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Bayboboyev Nabijon Gulomovich, Rakhmonov Husan Tojiyevich, Khamzayev Asrorkhon Almuhanovich, Akbarov Sherzod Batirovich, Namangan Institute of Civil Engineering, Uzbekistan E-mail: [email protected]
JUSTIFICATION OF PARAMETERS OF THE RUNNING WHEELS OF THE PRESEEDING SOIL TILLAGE ASSEMBLY
Abstract: Process of interaction of the driven wheel by soil taking into account of the friction force is considered in the course ofwork. Generalized design schemes are drawn up and analytical formulas in effort to justify the wheels' parameters of the preseeding soil tillage assembly. The results are shown in the form of graphics and appropriate conclusions are made.
Keywords: wheel, energy(power), assembly, machine, rolling, soil, sliding, friction forces, tractor, depth of track.
Introduction However, in these works in effort to study the issue on wheel
In order to implement any technological process an rolling the essential assumptions in the description of rolling energy(power) source, technical means and materials are of driven wheels on the deformable basis are applied. Often
the rolling of a wheel is described by the rolling coefficient « , which usually represents the value of displacement of the vertical reaction of base to the wheel [8, 9, 10]. Value of this coefficient is determined from experience and the value of this variable allows to calculate the wheel motion to certain extent. Another characteristic used to estimate wheel rolling is the resistance coefficient C to rolling, which is the ratio of thrust force P (enclosed to the wheel center) required to roll over the
wheel to vertical load onto the wheel Q.
p
C = P (1)
Q
Relation between values «and C as known is determined
required.
In agriculture, source of energy is the following: tractor, technical means of agricultural machinery and materials are mainly soil either agricultural crops.
In most cases, tractors and agricultural machinery moves throughout the material being processed i.e. throughout the soil. At the same time, a significant share of energy(power) is consumed on rolling over the assembly all over the field area.
In the course of rolling the assembly, the energy goes mainly for soil deformation under the action of machine wheels. Therefore, in effort to analyze the issue on energy(power) consumption in rolling, it is sufficient to study phenomena occurring in the soil when rolling the agricultural machine's wheels throughout it [1].
As you know, two types ofwheels exist: leading and driven. In its way the driven wheels are divided into free and running types. In this work the free type ofwheels are considered. Chassis differ from the loose wheels in that they are associated with any of mechanisms of the machine and part of the reactive torque occurring in the wheel, is transmitted to the machine mechanism (e.g. to the seeding unit of seeder)[l].
Thus, the energy consumed on rolling the agricultural machine or assembly, is mainly used for overcoming the reactive torque moment resulting from the deformation of soil at free wheel.
Main part
Theory of rolling the driven wheels has been considerably developed in the writings of such academicians: V. P. Gory-achkin [l] V. A. Zhelikovskiy [2] and continued specifying in works of M. G. Becker [3], V. V. Guskov [4] and had been developed in researches of other scholars[5, 6, 7, 8, 9, 10].
by the following dependency:
H = C • r (2)
where r - wheel radius.
By substituting in equation (2) the value C from equation (1) the equality of torques of the driving forces P and the load Q influencing on the wheel can be obtained:
P
u= — r
Q
Mentioned above dependencies, although allow you to calculate the wheel motion, but do not reveal the essence of wheel interaction with the soil in performance of any technological process.
When considering the interaction of wheel with soil, academician V. P. Goryachkin proposed a formula that determines the force onto rolling wheels in the form of:
P = 0,86"
where B - width of wheel, m; D - wheel diameter, m;
Q4
kBD2
(3)
k - is the volumetric coefficient of soil erosion (N/sm3) depending on the soil condition caused by humidity, soil composition and other factors.
Thus, the formula (3) allows to determine influence of k onto wheel traction resistance in case if data is Q, and D.
In the course of implementing analysis of the running gear of assembly in operation, along with in the course of implementing activities by using the formula (3), we performed a theoretical research of rolling resistance of wheel with its equal rolling throughout the field.
Unlike the works [4, 5] devoted to this issue, we adopted the calculation scheme (Fig.1), which took into account not only the normal movement, but also friction forces acting onto the wheel rim from the soil.
These forces are taken into account in the scheme (Fig. 1) by vectors dF and T. In accordance with design scheme, let's consider the infinitesimal little element of surface of the wheel rim bounded by angle d and wheel width B. It is obviously, that normal pressure dN and the friction force dF will influence onto this element.
Figure 1. Designed scheme of interaction of the wheel with soil
Figure 2. Forces influencing onto wheel
The friction force dF is caused by fact that if the instantaneous center of velocity is at the Pv point and directed against the rotation of the wheel (Fig. 2).
The variable of friction force dF is determined depending on depth of the track h, as points of wheel rim may slip or not slip relative to the soil. Gauge depth of track is determined as in the following way:
h <
Df 1 + f2
(4)
where D - is the wheel diameter; f - is the coefficient of sliding the wheel rim throughout the soil.
