Soil compaction management: Reduce soil compaction using a chain-track tractor

Journal of Terramechanics 89 (2020) 1–12

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Journal of Terramechanics journal homepage: www.elsevier.com/locate/jterra

Soil compaction management: Reduce soil compaction using a chain-track tractor Salavat Mudarisov ⇑, Ilshat Gainullin, Ildar Gabitov, Eduard Hasanov, Ildar Farhutdinov Federal State Budgetary Educational Establishment of Higher Education, Bashkir State Agrarian University, Ufa, Russia

a r t i c l e

i n f o

Article history: Received 12 June 2019 Revised 28 November 2019 Accepted 4 February 2020

Keywords: Agricultural machinery Support rollers Pressure on soil Strain gauge sensor Machine-tractor aggregate (MTA) Draw bar power Soil density

a b s t r a c t Modern agricultural production requires research for new design and layout plans of the track-chained mover, providing a reduction in soil compaction. One of many ways to improve the efficiency of machine-tractor aggregate (MTA) use is to improve the geometry of the support part of the chaintrack tractor. Flat geometry of the support part of a chain-track tractor with a semi-rigid suspension creates maximum pressure on soil with the first and last track rollers, which causes increased soil compaction. Research objective is to ensure the uniform pressure on soil from the tractor with a semi-rigid suspension by justifying the geometry of the supporting part of the track-chained mover. Based on experimental and theoretical studies a model of pressure distribution along the length of the support part was developed. Thus, the geometry of the support part of a track-chained tractor with a semi-rigid suspension was substantiated. Pressure decrease on soil and compaction reduction are achieved by changing the geometry of the support part and rational location of the tractor mass center. To achieve the elliptical geometry of the support part of a track-chained tractor with a semi-rigid suspension lower track rollers were placed at different heights. To test the formulas and to study the influence of the support part geometry, of the hitch height and the force on the hook of a track-chained tractor on soil compaction, experiments were conducted. As a model for experiment, the tractor actively used in agriculture was modernized; chain-track tractor T-170M1.0355 with flat and elliptical caterpillar bypasses. The pressure was measured directly by pressure sensors that were placed into the ground. Soil density in the track left by a track-chained tractor mainly depends on mover pressure and the number of impacts per pass. Track-chained mover makes two impacts on soil with the flat support part. If the support part geometry is changed, the number of impacts on soil is reduced to one. To create typical working conditions for T-170M1.03-55 track-chained tractor the third and fourth support rollers should be lowered by 9.5 ± 1.5 mm, the second and fifth-by 4.5 ± 0.5 mm relatively, which leads to a decrease in the maximum pressure on soil and reduces its compaction in the track left by the mover by 15–25%. Ó 2020 ISTVS. Published by Elsevier Ltd. All rights reserved.

1. Introduction Cultivation of agricultural crops is associated with multiple passes of machine-tractor units over the field. Soil becomes compacted when movers pass on it. This leads to the deterioration of the basic physical and physical-mechanical properties of the subsoil and topsoil layers, reducing crop yields and increasing energy consumption during agricultural operations (Ksenevich and Rusanov, 2000; Gainullin, 2001; Ksenevich et al., 2003; Hamza and Anderson, 2005; Holtkemeyer, 2005; Okunev and Kuznetsov, 2016; Aipov et al., 2018).

⇑ Corresponding author. E-mail address: [email protected] (S. Mudarisov). https://doi.org/10.1016/j.jterra.2020.02.002 0022-4898/Ó 2020 ISTVS. Published by Elsevier Ltd. All rights reserved.

The surface of a track chain is much bigger than the wheel surface contact area. Hence, the specific pressure that a track exerts on the soil is lower, compared to wheels, and even lower compared to the human foot. For agricultural tractors, the pressure range is between 0.045 and 0.060 MPa. In reality, however, the pressure is distributed unevenly: under the track rollers, it can be 2–3 times higher than the average pressure. The described effect depends on the type of suspension, namely, on the distance between the track rollers and on how uniform the tractor’s weight distribution across the track rollers is. This work aims to identify a track mover design such that helps avoid pressure unevenness and minimize the ground pressure. During assessment of the effectiveness of MTAs (machinetractor aggregates) in the performance of technological operations,

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it is significant that their movers meet the requirements of ensuring acceptable pressure on soil (Cueto et al., 2016; Edwin et al., 2018; Paulson et al., 2018). Various theoretical approaches and experimental methods are used to study the processes of interaction between tractor movers and the compaction of soil. Much attention is currently paid to improve the technical level and off-road capabilities of the undercarriage, reducing metal consumption and compacting effects on the soil. The issue of the mover pressure on soil was carefully analyzed. Using the results of the analysis, we developed new methods. These methods helped us to determine maximum scaled pressure of wheeled and chaintrack movers on soil. We also proposed calculating methods to determine the indicators of wheeled and metal chain-track movers providing the allowed influence on soil caused by machinery. Moreover, the indicators of the strain–stress soil state were calculated (Ksenevich and Rusanov, 2000). The level of soil compaction depends on the mass of the tractor, the type of mover used on the tractor, the type of soil and the technology of agricultural cultivation (Ksenevich and Rusanov, 2000; Gainullin, 2001; Hamza and Anderson,2005; Holtkemeyer, 2005; Gainullin et al., 2010; Taheri et al., 2015; Okunev and Kuznetsov, 2016; Paulson et al., 2018; Edwin et al., 2018) One of the main ways to reduce the compacting effect on soil is to improve the movers of MTAs. It is advisable to mainly use chain-track tractors in spring, during pre-sowing soil treatment and sowing. Studies of (Taheri et al., 2015) cover the most commonly used models of wheel interaction with deformed soils developed for wheeled vehicles. Janulevicˇius et al. (2018) studied the influence of air pressure in the front and rear tires on the rolling coefficient of the wheeled tractor and fuel consumption during wheat cultivation. El-Sayegh et al. (2018) presented an improved model of tire interaction with soil based on FEA-SPH modeling. In studies of Farhadi et al. (2018) a method for assessing the threedimensional (3D) track of pneumatic agricultural tires was developed. It is based on the formation of tire track with liquid plaster and the conversion of these forms to three-dimensional models using a 3D scanner. The work of Padmanabhan et al. (2018) proposed a model with the use of particle filtering to estimate terramechanichal parameters of wheel interaction with the ground. The proposed models of the wheel’s interaction with soil and the results of studies that were done by authors (Taheri et al., 2015; Janulevicˇius et al., 2018; El-Sayegh et al., 2018; Farhadi et al., 2018; Padmanabhan et al., 2018) can be used to model the interaction of rubber-reinforced tracks with the soil. However, they are not fit to be used with metal track movers. Bekker (1982) proposed methods of analysis ‘‘terrain-machine” in relation to the assessment of the off-road capabilities of vehicles. Vong (1982) studied the basics of the theory and design of wheeled and track-chained vehicles, as well as air cushion vehicles. Yang et al. (2016) proposed a method for calculating the traction of a track on soft ground. In the work of Edwin et al. (2018) the interaction with the soil tracked vehicle’s tracks is studied. A simple and general method for calculating the deformations of soil in the trail of tracked vehicles has been proposed (Edwin et al., 2018). In studies of Wang et al. (2016) the estimation of traction characteristics of marine tracked vehicles on the basis of laboratory mechanical tests has been made. In studies of (Bekker, 1982; Yang et al., 2016; Edwin et al., 2018; Wang et al., 2016), the interaction of the metal-tracked mover with soil, uneven distribution of soil reactions to the mover’s surface, traction characteristics and calculations are studied. Although the cited works consider the shift of the tractor weight relative to the axis of symmetry of the supporting surface, which is due to the traction force on the hook and the point of its application, the influence of the geometry of the supporting part of the tractor

