УДК 631.4; 631.31 THE SUBSTANTIATION OF THE TENSE STATE OF SOIL UNDER CONDITION OF ITS INTERACTION WITH WHEELS

Machine and tractor devices which consist of large tractors and devices corresponding to them, are widely used in the fields. The use of such machineandtractor devices results in reduction of both energy usage and labor inputs. But the wheels of large tractors deform and consolidate the soil that results in changes of healthy soil structure as well as in worsening of the agro-ecological soil condition. The use of large machineand tractor devices requires laying down of optimal constructional parameters for wheels. Optimized wheels will facilitate the decrease of both consolidation and devastation of the soil’s fertile layer. The paper considers the interaction between the soil and the wheels. The scheme for determining the distribution of tension in soil under condition of vertical loading, has been developed. The task for the calculation of the tense state of soil has been formed. This task makes it possible to determine the level of tension in soil under the wheels of machineandtractor devices. The determination of the level of tension in soil enables to determine and to substantiate the parameters of the wheel tires. The use of such tires will make it possible to provide the level of normal state of tension in soil lower than a permissible level. As follows from solving a reverse contact problem, and under condition of equal distribution of contact pressure, a mathematic model has been received. The received mathematic model makes it possible to perform a computer simulation of the effects of wheels’ width of the machine-and-tractor devices on tension which takes place in soil. The received model is universal and makes it possible to carry out the study of wheels of various standard sizes. A theoretical simulation of the performance of a machineand-tractor device has been made. The distribution of tension in soil environment is given.


Introduction
Large tractors are used in the fields. The use of such tractors makes it possible to raise productivity and reduce energy consumption, but they have a significant impact on natural environment. Currently, an experience on reducing the harmful effects of such machines on the environment at the cost of using biofuel [1] has been in practice. Also, under the pressure of heavy tractors' wheels on soil, appears a tense state which depends on the rate and the distribution of the external load and causes deformation, and as a result, soil environment's over-consolidation. Soil over-consolidation results in decrease in crop yields [2; 3], destruction of its structure [4; 5] and other negative effects [6]. That is why, the reducing of harmful effect of heavy tractors on the environment requires setting optimal design parameters of wheels.
The study of wheels' contact with soil showed that it is rather difficult to find a tense state in soil. It depends not only on loads which effect the wheels, but also on tractor's driving speed and on the parameters of a pneumatic tire [7; 8]. Sliding of a tire is of great importance as well [9]. In such type of study soil is treated as a tense and endless land which is limited by one horizontal surface [7; 10]. The soil environment is treated as homogeneous and isotropic one [8; 11]. But the results of the research obtained in above mentioned cases do not fully reflect the tense state of the soil environment. They will not help to determine the wheels' rational parameters either.

Materials and methods
The study of the fields of tension in vertical soil profiles, under condition of soil tension made by wheels, was done using the methods of numerical service simulating tests by means of a specially developed computer program ( fig. 1). This program made it possible to receive both the specifications of the distribution of the fields of tension and the numerical indexes of the rate of tension in separate, previously determined points of soil model on given scanning lines.
Further numerical modeling and service simulating test of a contact zone wheel-soil was performed on the algorithm, given on fig.2.  G kis normal load on the wheel, H; Dis external diameter of a tire, m, B minis minimum permissible width of a tire section, m: p wmaxis maximum permissible pressure in a tire, Pа; H -is height of a tire's section, m; С 1 , С 2 -is steel for a given type of a tire (С 1 =0.0012…0.0028•10 -5 Па -1 , С 2 =0.25…0.3 м -1 ); l -is distance between the wheels' extremities, m; n -is provisory amount of forces in a block of distributed tension; ΔВis spacing of width change of a tire's section, m; Δp w -is spacing of pressure change in a tire, Pа; h x -is normal deflection of a tire's dome, m; Вis real width of a tire section, m; σ х +σ уis a sum of normal tensions, Pа; τ ху -is tangent tensions, Pа; z w -is a relative ratio of deflection of a tire's dome; [z w ] -is a permissible deflection of a tire's dome 4 This program makes it possible to perform a computer simulation of the effects of MTA's wheels on the tension which appears in soil, as well as to choose their rational parameters.

