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1STUDY OF SEED MOVEMENT
1Normirzayev A.P., 2Bekmirzayev B.Sh.
1PhD, Candidate of Technical Sciences, associate professor 2Basic doctoral student Namangan Engineering-Construction Institute https://doi.org/10.5281/zenodo.13624413
Abstract. In the article, the speed of movement of seeds along the projection of the axes along the surface of the seeding device, the analytical connections for determining the absolute speed, as well as the expressions for calculating the laws of movement along the seed nest of the reel in the coordinate axes are presented.
F ^
Keywords: seed movement, lshq -friction force, G -gravity force, P -reaction force and
F
e -inertia force in seed movement, displacement of seed on the reel in the projection of coordinate axes and absolute speed as a function of time, angular acceleration.
The main part: Movement of seeds in the coil are fully described in their scientific works of Vasilenko P.M, Shevchenko I.A, Gevko B. M, Kirova A. A, Manchev A. V, Radugina N. P, Sisolina P. V and others.
In the study of seed movement, it can be seen in Figure 1 that the following forces act at
point O: Fishq -friction force, G -weight force, P -reaction force and Fe -inertia force in seed movement. The seed falls from the reel under the influence of gravity. Here is the force of gravity G = mg (1) is determined by the expression. Here: m - seed weight, kg; g -is the speed of free fall, m/c2
The coefficient of friction affecting the movement of the seed is determined when the force Fmax that moves it reaches its maximum value. It tries to balance the movement of the seed with the force of friction (f ■ G ■ sin p).
Figure 1. Scheme of the location of the seed relative to the side walls of the coil and the forces
acting at point O
Since the seed falls from the hopper to the roller under the slope, the initial velocity V"0of the seed can be considered equal to 0.
When determining the movement of the seed, the following points can be taken into account:
1. When the seed is moving, the air resistance forces are not taken into account, because it is smaller than the friction force during movement along the inclined plane and compared to the speed of the seed movement.
2. The mass of the seed is concentrated in its center of gravity [1; 44-b]. Methodology: When the reel reaches its maximum angular acceleration, the seed falls from
the slot. The seed falling on the reel is acted upon by a centrifugal force Fm = ma)2r and a
fictional force Fishq = fmg opposite to it. When the above forces are balanced, the seed will drop from the reel seat.
Fm = Fishq or m&2R = fmg (2)
If the friction angle P, formed due to mutual contact of the seeds, is variable, then the speed of seed's descent depends on its contact surface with the roller wall. Therefore, if P = 0, seed's falling speed is also equal to Vor = 0 at this point on the reel.
The inertial force when the seed reaches point O will be equal to
Fn = ma = ma>2 R
where: ® -is the angular speed of the coil rotation, rad/s R - coil radius, mm.
It can be seen from Figure 1 that the frictional force generated by the movement of the seed on the surface of the reel is directed in the opposite direction to the speed of the reel. The normal
force FumK ■ cosp causes the reaction force N acting on the seed. Based on these considerations,
the following expression can be written to determine the normal force
N = FumK C0SP (3) The friction force prevents the seed in contact with the surface of the reel from sliding [3].
FumK = f * G1 = f ■ m ■ g ■ SinP
where: Gx — G
(4)
component of gravity, H
P deviation angle, grad. G - the force of gravity acting on the seed, H
m- seed weight, kg f
J - coefficient of friction.
Therefore, in order for the seed to move when it is in contact with the surface of the reel, the following equation must be fulfilled [4].
FumK * C0SP > f * G1 (5)
When analyzing seed movement (Fig. 1), the following conditions should be taken into account.
1. After the seed leaves the nest, Ve force FumK is generated due to its weight m, which is
opposite to the speed a.
2. A movement of mg occurs when the seed falls off the reel [5].
Taking into account the above, we write the main equation of the movement of the seed with respect to the axis n normal [1; 45-b]
d 2 n
m-
= E F
¿—i x
dr y xi (6)
In this: y F xi - sum of active forces affecting the seed, H
y F
It can be seen from Fig. 1 that the forces acting on seed xi can be written as follows
[6]:
y Fx = Fn + G = FT + Fshq (7)
The seed starts moving at point M, and at this point the reaction force N is equal to 0. The force F acting on the movement of the seed is assumed to be proportional to the speed: F = f ■ mV
At point O, we write the equations of motion relative to the projection of the forces acting on the seed in the normal coordinate systems and n : mil = F sinp + Fn
(8)
m 1 = -G + Fishq C0SP
(9)
Taking into account expressions (3) and (4), expressions (8) and (9) can be written as follows:
mil = f ■ m V sinp + ma2 R
(10)
m i = mg + f ■ m ■ g ■ sinp
(11)
(11) we take conditions t = 0, Vx = 0, and X = 0 as initial conditions for the expression and then integrate the expression
m—VL = -f ■ m ■V sinp + ma2R (12)
(12) reduce both sides of the equation to m and make it look like this:
= -f ■ V sin p + g2R
dt n (13)
After separating the variables, we get the following view: dv
= dt
— f V • + (14)
We integrate equation (14) with speed up to V0 = 0 and t up to to = 0.
f
Jo
dv„
= f dt
o
30 C■ R - f -sinp- Vn After integration, we get the following equation:
1 9
--ln(c2 R - f ■ sinp V) = t + Ci
f ■Sinp
From this : C1 — constant integrator.