caterpillar on soil compaction is not taken into account. Zakhmatov et al. (1982) also tried solving the problem of choosing a rational geometry of the support surface of the tracked mover, however, these studies were incomplete. Comparative experimental studies have shown that pressure on soil caused by T-150 K, T-170M1.03-55 and K-701 tractors is 1.8. It is 2.6 and 3.5 times higher than pressure on soil that is caused by T-150 track-chained tractor. Further reduction of soil compaction and wear of T-170M1.03-55 tractor track chains is possible by justifying the geometry of the support part (Gainullin and Zaynullin, 2017; Gainullin, 2019). Thus, the problem of reducing soil compaction requires the search for new design and layout schemes of the tractor chassis, which will reduce soil compaction. They will also increase traction and pull force indicators. One of the ways to improve the efficiency of the MTA is to improve the geometry of the support part of the tracked tractor. To reduce the maximum pressure and the multiplicity of effects it is preferable to use a uniform distribution of pressure over the contact area of the support surface. Firstly, the uniform distribution does not create areas with extreme pressure, and secondly, the absence of areas with extreme pressure reduces the number of impacts to a minimum (to one). The pressure distribution can be significantly smoothed out by changing the geometry of the tractor support part. Research objective: ensuring uniform pressure on soil from the tractor with a semi-rigid suspension by justifying the geometry of the supporting part of the track-chained mover.

2. Research methods 2.1. Theoretical justification for the track-chained tractor’s support part geometry At Limited Liability Company ‘‘ChTZ-UralTRAK” for a number of years a chain-tracked tractor T-170M1.03-55 is being produced. This tractor is actively used in the main operations related to soil treatment and sowing of cereals, as well as road construction and agricultural operations. Experimental studies on the impact of tractor T-170M1.03-55 movers on soil showed, that the maximum pressure reaches 0.166 MPa. The diagram of pressure distribution along the length of the support surface has two local extremes in the zone of the 1st and 6th support rollers (Fig. 1, Table 1). This causes a double impact on soil in a single pass with a pressure exceeding the average pressure value, which causes increased in soil compaction and a decrease in tractor traction properties. The experiments were carried out in 2015–2017 at the test base of Cheliabinsk tractor factory (Gainullin, 2017). Fig. 1 is the diagram showing the main parameters of a trackchained mover and of normal pressure distribution p(x) in the longitudinal section of the supporting surface of T-170.M1.03–55 tractor: P is the load on a single mover, H; Phk is the pressure on the tractor hook, N; e is the eccentricity, m; L is the length of the support surface, m; |±a| is the half length of the support surface, m; hf is the displacement of the longitudinal component of the rolling force Pf from the reaction of the soil; C is the distance from the center of contact to the vertical component Phk. m; c is the angle between the force acting on the hook and the horizontal plane; v - tractor speed in m/s; hhk is the height of the trailer as relating to the support surface, m. Reduction of the maximum pressure from the track of the tractor on soil can be achieved by ensuring a uniform distribution of pressure on the contact area of the support surface of the mover with the soil. Based on the contact task of elasticity theory, the equation for geometry of the support part of a track-chained trac-

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Fig. 1. The main parameters of a track-chained mover and of normal pressure distribution p(x) in the longitudinal section of the supporting surface of T-170.M1.03–55 tractor.

Table 1 Normal pressure on soil from tractor movers T-170M1.03-55. Mode of exposure

Normal pressure (load) in soil, kPa h = 20 cm

Without load With an 80 kN load on the hook

h = 50 cm

h = 80 cm

A1

A2

A3

A1

A2

A3

A1

A2

A3

162.7 127.4

12.7 61.7

166.6 117.7

133.3 96.5

30.0 36.3

137.2 97.0

36.3 25.5

18.6 8.8

42.1 21.6

Note: Point A1 is the zone of the first support roller, point A2 is the middle of the support surface of the tractor; Point A3 is the zone of the sixth support roller.

tor with a semi-rigid suspension, which provides a uniform pressure distribution along the support surface is obtained by Eq. (1) (Gainullin and Zaynullin, 2017):

f ðxÞ ¼ 0; 5pav pbfxarcsinðx=aÞ þ A  ðB½xA=a2 þ arcsinðx=aÞg þ C ð1Þ where pav is the average pressure on soil caused by the tractor, kPa. pav = Ge/(2bL); Ge is the operating tractor weight, N. L is the length of the support surface of the tractor, m. b is the width of the track; pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b ¼ t1 þ t2 t1 ¼ ð2ð1  l21 Þ=pE1 ; t2 ¼ ð2ð1  l22 Þ=pE2 ; ¼ a2  x2 . E1 is the soil elasticity modulus, Pa. l1 is the Poisson’s soil ratio. E2 is the steel elasticity module of a track shoe, Pa. l2 is the Poisson’s ratio of the track shoe steel; a = L/2-is a contact half -width, m. x is the horizontal coordinate of the point of the support surface, m;   B ¼ P e þ uhk ðhhk coscþ ¼ csincÞ þ fhf . P ¼ Ge þ P hk cosc is the load on the single-piece mover, kN. Phk is the force on the hook, N. c is the angle between the force on the hook and the horizontal plane. uhk ¼ Phk=P is the coefficient of use of the hitch weight. e is the longitudinal coordinate of the tractor gravity center as relating to the length of a track on ground, m. hhk is the height of the trailer as relating to the support surface, m. f is the coefficient of resistance to the tractor movement, f = 0.07 0.15. . ... . . hf is the shift

