Source document: https://docs-lawep.s3.us-east-2.amazonaws.com/1697749758826.pdf (Georgia)
ANNALS OF AGRARIAN SCIENCE, vol.

13, no.

3, 2015 ИЗВЕСТИЯ АГРАРНОЙ НАУКИ, Том 13, Ном.

3, 2015 AGROENGINEERING АГРОИНЖЕНЕРИЯ INTERACTION OF THE UNDERCARRIAGE OF MOUNTAIN SELF-PROPELLED CHASSIS WITH THE SOIL BASED ON THE RHEOLOGICAL MODELS R.M.

Makharoblidze, I.M.Lagvilvava, R.M.

Khazhomia, B.B.
Khazhomia, B.B.

Basilashvili Agricultural University of Georgia 13 km, Ave., David Aghmashenebeli, Tbilisi, 0131 Georgia; r.makharoblidze@arguni.edu.ge; lagviigor@mail.ru; Mishkakhazhomia@mail.ru; b.basilashvili@agruni.edu.ge Received: 12.03.15; accepted: 15.05.2015 The work gives a mathematical model of interaction of the undercarriage of mountain tandem-wheeled self- propelled chassis with the soil.
A rheological model of Voigt and principal law of linear deformation are used as the deformation law of soils.

A calculation formula for the soil deformation by considering the relative location of the front steering and rear driving tandems wheels is deduced.

The soil deformation by ordinary biaxial and experimental undercarriages is compared.

interaction of the given type of undercarriages with the soil need further perfection.
RESULT AND ANALYSIS Unlike the mechanics of a continuous medium, admitting that a body is continuous, the soil mechanics considers the ground as a porous disperse medium, capable of changing its volume, i.e.

being compacted.
being compacted.

The theory of linear deformation of soils is based on the following preconditions: the relation between the pressure and the change of volume is directly proportional; the compaction of ground in time (consolidation) takes place as a result of the water movement through the ground pores; the ground has not only inter particle cohesion, but internal friction, too [3].

In reality, the behavior of soils under the load is much more complex.
They are able to change their deﬂ ected mode in time and have the relaxation and aftereffect properties.

Therefore, the design diagrams of interaction of the undercarriage of the machines with the soil must consider the rheological properties of the soil.

Let us evaluate the behavior of soils at repeated loadings by undercarriages of an experimental self-propelled chassis based on the rheological model of Voigt, which is parallel connection of linear-elastic and viscous elements [4].
A mathematical model of the law of deformation is expressed as follows: INTRODUCTION It is known that the traction and coupling properties of tractors and exhibited during the interaction with the soil, what on its turn results in the changed physical-mechanical properties of the soil.

In particular, there are compacted zones of signiﬁ cant sizes formed in the soil, which are concentrated along the both sides of traces of caterpillars or wheels.
As the soil compaction increases, the volume of air pores is reduced and gas exchange is declined having a negative impact on the course on the course of the biological processes and consequently, on the growth and germination of plants.

These negative consequences are particularly severe for perennial plantings, where the aggregates repeatedly travel along the permanent track.
The density of a root-inhabited soil layer exceeding its optimal value by several times reduces the crop yield signiﬁ cantly and accelerates the process of the plants drying out.

At present, the following methods to reduce the compacting impact of the wheels are widely used: reduction of pressure in tires; use of arch tires; doubling of tires; installation of rippers eliminating the surface compaction of soil.
The authors [1] consider the use of a multi-axis tractor for this purpose as a perspective choice.

Aiming at reducing the compacting impact on soil as well as expanding the functional capabilities, we have developed a self-propelled chassis, which consists of two balancers with four driving wheels at the ends, which transmit the rotation from the rotation from the driving axle by means of roller chains [2].
The methods of theoretical investigation of the process of 61 where H is the long-termed modulus of elasticity, H M 2 ; is the stress, H M 2 ; is the relative deformation; is the coefficient of viscosity, H c 2 ; M t as the time of deformation, sec.
A similar task when considering the interaction of multi-axis undercarriages with the soil in terms of spasmodically changing continuous stress 0 and constant time of load and unload is referred to in the work [1].

The diagram of the model loading is shown in Fig.

1.
1.

At the first loading with the front driving wheels, in case of stress constant in time const, the relationship (1), after integrated, gives the following expression: 1 H c e t 10 H , (2) Where H is the delay time of deformation.

Fig.

1.
Fig.

1.

Diagram of loading the undercarriage of mountain tandem-wheeled self-propelled chassis: 62 1 - balance reducer; 2 - driving half-axle; 3 - chain gear; 4 - axle of driving wheels; 5 - front driving tandem wheels; 6 - rear driving tandem wheels; 7 - of mountain self-propelled chassis; 8- front wheels.
At initial conditions t 0, IH 0, G 10 H we have 1 H e 10 H 1 , (3) i.e the movement takes place under the exponential law, whereas 3I asymptomatically approximates the value 10 H .
At unloading 10( 0) equation we can find the value of the deformation of inverse creeping from the The change of deformation in the period of first unloading is determined from this equation H d dt .
(4) 0 under the initial condition 0 t t 1 1 H We will have P 1 1 H e t T 1 1 H e .
(5) By putting equation (3) in equation (5), we gain: 1 P 10 H ) e T 1 (1 e , (6) i.e the maximum deformation 10 H diminishes under the demonstrative law.
At the repeated loading, the soil is deformed with the front wheels of a tandem of a balance carriage by the stress constant in the time 20 const and the determined by the following relation: 2 H C e t 20 H .

