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PUBLISHED DATE: - 24-12-2024
https://doi.org/10.37547/tajas/Volume06Issue12-05
PAGE NO.: - 21-27
DYNAMICS OF MOISTURE ABSORPTION IN
MOVING THREADS
B.B.Mirzabaev
Namangan Engineering-Construction Institute, Uzbekistan
N.Yu.Sharibaev
Namangan Engineering and Technological Institute, Uzbekistan
E.Y.Sharibaev
Namangan Engineering and Technological Institute, Uzbekistan
INTRODUCTION
The process of moisture absorption by moving
yarns consists of complex mechanisms that are
important for the production of high-quality
fabrics. By understanding the mechanisms of
moisture absorption and developing mathematical
models that describe these processes, textile
products can be optimized for different conditions
of use. The purpose of this article is to analyze
existing mathematical models describing the
process of moisture absorption by moving yarns
and to identify the main factors influencing these
processes.
In the works reviewed, he presented two models
describing the process of moisture transfer
through the fiber. These models make it possible to
predict how materials change under various
conditions, taking into account heat and mass
transfer [1]. Developed zero linear mathematical
models describing the processes of isothermal
moisture absorption. These models are used in the
analysis of various textile materials [2]. Presented
a mathematical model taking into account heat and
mass transfer when changing the density and
structure of the thread. The model is intended for
the analysis of materials used in extreme
conditions [3]. Studying the movement of moisture
through fabrics, he showed the importance of the
density and orientation of the threads. This model
takes into account the structural properties of the
RESEARCH ARTICLE
Open Access
Abstract
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material
[4].
Studying
leather
fabrics,
characterizing the physical and mechanical
properties of the yarn, he developed a model
analyzing the dynamic processes of moisture
absorption [5]. Proposed a model illustrating the
process of dynamic wet impregnation of two-layer
knitted fabrics. This approach is successfully used
to analyze sportswear [6]. Developed heat and
mass transfer models for multi-level textile
structures. The study showed that simplified
models can be effective in predicting the behavior
of fabrics [7]. Developed a model for predicting
phase transitions between liquid and vapor in
dynamic processes. This model is used in the
analysis of textile materials under complex
conditions [8]. He developed an empirical model
describing the transfer of heat and moisture in
multilayer textile structures [9]. Described a global
mathematical model describing motion taking into
account the effect of moisture on the physical
properties of the thread. This model is used to
predict the behavior of textiles under various
conditions [10].
On the loom, the fabric is woven by adding warp
yarn and feather tanda yarn. Before weaving, v1 is
the yarn speed on the loom v1, the yarn speed on
the loom v2. Before adding them, cold steam is
supplied for the purpose of humidification. Given
the steam speed, yarn speeds, air temperature and
relative humidity, we need to build differential
equations for the dependence of the moisture
absorption rate of the yarn on time. Based on these
models, the goal is to reduce the breakage of the
floor and hairy tan yarn based on the optimal
humidity values.
Main part
Hypotheses:
•
Yarn speed: ground yarn speed v1, hairy
yarn speed v2.
•
Steam velocity: cold steam velocity V.
•
Air temperature and relative humidity: air
temperature T, relative air humidity
ϕ
.
•
Moisture content: the amount of moisture at
time t of the thread M(t), and the equilibrium
moisture content ms under given conditions of
temperature and humidity.
Additional Hypotheses:
•
The rate of moisture absorption is
proportional to the difference between the
equilibrium moisture content and the current
moisture content.
•
The mass transfer coefficient depends on the
relative velocity between the filament and the
vapor.
•
Equilibrium humidity is known as a function
of temperature MS t and relative humidity.
Theoretical research
The change in yarn moisture content over time is expressed as follows:
𝑑𝑀
𝑑𝑡
= 𝑘(𝑀
𝑠
− 𝑀(𝑡))
(1)
Here:
•
k is the mass transfer coefficient, which depends on the relative velocity.