of the longitudinal component of the displacement force provoked by soil reaction, hf = 0,015...0,029, m. C = 0,027 ± 0,003, m is the coefficient, equal to the initial soil deformation determined empirically. The geometry of the support part depends on the following: tractor mass, length of the support part, mass center position, drive force and the point of its application, track material properties and soil type. During the research the following parameters were used: drive force (40–80 kN), bearing surface length (2,88 m), trailer height (0.4 m); eccentricity e = 0,165 m; track material which is carbon steel (steel 20, steel 45); loam soil; soil moisture (12–24%). If we calculate the pressure p(x) along the contact line of the supporting surface is constant and equal to the average pressure of the tractor T-170M1.03-55, the dependence (1) can be represented by a curve (Fig. 2). This curve shows the removal of points of the supporting surface of the tractor relative to the OX axis. The distance between each lower track wheel to be set is determined by measuring the height along with OY axis at the level of the lower track wheel along with OX axis (Fig. 2). The solution of the Eq. (1) allowed us to establish that for the chosen operating conditions of the chain-track tractor T170M1.03-55 with a semi-rigid suspension, the third and fourth support rollers should be lowered by 9.5 ± 1.5 mm, and the second

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Fig. 2. Removing points of the supporting surface of T-170M1.03-55 tractor from the horizontal axis along the contact length.

and fifth rollers should be lowered by 4.5 ± 0.5 mm. This will reduce soil compaction in the track by 15–25%. The mover consists of a track-chain 1 covering the drive wheel 2, the guide wheel 3, the supporting rollers 4, the middle 5, the intermediate 6 and the outer 7 support rollers. The middle 5 and intermediate 6 support rollers should be lowered according to the expression (1) by placing plates 8 and 9 that are h5 and h6 in thickness respectively. The plates should be placed under the axes of the support rollers (Fig. 3). Thus, less loaded intermediate rollers are located at different heights from the horizontal plane, after which the crawler will take an elliptical shape. Thus, less loaded intermediate rollers are located at different heights from the horizontal plane, after which the track-chain bypass will take an elliptical shape. 2.2. Models of pressure distribution on soil and justification for the horizontal coordinate of a chain-track tractor’s center of mass The pressure distribution equations p(x) for the plane (2) and elliptic (3) geometry of the support surface along the contact line are determined by the following equations (Gainullin, 2015):

  xðeþuhk ðhhk coscþcsincÞþfhf Þ P 1þ2 a2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pðxÞ ¼ p a2  x2

ð2Þ

pðxÞ ¼

1þ2

pcp xðeþuhk ðhhk coscþcsincÞþfhf Þ a2

ð3Þ

The curve of pressure distribution was made using Eq. (2), 3 and was based on the assumption of the contact patch length and the length of the contacted body: b = ka, where b is the half-length of the contact patch, b = 1.5 m; a is half the length of the body (mover support part), a = 1.44 m, k is the correction factor, k = 1.041 (Gainullin, 2015). At that, the interval of point coordinates was set within the following limits: x = b, b + 0,01b. Within the range of real pressures preal exerted on the steering wheel by the tractor, the linear relationship between preal and hhk can be described by the Heidecker’s formula, with some reservations. Thus, if the track stiffness is assumed high, the depth of the groove can be determined as a functional dependence that is transformed by reflecting the pressure in the ground through the contact pressure, the rolling surface area, and the tensile strength of the soil under the unconfined compression, with the pressure distribution The value of the eccentricity e which provides a uniform distribution of pressure along the support surface is determined by the following dependency:

  e ¼  uhk ðhhk cosc þ csincÞ þ fhf ; m

ð4Þ

For tractor T-170M1.03-55 with a pulling force on the hook of 80 kN (aggregation with a plow type PTC-12-40) and a trailer height of 0.4 m, the eccentricity value will be 0.165 m. Then the pressure distribution along the contact line of the support surface described by equation (1), with different forces on the hook according to the equation, will take the form of Fig. 4. As shown

Fig. 3. Elliptical track-chain bypass of T-170M1.03-55 tractor.

Fig. 4. The pressure distribution of the elliptical support surface of T-170 M1.03–53 tractor.

S. Mudarisov et al. / Journal of Terramechanics 89 (2020) 1–12

5

in Fig. 4 in the form of a track chain bypass, in the longitudinal section described by the Eq. (1), the nature of pressure distribution along the support surface varies, but does not exceed the maximum pressures than with a flat support surface (Fig. 5). 2.3. Experimental unit and measurements Measurement of ground pressure caused by the mover of the tractor was carried out using a force measuring sensors 20 State All-Union standard 15077-71 with special made attachments. Force-measuring strain-gauge sensors C 20 (hereinafter sensors) are designed to convert static and dynamic forces in the measured physical value (analog electrical signal). Sensors box frame is of a cylindrical form. The main sensors node is an elastic part of the box frame located inside of it. Strain gauges are attached to the elastic element and are connected to make a bridge circuit. The electrical circuit contains temperature-compensated elements which influence the output signal. The sensors were connected to the amplifier with a shielded wire to reduce extraneous electrical interference. The amplifier signals are received on the recording equipment. A portable multichannel measuring system MIC400D was used as a registration and measuring instrument. The MIC-400D measuring system is designed to register static and dynamic signals and to make express analysis of quick-changing analog signals going through independent measuring channels. The pressure sensors and strain gauges were calibrated before and after the measurements. The calibration characteristics approximated by a straight-line with the use of the least square’s method. A trench was made on the chosen site. At the bottom of the trench along its longitudinal axis, three sensors were installed. The first sensor was installed at a depth of 0.2 m, the second sensor was installed at a depth of 0.5 m and the third sensor at a depth of 0.8 m (Fig. 6). Distance between neighboring sensors:

Ls ¼ Kt t þ 0:25tt ¼ 3  0:203 þ 0:25  0:203 ¼ 0:66m

ð5Þ

where tt is the track chain step, K is one of natural numbers (1,2, 3), which is chosen according to Ktt > 0.5. In the course of research, the distribution of tractor pressure on soil was determined depending on the geometry of the support surface, the magnitude of the pulling force on the hook and its height of application. Loading of a moving tractor was done with the force of 40, 80 kN. This force was applied to the lifting trailer-type device with the help of a self-propelled dynamometer laboratory SDL-30,

Fig. 5. Pressure distribution of the flat support surface of T-170M1.03-55 tractor.

