Authors

  • Nafisa Odilkhonova
    Phd, Docent, Department Of Technology Of Textile Products, Namangan Institute Of Engineering And Technology, Namangan, Republic Of Uzbekistan
  • Lastochkin Pavel
    Phd Student, Namangan Institute Of Engineering And Technology, Uzbekistan

DOI:

https://doi.org/10.71337/inlibrary.uz.ijasr.130855

Keywords:

Unevenness semi-finished product spectrogram the coefficient of variation sliver

Abstract

The article describes the characteristics and types of unevenness of semi-finished products of spinning production, as well as their influence on the quality of the finished product. A technique for performing spectral analysis of semi-finished products and calculating the wavelengths of the spectrogram is described. A spectral analysis of such semi-finished products as carding sliver and sliver from the first and second stages of draw frames with a linear density of 4.9 Ktex with a coefficient of variation (CVm) equal to 3.29%, 3.71% and 2.97%, respectively, was performed. Their wavelength was calculated taking into account the filling parameters of the studied machines. The reasons and places of formation of unevenness of semi-finished products are revealed and their assessment was given.


background image

Volume 02 Issue 12-2022

156



International Journal of Advance Scientific Research
(ISSN

2750-1396)

VOLUME

02

I

SSUE

12

Pages:

156-165

SJIF

I

MPACT

FACTOR

(2021:

5.478

)

(2022:

5.636

)

METADATA

IF

7.356


















































A

BSTRACT

The article describes the characteristics and types of unevenness of semi-finished products of spinning
production, as well as their influence on the quality of the finished product. A technique for performing
spectral analysis of semi-finished products and calculating the wavelengths of the spectrogram is
described. A spectral analysis of such semi-finished products as carding sliver and sliver from the first and
second stages of draw frames with a linear density of 4.9 Ktex with a coefficient of variation (CVm) equal
to 3.29%, 3.71% and 2.97%, respectively, was performed. Their wavelength was calculated taking into
account the filling parameters of the studied machines. The reasons and places of formation of unevenness
of semi-finished products are revealed and their assessment was given.

K

EYWORDS

Unevenness, semi-finished product, spectrogram, the coefficient of variation, sliver, peak, amplitude, wave,
yarn, fiber

Journal

Website:

http://sciencebring.co
m/index.php/ijasr

Copyright:

Original

content from this work
may be used under the
terms of the creative
commons

attributes

4.0 licence.

Research Article

RESEARCH OF THE UNEVENNESS OF THE SPINNING

PRODUCTION’S SEMI

-FINISHED PRODUCTS BY THE METHOD

OF SPECTRAL ANALYSIS


Submission Date:

December 11, 2022,

Accepted Date:

December 16, 2022,

Published Date:

December 21, 2022

Crossref doi:

https://doi.org/10.37547/ijasr-02-12-23


Nafisa Odilkhonova

Phd, Docent, Department Of Technology Of Textile Products, Namangan Institute Of Engineering And
Technology, Namangan, Republic Of Uzbekistan

Lastochkin Pavel

Phd Student, Namangan Institute Of Engineering And Technology, Uzbekistan


background image

Volume 02 Issue 12-2022

157



International Journal of Advance Scientific Research
(ISSN

2750-1396)

VOLUME

02

I

SSUE

12

Pages:

156-165

SJIF

I

MPACT

FACTOR

(2021:

5.478

)

(2022:

5.636

)

METADATA

IF

7.356















































I

NTRODUCTION

One of the main tasks of the modern textile
industry is to identify and analyze the factors that
determine the quality of products, as well as the
reasons for the decline in its performance. The
solution to this problem is the provision,
regulation and quality management at all stages
of product formation.

The production of high-quality textile products
largely depends on the choice of raw materials
and the organization of technological processes.
However, it is not always possible to increase or
ensure the required quality of products by
selecting the appropriate raw materials. [1, 2].
This is due to the fact that there are not always
raw materials of the required quality in
production, and sometimes textile workers have
to use the raw materials that they have. Also,
high-quality raw materials have a high cost, which
negatively affects the cost of manufactured
products. Therefore, in order to achieve the
expected quality of spinning products, they often
resort to methods for studying the unevenness of
finished products and semi-finished products, the
reasons for its formation and the flow of
technological processes.

The main part

The unevenness of spinning products is a complex
phenomenon. For spinning products, there are
several types of unevenness, such as: unevenness
in linear density, unevenness in breaking load,
quadratic unevenness, etc.

