Issue 
BIO Web Conf.
Volume 17, 2020
International ScientificPractical Conference “Agriculture and Food Security: Technology, Innovation, Markets, Human Resources” (FIES 2019)



Article Number  00056  
Number of page(s)  4  
DOI  https://doi.org/10.1051/bioconf/20201700056  
Published online  28 February 2020 
Research of dynamics of turning of machinetractor aggregate with tractor on wheeledcrawler mover
^{1}
Kazan State Agrarian University, 420015 Kazan, Russia
^{2}
Bashkirian State Agrarian University, 450001 Ufa, Russia
^{*} Corresponding author: drgali@mail.ru
In the article theoretical preconditions of a description of dynamics of manoeuvrability of machinetractor, aggregates with a wheeledtracked mover are considered. For a machinetractor aggregate with halftracked progress theoretical formulas of determination of an actual turning radius, the moment of resistance of turn and torque for rotation are obtained. The theoretical preconditions are confirmed by experimental research of the manoeuvrability of the machinetractor aggregate with the tractor on a halftracked progress, made as the experimental sample. The dependences of the turn coefficient and the resistance coefficient of the turn are obtained, and the correlation coefficients and their significance have confirmed the existence of a stable connection between the changing parameter and the response function. Proceeding from theoretical and experimental research, it is possible to draw a conclusion that the manoeuvrability of the tractor with a wheeledcrawler mover does not concede to the tractor in the basic execution.
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
The main task of agricultural production of the country is to provide the population with food and raw materials of various industries, the implementation of which is directly related to the transfer of agroindustries to an industrial basis. This, in turn, requires a radical improvement in their material and technical equipment, both quantitatively and qualitatively. However, in recent years, enterprises producing tractors and various agricultural machinery have been in dire economic straits. On the other hand, as the statistics shows, the volume of agricultural production is increasing. In subsequent years, this process continued, and as a result, the need of agriculture for tractors and harvesters will 5...7 times exceed the level of their production [1–4].
In agriculture, the production process is intermittent, which creates certain difficulties for the uniformity of loading of specialized equipment and performance of technological operations in the agrotechnical time. The solution of this problem is a flexible changeover of the tractor, its versatility, that is, its fast retooling for other agricultural works, which are not typical of the basic variant of the tractor.
As practice shows, the less there are the tractors of different types and grades in one economy, the less there is necessary material and technical base on maintenance of their efficiency that influences, in the end, the cost of agricultural products [5]. In this regard, agriculture needs versatile tractors, which could easily and quickly be rebuilt constructively to perform works not typical of the basic version. In our opinion, the solution of the problem is to create a tractor on a semitrack based on MTZ.
2 Conditions, materials and methods of research
When studying the manoeuvrability of the machinetractor aggregate (MTA) with the tractor on the halftracked move, the important point is the determination of the minimum turning radius, the turning moment and the moment of resistance to the turn of the MTA.
The actual turning radius of the MTA depends on the ratio of the turning moment and the moment of resistance to the MTA turning. The greater the turning moment and the less the torque of the MTA, the smaller the actual turn radius of the MTA, which tends to the value of the geometric radius.
To determine the turning moment and the moment of resistance to the turn, the MTA conducted theoretical studies by schematic simulation of the turn of the tractor with a wheeltrack specifying the active forces on the tractor.
For confirmation of theoretical preconditions it is necessary to conduct experimental research. Since the maneuverability of the MTA significantly depends on the physical and mechanical characteristics of the soil, the following indicators of soil were determined for the experiment: density, humidity and hardness. The turning radius, the torque, the moment of resistance to the turn of the MTA were determined both on the basis of the serial and on the basis of the experimental tractor of MTZ 80PG.
To study the dynamics of turning was developed experimental installation with tractor with a wheeledcrawler mover on the basis of tractor MTZ80.
Experimental studies were conducted in the conditions of the land of Kazan state agrarian university. The condition of the soil during the experiments was controlled by density, humidity and hardness. Plots for experiments were selected horizontally, with a relative smooth surface. An agrotechnical structure of field surface includes a stubble, raw field, freshly ploughed field.
In the course of studies the values of the actual turning radii of the MTA were measured under different conditions (agrotechnical structure of the field surface, the angle of rotation of the steered wheels).