Fig. 6. Installation of pressure sensors into soil.

which is based on DET-250 tractor through a tensor with the output of the parameters to the recording equipment (Fig. 7). The longitudinal axis of the track coincided with the longitudinal axis of the sensors. The line for installation of the sensor was traced with contrast flexible cord. Parameters registration started when the first lower track wheel was 1 m from the first sensor. After the last lower track wheel passed 1 m from the sensor, the registration finished. During the repeated experiments, there were five passes with not changing tractor’s direction and the tractor speed was 0.7–10.2 km/h. To make measurements sensors were changed at least three times. There were used such transport and operating modes as idle motion and the mode when the towed load is 40 kN and 80 kN. Operating modes were tested while the tractor drove directly with stable thrust loading, created by the SDL-30 laboratory. A research test engineer gives a command from the SDL-30 laboratory to a tractor driver who begins movement and speeds up the tractor, placing the control lever to a setting of maximum fuel supply. After stabilizing the tractor’s engine speed, a research test engineer creates resistance to the tractor movement using the loading device of the SDL-30 laboratory. The control of the load is carried out according to the M-906 milli-ampermeter readings and to the calibration schedule of the strain gauge. When the time of the experience is over, a research test engineer gives a command to stop the tractor. In order to obtain an empirical model, the method of mathematical planning of the experiment was used (Lvovskiy, 1988; Lee et al., 2016). Its main task is to obtain a multifactor model of the object of study in the form of a regression equation. Levels of input factors and their variation intervals, coded designations were established based on theoretical studies and analysis of literature (Gainullin, 2001; Lee et al., 2016; Gainullin and Zaynullin, 2017b; Gabitov et al., 2018; Rakhimov et al., 2018) and are shown in Table 2.

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the shape of the support surface. The ellipse parameter was structurally realized using the following method: with the unchanged position of the 1st and 6th support rollers, the second and fifth support rollers were lowered by 5 mm, the third and fourth support rollers-by 10 mm. The rollers were lowered with the help of plates relative to the support surface of the trailer frame at zero variation levels, at variation levels +1: without changes in the position of the 1st and 6th support rollers, the second and fifth support rollers were lowered by 10 mm, the third and fourth support rollers-by 20 mm. As the plan of experiment, the plan for three factors of Box– Behnken experimental design was developed. Box–Behnken designs are experimental designs for response surface methodology, devised by George E. P. Box and Donald Behnken in 1960, to achieve the following goals: Each factor, or independent variable, is placed at one of three equally spaced values, usually coded as 1, 0, +1. (At least three levels are needed for the following goal.) The design should be sufficient to fit a quadratic model, that is, one containing squared terms, products of two factors, linear terms and an intercept. The ratio of the number of experimental points to the number of coefficients in the quadratic model should be reasonable (in fact, their designs kept in the range of 1.5–2.6). The estimation variance should more or less depend only on the distance from the centre (this is achieved exactly for the designs with 4 and 7 factors), and should not vary too much inside the smallest (hyper) cube containing the experimental points. (Gainullin and Zaynullin, 2017, 2017b). The experiment plan is presented in Table 3. With three factors, the plan suggests a conduction of 15 experiments, including 3 in the centre of the experiment. According to the plan, the first experiment N = 1 was realized according to the following factors: X1 = 1 is the bypass shape (support part geometry) 0,02 m; X2 = 1 is the hinge height 1050 m; X3 = 0 is the force on the hook 40 kN. The second experiment N = 2 was realized according to the following factors: X1 = 1 is the bypass shape (support part geometry) 0,02 m; X2 = -1 is the hinge height 1050 m; X3 = 0 is the force on the hook 40 kN. The remaining 3 to 15 experiments were implemented in accordance with Table 3. After all experiments and data processing, the regression coefficients of the second order were determined:

Fig. 7. Spot for strain-gauge link placement on self-propelling dynamometric laboratory SDL-30.

The main purpose of the factorial experiment is to obtain an empirical dependence of the tractor’s support surface pressure to soil on the ellipse parameter h, and the dependence of the trailer relative height to the support surface of hhk on the force generated on the hook Phk. Based on the obtained model, the influence level of the support surface shape was studied to assess the correction of the hypothesis proposed in the theoretical part. Reduction of soil compaction by a chain-track chassis with semi-rigid suspension is possible due to a more uniform distribution of pressure along the length of the support surface. This is achieved by changing

Y ¼ b0 þ

3 X

bi xi þ

i¼1

3 X

bij xi yj þ

X

bij x2i ;

ð6Þ

ij¼1

where E is the variable characterizing the object of study; xi is the first factor; b0, bi, bij, bii are the regression coefficients; j is the factor number, which is deferent from i.

Table 2 Levels and intervals of factor variation. Factor names

Notation

Shape of the bypass Suspension height Force on the hook

Variation levels

Interval

Nominal

Coded

1

0

+1

h, v hhk, v Phk, kNr

X1 X2 X3

0 220 0

0,01 635 40

0,02 1050 80

0,01 415 40

Table 3 The experiment plan. Experience number

Factors

N

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

X1 X2 X3

1 1 0

1 1 0

1 1 0

1 1 0

1 0 1

1 0 1

1 0 1

1 0 1

0 1 1

0 1 1

0 1 1

0 1 1

0 0 0

0 0 0

0 0 0

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Average value and root-mean-square regression of optimization parameters in every experiment were calculated by the following formulas:

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n P 2

Pm



ðY jðeÞ Y ij Þ

Yi ;S¼ m

Yj ¼

ð7Þ

1

1

m1

where m is the repeating of sampling; e is the number of repetitions; Y j the average value of the optimization criterion; S is the root-main-square regression. Gross errors were eliminated from the condition 