The unevenness that occurs in the first stages of
the spinning process can affect the flow of the
processes of subsequent stages of production, as
well as the quality indicators of the finished
product. The unevenness of spinning products in
linear density in many cases is one of its main
types. With the above complex change in the
properties of the product, no numerical values of
the unevenness can fully take into account and
evaluate its nature. So, for example: two products
can have the same numerical values of the
quadratic unevenness in linear density, but one of
them will have a periodic unevenness, and the
other will have an unevenness with a one-sided
increase in deviations or random. The reasons for
the formation of unevenness of these types are
different.

The use of such characteristics as amplitude
spectrum, unevenness gradient, correlation
function, and others makes it possible to reveal
the nature of the unevenness and its structure.
Quantitative assessment of the nature of the
unevenness, i.e., determination of the amplitude
and wavelengths found in the unevenness of the
product under study, the repeatability of
wavelengths, as well as the determination of
other characteristics, will help to better reveal the
phenomena that occur during the production of
semi-finished products and finished products [3].

The problem of studying the causes of
unevenness, as well as the influence of the
unevenness of spinning products on the course of


background image

Volume 02 Issue 12-2022

158



International Journal of Advance Scientific Research
(ISSN

2750-1396)

VOLUME

02

I

SSUE

12

Pages:

156-165

SJIF

I

MPACT

FACTOR

(2021:

5.478

)

(2022:

5.636

)

METADATA

IF

7.356















































further technological processes, has been dealt
with by many scientists. So, for example, in his
works, A. N. Soloviev studied statistical methods
for monitoring and analyzing product quality
using continuous monitoring and analysis of the
studied material properties using control-scatter
charts, as well as using graphs of the
autocorrelation function [4]. A. G. Sevostyanov, on
the other hand, studied the methods and means of
studying the unevenness of spinning products,
fabrics, knitted and non-woven fabrics, revealing
the essence of the unevenness and its types, based
on the correlation and spectral analysis of the
unevenness [5].

In the study of any one indicator of unevenness, it
turns out that the indicator of this unevenness
consists of a number of elementary unevenness.
Since the unevenness that occurs at the initial
stages of production changes in the subsequent
ones and, in addition, the unevenness of new
types is formed, and different types of
unevenness are interdependent [6]. Studies have
shown that all semi-finished products and the
yarn itself have unevenness, for example, in
thickness, which consists of several irregularities
that differ in length, waveform and vibration
amplitudes. Having arisen, any unevenness does
not disappear, it passes from one semi-finished
product to another and finally to yarn. Since the
product is folded and thinned in spinning
machines, its length increases in accordance with
the drawing, then various kinds of fluctuations in
thickness along the length of the incoming
product pass into the outgoing product, and the
wavelength of these oscillations increases in

proportion to the drawing, and the resulting
unevenness with shorter waves is superimposed
on longer waves of fluctuations in the thickness of
the incoming product [7]. The earlier unevenness
occurs in the course of the spinning process, the
longer the oscillation waves will be for the
corresponding component of unevenness in the
yarn. To a greater extent, this refers to
unevenness in the thickness of the product.

Research and analysis of the unevenness of
spinning products in order to evaluate the
operation of individual machines must be
accompanied by the determination of indicators
of changes in unevenness and the conditions for
their operation. [8,9].

Today, in modern spinning mills, the definition of
unevenness, as well as the analysis and nature of
its origin, is determined by the method of spectral
analysis. The essence of spectral analysis lies in
the study of fluctuations in the thickness of the
product, including waves (thickening and
thickening) of various lengths and amplitudes,
which are mutually combined and superimposed
on one another. Using this method, waves of the
same length, but different amplitudes, and vice
versa can occur. The task of this method is to
decompose complex fluctuations in the thickness
of the product into the simplest components
(harmonics) with the subsequent construction of
a spectrum of wavelengths of various amplitudes.
To construct a spectrogram, the amplitude
corresponding to the wavelength is plotted along
the ordinate axis, and the wavelength is plotted
along the abscissa axis. [10, 11]


background image

Volume 02 Issue 12-2022

159



International Journal of Advance Scientific Research
(ISSN

2750-1396)

VOLUME

02

I

SSUE

12

Pages:

156-165

SJIF

I

MPACT

FACTOR

(2021:

5.478

)

(2022:

5.636

)

METADATA

IF

7.356















































Some modern devices, such as Uster Tester or
Evenness Tester, have special modules that allow
you to carry out harmonic analysis and obtain the

spectrum of waves of the unevenness of the
product under study by recording them in the
form of a spectrogram shown in Figure 1.

