A

Seminar On

THE PREDICTION OF TRACTIVE PERFORMANCE

ON SOIL SURFACES

Presented by

Mr. Yogesh Dilip Sawant (13AG61R15)

DEPARTMENT OF AGRICULTURAL AND FOOD ENGINEERING

IIT, KHARAGPUR.

Introduction:

DRIVE TVRES for agricultural tractors are required to

provide traction on agricultural soils, to support the vehicle,

and to provide a minimum resistance to movement over the

surface in the intended direction of travel.

Different approaches have been suggested for predicting

tractive performance, however, they all rely on some soil

strength parameter and generally assume a uniform

distribution of shear stress between the tyre and the soil.

A new approach to the traction prediction equation is

described.

To develop a new approach to the traction prediction

equation.

To compare prediction equation with the widely used

Wismer and Luth equation and measured data obtained by

Wittig.

Objectives:

Bekker was one of the first to suggest such a relationship:

Janosi and Hanamoto proposed a simpler equation to describe the

asymptotic curves of shearing stress versus soil deformation

where K is a soil deformation modulus

Wismer and Luth suggested an equation for traction

They used cone index (based on cone penetrometer resistance) as a

measure of topsoil strength properties

Gee-Clough suggested a similar empirical equation for

traction. The principal terms CT and (CT)max were defined in

terms of the vehicle mobility number.

Mobility number is based on cone penetrometer resistance, tyre

dimensions and tyre deflection.

Brixius developed several prediction equations for bias ply tyres

operating in cohesive-frictional soils.

These equations contained more wheel parameters and were a

result of testing that was conducted in a wide range of soil

types.

However, they also depend on cone index which seems to be an

insufficient parameter for defining soil strength for traction

prediction purposes.

Prediction using cone index showed poor correlation between

measured data and predicted values for traction coefficient at 20%

slip.

However, a similar comparison using data obtained from plate

sinkage tests gave better correlations.

The investigation suggested that soil shear strength and soil rubber

friction were likely to be important variables in predicting

coefficient of traction.

Dwyer et al. conducted traction tests in which they used a cone

penetrometer as well as a soil shear meter to measure soil

parameters

Wittig proposed the use of a single wheel tester (SWT) for

determining a soil strength parameter in predicting tractive

performance

Different normal loads were applied to the SWT and the

maximum torque that could be developed was measured.

The general form of the equation used was:

where a and b are empirical constants.

This method was shown to give more accurate predictions on

Vienna loam soils than the cone penetrometer approach of

Wismer and Luth.

Upadhyaya and Wulfsohn developed a fully instrumented device

capable of measuring soil sinkage and shear

It was employed to conduct in situ sinkage and shear tests

They had conducted field tests for three different types of radial

tyre on five different soils with three axle loads.

They obtained a prediction equation for different soils and

loading conditions and concluded that soil conditions had the

greatest effect on the outcomes of their study.

Another interesting approach suggested by Janosi and Hanamoto

whereby the thrust is assumed to act similar to the shear force, in a

horizontal plane under the traction device:

Where,

F is the maximum shear force

P is pull

Ravi Godbole etal proposes a modified form of previous equation,

For uniform normal pressure a is independent of x and is equal to

W/bl

where bl = A, the contact area, assuming a rectangular contact

patch.

The final form of the equation is

Material and Methods:

Thus for the contact patch length,

The tyre numeric was defined as follows,

where p is inflation pressure

Krick established the following empirical prediction equation for

deflection, f:

For the purposes of this investigation, Krick's equation was re-evaluated

using the section height S instead of tyre section width B

Krick proposed his equation based upon the experimental data of

the most commonly used agricultural tyres.

For Small tyres:

Final equation for small tyres:

Final equation developed for prediction of traction:

Soil Testing•

The shear tests conducted can be categorized as consolidated

undrained tests.

Soils were collected from two sites. Four samples of each soil

were used for testing. Each sample was tested at five levels of

normal stress.

Fig.Shear displacement curves for different normal stress levels.

Fig. Plot of shear stress vs normal stress for soil 1.

Fig. Plot of shear stress vs normal stress for soil 2.

Deflection calculations:

Contact length and deflections were calculated at a given axle

load from the formulae given earlier.

The validity of these calculations was checked with the

empirical equation suggested by Painter.

This equation is of the form,

f is the tyre deflection, p tyre inflation pressure

ao ,a2 etc. are empirical constants.

Using Painters equation the value of deflection is f= 0.102 m.

This compares quite well with the deflection value of 0.0969

m determined from the equation for the deflection give earlier.

Using this equation gives an area A = 0.2252 m2 which compares

reasonably well with our calculated value of A = 0.2985 m 2.

Contact area calculations:

Area calculations were made using the formulae developed in

the earlier section assuming a rectangular contact patch.

Painter has suggested a similar empirical equation for contact

area,

D is the outside diameter of the tyre,

C is the tyre cross section equivalent diameter of curvature,

f is the tyre deflection

Results and discussion:

The difference between the P/W values obtained by actual measurement

and those obtained by using the modified equation can be explained as

follows:

(1) The testing conducted by Wittig was done in 1990 whereas the

authors conducted their soil tests from samples collected in 1992 at

the same locations

(2) Changes in the conditions of the soil and crop residue may have

resulted in different Tmax valúes.

(3) The contact area A is either calculated by formulae or checked using

empirical relationships. This may differ from the exact value for

contact area. In addition, effects such as soil wall build up around the

tyres and soil topography may affect the area term

(4) The contact length term used in the prediction equations may

differ from actual values.

Conclusions:

The equation predicts traction coefficient more accurately than

some other methods and justifies the use of the soil deformation

modulus in traction studies.

Soil deformation modulus is a good estimator of soil strength and

has relationship with normal stress levels.

Expressions developed for contact lengths and area provide results

that are consistent with other models.

References:

M. BEKKER, Off the Road Locomotion. The University of

Michigan Press (1960).

Z. JANOSl and B. HANAMOTO, The analytical determination

of drawbar pull as a function of slip for tracked vehicles in

deformable soils. First Int. Conf. Mechanics of Soil-Vehicle

Systems, Torino-St. Vincent (1961).

R. WISMER and H. LUTH. Off-road traction prediction for

wheeled vehicles. Trans. ASAE 17 (1), 8-14 (1974).

V. Wlx'rlG, Prediction of tractor drawbar pull on agricultural

soils. M.S. Thesis, Dept of Agricultural Engr, South Dakota State

University, Brookings, SD 57007, unpublished (1990).

THANK YOU