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Application of Spectral Analysis in Spinning Measurements

Publicado en línea: 22 Sep 2022
Volumen & Edición: AHEAD OF PRINT
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Detalles de la revista
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Revista
eISSN
2300-0929
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19 Oct 2012
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4 veces al año
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Inglés
Introduction

The fiber stream is a term often used in technological spinning processes. It denotes a certain arrangement of fibers, characterized by varying degrees of ordering, parallelization (straightening and parallel arrangement of fibers), evenness of the linear mass, and blending. The fiber stream can represent, for example, spinning intermediate products such as sliver or roving, but yarn is also a fiber stream. With respect to the quality of flat textile products, the evenness of fiber distribution over the length of the stream is the most important quality parameter of yarns.

Analysis of the distribution of fibers in the yarn, i.e., the assessment of irregularity of the linear mass of the fiber stream, should take into account certain universal principles. First of all, it is assumed that a properly conducted spinning process is stationary in character. This means that the test results do not depend on the choice of the zero point of measurement on the length of the fiber stream, and thus, the starting moment of the measurement can be freely selected.

Three types of analysis are commonly used to assess the unevenness of the linear mass distribution of the fiber stream:

harmonic analysis of the distribution of linear mass over the fiber stream

analysis of the distribution of linear mass in the fiber stream by the moving average method

correlation analysis of the linear mass distribution of the fiber stream.

The most commonly used method is harmonic analysis due to the commonly used equipment, which facilitates and significantly accelerates such analysis and, most importantly, eliminates subjective assessment.

Ideal Fiber Stream Model

An ideal fiber stream is a collection of straight fibers, arranged in parallel along a straight line according to a certain conventional statistical scheme. This is a special case of a real fiber stream, possible to obtain under ideal technological conditions. Only an ideal model of a stream composed of fibers differing in length and linear mass, but of constant thickness along their axis, can be of practical importance. The variance sn2 s_n^2 of the number of fibers in the cross-section of the thus formed fiber stream is equal to the average number n¯ \bar n of fibers in the cross-section of the stream [10]: sn2=n¯ s_n^2 = \bar n

This determines the basic property of a quantity subject to Poisson distribution. Hence, the coefficient of variation CVn of the number of fibers in the stream cross-section is as follows: CVn=snn¯=n¯n¯=1n¯ C{V_n} = {{{s_n}} \over {\bar n}} = {{\sqrt {\bar n} } \over {\bar n}} = {1 \over {\sqrt {\bar n} }}

Since it has been assumed that the fibers have the same linear masses, the coefficient of variation of the linear mass (thickness) of the stream is equal to the coefficient of variation of the number of fibers CVn. It can be proved that if fibers of constant thickness are arranged in an ideal stream built according to the Poisson distribution, then the variance of the number of fibers in the cross-sections depends on the average number of fibers in the cross-sections and is independent of the unevenness of the length of these fibers.

Taking into account the fact that under real conditions the fibers have not only different lengths but also different linear masses (thicknesses), the unevenness of the ideal fiber stream CVT is described by the Martindale formula: CVT=100n¯1+0,004CVd2[%] C{V_T} = {{100} \over {\sqrt {\bar n} }} \cdot \sqrt {1 + 0,004 \cdot CV_d^2} \left[ \% \right] or CVT=100n¯K[%] C{V_T} = {{100} \over {\sqrt {\bar n} }} \cdot K\left[ \% \right] where

n¯ \bar n is the average number of fibers in the stream cross-section and

CVd is the coefficient of variation in fiber diameter.

The K-factor depends on the physical and mechanical parameters of the fibers. Its value is primarily influenced by the length and linear mass of the fibers and their mechanical strength parameters (especially bending stiffness). The examples of K-factor values for the selected fibers are:

K = 1.02 for chemical fibers,

K = 1.06 for cotton fibers,

K = 1.12 for wool fibers,

K = 1.26 for flax fibers.

For a multicomponent blend, the variance of the total cross section of the fiber stream will be equal to the sum of the variances of the component streams. In this case, the irregularity of the ideal fiber stream CVT is as follows: CVT=u12CVT12+u22CVT22++uk2CVTk2 C{V_T} = \sqrt {u_1^2 \cdot CV_{T1}^2 + u_2^2 \cdot CV_{T2}^2 + \cdots + u_k^2 \cdot CV_{Tk}^2} where CVTi is the coefficient of variation of the linear mass of the ith component stream calculated according to the Martindale formula, uiisthevolumeormassfractionsofcomponentsintheyarn. {u_i}\,is\,the\,volume\,or\,mass\,fractions\,of\,components\,in\,the\,yarn.

