specific fuel consumption decreased with increasing wheel load at a tyre pressure of 160 kPa.
The results of this study may provide helpful indications for an appropriate choice of tractor configuration on cohesive soils in order to optimise tractor performance, thereby saving time and reducing the costs of tillage management.

Conclusions
The present study aimed to analyse the effects of variations in tyre inflation pressure and wheel load on the traction performance of a 65 kW MFWD tractor on an agricultural clay (C) Vertic Cambisol.
In the conditions examined, although the tractor developed higher drawbar pull both when tyre inflation pressure was decreased and wheel load was increased, only the decrease in tyre pressure produced improvements in terms of coefficient of traction, tractive efficiency, power delivery efficiency, and specific fuel consumption, while the only significant benefit due to the increase in wheel load was a reduction in the specific fuel consumption at a tyre pressure of 160 kPa and a slip of under 15%.A mechanistic interpretation of these results proposed.
Two equations describing the relationships power delivery efficiency-wheel slip and specific fuel consumption-wheel slip were presented.
The results of this study may provide helpful indications for an appropriate choice of tractor configuration, as well as for the reasonable control of wheel slip, with a view to optimising traction performance on cohesive soils, thereby saving time and reducing the costs of tillage management.
is the maximum value of the horizontal coordinate according to Figure1.
Figure 2. Forc Figure 4. Lay Figure 7. and th Figure 9 sh pressure (f base is ass Tyre press increase in Figure 1

Table 1
B , θ B , a ic fuel consum