Figure 1. Spectrogram

On the spectrogram shown in Figure 1, we can see

the logarithmic scale of the wavelength lgλ along

the abscissa and the mean amplitude A along the
ordinate. The figure also shows the curve of
product I, which has an unevenness formed due
to defects in the working parts or incorrect
optimization of the technological parameters of
machines, which are expressed in the
spectrogram as peaks (1,2,3,4,5,7). Each of the
peaks has a certain length, and by their size it is
possible to determine in which machine node the
unevenness of the product has formed by
calculating the wavelength responsible for one or
another working part of the machine. Under the
Roman numeral II on the spectrogram is shown a
curve of a perfectly flat product, for a visual
representation of deviations in the unevenness of
a real spinning product [12, 13]. In the production
of yarn in a spinning system consisting of six

stages, the spectrum of all waves that make up the
unevenness of the yarn can be divided into four
main groups:

1)

1) The widest waves (up to Zsm.) - they are

formed by a slight curvature of the cylinders of
spinning machines.

2)

The short waves (from 3sm. to 50sm.) - are

caused by the eccentric rotation of the rollers and
cylinders of the spinning machine drafting
system, which create uneven yarns due to the
formation of freely moving (floating) fibers.

3)

The medium waves (from 50sm. to 5m.) -

are formed due to the presence of defects in the
drafting system of the draw frame;

4)

The longest waves (more than 5m.) -

indicate a defect in the drafting system of draw


background image

Volume 02 Issue 12-2022

160



International Journal of Advance Scientific Research
(ISSN

2750-1396)

VOLUME

02

I

SSUE

12

Pages:

156-165

SJIF

I

MPACT

FACTOR

(2021:

5.478

)

(2022:

5.636

)

METADATA

IF

7.356















































frame (rollers, cylinders rotate eccentrically, i.e.,
crookedly).

5)

indicate a defect in the drafting system of

tape machines (rollers, cylinders rotate
eccentrically,).

Unevenness analysis by spectral analysis can be
carried out both for all stages of spinning, and for
semi-finished products separately. In production,
spectral analysis of yarn is most often performed
from a ring spinning and winding machine,
analysis of semi-finished products such as sliver
or roving is performed much less frequently. The
data of these laboratory studies of finished
products and semi-finished products allow
technologists to identify process failures and
show at what stage of production the quality of
the product is deteriorating.

In the spectral analysis of one semi-finished
product, it is first checked on a test device, and
then the wavelength is calculated, which is
responsible for the correct operation of one or
another element of the machine during the
production of the semi-finished product.

Results and Discussions

In our study, we present a spectral analysis of
semi-finished products using the Uster Tester
laboratory device, and also describe a method for
calculating wavelengths for analyzing the
resulting spectrogram of semi-finished products
(Tables 1,2 and 3), which gives us an idea of the
operation of the working parts of machines and
their malfunctions.

Table 1. Calculation of the waves of the card sliver

Machine

name

Areas that create unevenness

Wavelength calculation

C

ard

ing

mac

hine

Taker-in

12

,

0

600

/

72

/

1

1

=

=

=

n

V

p

m.

Cylinder

2

,

0

360

/

72

/

2

2

=

=

=

n

V

p

m.

Doffer

2

,

7

10

/

72

/

3

3

=

=

=

n

V

p

m.

Flats

3

,

34

1

,

2

/

72

/

4

4

=

=

=

n

V

p

m.

Stripping roller

3

,

21

14

,

3

8

,

6

5

5

=

=

=

d

sm.

To determine the reasons for the formation of
unevenness in semi-finished products, as well as
to determine and control the operation of the
working parts of machines, we compared the

calculated wavelength data obtained by us with
the spectrogram. If sharply prominent peaks
were present on the spectrogram along the
ordinate axis, then we, having determined on the


background image

Volume 02 Issue 12-2022

161



International Journal of Advance Scientific Research
(ISSN

2750-1396)

VOLUME

02

I

SSUE

12

Pages:

156-165

SJIF

I

MPACT

FACTOR

(2021:

5.478

)

(2022:

5.636

)

METADATA

IF

7.356















































abscissa axis to which wavelength they belong,
determined the place of formation of product
unevenness, i.e., malfunction of any working part
or incorrect filling parameters of the machine we
are studying.

