| Abstract |
|
 |
How Did We Construct The General Equation For Estimating Yarn Tenacity? |
|
|
 |
Many years ago Peirce (1) spelt out the basic purpose of a general equation for yarn tenacity: it should provide us with algebraic expressions that will help trace the well-known twist-tenacity curves of yarns, similar to the ones in Figure A - i. |
|
|
|
|
|
|
|
Figure A-i Typical inverted parabola of T.M. – CSP plots
Karnak cotton; NE 18, 36, 72. |
|
|
|
We ensured that our general equation fulfils this fundamental requirement by structuring the equation on the basis of the characteristic features of the phenomenon of yarn breakage in tenacity testing. These features are:- |
|
|
|
 |
Yarn tenacity is the manifestation of fibre tenacity. |
|
Yarn tenacity (g/t) is, however, never equal to fibre tenacity (g/t), but is only a fraction of fibre tenacity—generally less than half the zero-gauge fibre tenacity. There are many reasons for this. |
|
The linear density of a cotton yarn is highly variable along its length. At the place of break, therefore, the number of fibres will only be a fraction of the number of fibres corresponding to the average count of the yarn. In other words the yarn count at the place of break will be much finer than the average count. Yarn tenacity is, however, reckoned on the average yarn-count, and not on the count at the place of break. Yarn tenacity can, therefore, be only a fraction of cotton fibre tenacity. |
|
Further, of the fibres present at the place of break, only a fraction may break and contribute to yarn tenacity, while the rest may slip. |
|
The fibres at the place of yarn break that break themselves and contribute to yarn tenacity, may not break at ‘zero-gauge’, but at some finite gauge. |
|
Quite likely, the gauge-length of fibre breakage when yarn fails in testing should decrease with increasing twist. The appropriate gauge-length of cotton tenacity to use in the prediction equations for yarn tenacity should, therefore, decrease asymptotically with increasing levels of twist in the yarn. |
|
Now, as the test length is decreased, cotton fibre-bundle tenacity is known to increase asymptotically to the zero-gauge value. |
|
There is a subtle difference between the way fibres are broken in the determination of bundle-strength and the way fibres are broken in the determination of tensile strength of yarn. In the manual method of determination of fibre-bundle tenacity all the fibres in the bundle under test, without exception, bridge the entire distance between the clamps, and therefore share the applied load. As against this, in yarn-test some fibres in the yarn-element that breaks may have one end lying within the break-zone and may not, therefore, share the applied tensile load; the number of such fibres will conceivably depend on the fibre-length distribution. This has to be taken into account in the construction of the equation. |
|
There is one more reason for the yarn tenacity falling short of the fibre-bundle tenacity. This is the obliquity of the fibres in the twisted yarn to the yarn-axis, which is the direction in which tensile stress is applied in the determination of yarn tenacity. |
|
|
|
|
|
|
|
|
This analysis led us to the following structural equation for yarn-tenacity: |
|
|
|
CS = Z x R x F(1) x F(2) x F(3) x F(4),
where,
CS is the yarn-tenacity in terms of the English count strength product,
(NE) x (lbs.),
Z is the fibre-bundle tenacity at zero-gauge (g/tex),
R is a numerical conversion factor to adjust for the units in use
in expressing fibre-bundle tenacity and yarn tenacity, well as for the differences in testing procedures,
F(1) is the available number of load bearing fibres at the place of break,
expressed as a fraction of the average number of fibres
corresponding to the count of yarn,
F(2) is the fraction of fibres at the place of break
which break themselves as against the remaining
which slip when yarn breaks in tensile testing,
F(3) is the fraction of zero-gauge fibre-bundle tenacity available at the gauge-length at which fibre-bundles break when yarn breaks in tensile testing ,
F(4) is the correction to take into account the angle made by fibres
to the direction of tensile loading in yarn testing. |
|
|
|
There is one other obvious requirement of a general equation for yarn tenacity. The equation should have the provision to allow for the contribution of the drafting system used to spin the yarn. For, even from the same cotton, different drafting systems are well known to yield yarns that differ in yarn tenacity. The term for the contribution of the drafting system can conveniently be included in the algebraic expression for the irregularity fraction. |
|
|
|
Some important points emerge from the foregoing analysis. |
|
|
|
|
To obtain accurate estimates of yarn CSP at different twists we need to be able to estimate the fibre tenacity at any finite gauge length over a wide range of values. For this we need to have the tenacity measured not only at 3-mm., but also at zero gauge. |
|
In the general equation the number of fibres at the place of break is an important fundamental variable. Now, the number of fibres at the place of break is a fraction of the average numbers of fibres in the cross-section of the yarn. The number of fibres in the cross-section can only be calculated from yarn count and fibre fineness, millitex, not micronaire index. Therefore, micronaire index is not appropriate for use in the general equation; we need the gravimetric fibre fineness, millitex. (Fortunately, instrumental evaluation of fibre millitex is today there for the asking.) |
|
|
|
|
We have now to formulate the algebraic expressions for F1, F2, F3 and F4 in terms of these fibre parameters. For this we need data on fibre and yarn tests of a number of disparate cottons. Brown and co-workers (7) have provided such data. In our first attempt to formulate expressions for the general equation we made use of these data. We were able to construct a general equation that gives yarn CS estimates of acceptable accuracy over a range of values of yarn count and twist. |
|
|
|
A scrutiny of the of errors of individual estimates of CS, however, led to the conclusion that a single measure of fibre length, upper half mean length (UHML) in this case, is, perhaps, not adequate to take into account the contribution of fibre length to the translation of fibre tenacity into yarn tenacity. Earlier investigations in ATIRA (31) had shown that we can characterize cottons for their propensity to incur drafting irregularity by the use effective length, %-age fibres shorter than 12-mm, %-age fibres longer than 24-mm. The investigations also led to an important conclusion: these three length parameters could be used to construct a floating-fibre index, Q, which could then be used along with fibre-fineness to estimate accurately the frequencies of Uster thin and thick places in the yarn – Table - -iv. |
|
|
|
We, therefore, decided to use these insights to improve upon the general equation for yarn tenacity that was constructed from Brown’s data. We selected 12 Indian cottons to cover a wide range of fibre length, fineness, and tenacity. We tested these cottons for the following fibre characteristics, that we have identified are required to construct the general equation: L, the Baer sorter effective length in mm; S, the percentage fibres by number shorter than 12 mm; B the percentage fibres longer than 24 mm; H, the fibre fineness in millitex; Z, the zero-gauge bundle tenacity in g/t; F, the 1/8-in. (3.2 mm) bundle tenacity in g/t. We carried out two spinnings from these cottons: in the first we spun each of five cottons to one or more count, each count at more than three twists; in the second each of the twelve cottons to three counts at the same twist. |
|
|
|
Starting with the general equation derived from Brown’s data, we made modifications to the algebraic expressions to incorporate the three cotton parameters that we have identified as necessary to characterize cottons for yarn irregularity. We also made minor adjustments in the algebraic expressions to allow for the differences in the fibre test procedures between Brown’s and ATIRA sets of data. We were able get accurate estimates of yarn CS for the ATIRA data from the two spinnings as well.
|
|
|
|
|
|
|
|
|