The ideal stream provides the standard for real streams. The relationship between the ideal and the actual stream is illustrated by the Huberty index (the so-called index of irregularity): I=CVRZCVT=CVRZn¯100K I = {{C{V_{RZ}}} \over {C{V_T}}} = {{C{V_{RZ}} \cdot \sqrt {\bar n} } \over {100 \cdot K}} where

CVRZ is the actual irregularity of the linear mass of the fiber stream determined for short sections:

CVT is the theoretical irregularity of the linear mass of the fiber stream calculated from the Martindale formula.

For the ideal process, the Huberty index I=1.

The values of the Huberty index depend on the technological process and the type of processed fibers, and for exemplary yarns they are as follows [10]:

- for carded cotton yarn 1.8 ÷ 2.6
- for combed cotton yarn 1.3 ÷ 1.6
- for yarns of man-made staple fibers 1.5 ÷ 2.2
- for worsted woolen yarn 1.1 ÷ 1.4
- for carded woolen yarn 1.4 ÷ 2.1.

During the technological process, along with the consecutive phases of yarn production, the Huberty index is reduced asymptotically, which is illustrated by the example of Figure 1.

Figure 1

The Huberty index in the consecutive phases of spinning. 0, raw material; 1, fiber pre-treatment machines; 2, carding machines; 3, drawing machines; 4, drawing machines of the second passage; 5, roving machines; 6, spinning machines.

The Huberty index is the greatest for the disordered fiber structure (phase 0) at the beginning of the technological process. In each subsequent phase of fiber processing, this coefficient should be lower, as a result of fewer and fewer fibers in the stream cross section and better and better parallelization of fibers. The disruption of this trend, as illustrated in Figure 1 in the third phase of spinning (dashed line), suggests irregularities in the technological process (in phase 3), which will certainly have a negative impact on the quality of the yarn.

Spectral Analysis in Spinning Measurements

The fiber stream traveling through any spinning machine comes into contact with many working elements, which for the most part are of a rotating nature (working rollers, cylinders, spindles, rotors, etc.). Any possible defect of such elements (e.g., damaged cover of the upper rollers of the drawing apparatus) causes interference in the fiber stream. Such disturbances are periodic, i.e., repeated regularly at the intervals equal to the circumference of the damaged rotating element. Even if the irregularity appears in the fiber stream leaving the machine at any stage of the technological process, it is very difficult to remove in the subsequent phases of processing. The error goes to the yarn, the quality of which is thus reduced [8, 14]. The disturbance in the fiber stream is usually so small that it is impossible to observe without specialized equipment. It becomes apparent only during the production of flat textile products in the form of weft or warp stripes in fabrics, or strippedness caused by uneven meshes in knitted fabrics. The process of finishing such a product, e.g., by dyeing, makes the resultant irregularities even more visible [7].

Figure 2 presents the scheme of creating stripes in fabrics due to periodic irregularity of the yarn linear mass distribution (periodic thickening).

Figure 2

The scheme of weft and/or warp stripes creation in fabrics.

The periodic irregularity of the yarn linear mass distribution is not always visible in flat textile products in the form of stripes [6,9,11]. It can manifest, e.g., as the “moiré” effect (Figure 3), irregularities visible when winding yarn on a contrast plate (Figure 4), or a simulation of the appearance of the fabric or knit after yarn analysis on the Uster testing device (Figure 5).

Figure 3

A “moiré” effect

Figure 4

View of the yarn on a contrast plate obtained on the Uster apparatus

Figure 5

Fabric appearance simulation

The Uster Tester, among others, is used to analyze the mass distribution in the fiber stream. The measurement is performed between the covers of the capacitor, in which changes in capacitance occur under the influence of momentary changes in the linear mass of the sliding fiber stream. Such instantaneous changes in the capacitor capacitance are proportional to the instantaneous changes in the thickness of the fiber stream and are mapped in the form of a mass diagram. On the basis of the obtained results, the Uster device performs harmonic analysis, i.e., it breaks down the mass diagram into harmonic components along with the determination of their amplitudes and lengths of periods (waves), and then, using spectral analysis, draws a spectrogram in the form of an amplitude spectrum. It is spectral analysis that makes it possible to detect the hidden periodicity in the distribution of linear mass of the studied fiber stream [1, 2, 12]. An example of a spectrogram obtained with the Uster device is shown in Figure 6.