Figure 2 shows the spectrogram of a carding
sliver with a linear density of 4.9 ktex, which has
a coefficient of variation (CVm) of 3.29%, which
corresponds to the Uster Statistic 2018 standard

of 95%. The spectrogram shows that on the
logarithmic wavelength plotted along the
abscissa axis, which is slightly more than one
meter, there is a sharply prominent peak.
Comparing this with our calculations presented in
table 1, we came to the conclusion that the
deterioration of the coefficient of variation of the
card sliver is due to a slight fault in the area of the
cylinder of the carding machine.

Figure 2. Spectrogram of card sliver 4.9 ktex

Table 2. Calculation of the wavelength of the sliver of the 1-st stage

Machine

name

Areas

that

create

unevenness

Wavelength calculation

Dr

aw f

ra

me

Front roller

14

14

,

3

4

,

4

1

1

=

=

=

d

sm.

Front cylinder

13

14

,

3

4

2

2

=

=

=

d

sm.

Middle roller

115

2

,

7

14

,

3

08

,

5

1

3

3

=

=

=

D

d

sm.

Middle cylinder

45

2

,

7

14

,

3

2

1

5

,

4

5

,

4

=

=

=

D

d

sm.

Back roller

104

56

,

7

14

,

3

4

,

4

6

6

=

=

=

um

D

d

sm.


background image

Volume 02 Issue 12-2022

162



International Journal of Advance Scientific Research
(ISSN

2750-1396)

VOLUME

02

I

SSUE

12

Pages:

156-165

SJIF

I

MPACT

FACTOR

(2021:

5.478

)

(2022:

5.636

)

METADATA

IF

7.356















































Back cylinder

104

56

,

7

14

,

3

4

7

7

=

=

=

um

D

d

sm.

Drawbox drive

6

8

Drafting waves

10

1

.

4

~

9

sm.

The spectrogram of the sliver from the first stage
draw frame with a linear density of 4.9 ktex
having a coefficient of variation (CVm) equal to
3.71%, which corresponds to the Uster Statistic
2018 standard of 95%, is shown in Figure 3. It can
be seen from the spectrogram that the nature of
the peaks on the logarithmic wavelength plotted
along the abscissa axis differs significantly, i.e., in
the length interval from 5 sm. to 10 sm., we can

notice a sharp increase in peaks. But this
amplitude jump is acceptable for this stage, as the
initial addition and drafting of several slivers is
performed here. But the prominent peak at a
wavelength equal to more than 25 sm., comparing
with the calculation values from table 2, tells us
that there is a small malfunction on the machine
in the pre-drawing zone of the drafting system.

Figure 3. Spectrogram of the sliver of the 1-st stage 4.9 ktex.

Таблица 3. Calculation of the wavelength of the sliver of the 2

-nd stage


background image

Volume 02 Issue 12-2022

163



International Journal of Advance Scientific Research
(ISSN

2750-1396)

VOLUME

02

I

SSUE

12

Pages:

156-165

SJIF

I

MPACT

FACTOR

(2021:

5.478

)

(2022:

5.636

)

METADATA

IF

7.356















































Machine
name

Areas that create
unevenness

Wavelength calculation

D

ra

w fr

a

me

Front roller

10

14

,

3

4

,

3

1

1

=

=

=

d

sm.

Front cylinder

11

14

,

3

5

,

3

2

2

=

=

=

d

sm.

Middle roller

78

2

,

7

14

,

3

4

,

3

1

3

3

=

=

=

D

d

sm.

Middle cylinder

79

2

,

7

14

,

3

5

,

3

1

5

,

4

5

,

4

=

=

=

D

d

sm.

Back roller

80

56

,

7

14

,

3

4

,

3

6

6

=

=

=

um

D

d

sm

Back cylinder

95

56

,

7

14

,

3

4

7

7

=

=

=

um

D

d

sm.

Drawbox drive

6

8

Drafting waves

10

1

.

4

~

9

sm.