Y jðeÞ  Y j >t S

ð8Þ

where t is the Student’s criterion for the significance of 0.95. Regression coefficients for Boks-Benkin plan were calculated: 



b0 ¼ Y 0 ; Y 0 ¼ bij ¼ B

n X

Pn0 1

n0



x2ij Y j þ C 1

j¼1

bik ¼ D1

Y0

n X

; bi ¼ A

n X

j¼1

j¼1

P 1 ¼ 68;6  30;05  x1  12;19  x2  27; 54  x3 þ 15;77  x1 2 þ 1;4  x2 2 þ þ1;55  x3 2 þ 32; 12  x1  x2 þ 19;37  x1  x3  4; 7  x2  x3 ; ð11Þ Regression equation for the center part of the mover’s support surface (point 2):

2;95  x23  23; 75  x1  x2  10  x1  x3 þ 1; 95  x2  x3



x2ij Y 

Based on the realization of the plan and processing of the experimental results, the pressure dependences on the factors for the front, center and rear points of the reference surface are obtained (points A1, A2, A3 are shown in Fig. 1). After elimination of major errors, calculations of regression coefficients of the second-order model, which characterize the influence of the accepted factors (according to the experimental plan) on the pressures at three points are carried out. Regression equation for the front edge of the mover’s support surface (point 1):

P2 ¼ 78 þ 27; 9  x1 þ 3; 45  x2 þ 5; 65  x3 þ 15;05  x21 þ 22;05  x22 

xij Y j ;

j¼1 p X n X

3. Results of experimental studies

Y0 p

;

ð12Þ

ð9Þ

Regression equation for the tail part of the mover’s support surface (point 3):

ð10Þ

xij xkj Y j

j¼1

where i is the factor number; p is the number of factors; j is the experiment number; k is the experiment number that is not equal to i (k – i). The values of the coefficients are presented in Table 4. Experiment is carried out when the Kochren criterion is Gcalc < Gtabl.

P3 ¼ 86;2  24;6  x1 þ 10;44  x2 þ 47;44  x3 þ 48;76  x21 þ 32;49  x22  0;26  x23  15;3  x1  x2 þ 9;55  x1  x3 þ 6;12  x2  x3 ð13Þ The significance of regression coefficients was tested using Student’s t-criterion by determining the confidence interval for each type of coefficients at the significance level of 0.95. The coefficient is considered statistically significant provided that the absolute value of the coefficient is greater than the confidence interval:

tSyh jbi j < Dbi ¼  pffiffiffiffi : N

2.4. Soil compaction test The experiments were conducted on a field prepared for sowing. The characteristics of the research conditions are presented in Table 5. After installation of the sensors, the uniformity of the soil layer was restored. Soil hardness is controlled by Reviakin’s hardness meter. Moisture content and density were determined by the gravimetric method.

Table 4 Constant coefficients from Box-Benkin’s calculation formulas plan (Gainullin and Zaynullin, 2017, 2017b). A

B

C1

D1

q

D

1/8

1/4

1/16

1/4

2

1/4

ð14Þ

Main evaluation results are presented in Table 6. Taking into account the results of evaluating the significance of the regression coefficients, the equations will take the following form

P1 ¼ 68; 6  30; 05  x1  12; 19  x2  27; 54  x3 þ 15; 77  x21 þ ; þ32; 12  x1  x2 þ 19; 37  x1  x3  4; 7  x2  x3 ð15Þ P2 ¼ 78 þ 27; 9  x1 þ 5; 65  x3 þ 15; 05  x21 þ 22; 05  x22 23; 75  x1  x2  10  x1  x3

;

ð16Þ

P3 ¼ 86;2  24;6  x1 þ 10;44  x2 þ 47;44  x3 þ 48;76  x21 þ 32;49x22  15;3  x1  x2 þ 9;55x1  x3

;

ð17Þ Table 5 Condition characteristics of laboratory and field experiments. Condition indicator

Value

Relief of the field, angle of the slope, degrees

3° Salt washed, medium-humic

Soil type Soil moisture level in a layer, % In a layer from 0 to 30 cv, % Soil hardness, MPa In a layer of 0–30 cm Metrological conditions Air temperature, °C Relative air humidity, %

12–24 0.5. . .1.4 20. . .26 72. . .92

Note: The soil type was determined according to the tractor operating conditions, the Ural region, Russian Federation.

Equations (15), (16), (17) show the system, which describes the distribution of pressure on soil in three spots depending on factors x1, x2, x3:

8 P1 ¼ 68; 6  30; 05  x1  12; 19  x2  27; 54  x3 > > > > þ15; 77  x21 þ 32; 12  x1  x2 þ > > > > > þ19; 37  x1  x3  4; 7  x2  x3 > > > > > P ¼ 78 þ 27; 9  x1 þ 5; 65  x3 þ 15; 05  x21 < 2 þ22; 05  x22  23; 75  x1  x2  > > > 10  x1  x3 > > > > > P3 ¼ 86; 2  24; 6  x1 þ 10; 44  x2 þ 47; 44  x3 > > > > > þ48; 76  x21 þ 32; 49  x22  > : 15; 3  x1  x2 þ 9; 55  x1  x3

ð18Þ

8

S. Mudarisov et al. / Journal of Terramechanics 89 (2020) 1–12

change in pressure on soil only in a specific section of the support surface, to find out the parameters, (ensuring stable pressure along the length of the support surface) total pressure difference at the outer points relative to the central section was accepted (point2) (look at Fig. 2). This criterion is determined by the expression:

We transform these equations in decoded form, replacing the variables x1, x2 and x3 in the system of equations (18) with the corresponding expressions.

x1 ¼

h  h0 ; Dh

x2 ¼

a  a0 ; Da

x3 ¼

Pkp  P0kp : DPkp

ð19Þ

After reorganization the equation system takes the following form

DP ¼ jP2  P1 j þ jP2  P3 j:

8 P1 ¼ 221; 93  13010; 3  h  95; 46  hhk  0; 99  Phk > > > 2 > > þ157700  h þ 7740; 92  hhk  hþ > > > > > þ48; 42  h  Phk  0; 282  hhk  Phk > > > > > P ¼ 64; 76  4413; 75  h  105; 36  hhk þ 0; 391  P hk > 2 < 2 2 þ150500  h þ 128; 1  hhk  > > > 5723; 75  h  hhk  25  hhk  Phk > > > > > > P ¼ 157; 72  10766; 1  h  177; 42  hhk þ 0; 945  Phk 3 > > > 2 2 > > þ48760  h þ 188; 77  hhk  3687; 3  h  hhk þ > > : þ23; 87  h  Phk