In this case, the friction force is determined by below formula:
dF = dN • tg /a (5)
where a is angle between dN and equally acting dr that determines dF friction force.
For rim points allocated higher than the h value, the friction force determined by the formula (4) is equal to:
dF = dN • tgP= dN • f (6)
where P is the friction angle of wheel rim throughout soil.
In effort to determine depth of h track depending on load onto wheel Q. Let's design the forces enclosed to wheel on the y axis after we got
max
£ y = Q +J (dN ■ cos0 + dF ■ sin0 (7)
0
where dF = q • ds, in which q is specific normal pressure of the soil on wheel at A point, at N/ sm3; ds is the infinitesimal little element of the wheel rim surface at A point.
ds = Orb.
When we make variation in the specific pressure q on wheel rim can be obtained base on the cosine law, i.e., in the event if at Pv point of the wheel (Fig. 1) influence the maximum specific pressure qmax, then at A point it is determined by equation
q = qmax ■ cos(0-0o) ~ qmax ' C°S^ (8)
In its turn, qmax value depends on gauge depth h of track that is, also depends on 9 angle.
This dependence is determined by the equation:
qmax = kr(COS^0 - C0s^max) ~ kr ' (1 - C0S^max) (9)
Equation (8) is derived from the condition of linear dependence of the soil resistance against crumbling from h track depth, that is qmax = k ■ h [8]. Considering equation (8) and (9), the elementary normal pressure dN is determined by the equation:
dN = kB ■ r2(1 - cosOmax)cosO-dO (10)
By substituting dN and dF value from equations (5), (10) into formula (7) we will obtain
max
Q = kBr2(1 -cos0max)• J cos0-dd
0
After integration activity of setting the limits of integration, we will obtain
Q = k • B -r 2(1 - cOS^max) • Sin^max (11)
By replacing 9 angle through h depth of track gauge, we will obtain
Q = k ■ B ■ h -V2rh - h2
(12)
Equation (12) determines h gauge depth of track, depending on the condition of soil characterized by k, in the event if data is Q, r and B.
Materials and results of the research
Let's consider the equation of torque moments of all forces influencing at the wheel relatively to the wheel center. Let's set that the wheel rim in addition to dF forces that equate the torque moment of dF forces should influence. This is the t coupling force.
Moment of the clutch force t is equal to moment of dF friction forces relative to the wheel center, from where it follows the below formula:
0 2
T = J dF = J dN-tg-
00
When we substitute dN value from the equation (10) and
9
replace tg— into (cos9)/sin9, we obtain
«max Q dmax Q
T = i dN ■ tg- =i k ■ B ■ r2 (1 - cosd ) • cos0-tg-■ dd =
0 2 00 2
= kBrh (1 -cos0 + ln1 + COS0max) = k-B-r-h (- + ln)(13) 2 r 2r
In effort to determine the traction resistance of P wheel, we will design the forces enclosed to the wheel on X-axis, then we obtain:
£X = P - T - J (dN ■ sin0 — dF ■ cos0)
(14)
By substituting the value dN, dF and T from equations (5), (10) and (13), after integration and substitution of integration limits from zero to qmax, we obtain the following
P = kBr2 • 2(1-cos0 )2 = 2kBh2 (15)
v max' v '
On the (fig. 3) svariations in the values of P traction resistance are shown, that are determined base on (15) equation with (12) equation
1 - in case when wheel diameter - D = 0.45 m; 2 - in case when wheel diameter - D = 0.75 m Figure 3. Dependency of traction resistance of the assembly from the wheel diameter and k coefficient
From above graphics it can be seen that the traction resistance increases significantly by decreasing in the resistance of soil to crumbling and the wheel diameter.
In comparing these graphics there can be shown in case if the running wheels of the assembly are replaced into the wheels with increased diameter possibly to reduce signifi-
cantly the traction resistance of wheels and to improve significantly the aggregation of the agricultural machines.
Summary
1. The formula for determining the traction resistance of the assembly is obtained taking into account of friction force of the soil and the wheel diameter.
2. Traction resistance significantly increases by decreasing in the soil resistance to crumbling and the wheel diameter. Decreasing in the traction resistance ofwheels, and substantially improve the aggregation the agricultural machines are implemented by practicing the running wheels of the increased diameter.
References:
1. Goryachkin V. P. Collection of works in - Vol. 3.- Moscow. "Kolos". - 1968.
2. Zheligovsky V. A. Elements of the theory of soil tillage machines and mechanical technology of the agricultural materials.-Tbilisi,- 1960.- 146 p.
3. Bekker M. G. Introduction to the theory of terrain-machine systems/ M. G. Bekker; Translated from English. Vladimir Guskov.- M: Mechanical Engineering,- 1973.- 519 p.
4. Tractors: theory/ V. V. Guskov, N. N. Velev, I. E. Atamanov, N. F. Bocharov, I. P. Ksenevich, under general edition of B. V. Guskov.- M: Mechanical Engineering,- 1988.- 376 p.
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