(15)
(16)
1
lnC R
- - .
- j - sinp Then we can write equation (16) as follows:
1 — .2„ ^ . 1 jn»2r = t
f -sinp
ln(c R- f -sinp-V) +
f -sinp
(17)
ln
(17) as a result of mathematical changes, we make the expression look like this:
^c2R - f -sinp- V ^
V
co2 R
= -t-f -sinp
J
(18)
ln X 2'X e using the fact that is equal to , the expression (18) can be written as follows:
J2 ti .c tz ,.,2 n -t■ f -sinp
cCR - f - sinp-V =cR - e" J-s
(19)
After mathematical transformations of the expression (19), we determine the speed of
Vn T
movement of the seed on the reel for the projection on the axis 1 _ c2R(1 - e- - f ■sinp)
n = r •
f -sinp (20)
To determine the displacement of the seed in the projection on the T axis, we replace the
V =
dS„
expression (20) with the variable dt . Then we get the following expression:
dSn c2 R(1 - e - ■f ■sinp)
dt f -sinp
We integrate the expression (21):
c2 R(1 - e - f - sinp)
(21)
f dS = f
dt
f -sinp
After integration, expression (22) becomes:
V R(1 - e - f - sinp)
(22)
s>< =f-
f -sinp
dt
n
0 R(1 - e- f sin^) SB =--- • t + c3
f • sln^ (23)
c3 - constant of integration is found by expression (23) based on initial conditions. It will be equal to c3 = 0. The equation then becomes:
0 R(1 - e ~vf sin^)
Sn =—--• t
f • slnç (24)
(24) we give the final expression based on initial conditions: t = 0 Sn = 0 VT = 0 of
the equation of motion relative to the projection of the forces acting on the seed onto the T axis of the vector expression as follows [3; 48-51-b]:
V= g(sln^- f )t (25)
V t m / c
Here: T - the speed of the reel on the projection of the seed on the 1 axis,
The speed of movement of the seed on the reel is equal to the sum of the speeds of its projections on the coordinate axes
—t ■ f -sin^ -
V = JÏ[+Vn
f__2
¿y2 R(1 — e
—t- f -sin^ \
f ■ sinç
+ (g (sin^ — f )t )
(26)
Result: To determine the speed of movement of seeds along the surface of the roller of the
n r
sowing device along the projection of the normal and axes and the displacement of the seed on the roller in the projections of the coordinate axes, we calculate the numerical solutions using
the Microsoft Excel program. We perform calculations on the values in the G 6,14Pad / c,
, fc[0;0,5]; V0[0;1,25]; g = 9.8m/c2
interval and build the graph shown in
^ = [0...0,86]; lC[°;°,5]; ' 0> Figure 2 based on the obtained results.
From the graph in Figure 2, the movement of the seed in the axes of normal coordinates
n moves 0.01 m in 0.1 s, 0.04 m in 0.2 s, and 0.1 m in 0.3 s.
From the graph in Figure 3, the absolute speed of the seed in motion is 7.3 m/s when the spool is 0.1 s, 4.5 m/s at 0.3 s, and 4.3 m/s at 0.5 s.
Sn m
V, m/c 8
0,2
t, c
0,1
0,2
0,3
0,4
t, c
0,5
2
2
6
4
2
0
0
Figure 2. The graph of the time Figure 3. Time dependence graph of the
dependence of the displacement of the seed absolute speed of the seed falling into the slot on the reel in the projection of the of the reel in the coordinate axes
coordinate axes
Conclusion: Based on the above, it can be said that the speed of movement of seeds along the surface of the roller of the sowing device along the normal and axis projection (25), analytical connections for determining the absolute speed (26), as well as the expressions (24) for calculating the laws of movement along the seed nest of the roller received.
REFERENCES
1. Teterina O.A. Justification of the parameters of the device for pre-sowing treatment of seeds with hot fog of humates. Dissertation for the degree of candidate of technical sciences. Ryazan 2019. - 138 p.
2. A. V. Machnev et al. Studies of seed movement on the surface of an equal-speed worm of a reel sowing apparatus. Technical science. Niva Povolzhya No. 4 (29) 2013. P.48-51
3. Normirzaev AR, Bekmirzaev Sh. Double-row seeder for planting legumes. Fergana FarPI scientific and technical magazine. 2022. Special issue - 2021. 56-61.
4. Bekmirzaev Sh B. Normirzaev AR. Nuriddinov A. Basing the dimensions of the working part of the mini seeder for planting granular seeds. Namangan Engineering and Construction Institute Journal of Mechanics and Technology. SPECIAL ISSUE 2022, No. 1 (1). 80-p
5. Bekmirzaev Sh B. A study of the forces influencing the sowing of leguminous seeds. Namangan Engineering and Construction Institute Journal of Mechanics and Technology. SPECIAL ISSUE 2022, No. 1 (1). p. 96
6. Sh.B. Bekmirzaev, A.R. Normirzaev. Determine the size between the reel and the seed returner. Scientific and technical journal of Namangan Institute of Engineering Technology. Volume 7, Special Issue 2, p. 2022.29.