On the spectrogram of the sliver of the second
stage draw frame tape (Fig. 4.) with a linear
density of 4.9 ktex, which has a coefficient of
variation (CVm) equal to 2.97%, which
corresponds to the Uster Statistic 2018 standard
of 25%. We can notice that at the logarithmic
wavelength plotted along the abscissa axis in the
length interval from 5 sm. to 10 sm., compared
with the spectrogram of the sliver of the first

stage draw frame, the peaks are no longer sharply
distinguished by their amplitude, but there is only
one peak at a length after 10 sm., comparing this
value with the value calculated by us from table 3,
we can conclude that the load on the rollers of the
drafting system of the draw frame of the second
stage is applied unevenly, i.e. or it is low, or the
load on the rollers is applied with periodic
changes.

Figure 4. Spectrogram of the sliver of the 2-nd stage 4.9 ktex


background image

Volume 02 Issue 12-2022

164



International Journal of Advance Scientific Research
(ISSN

2750-1396)

VOLUME

02

I

SSUE

12

Pages:

156-165

SJIF

I

MPACT

FACTOR

(2021:

5.478

)

(2022:

5.636

)

METADATA

IF

7.356















































Comparing all three spectrograms presented
above, we can notice a decrease in the amplitude
of the waves and peaks that determine the
unevenness of the semi-finished products, and
this tells us that the unevenness from stage to
stage is decreasing. This reduction in unevenness
occurs due to the addition and drafting of the
product, but does not remove it completely. As
mentioned

above,

«Having

arisen,

any

unevenness does not disappear, it passes from
one semi-finished product to another and finally
to yarn. Since the product is folded and thinned in
spinning machines, its length increases in
accordance with the drawing, then various kinds
of fluctuations in thickness along the length of the
incoming product pass into the outgoing product,
and the wavelength of these oscillations increases
in proportion to the drawing, and the resulting
unevenness with shorter waves is superimposed
on longer waves of fluctuations in the thickness of
the incoming product». Based on this, the
coefficient of variation of the sliver of the second
stage is only 2.97% which corresponds to 25%
according to Uster Statistic 2018, and not 2.69%
which corresponds to 5% according to Uster
Statistic 2018. To achieve this improvement, the
unevenness of the semi-finished products, i.e.,
decrease in the coefficient of variation and its
value approaching 5% according to Uster Statistic
2018, it is necessary to correct the shortcomings
of the processes identified by us through the
analysis of spectrograms of semi-finished
products of spinning production.

C

ONCLUSION

Thanks to our research, we studied such a factor
as the unevenness of spinning products, its types
and characteristics, as well as the principle of its
determination by the method of spectral analysis.
Which helped us understand the nature and
causes of the formation of unevenness in the
semi-finished products we studied.

Based on the results of our spectral analysis, we
determined the causes of the unevenness of the
products we studied, such as: carding sliver, sliver
from the first and second stages. Summarizing all
of the above, it can be noted that with the help of
spectral analysis of semi-finished products, it is
possible to identify and eliminate defects and
malfunctions that affect the efficiency of spinning
processes in the shortest possible time. Since, in
comparison with other methods for determining
unevenness, spectral analysis gives a more
accurate result in determining the occurrence and
cause of unevenness in the product.

R

EFERENCES

1.

Одилхонова, Н. О., & Азизов, И. Р. (2020).
Влияние

степени

подготовки

волокнистых отходов на качество
смесовой

пряжи.

Universum:

технические науки, (7

-2 (76)), 15-18.

2.

Азизов, И. Р., & Одилхонова, Н. О. (2020).
Анализ

методов

прогнозирования

прядильной способности волокон.
Universum: технические науки, (12

-2

(81)), 48-51.

3.

Жуков, В. И., & Титова, У. Ю. (2009).
Определение показателей качества


background image

Volume 02 Issue 12-2022

165



International Journal of Advance Scientific Research
(ISSN

2750-1396)

VOLUME

02

I

SSUE

12

Pages:

156-165

SJIF

I

MPACT

FACTOR

(2021:

5.478

)

(2022:

5.636

)

METADATA

IF

7.356















































продуктов прядильного производства
с помощью установки КЛА

-

М: метод.

указ. Кострома: Изд

-

во КГТУ.

4.

Кирюхин, С. М., & Соловьев, А. Н. (1977).
Контроль и управление качеством
текстильных материалов. М.: Легкая
индустрия, 312.

5.

В.К. Крючкова, С.С. Максудов и др.
(1993).

Пути

повышения

конкурентоспособности
хлопчатобумажной пряжи и тканей.
Ташкент. ГФНТИ.