To determine the nature of influence of the height of the trailer hhk on the pressure difference DP, we take the specific values of the ellipse parameter - h and the force on the hook Phk. The height of the trailer relative to the reference surface is taken as an argument of function with the limits of variation according to the experiment plan: hhk = 0,635 ± 0,415 m. Nature of the change in pressure difference is shown in Fig. 8. The nature of influence of the trailer’s height on the pressure difference when changing the parameters h and Phk is similar. This is obvious because as the height of the trailer increases, the torque

ð20Þ

ð21Þ

where h is the thickness of the plate in the middle of the tractor’s support surface, m; hhk is the height of the trailer in relation to the support surface, m; Phk is the force on the hook of the tractor, kN. To check the adequacy of the equations obtained, calculations of the Fisher criterion were made. These calculations were compared with table values at the significance level of 0.95: – for equation 1 (point 1): F calc ¼ 0; 57 < F table ¼ 2; 5; – for equation 2 (point 2): F calc ¼ 1; 07 < F table ¼ 2; 5; – for equation 3 (point 3): F calc ¼ 0; 22 < F table ¼ 2; 5. The study of dependencies in the presence of three variables is very difficult. Therefore, we considered each of the parameters separately. It is obvious that the pressure of the support surface is influenced by the force on the hook and the height of the trailer relative to the support surface. At the same time, the height of the trailer is a design parameter that has a specific value. The goal of the research was to determine this design parameter - hhk and the ellipse parameter (plate thickness) - h, which provides a stable pressure of the tractor’s support surface along its entire length. Since each of the obtained empirical equations characterizes the

Fig. 8. Dependence of pressure differences DP on the height of the trailer: with h = 0, Phk = 0.

Table 6 Evaluation of the significance of regression coefficients by t criterion. In point 1 Empirical equation of points

Regression coefficients b0

b1

b2

b3

b11

b22

b33

b12

b13

b23

1

2

3

4

5

6

7

8

9

10

11

Coefficient value Confidence interval Assessment of the importance

68.6 30.05 6.07 3.72 important

12.2

27.5

15.78 6.07

1.4

1.55

4.7

not important

not important

32.13 19.37 2.02 important

Coefficient

b0

b2

b3

b11

b22

b33

b12

b23

Coefficient value Confidence interval Assessment of the importance

78 27.9 5.65 3.35 important

3.45

5.65

15.05 22.1 5.65 important

2.95

23.8 10 4.89 important

In point 2 b1

not important

b13

1.95 not important

In point 3 Empirical equation of points

Regression coefficients b0

Coefficient value Confidence interval Assessment of the importance

b1

86.2 24.6 8.12 4.97 important

b2

b3

b11

b22

b33

b12

10.44

47.4

48.76 8.12

32.5

0.26

15.3 9.55 7.03 important

not important

b13

b23 6.125 not important

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S. Mudarisov et al. / Journal of Terramechanics 89 (2020) 1–12

acting on the frame of the tractor is also being increased. This helps to increase the pressure of the back of the support surface on the soil; the lower the height of the trailer, the more even the pressure on soil along the support surface. However, the height of the trailer is limited by the design features of the tractor, the working conditions and the design of the hinged mechanism of agricultural machines. Further decrease in height requires changes in the design of the hinged mechanism of agricultural machines, but this is not acceptable. Thus, we take the height of the trailer relative to the support surface equal to 0.35 m. At a trailer height of 0.35 m. the system of Eq. (20) after conversion will take a simplified form: 8 2 > < P 1 ¼ 188;52  10300; 98  h  1;09  P hk þ 157700  h þ 48;42  h  P hk 2 P 2 ¼ 43;57 þ 2410;44  h þ 0;391  P hk þ 150500  h  25  h  P hk > : 2 P 3 ¼ 118;75  12056; 65  h þ 0; 945  P hk þ 487600  h þ 23; 87  h  P hk ð22Þ This system of equations characterizes the influence of the ellipse parameter h and the force on the hook-on pressure at points 1, 2 and 3. The dependence for the average force on the hook (Phk = 40 kN) is shown in Fig. 9. The figure shows that the ellipse parameter significantly impacts the amount of pressure. In this case, the pressure at point 1 decreases when parameter h is increased, at point 2 - increases, and at point 3 - has a pronounced minimum in the vicinity of the values: h = 0.01–0.013. For further calculations, we simplified the system of equations (22), taking the force on the hook Phk = 40 kN, which corresponds to the average value (this is due to the fact that the main technological operations are performed at a force of 40. . .50 kN. The maximum force on the hook – 70. . .80 kN and it is created only when performing energy-intensive operations, such as plowing). Given the value Phk = 40 kN the Eq. (22) takes the following form:

8 2 > < P1 ¼ 144; 97  8364; 18  h þ 157700  h 2 P2 ¼ 59; 22 þ 1410; 44  h þ 150500  h > : 2 P3 ¼ 156; 55  11101; 65  h þ 487600  h

ð23Þ

Since the system of equations characterizes the impact on soil at different points of the support surface, it is very difficult to estimate how even the pressure is with one or another value of the ellipse parameter. In order to determine the most preferred value of the ellipse parameter, which provides a more stable distribution of pressure on the support surface, we take the criterion of the average pressure on the soil:

Fig. 9. The dependence of pressure on soil in the front (point 1), center (point2) and rear (point 3 parts of the support surface from ellipse parameter h, with a force on the hook of Phk = 40 kN.