The relative velocity Vratio is defined as follows:
𝑣
отношение 𝑣
= |𝑣
𝑖𝑝
− 𝑣
пар
|
(2)
The mass transfer coefficient K is proportional to the relative velocity:
𝐾 = 𝑘
0
≤ 𝑣
𝑣
(3)
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Here:
•
k0 is an experimentally determined proportionality coefficient.
we substitute K into the differential equation:
𝑑𝑀
𝑑𝑡
= 𝑘
0
≤ 𝑣
𝑣
(отношение 𝑀
𝑠
− 𝑀 (𝑡))
(4)
For floor thread (V1):
𝐷𝑀
𝑑𝑡
= 𝑘
0
℃ |𝑣
1
− 𝑣
пар
|(𝑀
𝑆
− 𝑀(𝑇))
(5)
For hairy warp yarn (V2):
𝐷𝑀
𝑑𝑡
= 𝑘
0
℃ |𝑣
2
− 𝑣
пар
|(𝑀
𝑆
− 𝑀(𝑇))
(6)
The equilibrium humidity function MS of air temperature T and relative humidity ϕ:
𝑀
𝑠
= 𝑓 (𝑇, 𝜙)
(7)
This function is based on the sorption isotherms of the thread material.
Based on the above, we will compose general differential equations:
𝑑𝑀
1
𝑑𝑡
= 𝑘
0
∙ |𝑣
1
− 𝑣
𝑏𝑢𝑔′
|(𝑓(𝑇, 𝜙) − 𝑀1(𝑡))
𝑑𝑀
2
𝑑𝑡
= 𝑘
0
∙ |𝑣
2
− 𝑣
𝑏𝑢𝑔′
|(𝑓(𝑇, 𝜙) − 𝑀2(𝑡))
(8)
These differential equations describe the change in
yarn moisture content over time, taking into account
yarn speed, steam speed, air temperature and relative
humidity.
To solve these equations analytically, we rewrite the
differential equations so that the variable is discrete,
and find the general solution using the integral. This is
a first-order linear differential equation involving the
variable a and time t. We break this down into
individual variables:
𝑀1(𝑡)
𝐷𝑀
1
𝑓(𝑡,𝜙)−𝑀
1
(𝑡)
= 𝑘
0
℃ |𝑣
1
− 𝑣
пар
|𝑑𝑡
(9)
This is a first order linear differential equation with time t. We break this down into individual
variables:
, связанное с переменной 𝑀1(𝑡)
∫
1
𝑓(𝑇,𝜙)−𝑀
1
(𝑡)
𝑑𝑀
1
= ∫ 𝑘
0
∙ |𝑣
1
− 𝑣
𝑏𝑢𝑔′
|𝑑𝑡
(10)
We solve the integral on the left:
−ln|𝑓(𝑇, 𝜙) − 𝑀
1
(𝑡)| = 𝑘
0
∙ |𝑣
1
− 𝑣
это𝑔
′
| ∙ 𝑡 + 𝐶
1
(11)
Where is the integral constant. Writing in exponential form, :
𝑐
1
представим 𝑀1(𝑡)
𝐹(𝑇, ′) − 𝑀
1
(𝑡) = 𝑐
1
𝐸
𝐾
0
′|𝑣
1
−𝑣
это𝑔′
|′ 𝑇
(12)
Now let's select M1 t separately:
𝑀1(𝑡)
𝑀
1
(𝑡) = 𝑓(𝑇, 𝜙) − 𝐶
1
𝑒
𝑘
0
∙|𝑣
1
−𝑣
это𝑔′
|∙𝑡
(13)
Using the initial conditions, . For example, at t=0 m1(0)=m1,0:
мы находим 𝑐
1
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𝑀
1,0
= 𝑓(𝑇, 𝜙) − 𝐶
1
(14)
𝐶
1
= 𝑓(𝑇, 𝜙) − 𝑀
1,0
(15)
Final decision:
𝑀
1
(𝑡) = 𝑓(𝑇, 𝜙) − (𝑓(𝑇, 𝜙) − 𝑀
1,0
)𝑒
𝑘
0
∙|𝑣
1
−𝑣
это𝑔′
|∙𝑡
(16)
Application for hairy yarn
𝑑𝑚
2
𝑓(𝑡,′)−𝑚
2
(𝑡)
= 𝑘
0
℃ |𝑣
2
− 𝑣
пар
/ 𝑑𝑡
(17)
This is a first order linear differential equation with time t. We break this down into individual
variables:
, связанное с переменной 𝑀1(𝑡)
∫
1
𝑓(𝑡,𝜙)−𝑚
2
(𝑡)
𝑑𝑚
2
= ∫ 𝑘
0
℃ |𝑣
2
− 𝑣
пар
|𝑑𝑡
(18)
We solve the integral on the left:
−ln|𝑓(𝑇, 𝜙) − 𝑀
2
(𝑡)| = 𝑘
0
∙ |𝑣
2
− 𝑣
это𝑔
′
| ∙ 𝑡 + 𝐶
2
(19)
Where is the integral constant. Writing in exponential form, :
𝑐
1
представим 𝑀1(𝑡)
𝑓(𝑇, 𝜙) − 𝑀
2
(𝑡) = 𝐶
2
𝑒
𝑘
0
∙|𝑣
2
−𝑣
это𝑔′
|∙𝑡
(20)
Now let's select M1 t separately:
𝑀1(𝑡)
𝑀
2
(𝑡) = 𝑓(𝑇, 𝜙) − 𝐶
2
𝑒
𝑘
0
∙|𝑣
2
−𝑣
это𝑔′
|∙𝑡
(21)
Using the initial conditions, . For example, at t=0 m1(0)=m1,0:
мы находим 𝑐
1
𝑀
2,0
= 𝑓(𝑇, 𝜙) − 𝐶
2
(22)
𝐶
2
= 𝑓(𝑇, 𝜙) − 𝑀
2,0
(23)
Final decision:
𝑀
2
(𝑡) = 𝑓(𝑡, ′) − (𝑓(𝑡, ′) − 𝑚
2,0
)𝐸
𝐾
0
′|𝑣
2
−𝑣
это𝐺′
|′ 𝑇
(24)
RESULTS
Based on these models, based on the change in the
speed of cold steam, it becomes possible to see in
graphic mode the degree of moisture absorption of
strands on the floor and hairy tan. Figure 1.
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Figure 1.The degree of water absorption of a thread based on the change in steam
velocity
B graph illustrating the moisture absorption rate
for the Warp floor thread and the Warp hair thread