3 The results of the study
The geometric turning radius of the MTA (Fig. 1) depends on the angle of rotation of the steered wheels [6]:
$${R}_{r}=L\xb7ctg\alpha ,$$(1)
R_{r} – geometric turning radius of the MTA, m; L – distance between axles of leading and driven tractor wheels, m; α – the average angle of rotation of the steered wheels, degree.
The actual radius of the turn of the MTA with the wheeledcrawler mover, unlike the geometric radius of rotation, depends on many factors: the coefficient of coupling of the mover with the soil, the coefficient of rolling resistance, the speed of the movement of the MTA, the distance between the tractor tracks, the force on the hook, the longitudinal distance between the axles of the tractor, the average angle of rotation of the steered wheels, the redistribution of weight between the front and rear axles of the tractor, the redistribution of weight between the outer and inner wheels, the length of the supporting surface caterpillar with soil, humidity and soil density, the stress of soil compaction, the design parameters of the front steered wheels.
The MTA moves at a constant speed and on a circular trajectory with a constant turning radius. The tangential traction force of the rear caterpillars is transferred to the tractor’s skeleton in the form of the equivalent force of the P_{k} (Fig. 1), which is directed forward along the axis of the tractor. This pushing force of P_{k} is transferred to the front axle and front wheels.
In the spot of the contact of the controlled wheel with the soil, there are reactions, the equivalent force of which equals the pushing force of the P_{k} and opposite it is directed. Each of these forces can be decomposed into two components. The reactive force component R_{f} of the R_{k} is the force of wheel rolling resistance. The force component R_{t} the force creates a turning moment of the MTA M_{t} around the point “O”:
$${M}_{t}={R}_{t}\xb7cos\alpha \xb7L={G}_{t}\xb7{\varphi}_{c}\xb7cos\alpha \xb7L,$$(2)
G_{t} – vertical load on the front axle of the tractor, N; φ_{c} – wheel coupling coefficient with soil.
In addition, the following forces also operate on the tractor: centrifugal force of the P_{c}, which arises as a result of moving the tractor carrier system with some angular velocity ω_{t} around the centre of the rotation point “Ot”; tangent forces of the P_{K}1 and P_{K}2, respectively on the running and lagging tracks; force on the hook of the P_{fh}.
The moment of resistance to the turning of M_{rt} around the point “O”:
$$\begin{array}{c}{M}_{\mathit{rt}}={R}_{f}\xb7sin\alpha \xb7L+{P}_{c}\xb7cos{\gamma}_{c}\xb7a+\\ +\frac{\mu \xb7{G}_{l}\xb7{L}_{\mathit{cat}}}{4}+{P}_{\mathit{fh}}\xb7sin\psi \xb7b\\ \end{array}$$(3)
γ_{c}– the angle between the direction of centrifugal force of the P_{c} and the line passing through the center of rotation “O_{t}” and point “O”, deg.; a – distance from the rear axle to the center of gravity of the tractor, m; μ – the cast to value of a coefficient of resistance to turn; G_{l} – vertical load on the rear axle of the tractor, kN; ψ– angle between the direction of action of the hook force of the P_{fh} and the axial line of the tractor, deg.; b – distance from the rear axle to the coupling device (hook), m.
The strength of wheel rolling resistance depends on soil properties and vertical load on steered wheels:
$${R}_{f}={G}_{t}{f}_{r},$$(4)
f_{r} – coefficient of wheel rolling resistance on the soil.
The centrifugal force of the P_{c} is known to be directly proportional to the weight of the tractor, the square of the rate of movement of the MTA and inversely proportional to the radius of the center of gravity rotation:
$${P}_{c}=\frac{G{v}^{2}}{g\xb7{R}_{c},}$$(5)
G – tractor weight, kN; g – acceleration of the free fall, m/c^{2}; R_{c} – radius of the turn of the center of gravity of the tractor, m.