Figure 6

A sample spectrogram.

D – dominant wavelength)

The individual bands on the spectrogram are an image of harmonic components, i.e., their relative amplitudes and wavelengths mapped on a logarithmic scale. The band is hatched when the harmonic component is repeated more than 25 times during the measurement, and unhatched when there are from 6 to 25 such repetitions. The longer the fiber stream is studied, the more harmonic components in the form of striations will appear on the spectrogram (at higher wavelengths), which enables a more accurate assessment of the technological process.

Each drawing mechanism in spinning machines introduces a certain short-term unevenness in the fiber stream, which is reflected on the spectrogram in the form of a drawing wave at small wavelengths; the individual harmonic components have slightly higher amplitudes. The dominant wavelength λD (Figure 6) depends on the length of the processed fibers: λD=(2÷3)ι¯fortheyarnspectrogram {\lambda _D} = \left( {2 \div 3} \right) \cdot \bar \iota \,{\rm{for}}\,{\rm{the}}\,{\rm{yarn}}\,{\rm{spectrogram}} λD=(3÷5)ι¯forthesilverorrovingspectrogram {\lambda _D} = \left( {3 \div 5} \right) \cdot \bar \iota \,{\rm{for}}\,{\rm{the}}\,{\rm{silver}}\,{\rm{or}}\,{\rm{roving}}\,{\rm{spectrogram}}

Errors on the Spectrogram and the Reasons for Their Occurrence

Any disturbances in the proper course of the technological process are reflected on the spectrogram in the form of so-called “chimneys” and “humps.” A sample spectrogram of the yarn produced in a disrupted process is presented in Figure 7.

Figure 7

A sample spectrogram of yarn from a disrupted technological process.

(λD, dominant wavelength; λK, wavelength of the chimney; λG, wavelength of the humps; K, height of the chimney; B, height of the “base”).

A mechanical error in the operation of the machine appears on the spectrogram in the form of a chimney—one of the harmonic components of the mass distribution of the fiber stream has a higher amplitude than the other components. According to the data provided by the Uster device manufacturer [13]:

K ≥ B/2 – in the woven or knit fabrics there are clusters of yarn sections giving the effect of spots;

K ≥ B – a very serious error requiring immediate interruption of production.

The wavelength of such a harmonic component depends on the diameter d of the damaged element and on the draft R between the defectively working element and the measuring point: λK=πdforthedeliveryrollerofthemachine {\lambda _K} = \pi \cdot d\,{\rm{for}}\,{\rm{the}}\,{\rm{delivery}}\,{\rm{roller}}\,{\rm{of}}\,{\rm{the}}\,{\rm{machine}} λK=πdRfortheremainingtractionsystemrollers. {\lambda _K} = \pi \cdot d \cdot R\,{\rm{for}}\,{\rm{the}}\,{\rm{remaining}}\,{\rm{traction}}\,{\rm{system}}\,{\rm{rollers}}{\rm{.}}\,

The most common harmonic components on the spectrogram caused by mechanical defects include:

eccentricity of rollers

deformation of the lagging of the upper rollers

non-parallel alignment of the rollers

faulty or damaged grooving of the bottom rollers

torsional and transverse vibrations of the rollers

damage in the drive (damaged gears, incorrect meshing of gears, dirty gears, damaged drive belts, etc.)

damaged or worn bearings

damaged belts of the drawing mechanism.

Mechanical defects can cause the occurrence of periodic errors of the following types:

sinusoidal – a single or less often double chimney on the spectrogram

non-sinusoidal – on the spectrogram, a chimney at the basic wavelength and several smaller chimneys at the λ/2, λ/3, λ/4 wavelengths (e.g., damaged surface of the drawing roller, incorrect connection of belts in the drawing mechanism, oscillation of silk tension when winding the yarn on the spindle, accumulation of microdust in the rotor groove of the spindleless spinning machine).

The appearance of double chimneys on the spectrogram is a result of insufficient measurement accuracy of the Uster Tester. The probability of their appearance decreases with increasing the number of measuring channels in the device [3,4,5].