(7) Here the constant C is determined from the initial conditions 2 H 1 P C , 1P 20 H .
63 t T 1 0 T , 1 Then from expression (7) we again: 2 H P 1 2 0 H e 0 H 0 2 H 2 1 e 1 P e .
(8) By putting the value 1 p in equation (8), after the conversion, we gain: 2 H 1 e 1 H 0 1 0 2 T 1 e .
(9) At the second unloading 20( 0) the change of deformation is determined from equation (4) under the initial condition t 2 We have T T T 1 2 1 T 2 0 2 H .
P 2 2 H e T 2 1 e 1 H 0 1 0 2 T 2 e , T 1 e 2 P 1 e 1 H 0 1 0 2 T 2 e T 1 e .
(10) The third time , the compacted trace of soil is deformed with the rear wheels of the balance carriage by the stress constant in time 20 const and the deformation is determined by the relation: 3 H C e t 30 H .

(11) Here the constant C is determined from the initial conditions t T T T T 2 1 1 2 0 2 P .
From expression (11) we again Then from equation (11) we will gain 2P 30 .

 3 H 2 P 0 3 e 0 3 H 0 3 H 1 e 2 P e .
Then, after putting the value 2P from the equation (10) and after relevant conversions, we gain: 64 3 H 1 e 1 H 0 0 3 T 2 e 2 0 1 e T T 1 2 .
(12) The technological working tools on spars of a mountain self-propelled chassis can be positioned in the manner as to observe the following condition 0 0 .
0 3 0 1 2 Then the subsidence of the deformed trace after three passages of wheels, according to expression (12), will be: 3 H 1 e 0 H T 2 T T 1 2 e 1 e .
(13) For a biaxial of mountain self-propelled chassis of a serial production, the subsidence of the deformed trace, according to expression (9), will be 2 H 1 e 0 H T 1 e 1 .
(14) The duration of the period of loading , where l is the length of support point of wheels (m), is the aggregate speed (m/sec).

The duration of the period of loading and unloading /l v T 1 ( L d ) / v , T for serial chassis 1 L v , where L is the base of the self-propelled chassis (m), d is a half distance between the centers of tandem wheels (m), T 2 2d v is the duration of the second period of loading and unloading, (m).
Let us analyze the impact the increase of the number of supports with the area KF has on the track-formation under the constant general load ,GenG i.e.

 0 F K 1 0 F K 2 0 F K 3 0 F Gen 3 0 F G 0 Gen , if F K 1 F K 2 F K 3 F 0 .
By considering these assumptions, let us write down relation (13) as follows: 3 H l v 1 e G GEN 3 F H 0 2 d v L d v e 1 e (15) Similarly for the serial chassis, we have: 2 H l v 1 e G Gen 2 F H 0 L v 1 e (16) 65 By dividing expression (16) by expression (15), we will gain coefficient of the change of the track depth as a result of increasing number of tandem wheels of the experimental self-propelled chassis to three.
We have: K 2 3 H H 3 2 1 1 e d 2 v L v e L d v e .

(17) For example, we admit that =1, L 2,55 m, d 546 m, v 51 km / h =1,39 m / sec.

with these values we gain the coefficient K 1, 2.

This is the value by which the track depth diminishes for the of mountain self-propelled chassis if compared with a serial one.
For comparison, let us make a similar assessment of the behavior of soils based on a more general law of linear deformation [3].

E d dt H d dt , (18) here E is the instantaneous modulus of elasticity, N/ 2m ; E is the relaxation time, sec.

We admit that at every loading with the duration of , the load is kept constant 0.
At the first loading, 0 const .

E d dt H 0 , (19) and deformation 1H is determined by solving equation (19) as follows: 1 H C e Ht E 0 H C e t 0 H , (20) here the notation is accepted.
E H Unlike the model of Voigt, at the moment of applying the stress 0 an initial deformation 0 10 H , appears instantly and therefore, at t 0 from (20) we gain: C 0 0 e H Then, by considering that the time of loading t 1 1 H E 0 H 0 1 .

H 66 e .
(21) At the first unloading ( 0 ) the deformation of inverse creeping can be found from the 0 equation E d H dt t C e .

 1 P 0, (22) Here we deduce the constant C by the following consideration.

Let the value IH IH 0 and the stress 0 at the moment of unloading t t 0 At the same moment of time 0t , T .
1 owing to instant reduction of stress by value 0 , the deformation will be instantly reduced to the value 1 H t ( 0 ) 1 Ho 0 E .