Pav ¼

P1 þ P2 þ P3 3

ð24Þ

or

Pav ¼ 120; 245  6018; 46  h þ 265266; 67  h

2

ð25Þ

Graphically, the dependence (25) is shown on Fig. 10. Let’s differentiate the Eq. (25):

dh Pav ¼ 6018; 46 þ 530533; 34  h h

ð26Þ

Equating the derivative to zero, we determine the ellipticity parameter h:

dh Pav ¼ 0 h

 6018; 46 þ 530533; 34  h ¼ 0 h ¼ 0; 0113M ð27Þ

Thus, the ellipse parameter, which provides a stable pressure distribution along the support surface, is equal to h = 0.0113 m. This is confirmed by theoretical studies, according to the results of which the optimal parameter should be 0.011 m. Fig. 10 shows that the proposed geometry of the crawler track drive when the tractor works on a medium loam soil field prepared for sowing reduces the maximum pressure on the soil from 120 kPa to 85 kPa. Substituting the accepted values h = 0,011 m (ellipticity parameter) and hhk = 0,35 m (trailer height) into the equation (22), after the reorganization we obtain a system of equations with parameters. These parameters provide a more stable distribution of pressure on soil along the support surface of the tractor:

8 > < P1 ¼ 94; 29  0; 556  Phk P2 ¼ 88; 301 þ 0; 116  Phk > : P3 ¼ 45; 124 þ 1; 21  Phk

ð28Þ

After approximation of the equation system (28) when the force on the hook is known, we take as an argument the longitudinal coordinate of the point on the support surface X with respect to the center of coordinates 0, i.e. the center of the reference surface (Fig. 1). Then the equations characterizing the pressure at each point will take the form: with Phk ¼ 0 kN with Phk ¼ 40 kN with P hk ¼ 80 kN

p ¼ 63; 09 þ 49; 795  X  18; 594  X 2 ; p ¼ 30; 755 þ 51; 497  X  10; 202  X 2 ; p ¼ 1; 58 þ 53; 2  X  1; 81  X 2 ;

Fig. 10. Dependence of the maximum pressure of the tractor’s support surface on soil from the ellipticity parameter h where Phk = 40 kN.

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S. Mudarisov et al. / Journal of Terramechanics 89 (2020) 1–12

where p is the amount of pressure in soil, kPa; X is the longitudinal coordinate of the support surface point, m (U ¼ 1; 44M ). The nature of pressure distribution corresponds with the theoretical results obtained earlier, which confirms the assumption that it is possible to reduce the pressure on soil by changing the geometry of the tractor’s support surface. Density in the track of T–170.M1.01–55 tractor with a flat and ellipse support part calculated the following dependence, which takes into account the characteristics of the soil, the mover type, the number of impacts on soil from variable loads:

qt ¼ q0 H=ðH  hÞ

ð29Þ

where pt, p0 is the soil density, respectively, after compaction and before it, g/cm3; H is the distance from the soil surface to the solid bedding layer (is the depth of deformation) H = 0.30 m; h is the depth of the track (soil settlement), m. The depth of the track h was figured out using the following equation (for the conditions of the Ural region of the Russian Federation):

h ¼ x  b  pmax  ð1  t2 Þ  ð1 þ v  lgNÞ=E0 ;

ð30Þ

where t and E0 are accordingly the coefficients of lateral expansion and the volume expansion module. x is the coefficient, which depends on the size and shape of the mover’s support surface:

- ¼ ð0:92 þ 0:3L=bÞ2=3 ; for a track-chain mover with L/b < 7, and

L/b > 7 x = 2.15, forT-170M1.03-55 tractor the relation L/b = 2.88/

0.51 = 5.65 it follows herefrom - ¼ ð0:92 þ 0:3  5:65Þ2=3 ¼ 1:9. b is the width of the mover, m. L is the tractor’s support surface lenght, m. pmax is the maximum pressure on soil. kPa; v is the coefficient of accumulation intensity of irreversible deformation under repeated loads which is figured out by the next dependency: v ¼ tgbð1=ðq1  q0 ÞÞ, where b is the angle of inclination of the linear function q ¼ f ðlgNÞ. q1 is the soil density after a single load is applied. Usually 0:2 6 x P 2:5, if the v value is not determined, in approximate calculations it is recommended to take v = l,0. N is the number of repeated loads caused by the mover (it corresponds to the number of sections with increasing pressure on the pressure distribution of the mover). In order to take into account the uneven pressure over the contact area, the depth of the trace (30) was presented as the sum of deepening values of the trace after each mover passes sequentially the one after the other.

h ¼ h1 þ h2 þ ::: þ hi

xbð1  v 2 Þ E0

4. Discussion Soil compaction caused by a tractor mover depends on not only the tractor average pressure on soil, but also more on the design of the mover and the contact stresses generated in the support parts during the interaction. The maximum pressure can exceed the average pressure of the tractor by two or more times. In particular, the T-170M1.03-55 tractor reaches up to 0.166 MPa and extreme pressure values are offset to the edges of the contact points. The solution of the modeling problem was obtained using the theory of elasticity methods, when interacting with a perfectly homogeneous and elastic environment. In this case, such an assumption may seem unjustified, since the soil does not belong to materials

ð31Þ

where h1, hi is the track depth after the 1st passage of the imoveror after conversion

h¼

with a stable pressure distribution soil compaction value is reduced by 15. . .25%. The change in soil density in the trail of T170M1.03-55 tractor depending on uhk (under the conditions t = 0.3; E0 = 16 MPa; q0 = 0.95 g/cm3; H = 0.30 m) has the following form shown on Fig. 11. Experimental values of soil density after the T-170M1.03-55 tractor, with regard to the soil depth, are shown in Fig. 12. To make the experiments, we used a field prepared for sowing. Before the experiment, the field was subjected to harrowing and pre-sowing cultivation to the depth of 16–18 cm with soil moisture ranged between 31.7. . .37.5%. T–170.M1.01–55 tractor with flat and elliptical support part was loaded by flat and elliptical crawler rim which force is 42. . .44 kN. With a load of 80 kN, the soil density difference at the depth of 0.30 m along with the track was 25%. The same value at idle motion of the tractor was 15%.

 ðp1 þ v

N X fpiþ1 ½lgði þ 1Þ  lgðiÞgÞ

Fig. 11. Change of soil density in the trail of T-170M1.03-55 tractor: h is a flat track-chain bypass; h is an elliptical track-chain bypass.

ð32Þ

iþ1

After reformation of the Eq. (29) with (32) we obtained:

qt ¼

H H

xbð1m2 Þ E0

 ðp1 þ v  p2  lg2Þ

 q0

 for a flat support surface

qt ¼

H m Þ  ðp1 Þ H  xbð1 E0 2

ð33Þ

 q0

 for and elliptical support surface

ð34Þ

p1, pi+1 is the maximum pressure of the first and the following mover (according to the pressure distribution, Pa. Comparative calculations of soil density using formulas (33,34) on the trail and experimental studies of T-170M1.03-55 tractor with an elliptical bypass for different types of soil showed that

Fig. 12. Statistics for soil density along the furrows after the T-170M1.03-55 tractor: h – flat track-chain bypass; h – elliptical track-chain bypass; 4 – out of the tracks.