A technological error in the operation of the machine appears on the spectrogram in the form of a hump, which occurs when several adjacent harmonic components of the mass distribution of the fiber stream have a higher amplitude than the other components. The maximum wavelength of harmonic components with an increased amplitude value depends on the average length ι¯ \bar \iota of the processed fibers and on the draft R between the faulty driving zone and the measuring point. λG=(2÷3)ι¯Rfortheyarnspectrogram {\lambda _G} = \left( {2 \div 3} \right) \cdot \bar \iota \cdot R\,{\rm{for}}\,{\rm{the}}\,{\rm{yarn}}\,{\rm{spectrogram}} λG=(3÷5)ι¯Rforthesilverorrovingspectrogram. {\lambda _G} = \left( {3 \div 5} \right) \cdot \bar \iota \cdot R\,{\rm{for}}\,{\rm{the}}\,{\rm{silver}}\,{\rm{or}}\,{\rm{roving}}\,{\rm{spectrogram}}{\rm{.}}

Harmonic components on the spectrogram caused by technological defects are formed as a result of improper movement of fibers in the drawing zone. The reasons may include:

poor composition fiber blend (e.g., too high a proportion of short fibers)

too long distances between the rollers of the drawing mechanism

poor selection of the total draft and partial drafts

too low load on the upper drawing rollers

too wide condensers

sliding strips of drawing mechanism rollers.

On the spectrogram obtained for yarn, it is possible to detect irregularities in the work, not only of the spinning machine, but also of the machines involved earlier in the technological process. The causes of the appearance of stretch waves (chimneys and humps) are dependent on the wavelength:

waves up to 3 cm – in spinning machines, vibration of the rollers, damaged grooving of the rollers, unevenness of fibers in the blend

waves 3–50 cm – in spinning machines, mechanical damage to the drawing rollers, eccentricity of the rollers, technological errors in the drawing zones; in roving machines, mechanical damage to the drawing rollers, vibration of the rollers

Waves 50 cm–5 m – in roving machines, mechanical damage to the drawing rollers, vibration of the rollers

waves above 5 m – in drawing frames, mechanical damage to the drawing rollers, technological errors in the drawing zones.

Mechanical defects in the operation of spinning machines can also be detected using the tachometric method. For this purpose, a tachometer (revolution counter) is used, or kinematic calculations of the drive elements of the machine are performed.

If the wavelength of the chimney on the spectrogram is λ, then this wave will occur on the length of the fiber stream, leaving the machine in a unit of time as many times as the number of revolutions of the defective roller per unit of time. If the speed of the fiber stream release by the machine is Vd, then the rotational speed nw of the defective element (roller, gear, etc.) is nw=Vdλ {n_w}\, = \,{{{V_d}} \over \lambda }

By means of a tachometer or kinematic calculations, an element with the calculated rotational speed nw is searched for in the machine. The tachometric method allows one to detect defective elements only of the machine from which the analyzed product comes.

Errors within the range of very small wavelengths (λ < 5 cm) may also appear on the spectrogram. The causes of such errors may include:

vibration of the machine and/or the drawing rollers (an error difficult to detect)

faulty grooving of the driving rollers (irregular or too deep grooves); bundles of fibers are captured at intervals of the groove scale t (the harmonic component on the spectrogram is easier to detect by obtaining a spectrogram for the next machine in the technological line because the wavelength increases significantly under the influence of the draft R between the defective shaft and the measuring point),

λ=tR \lambda = t \cdot R

Most drawing mechanisms in spinning machines are equipped with belts to control the movement of the fibers. A damaged belt can also be a source of error in the operation of the machine, and the wavelength of such an error is recorded on the spectrogram as λ=ιR \lambda = \iota \cdot R where l is the belt length and R is the draft between the damaged belt and the measuring point.

Incorrect meshing of the drive wheels may also be the cause of the error visible on the spectrogram. As a result of too small or too long a distance between the cooperating gears, a harmonic component with a wavelength λ appears in the fiber stream coming out of the machine: λ=Vdnwz \lambda = {{{V_d}} \over {{n_w} \cdot z}} where Vd is the linear velocity of fiber stream release from the machine, nw is the rotational speed of the faulty gear, and z is the number of teeth in the defective wheel.