Results and discussion
A numerical solution of the task on determining the tense state of soil is possible under condition of using the iteration method. In the first approaching, soil is considered as elastic semi-space limited by horizontal surface. The accepted environment of a soil model is isotropic. Under these conditions was used the solution of Bussinesk's task. According to this method, the distribution of tense in a massive is symmetric about x axis. To develop a mathematic model of a tense state from a few blocks of distributed load, it was represented as a superposition n of forces exerted on corresponding points ( fig. 3). Р 1 , Р 2 ,…,P iare the value of corresponding unit forces, H; ais the distance of block beginning from the beginning of coordinates, m; dais spacing among forces in a block, m; l 1 , l 2is blocks' width, m; σ х , σ у , τ ухare normal and tangent tenses in elementary semi-space M, PА; nis a number of forces in a block of distributed load As a result, a mathematic model of tense state was received from two blocks of distributed load in the form of: where G -is loading on the wheels' axe, H; l iis the width of a plot on which the distributed load was exerted, m k іis a weight coefficient which is determined as: k i =P i /P 0 (Р 0according to rationing will be: P 0 =Gl/(l 1 +l 2 +l 3 )); х, уare coordinates of an elementary plot of semi-space M ( fig.1) for which the indexes of normal and tangent tenses are determined, m. According to the system (1), a sum of normal tenses, which characterizes the change of a tense state of the environment that is under investigation, under the weight of a pair of wheels, is determined on a vertical surface of soil semi-space as: І І =σ I =σ х +σ у , where I I -is an invariant of a full tensor of tensions (a sum of normal tensions qi), Pа. And a maximum shifting tension τ max in a particular point of this surface will be: (1) The solutions of the equation make it possible to replicate a numerical model and imitation experiment to study the tense state of compacted soil profile according to the condition: where G iis a weight of a machine and tractor unit that falls on wheel, H; q iis і-wheel's pressure on the soil surface, Pа; l opt -is an optimal wheel's footprint area, m 2 ; σ н -is the boundary of soil's current, Pа; [τ]is permissible tangent tenses, Pа. The application of a system (1) makes it possible to replicate a numerical experiment on optimization of the constructive and performance parameters of a mobile farm vehicle's wheel as to minimization of the levels of intensity of soil environment's tension.

Fig. 4. Change of a sum of normal tensions (a) and tangent tensions (b) at depth
When solving the system (1), the change of the intensity level of soil environment tension at depth H=x, depending on the width b of wheel's footprint area contact with soil ( fig. 4), was determined.
The current's boundary of sod-podzol sandyloam soil which does not cause the non-renewable changes of the structural state of soil's root layers, for soil layer 0…10 is  н <0.113 MPa. Permissible tangent tensions (taking into account the moment of rolling) are τ<0,021 MPa. Taking this into account, it has been found that under maximum load on a wheel up to 28 kH (common to tractors of pulling power type 3) the width of a contact footprint has to satisfy the condition b≥0.55 m.
When choosing the type of tires which satisfy this requirement, the normal and relative tires' deflections and the width of a contact footprint depending on pressure in a tire ( fig. 5) were analyzed and a system (4) was received.  On the basis of the above mentioned characteristics of sod-podzol sandy loam soil, by means of the analysis of the numerical experiment's results, it has been determined that the use of a tire of type 28.1R26 for a tractor of pulling power type 3 under operating pressure р w =0.073 MPa, does not cause non-renewable changes of the structural state of the agricultural soil layers.

Conclusions
The results of the scientific research and of the practical experience testify to a close correlation link between a compressing effect of the drive systems of energy charged mobile agricultural machinery and the processes of upper soil degradation. The decline of the levels of technogeneous compression of mobile agricultural machinery on soil can be achieved by means of complex optimization of the construction parameters of the mobile machinery's wheels and by a corresponding standardization of their operating features.
A numerical simulation experiment made it possible to determine the basic rational parameters of a tractor's wheel of pulling power type 3, used while cultivating sod-podzol sandy loam soils: working pressure in a tire is 0.075 MPa, a minimal width of a contact footprint is 0.55 m. Under these conditions the compressing tensions in soil under the wheel are lower than a tension boundary of formchanging of the microstructure and do not exceed 0.113 MPa.