The American Journal of Applied Sciences
26
https://www.theamericanjournals.com/index.php/tajas
TYPE
Original Research
PAGE NO.
26-30
10.37547/tajas/Volume07Issue06-05
OPEN ACCESS
SUBMITED
22 April 2025
ACCEPTED
18 May 2025
PUBLISHED
20 June 2025
VOLUME
Vol.07 Issue06 2025
CITATION
Sodikjanov Jaxongirbek Shukhratbek oglu. (2025). Enhancing the Operation
of The Ginning Machine Chamber to Improve Efficiency. The American
Journal of Applied Sciences, 7(06), 26
–
30.
https://doi.org/10.37547/tajas/Volume07Issue06-05
COPYRIGHT
© 2025 Original content from this work may be used under the terms
of the creative commons attributes 4.0 License.
Enhancing the Operation
of The Ginning Machine
Chamber to Improve
Efficiency
Sodikjanov Jaxongirbek Shukhratbek oglu
Andijan State Technical Institute, Uzbekistan
Abstract:
In this work, a mathematical model of the
pulsating forces acting on the working chamber of a
cotton‐cleaning machine was developed and analyzed.
It was demonstrated that maximum productivity is
achieved by installing triangular accelerators at a 60°
angle, which eliminates sequential impulses and
prevents unnecessary collisions.
Keywords:
Ginning machine, accelerator, efficiency,
mathematical model.
Introduction:
"In order to prevent the raw material
from accumulating in the middle of the working
chamber of the saw gin, triangular, rectangular and
pentagonal separators are installed inside the working
chamber, which serve to reduce the density of the
cotton gin in the working chamber. In addition,
separators of various shapes are installed, which allow
the separated seeds to come out as a result of the
impact of the cotton gin on the surface of these
separators. This serves to evenly separate the seeds
from the cotton gin in the working chamber. As a result
of theoretical analysis of this process, the issue of
ensuring the uniformity of the density of the cotton gin
was considered.
The directions of external forces acting on the cotton
ball in the working chamber are given - the weight of the
cotton ball,
𝑃 = 𝑚 ⋅ 𝑔
𝐹
𝑒𝑙
= 𝜇 ⋅ (𝜗 ⋅ 𝑡 − 𝑆̆)
-
the
elastic force of the accelerator acting on the cotton ball,
where: - the coefficient of elasticity between the cotton
ball.
𝜇
𝐹
𝑖𝑠ℎ𝑞
= 𝑓 (
𝑚⋅𝜗
1
2
𝑅
+ 𝑚 ⋅ 𝑔)
-the friction force
generated by the cotton ball on the surface of the
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The American Journal of Applied Sciences
working chamber
here:
𝑚⋅𝜗
1
2
𝑅
–
centrifugal force;
–
coefficient
of friction.
𝑓
We analyze the state of a piece of cotton
moving along an arc in a working chamber under the
influence of external forces. The differential equation of
motion resulting from the action of a straightener-
accelerator on the piece of cotton is expressed as
follows
𝐴𝐵̆ = 𝑆̆𝑆̆ = 𝑅 ⋅ 𝜙
1
𝑚 ⋅ 𝑅 ⋅ 𝜙̈
1
= 𝐹̄
эл
+ 𝑃 − 𝐹̄
иш
(1)
(1)
We form the equation using the external forces acting on the cotton ball in the working
chamber above
𝑚 ⋅ 𝑅 ⋅ 𝜙̈
1
= 𝜇(𝜗 ⋅ 𝑡 − 𝑆̆) + 𝑚 ⋅ 𝑔 −
𝑓⋅𝑚⋅𝜗
1
2
𝑅
(2)
Since in equation (2) and
𝑆̆ = 𝑅 ⋅ 𝜙
1
𝜗 = 𝜔 ⋅ 𝑅 = 𝜙̇
1
⋅ 𝑅
𝑚 ⋅ 𝑅 ⋅ 𝜙̈
1
= 𝜇 ⋅ 𝑚 ⋅ 𝑅 ⋅ 𝜙
1
2
̇
2
+ 𝑚 ⋅ 𝑔 −
𝑓⋅𝑚⋅𝜗
1
2
𝑅
(3)
Equation (3) is integrated under the following initial conditions. If the working chamber is a circular