Since λ takes small values in this case, it is better to locate the improper meshing defect of the wheels on the spectrogram in the next technological phase, λ=VdRnwz \lambda = {{{V_d} \cdot R} \over {{n_w} \cdot z}} where R is the draft in the next technological phase.

Errors on the spectrogram can be caused by defects in the twisting and winding system of the roving or spinning machine. The reasons for this type of error may include:

eccentric setting of spindles

damaged spindle bearings

wings set eccentrically in relation to the bobbin.

The wavelength of the harmonic components on the spectrogram (chimneys) depends on the diameter of the bobbin from which the fiber stream for testing is sampled and fall within the following range: λmin=πdmin÷λmax=πdmax, {\lambda _{min }} = \pi \cdot {d_{min }} \div {\lambda _{max }} = \pi \cdot {d_{max }}, where dmin is the empty bobbin diameter and dmax is the maximum winding diameter.

Spectral Analysis of Linear Textile Products in Practice

When performing spectral analysis of yarn or any intermediate spinning product, it is not enough to have only a spectrogram obtained on the Uster Tester device. It is also necessary to know the parameters of the technological process such as: diameters and speeds of rollers of the drawing mechanism, length of strips in the drawing mechanism, intermediate drafts, rotational speeds of individual drive wheels, release speed of machines, etc. The values of these parameters are usually known and once measured or calculated, they can be used repeatedly to carry out such analyses for a particular technological process.

An example of spectral analysis of worsted yarn, made of a wool and polyamide fiber blend 70/30 of an average length of 80 mm, based on the spectrogram obtained in Figure 8, is presented below.

Figure 8

A spectrogram of wool-polyamide yarn (70/30) obtained from the Uster Tester 6 device.

A diagram of the drawing mechanism of the spinning machine from which the yarn was taken for analysis is shown in Figure 9.

Figure 9

Diagram of the drawing mechanism of the spinning machine.

The operating parameters of the spinner and the rotational speeds of the selected drive wheels, the work of which seemed incorrect after assessing the condition of the machine drive, are presented in the box.

The yarn spectrogram (Figure 8) clearly shows two chimneys, i.e., harmonic components of the distribution of the yarn linear mass, whose amplitudes are much higher, as well as a hump resulting from a technological error. The chimneys occur at λk1 ≈ 15 cm and λk2 ≈ 4 m wavelengths, while the maximum amplitude of the hump corresponds to the wavelength of λg3 ≈ 3 m.

Mechanical damage to the roller of the drawing mechanism results in the appearance of a chimney on the spectrogram at the following wavelength:

λ1 = π · d3 = π · 50 = 157 mm = 15.7 cm – for the delivery roller

λ2 = π · d2 · R = π · 32 · 15 = 1507 mm ≈ 1.5 m – for the intermediate roller

λ3 = π · d1 · R = π · 42,5 · (2 · 15) = 4004 mm ≈ 4 m – for the feeding roller

Mechanical damage to the belts in the drawing mechanism results in the appearance of a chimney on the spectrogram at the following wavelength:

λ4 = l · R = 167 · 15 = 2505 cm ≈ 2.5 m – for the top belt

λ5 = l · R = 267 · 15 = 4005 cm ≈ 4 m – for the bottom belt

Mechanical damage or error in the operation of the drive wheels results in the appearance of a chimney on the spectrogram at the following wavelength:

λ6 = Vd/nz1 = 0,2/1,27 = 0.157 m = 15.7 cm – for the Z1 drive wheel

λ7 = Vd/nz2 = 0,2/2 = 0.1 m = 10 cm – for the Z2 drive wheel

λ8 = Vd/nz3 = 0,2/0.5 = 0.4 m = 40 cm – for the Z3 drive wheel

Technological error in the work of the drawing mechanism results in the appearance of a hump on the spectrogram at the following wavelength:

for the output zone λG=(2÷3)ι¯=(2÷3)80=160÷240mm=16÷24cm {\lambda _G} = \left( {2 \div 3} \right) \cdot \bar \iota = \left( {2 \div 3} \right) \cdot 80 = 160 \div 240\,mm = 16 \div 24\,cm

for the feed zone λG=(2÷3)ι¯R=(2÷3)8015=2400÷3600mm=2.4÷3.6m {\lambda _G} = \left( {2 \div 3} \right) \cdot \bar \iota \cdot R = \left( {2 \div 3} \right) \cdot 80 \cdot 15 = 2400 \div 3600\,mm = {\bf{2.4}} \div {\bf{3.6}}\,\boldsymbol{m}

The analysis of errors visible on the yarn spectrogram in the form of chimneys and humps allows one to determine the probable causes of their formation.