S. Mudarisov et al. / Journal of Terramechanics 89 (2020) 1–12

having such characteristics. However, the complications connected with the soil structure heterogeneity do not change the general nature of the conclusions obtained using the theory of elasticity. There are no elastic elements between the track-chain trolley and the support rollers. Thus, the rigidity of the ‘‘mover-soil” contact is almost completely determined by the soil properties taking into account the rigidity of the chain track. To describe pressure distribution along the support surface of a chain-track mover with a semi-rigid suspension we propose to use the mathematical model obtained based on the elastic contact problem. This model can be used to calculate the pressure distribution along with the contact length, when changing the pulling force on the hook, the height of the trailer, the displacement of the center of gravity of the tractor. By changing the geometry of the support surface of the chaintrack mover with a semi-rigid suspension and during the rational location of the center of mass of the tractor relative to the axis of symmetry of the support surface, it is possible to reduce the pressure of the mover on soil. The elliptical geometry of the support surface f(x) depends on the following parameters: the weight of the tractor, the length of the support surface, the location of the mass center, the magnitude of traction force and its application point, the material properties of the chain-track and of soil. The elasticity parameter obtained from the experimental data and which provides stable pressure distribution along the support surface equals to h = 0.0113 m. This confirms the results of theoretical studies. As a result of these studies the optimal parameter was obtained and it is 0.011 m. Elliptical geometry of the chain-track tractor’s support part with a semi-rigid suspension is achieved with the installation of support rollers at different height, this is the main advantage of this method. The uneven distribution of pressure along the length of the support part is influenced by the tractor equal weight displacement (eccentricity - e) caused by the pulling force on the hook as relating to the symmetry axis of the support surface. For a chain-track tractor designed to work with the pulling resistance on the hook during the engineering process, it is necessary to put the mass center in front of the middle of the length of the support surface. In particular, this value for T-170M1.03-55 tractor is 0,165 m. The obtained eccentricity equation is consistent with the well-known expressions for determining the horizontal coordinate of the tractor’s center of mass (Bekker, 1982; Vong, 1982; Ksenevich et al., 2003). The nature of pressure distribution on soil of the experimental studies is consistent with the theoretical results, which confirms the assumption that it is possible to reduce the pressure on soil by changing the geometry of the tractor’s support part. The elliptical geometry of the crawler mover reduces the maximum pressure from 120 kPa to 85 kPa when the tractor is working on a field prepared for sowing with medium-loamy soil. Numerous studies of soil density effect on crop yields have shown that density is one of the important agrophysical characteristics of soil that determine its fertility (Ksenevich and Rusanov, 2000; Gainullin, 2001; Ksenevich et al., 2003; Hamza and Anderson, 2005; Holtkemeyer, 2005; Gainullin et al., 2010; Khaliullin et al., 2010; Elaoud and Chehaibi, 2011; Nawaz et al., 2013; Elaoud et al., 2014; Cueto et al., 2016; Okunev and Kuznetsov, 2016; Edwin et al., 2018; Gabitov et al., 2018; Paulson et al., 2018; Rakhimov et al., 2018; Pulido-Moncada et al., 2019). The soil density in the track left by a chain-track tractor mainly depends on the magnitude of the pressure of the mover and the number of impacts in one pass. With each pass of the chain-track mover, the number of effects on each elementary track pad will be the same as the number of sections of the support part with

11

extreme pressure. For a chain-track mover with a semi-rigid suspension and flat support part there are two effects on soil. When changing the geometry of the support surface with a pressure distribution with one extreme value, the number of impacts is reduced to one. The influence of multiple passes on soil compaction and its structure is established for wheel movers (PulidoMoncada et al., 2019). 5. Conclusion Experimental studies on the impact of T-170M1.03-55 tractor movers on soil determined that the maximum pressure reaches 0.166 MPa. Expressed extreme pressure diagrams in the zone of the 1st and 6th support rollers, cause a double impact on soil in one pass along the track of the mover, which causes increased soil compaction with a corresponding decrease in traction properties of the tractor. To achieve the elliptical geometry of the support part of a crawler tractor with a semi-rigid suspension, lower track wheels were set at different heights. To provide typical working conditions of the T-170M1.03-55 crawler tractor with semi-rigid suspension, the third and the fourth lower track wheels should be placed 9.5 ± 1.5 mm lower, and the second and the fifth ones 4.5 ± 0.5 mm lower. When a crawler tractor is on the medium loam soil field prepared for sowing, the elliptical geometry of its track drive reduces both the maximum pressure from 120 to 85 kPa, and the load on outer lower track wheels by evenly distributing pressure on the soil. The elliptical geometry of the support surface of a chaintrack tractor with semi-rigid suspension is achieved by installing support rollers at different heights. Based on the contact problem of the elasticity theory, a model of pressure distribution under the support surface of the mover is developed. It takes into account the influence of the mover’s geometry the, the location of the center of mass, the magnitude and point of application of traction resistances acting on the tractor. An Eq. (1) to describe the geometry of the support part of a chain-track tractor with a semi-rigid suspension is proposed. It provides a stable distribution of pressure along the support surface. The location of the tractor’s center of mass from the load mode and the geometry of the support surface of the mover is justified. For T-170M1.03-55 tractor with a pulling force of 80 kN and a trailer height of 0.4 m, the mass center should be located at 0.165 m forward from the middle of the support surface. Laboratory and field tests showed that the proposed geometry of a chain-track mover when the tractor is working on a field prepared for sowing, with medium-loamy soil reduces the maximum pressure on the soil from 120 kPa to 85 kPa. It also reduces the load on the extreme support rollers by evenly distributing the pressure on soil. The influence of T-170 M 1.03.55 tractor’s support surface geometry on soil compaction was determined. With the justified knowledge of the above, stable pressure distribution across the track rollers was ensured and the soil compaction in the groove was reduced by 15. . .25%. Thus, the mover pressure on soil, and consequently reduction in compaction can be achieved by changing the geometry of the support part of a track-chain tractor with a semi-rigid suspension, as well as by the rational location of the tractor’s center of mass relative to the support part. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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