The radius of rotation of the tractor center of gravity is always slightly larger than the geometric turning radius R_{r} and with the formula (1):
$${R}_{\mathit{cg}}=\sqrt{{a}^{2}+{R}_{r}^{2}}=\sqrt{{a}^{2}+L\xb7ct{g}^{2}\alpha}.$$(6)
Therefore, equation 8 will take the following form:
$${P}_{c}=\frac{G{v}^{2}}{g\xb7\sqrt{{a}^{2}+{L}^{2}}\xb7ct{g}^{2}\alpha}.$$(7)
Let us consider the triangle with the vertices of the DSO_{t}, from which we define the formula component (3):
$$cos{\gamma}_{c}=\frac{{R}_{r}}{{R}_{c}}=\frac{L\xb7ctg\alpha}{\sqrt{{a}^{2}+{L}^{2}\xb7ct{g}^{2}\alpha}}.$$(8)
The cast to value of a coefficient of resistance to turn p depends on physical and mechanical properties of a soil, structure of caterpillars and depth of their immersion in soil. However, the maximum influence on this coefficient is the turning radius (the smaller the turning radius, the greater the coefficient of μ).
In the indicative calculations of the value of coefficient μ at different radii of turning, it is possible to apply the empirical formula of A. O. Nikitin [7]:
$$\mu =\frac{{\mu}_{max}}{{[c+(1c)\xb7({\rho}_{t}+0,5)]}^{,}}$$(9)
μ_{max} – the highest value of the coefficient of resistance turn, (the denser the soil, the smaller the value of the coefficient μ_{max} (0.7... 1.0)); ρ_{t} – relative turning radius; c – depends on soil conditions (the denser the soil, the greater the value of c (0.75... 0.9)).
The relative radius of rotation is determined by the formula:
$${\rho}_{t}=\frac{{R}_{r}}{B}\xb7$$(10)
B – distance between the tractor’s gusinians, m.
In movement of the MTA along the curvilinear trajectory the onhook force of the P_{fh} will be directed not to an axis of the tractor, and under some angle ψ. Breakdown of the onhook force of the P_{fh} into two components: transverse P_{fh}· sin ψ and longitudinal P_{fh}·cos ψ. The transverse component of the onhook force is directed towards the lagging caterpillar and in relation to the point of “O” gives the moment of resistance to the turn of the MTA.
Under the action of the longitudinal component of the on hook force the load is redistributed along the axes of the tractor. The redistribution of load on axes, first of all, depends on the type of agricultural machine and the way of regulation.
The vertical load on the front axle, taking into account the effort on the hook, will be:
$${G}_{t}={G}_{t}^{0}{P}_{\mathit{fh}}\frac{{h}_{h}}{L},$$(11)
${G}_{t}^{0}$ – vertical load on the front axle without taking into account the on hook force, kN; h_{h} distance from the ground to the point of the trailer, m.
The hook force of the P_{fh} will load the rear axle as follows:
$${G}_{l}={G}_{l}^{0}+{P}_{\mathit{fh}}\frac{{h}_{h}}{L}+{P}_{\mathit{fh}}\xb7tg\beta ,$$(12)
${G}_{l}^{0}$ – the vertical load on the rear axle without regard to the on hook force, kN; β – angle between the horizontal plane and the line of traction force, deg.
Thus, the hook force of the P_{fh}, loading the rear leading caterpillar, increases traction properties of the tractor, but at the same time, unloading the front driven wheels, worsens the controllability of the MTA.
The angle between the direction of the action of the P_{fh} and the axial line of the tractor ψ depends on the angle of rotation of the steered wheels a, namely – the greater the angle of a, the greater the angle of ψ.