For a chimney located at wavelength λ1 = 15.7 cm, it is due to damage to the output roller (upper / lower) or the Z1 drive wheel.

For a chimney located at wavelength λ2 = 4 m, it is due to damage to the feeding roller (upper / lower) or the lower belt in the drawing mechanism.

For a hump, the maximum amplitude of which falls on the wavelength λg3 ≈ 3 m, it is due to an incorrect operation of the feeding zone of the drawing mechanism.

It is noteworthy that the reason for the appearance of a chimney on the spectrogram cannot always be clearly identified. This is applicable also to the case under consideration. If the upper and lower rollers have the same diameter (which happens very rarely), then only a direct assessment of their condition on the machine allows one to identify the site of damage more accurately. Additionally, the drive wheels of the machine or the belts controlling the movement of the fibers in the drawing mechanism can yield an error at the same wavelength on the spectrogram as the damaged roller of the drawing mechanism.

Summary

Spectral analysis of the linear mass distribution of the fiber stream based on the results obtained on the Uster Tester is the simplest and fastest method of assessing the quality of linear textile products already at the stage of their manufacture. Any irregularities in the spectrogram structure for the analyzed fiber stream are the result of either mechanical damage or technological errors in the operation of spinning machines. Analysis of the spectrogram allows one to detect and locate these errors and damages with fairly high accuracy, which makes it possible to eliminate them. To perform spectral analysis, it is required to have a thorough knowledge of the technological process, the operating parameters of the machines in the technological line, and the kinematics of the drives of the individual machines. A spectrogram of any fiber stream contains the entire history of its production, which makes it possible to detect errors also in earlier stages of processing. However, spectral analysis does not always give unambiguous results. It is often necessary to verify the obtained results directly on the machine in order to identify a malfunctioning element or zone.

Spectral analysis is currently the basic tool for assessing the quality of flat textile products already at the stage of yarn formation.

Figure 1

The Huberty index in the consecutive phases of spinning. 0, raw material; 1, fiber pre-treatment machines; 2, carding machines; 3, drawing machines; 4, drawing machines of the second passage; 5, roving machines; 6, spinning machines.
The Huberty index in the consecutive phases of spinning. 0, raw material; 1, fiber pre-treatment machines; 2, carding machines; 3, drawing machines; 4, drawing machines of the second passage; 5, roving machines; 6, spinning machines.

Figure 2

The scheme of weft and/or warp stripes creation in fabrics.
The scheme of weft and/or warp stripes creation in fabrics.

Figure 3

A “moiré” effect
A “moiré” effect

Figure 4

View of the yarn on a contrast plate obtained on the Uster apparatus
View of the yarn on a contrast plate obtained on the Uster apparatus

Figure 5

Fabric appearance simulation
Fabric appearance simulation

Figure 6

A sample spectrogram.(λD – dominant wavelength)
A sample spectrogram.(λD – dominant wavelength)

Figure 7

A sample spectrogram of yarn from a disrupted technological process.(λD, dominant wavelength; λK, wavelength of the chimney; λG, wavelength of the humps; K, height of the chimney; B, height of the “base”).
A sample spectrogram of yarn from a disrupted technological process.(λD, dominant wavelength; λK, wavelength of the chimney; λG, wavelength of the humps; K, height of the chimney; B, height of the “base”).

Figure 8

A spectrogram of wool-polyamide yarn (70/30) obtained from the Uster Tester 6 device.
A spectrogram of wool-polyamide yarn (70/30) obtained from the Uster Tester 6 device.

Figure 9

Diagram of the drawing mechanism of the spinning machine.
Diagram of the drawing mechanism of the spinning machine.

j.aut-2022-0019.tab.001

- for carded cotton yarn 1.8 ÷ 2.6
- for combed cotton yarn 1.3 ÷ 1.6
- for yarns of man-made staple fibers 1.5 ÷ 2.2
- for worsted woolen yarn 1.1 ÷ 1.4
- for carded woolen yarn 1.4 ÷ 2.1.

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