segment on the surface, equation (3) is integrated up to the moment, where is determined from the condition
𝜙
1
(0) = 0𝜙̇
1
(0) = 0𝜙̇
1
⋅ 𝑅𝑡 = 𝑡
0
𝜙
1
(𝑡
0
) = 𝜙
𝜙̈
1
−
𝜇⋅𝑡
𝑚
⋅ 𝜙̇
1
+
𝜇
𝑚
⋅ 𝜙
1
=
𝑔
𝑅
−
𝑓⋅𝜗
1
2
𝑅
2
(4)
By introducing definitions into equation (4), we obtain a differential equation,
𝑛 = −
𝜇⋅𝑡
2⋅𝑚
𝑘 = √
𝜇
𝑚
𝜙̈
1
+ 𝑛 ⋅ 𝜙̇
1
+ 𝑘
2
⋅ 𝜙
1
= 0
(5)
We define the solution of the homogeneous equation (5) as follows
𝜙
1
= 𝑒
𝜆⋅𝑡
𝜆
2
+ 𝑛 ⋅ 𝜆 + 𝑘
2
= 0
(6)
This means that from the definition and when the solution to equation (5) is as follows
𝜆
1/2
= −𝑛 ±
√𝑛
2
− 𝑘
2
𝑘
1
= √𝑛
2
− 𝑘
2
𝑛 < 𝑘
𝜙
1
= 𝑒
−𝑛⋅𝑡
⋅ (𝐶
1
⋅ 𝑠𝑖𝑛( 𝑘
1
⋅ 𝑡) + 𝐶
2
⋅ 𝑐𝑜𝑠( 𝑘
1
⋅ 𝑡))
(7)
We define the initial and boundary values of the constant values S1 and S2 in expression
𝜙(0) = 𝜙
0
; 𝜙̇(0) = 0
(8).
𝜙̇
1
= −𝑛 ⋅ 𝑒
−𝑛⋅𝑡
⋅ (𝐶
1
⋅ 𝑠𝑖𝑛( 𝑘
1
⋅ 𝑡) + 𝐶
2
⋅ 𝑐𝑜𝑠( 𝑘
1
⋅ 𝑡)) + 𝑒
−𝑛⋅𝑡
⋅ (𝐶
1
⋅ 𝑘
1
⋅ 𝑐𝑜𝑠( 𝑘
1
⋅ 𝑡) −
𝐶
2
⋅ 𝑘
1
⋅ 𝑠𝑖𝑛( 𝑘
1
⋅ 𝑡))
(9)
Using the initial conditions above, we substitute these values into equation
С
1
= −
𝜙
0
𝑘
1
, 𝐶
2
= 𝜙
0
(10).
𝜙
1
= 𝑒
−𝑛⋅𝑡
⋅ (−
𝜙
0
𝑘
1
⋅ 𝑠𝑖𝑛( 𝑘
1
⋅ 𝑡) + 𝜙
0
⋅ 𝑐𝑜𝑠( 𝑘
1
⋅ 𝑡))
1
1
=
R
L
(11)
The results of the calculation of the motion of the
accelerator along the AB arc during the transfer of the
cotton piece, the analysis of the effect of the various
geometric shapes of the accelerators installed in the
working chamber on the cotton piece, are presented in
graphs in terms of rotation angles - coverage angles in
terms of eliminating jams of cotton pieces in the
working chamber [1-4].
𝜙
1
𝜙
The cotton pieces are separated by the time of changing
the angle, preventing clogging in the working chamber.
If the laws of motion of cotton pieces are known, the
efficiency of separating seeds from them can be
determined.
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The American Journal of Applied Sciences
a) evenly
b) 60
oh
With C
1-seed comb; 2-front apron; 3-lower apron; 4-lower beam;
5-upper beam; 6-straightener-accelerators
Figure 1. Scheme of the movement of various accelerators installed in the working chamber of a
sawmill.
The graphs above show the trajectories of the effects
of various geometric shapes of accelerators installed in
the working chamber on a piece of cotton. The graphs
also analyze the dependence of the spread of a piece
of cotton on the angle of coverage without changing its
density along the arc AB during uniform transfer.
Formalization: impulsive field
If the worker is in the cell
N
If two accelerators are placed and their angles with respect to the center are
θi
= iθ,
I
= 0,1,...,N − 1,
The total impulsive force is divided by the method
,
here
F
0
—
elastic impulse amplitude of each accelerator,
ω
—
rotor bur speed.
Insertion into a differential equation
From the basic equation (1)
–
(3):
mx
¨ + kx + µmg − mō2r = F(t).
For analysis, separating the constant additions, leaving only the impulsive part:
.
System response: Green's function
Free resonant frequency, transfer function, Stationary impulse response:
N−1 xss(t) = X F0 H(ω)e−j(ωt−ith). i=0
Amplitude coefficient:
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.