based on the change in speedV (Fig. 1.). The graphs
show the degree of moisture absorption by the
threads within 1 second. You can see how the
moisture content in the warp threads depends on
the speed of the steam.
B graph illustrating the degree of moisture
absorption
for
a
threadBasicsand
hairy
threadBasicswith respect to time in relation to
speed is shown in Fig. 2. In this graph you can see
how the rate of moisture absorption by the threads
changes over time for different steam speeds.
Figure 2.Change in moisture absorption level over time
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To select the most optimal evaporation rate, we
analyze the degree of moisture absorption and the
time it takes to reach the state of moisture
equilibrium. The optimal rate should be such that
the strands absorb enough moisture to the target
level, and this process should occur in the shortest
possible time.
Analysis
To select the optimal speed, let's consider the
following aspects:
1.
Achieving target humidity levels: We must
quickly and efficiently achieve the target moisture
level of the yarn. The target moisture level Ms
should be close to the equilibrium moisture Ms.
2.
Stabilization of humidity levels: The change
should slow down or stabilize after these strands
reach some maximum moisture absorption. This is
called a state of equilibrium and usually indicates
that there is no excessive moisture absorption.
CONCLUSION
From the graphs above we can see the change in
humidity over time for different steam speeds. For
analysis, let's look at several key indicators:
•
Delivery speed period: We must ensure that
the yarn reaches the target moisture content as
quickly as possible.
•
Time to reach steady state: Once the
humidity level reaches the target level, it should
enter a stable state.
•
Low steam speed (0.5 m/s): The process of
moisture absorption is very slow and takes time.
This means that at low steam speeds, the threads
cannot absorb moisture sufficiently and this
process takes too long.
•
Average steam speed (1.0-1.5 m/s): At these
speeds, the moisture absorption process is faster,
the process of reaching the target humidity level is
relatively fast, and the moisture absorption rate is
stabilized.
•
High steam speed (2.0 m/s): At this speed,
moisture absorption is fast, but at very high speed,
excessive moisture absorption or over-absorption
may occur. In this case, the dryness of the threads
decreases and excessive moisture is observed,
which can cause problems in the weaving process.
Optimal Steam Speed
:
The most optimal result is observed at medium
steam speeds (1.0 - 1.5 m/s). At this speed:
•
Fast and effective moisture absorption: the
threads absorb moisture quickly and sufficiently.
•
Achieving balance: The humidity level is
reached faster, ensuring a stable moisture level in
the strands.
Each strip represents the process of moisture
absorption by the yarns at a certain steam velocity.
It has been shown that the moisture absorption
levels of the floor tanda yarn and the hairy tanda
yarn differ and change over time.
The optimum steam speed should be around 1.0 -
1.5 m/s. At this speed, the yarn is effectively
moistened, the moisture quickly reaches the
equilibrium level and does not cause problems
during the weaving process. At a very low speed,
moisture absorption occurs slowly, and at a very
high speed, the yarn may become wet, which will
affect the quality.
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