The turning radius of the trailer point of the R_{fh} is slightly larger than the geometric radius of the R_{r} (see Figure 1):
$${R}_{\mathit{fh}}=\sqrt{{b}^{2}+{R}_{r}^{2}}=\sqrt{{b}^{2}+{L}^{2}\xb7ct{g}^{2}\alpha ,}$$(13)
Let us consider the triangle with the vertices of the SO_{t}E, from where we define the component of the formula (3), while taking into account that the shift of the center of turning (from point “O” to point “ O_{t}”) will change the angle of ψ and therefore change the value of sin ψ and this change can be taken into account by the introduction in the formula of correction coefficient k:
$$sin\psi =\frac{k\xb7b}{\sqrt{{b}^{2}+{L}^{2}\xb7ct{g}^{2}\alpha}}\xb7$$(14)
It is difficult to determine exactly the k coefficient value. Therefore, we assume that the center of turning is shifted in this way (see Figure 1):
$$\frac{C{O}_{t}^{{}^{\prime}}}{B{O}_{t}^{{}^{\prime}}}=\frac{L}{b}=\text{k.}$$(15)
Subject to expressions 4...14, formula 3 will take the following form:
$$\begin{array}{c}{M}_{\mathit{rt}}=\left({G}_{t}^{0}{P}_{\mathit{fh}}\frac{{h}_{h}}{L}\right)\xb7sin\alpha \xb7L+\frac{G{v}^{2}\xb7L\xb7ctg\alpha \xb7a}{g\xb7{a}^{2}+{L}^{2}\xb7ct{g}^{2}\alpha}+\\ +\frac{{\mu}_{max}\xb7{L}_{\mathit{cat}}\xb7\left({G}_{l}^{0}+{P}_{\mathit{fh}}\frac{{h}_{h}}{L}+{P}_{\mathit{fh}}\xb7tg\beta \right)}{4\xb7\left[c+(1c)\xb7(\frac{{R}_{r}}{B}+0,5)\right]}+\frac{{P}_{\mathit{fh}}\xb7L\xb7b}{\sqrt{{b}^{2}+{L}^{2}\xb7ct{g}^{2}\alpha}}\xb7\\ \end{array}$$(16)
Let us introduce a concept such as the coefficient of turning of the K_{R}, which is equal to the ratio of the actual radius to the geometric:
$${K}_{R}=\frac{{R}_{f}}{{R}_{r}},$$(17)
R_{f} – the actual turning radius of the MTA, m.
When K_{R} = 1, the ability to rotate is considered normal, when the K_{R} < 1 – redundant and at the K_{R} > 1 – insufficient.
The ratio of the moment of resistance of the turn and the turning moment shall be denoted as a factor of resistance to rotation K_{m}:
$${K}_{m}=\frac{{M}_{\mathit{rt}}}{{M}_{t}}.$$(18)
Using formulas 1, 2 and 16, the geometric radius values are obtained, turning moments and moments of resistance turn. As a result of joint mathematical processing on the developed program on the computer [8, 9], empirical formulas of dependence of the coefficient of turning from the factor of resistance of a turn on various agrotechnical structure of the field surface have been received. Force on a hook changed from 0 to 10 kN, at the speed of the MTA movement of 2 m/s, which are presented in Table 1. The relationship between the changing parameter and the response function was determined by the correlation coefficient. The coefficient value is evaluated by the correlation coefficient error m_{R} indicator from the following condition [10]:
The study of the maneuverability of both types of MTA came down to the fact that the actual radii of turns were measured at various operational factors.
Fig. 1. The scheme of forces acting on the tractor with the wheeledcrawler mover at its turning in the composition of the MTA. 
Empirical dependence of the coefficient of turning and the factor of resistance turn.
4 Conclusion
The necessity of universal tractors is grounded, which can be easily and quickly reconstructed for the performance of works not typical for the basic version of this tractor.
Experimental research on different agrotechnical structures of the field surface, hook loads and rotation angles of control wheels was carried out on the pilot sample of the tractor with wheeledtracked progress.
The dependencies of the turning coefficient and the resistance factor have been obtained, and the correlation coefficients and their significance have confirmed the existence of a stable connection between the changing parameter and the response function.
Eith equal operational conditions the actual turning radius of the MTA with the tractor with the wheeltrack stroke, as a whole, exceeds the analogous indicator of the MTA with the tractor with the wheel stroke by 3.5%.
In the raw field and freshly ploughed field at the hook loads of more than 5...6 kN, the turn radius of the MTA with the tractor on the wheeltrack move begins to increase more intensively than that at the MTA with the basic tractor. The inverse picture is observed on the stubble – the actual turning radius of the MTA with the base tractor, under hook loads over 5 kN, starts to grow more intensively and at some operational factors exceeds the actual turning radius of the MTA with the tractor on a wheeltrack move.
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All Tables
Empirical dependence of the coefficient of turning and the factor of resistance turn.
All Figures
Fig. 1. The scheme of forces acting on the tractor with the wheeledcrawler mover at its turning in the composition of the MTA. 

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