Optimal turn:
θ
=60◦
theta=60°. If
N
= 6if,
θ
= 2π/6 = 60◦
Then: Equal distribution of impulses: the recovery
terms are equal to zero[5-9].
,
Reduction of amplitude dispersion: i.e. avoidance of resonance.
In this case, congestion and damage will be minimal.
Performance indicators
Dispersion:
θ
= 60◦
at
D
= 0, in other corners
D >
0.
.
Congestion index
TI
and density retention index
DS
:
TI
60
◦
≈ 0,
DS
60
◦
≈ 1.
Real momentum distribution (in Maple graphs):
TI <
0.05,
RE >
95%
[1]
.
Figure 2. Dispersion
D
(θ)
graph
Dispersion
function
N
=
6for. The first zero point (
θ
= 60◦
):
D
(60◦) = 0
-
momentum dispersion disappears, oscillations are
minimized. The second zero point (
θ
= 120◦
): the second
periodic zero of the function, but in this case the side
lobes are larger. Side lobes and maximum peaks:
θ
→
0◦
at
D
≈ 6
is, all the pulses are added together and a
maximum oscillation occurs. Then it decreases linearly,
reaches zero, and at 120° zero occurs again. Conclusion:
The 60° configuration distributes the pulses at once,
eliminating the oscillation. There is also a zero at 120°,
but the synchronicity weakens.
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The American Journal of Applied Sciences
Figure 3. Normalized amplitude
A
(θ)
graph
Normalized amplitude
A
(θ)
function
N
= 6for. The
minimum amplitude (
θ
= 60◦
):
A
(60◦) ≈ 0
-pulses
destructively cancel each other, the system “relaxes”
to oscillation. Side lobe amplitudes: The amplitude
increases in the range 90°
–
100°, the synchronism is not
sufficient. There is another minimum at 120°, but the
pulse interval here is long. Resonance avoidance: Side
lobe maxima occur at unfavorable angles, increasing
the risk of damage. Combined analysis:
θ
= 60◦
also
D
(θ)
= 0, both
A
(θ) ≈ 0
: - the zero-dispersion and zero-
amplitude points coincide. 6 accelerators act with a
synchronous rhythm, at equal intervals:
1.
Jamming does not occur.
2.
Mechanical damage will be minimal.
3.
Seed
separation
efficiency
is
maximized.
CONCLUSION
The working chamber clearly shows triangular diffuser-
accelerators
60
◦
should be installed with a twist. The
rotor speed should be maintained at values that are far
from the side lobes (about 70 rpm). To reduce the
coefficient of friction, the surface should be improved
by polishing or coating.
The triangular separators distribute the impulse
symmetrically at a 60° angle. This ensures that the
cotton pieces are conveyed in a stable and dense
manner. As a result, blockages and damage are
minimized, and the efficiency of the separation of the
seeds is maximized.
REFERENCES
A. Nurmatov, B. Kadyrov. "Dynamics and optimization
of sawing machine"
—
Journal of Mechanical
Engineering, 2024, No. 3, p. 45
–
53.
1.
C. Davies, E. Forbes. "Impulse Mechanics in Textile
Carding"
—
Textile Engineering Review, 2023, Vol. 12,
No. 2, pp. 112
–
120.
2.
G. Huang. "Maple-Based Modeling of Carding Chamber
Dynamics"
—
Applied Mechanics Letters, 2022, Vol. 18,
No. 4, pp. 301
–
308.
3.
I. Johansson. "Friction Reduction Techniques for High-
Speed Carding Machines"
—
Mechanical Systems
Journal, 2021, Vol. 27, No. 1, pp. 67
–
75.
4.
K. Lee, M. Novak. "Vibration Smoothing by Symmetric
Impulse Distribution"
—
Journal of Sound and Vibration,
2020, Vol. 465, pp. 115
–
127.
5.
L. Petrova, S. Ivanov. "Theory of impulse balance and
textile machines"
—
Vestnik Technologiy, 2019, No. 5, p.
89
–
98.
6.
D. Smith. "Optimization of Multi-Rotor Impacts in
Carding Chambers"
—
Journal of Mechanical Science,
2020, Vol. 45, No. 7, pp. 785
–
794.
7.
M. Yusupov. "Impulse-power relations and methods of
avoiding resonance"
—
Collection of scientific papers,
2021, p. 102
–
110.
8.
R. Zeinalli. "Carding Machine Design: Geometric
Configurations and Performance"
—
International
Journal of Textile Science, 2022, Vol. 6, No. 3, pp. 56
–
68.