(23) Further, the deformation will change smoothly under the law (22).

At the same time, the constant C is to be determined from the initial condition (23).
We will again 1 P 1 Ho 0 E e T 1 , or by considering expression (21), we will gain 1 P 0 0 H E 1 e T 1 e .
(24) At the second loading, at the moment t T i T i , the law of deformation is determined by expression (20), but when determining the permanent integration of C the instant appearance of the initial deformation as well as the value of pre-initial deformation 01P should be considered.
Then at the second loading, the soil deformation will take place under the law C 0 0 E H 1 .Po 2 H 0 0 H E E 0 1 Po e (25) By putting the value P 1 1 P 0 from expression (24) in (25), after single-valued conversions, we will gain the calculation formula: 67 2 H 0 0 0 E E H 1 e T 1 1 e .
(26) The second unloading will take place in the period t T .

2 By reasoning similarly as in case of the first loading, we arrive at the law of deformation for the second unloading 2 P 2 Ho 0 E e T 2 .
(27) By putting the value 2 H 0 2 P 0 in (23), we gain: 2 P 0 0 H E 1 e T 1 1 e T 2 e .
(28) Before starting the third loading at the moment the t the pre-initial deformation will be .P If considering the instant appearance of the initial deformation 0 02 E too, the permanent integration of C in the law of deformation (20) is determined by expression Then at the third loading, the deformation of the soil is determined by expression C 2Po 0 0 H E .
3 H 0 0 0 H E H 2 Po e .
(29) By outing the value P 2 2 P 0 following calculation formula: from expression (28) in (29), after conversions, we gain the 3 H 0 0 H E E 0 1 e T 2 T T 2 1 e 1 e .
(30) Thus, the subsidence of the deformed trace of soil after the passages of two wheels of the mountain and serial chassis is determined by the expression: 0 H 2 1 E 1 1 H E 1 e T 1 1 e .
(31) The subsidence of the trace of soil after the passages of three wheels, positioned on one side of an experimental adaptive self-propelled chassis will be as follows: 0 H 3 1 E 1 1 H E 1 e T 2 T T 1 2 e 1 e .
(32) 68 If comparing the depths of traces of serial and experimental self-propelled chassis by the methods referred to when deducing the coefficient K (17), we will gain .
(33) In the numerator and denominator, we may admit that summand 1 / E Then, we will have: 0.

K 3 2 1 1 e T 2 T 1 e T T 1 2 e .

(34) If considering the values 1T and 2T given above, the results of calculation by the formulae (34) and (17) will in fact be the same.
Thus, we may prove that the subsidence of the trace of soil after a passage of six-wheeled of mountain self-propelled chassis will be 20% less than after the passage of a four-wheeled serial self-propelled chassis.

CONCLUSION The work gives the theory of interaction of the undercarriage of mountain tandem-wheeled self-propelled chassis with the soil.

A rheological model of Voigt and principal the law of linear deformation are used as the deformation law of soils.
A calculation formula for the soil deformation by considering the relative position of the front steering and the rear driving tandem wheels is deduced.

A numerical example is used to demonstrate the reduction of the depth of trace after the passage of three tandem wheels of mountain chassis as compared with that of serial chassis.

REFERENCES 1.

Kacikin V.V., Gorin G.S and others.

Perspective Power Means for Agricultural Manufacture // “Science and engineering”, Minsk, 1982, 270 pp.

(in Russian).

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Makharoblidze R.,M.

Lagvilava I.,M.

Kobakhidze A.,B.

Asatiani O.,G.

Impact of Assembling an Adapted Self-propelled Chassis on Normal Reactions of the Track Movers with the Soil // Problems of Mechanics, 3(40), Tbilisi, 2010, №3 (40), pp.

64-71 (in Georgian).

3.

Vialov S.S Heology of a Basis of the Mechanics a Ground // “Vishaia Skola’’, M., 1978, 445 pp.

(in Russian).

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Rdjaniicin A.R.


The Theory of Slipping // “Publishing House of the Literature on Construction”, M., 1968, 414 pp.

(in Russian).

ВЗАИМОДЕЙСТВИЕ С ПОЧВОЙ ХОДОВОЙ СИСТЕМЫ ГОРНОРАВНИННОГО САМОХОДНОГО ШАССИ НА ОСНОВЕ РЕОЛОГИЧЕСКИХ МОДЕЛЕЙ Р.М.

Махароблидзе, И.М.

Лагвилава, Р.М.

Хажомия, Б.Б.

Басилашвили Предлагается математическая модель взаимодействия с почвой ходовой системы адаптивного самоходного шасси.
В качестве закона деформации почвогрунтов используется реологическая модель Фойгта и основной закон линейного деформирования.

Выведена расчетная формула деформации грунта с учетом взаимoрасположения передних управляемых и задних ведущих тандем колос.

Дается сравнение деформации почв обычными двухосными и экспериментальными ходовыми системами.

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