6.

Севостьянов, А. Г. (1962). Методы
исследования неровноты продуктов
прядения. М.: Ростехиздат, 5. 385 с.

7.

Поздняков, Б. П. (1978). Методы
статистического

контроля

и

исследования

текстильных

материалов. М.: Легкая индустрия, 4.

8.

Азизов, И. Р., Одилхонова, Н. О., &
Ласточкин, П. Д. (2021). Исследования и
анализ неровноты полуфабрикатов
прядильного производства. Universum:
технические науки, (4

-2), 57-59.

9.

Odilkhonova, N., & Pavel, L. (2021).
Change in technological and qualitative
indicators of card sliver from low-grade
fiber and fibrous waste during the carding
process on modern carding machines.
Innovative Technologica: Methodical
Research Journal, 2(12), 164-176.

10.

Соколов, И. В., Завалишин, И. В., &
Кушнир, К. П. (2021). Исследование
комплекса факторов, влияющих на
точность технологических процессов

раскроя деталей швейных изделий.
ББК 94.3 я431 С 56, 34.

11.

Ласточкин, П. Д., & Мелибоев, У. Х.
(2022). Исследование ориентации и
распрямленности волокон в ленте
методом

разрыва.

Universum:

технические науки, (9

-2 (102)), 38-41.

12.

Борзунов, И. Г., Бадалов, К. И., Гончаров,
В. Г., Дугинова, Т. А., Черников, А. Н., &
Шилова, Н. И. (1982). Прядение хлопка
и химических волокон: Учебник для
втузов.

-2-

е изд., перераб. и доп. М.:

Легкая и пищевая пром

-

сть.

13.

Виноградов,

Ю.

С.

(1964).

Математическая статистика и ее
применение

к

исследованиям

в

текстильной промышленности. М.:
Легкая индустрия, 312.

References

Одилхонова, Н. О., & Азизов, И. Р. (2020). Влияние степени подготовки волокнистых отходов на качество смесовой пряжи. Universum: технические науки, (7-2 (76)), 15-18.

Азизов, И. Р., & Одилхонова, Н. О. (2020). Анализ методов прогнозирования прядильной способности волокон. Universum: технические науки, (12-2 (81)), 48-51.

Жуков, В. И., & Титова, У. Ю. (2009). Определение показателей качества продуктов прядильного производства с помощью установки КЛА-М: метод. указ. Кострома: Изд-во КГТУ.

Кирюхин, С. М., & Соловьев, А. Н. (1977). Контроль и управление качеством текстильных материалов. М.: Легкая индустрия, 312.

В.К. Крючкова, С.С. Максудов и др. (1993). Пути повышения конкурентоспособности хлопчатобумажной пряжи и тканей. Ташкент. ГФНТИ.

Севостьянов, А. Г. (1962). Методы исследования неровноты продуктов прядения. М.: Ростехиздат, 5. 385 с.

Поздняков, Б. П. (1978). Методы статистического контроля и исследования текстильных материалов. М.: Легкая индустрия, 4.

Азизов, И. Р., Одилхонова, Н. О., & Ласточкин, П. Д. (2021). Исследования и анализ неровноты полуфабрикатов прядильного производства. Universum: технические науки, (4-2), 57-59.

Odilkhonova, N., & Pavel, L. (2021). Change in technological and qualitative indicators of card sliver from low-grade fiber and fibrous waste during the carding process on modern carding machines. Innovative Technologica: Methodical Research Journal, 2(12), 164-176.

Соколов, И. В., Завалишин, И. В., & Кушнир, К. П. (2021). Исследование комплекса факторов, влияющих на точность технологических процессов раскроя деталей швейных изделий. ББК 94.3 я431 С 56, 34.

Ласточкин, П. Д., & Мелибоев, У. Х. (2022). Исследование ориентации и распрямленности волокон в ленте методом разрыва. Universum: технические науки, (9-2 (102)), 38-41.

Борзунов, И. Г., Бадалов, К. И., Гончаров, В. Г., Дугинова, Т. А., Черников, А. Н., & Шилова, Н. И. (1982). Прядение хлопка и химических волокон: Учебник для втузов.-2-е изд., перераб. и доп. М.: Легкая и пищевая пром-сть.

Виноградов, Ю. С. (1964). Математическая статистика и ее применение к исследованиям в текстильной промышленности. М.: Легкая индустрия, 312.