Can We Modify the General Equation to Accept HVI Data?

The reader is now most likely to raise a question. Can we modify The General Equation to calculate CSP of ring-spun yarn from HVI data?

Before we begin to answer this question, let us recapitulate some tenable premises that are fundamental to  The General Equation:

Figure –A –vi Contd.  Fibre Length Distribution of S – 4 Cotton

Figure A – vii Plot of HVI tenacity against UHML

Now HVI does not provide on any of the following data: the %-ages of fibres at the two critical lengths; fibre-tenacity at two different gauge-lengths; fibre millitex. Furthermore, in the fibre-tenacity testing by HVI there is a likelihood of some percentage of fibres in the bundle under test having a free end within the test length. Would not this %-age be more for a short-fibre cotton than for a comparatively long cotton? Again would not this %-age be more for a cotton that is much more variable in length than that for a very uniform cotton? A plot of SITRA HVI tenacity values against the HVI UHML shows a striking trend of the tenacity increasing with length – Figure – A -vii. Such a prominent trend is not generally observed with conventional tenacity tests. One can argue that this very feature of the fibre-bundle test by HVI, of there being free fibre-ends in the bundle that breaks, can perhaps make it quite suitable for estimating yarn tenacity, the test for which shares the feature with HVI fibre-tenacity test. One has then to rewrite the expression for F₃ taking this aspect into consideration. One has to ponder over these points and questions before one rushes to modifying The General Equation, for use with HVI data.

Having said this, we yielded to the exigency in the situation.

We made use of SITRA data (3) in our attempt to modify HVI data so that they can be substituted in The General Equation to estimate the CSP  of ring-spun yarns of optimum T.M.. We proceeded along the following steps:

Figure – A – viii Plot of HVI Tenacity Adjusted to Remove Length Related Bias and Manual Test Tenacity of Similar Cottons Against Length

NOTE: With The SITRA equation errors are on either side, positive and negatie,
in the first half of the plot, but positive errors  predominate in the second half of the plot; with the Modified General Equation there is hardly any  bias.

Points               1 to 21             22 to 39           40 to 60           61 to 75        76 to 90
Cotton              SUVIN             DCH                  MCU5               LK                 S-4

Points               91 to 102         103 to 111       112 to 117       118 to 123
Cotton              MECH             LRA                 RCH                V 797

EST: estimated; EL: effective length; H: fibre fineness, millitex;
Z: zero-gauge Stelo level fibre-bundle tenacity;
G: gauge-length parameter of tenacity; F: Stelo level 1/8-in gauge tenacity;
Q: floating fibre index, a function of HVI UHML and ML

Table – A – ix  Conventional Fibre Test Data
on Cottons Comparable to those in Table – A - viii

Figure A - ix compares the errors in the estimates of CSP from the two methods, the SITRA equation and the modified general equation.

The inference is clear: we can successfully modify The General Equation to use HVI data for estimating CSP of ring-spun yarns of optimum T.M.; there is a possibility of extending this method to the estimation of CSP at values of TM other than the optimum. Considerable work, however,  needs to be done  to realize this.

On the basis of published data (16), we made an attempt to modify The General Equation to use it to predict rotor yarn CSP from HVI data. Unlike in the case of SITRA data, these data do not exhibit a marked increasing trend of fibre-tenacity with increasing fibre-length..

The modified equation (17) gives estimates of acceptable accuracy for cottons ranging in CSP from 1232 to 2807 at NE 10.1, and T.M. 5.3. – Table x.

The modification of the General Equation to predict rotor yarn CSP from HVI length, uniformity ratio, tenacity and micronaire seems a distinct possibility.

In the span of two decades electronics has taken over our lives, as much as we have taken to electronics. Electronics is ubiquitous: keeping abreast with news from around the world, booking air-tickets, getting the yearly medical check-up, all these remind us of electronics.

Come to think of it, even a modest 50,000-spindle mill exporting yarn is a show-case for electronics: auto-levelers, yarn clearers, evenness testers, and so on. But what about cotton purchase? How much does a 50,000-spindle mill spend a day  on cotton? And how do we decide as to whether to buy or not to buy a lot on offer? What equipment do we have? What tests do we get done? Any computer interface for graphic presentation of what yarn we can spin from the just tested cotton?

The General Equation for estimating cotton yarn tenacity, is the outcome of work that was carried out in ATIRA during the period 1985 to 1991. Part II of this monograph gives a detailed account of the work. The publication after a lapse of almost fifteen years is justifiable. There is a greater chance of the acceptance of the General Equation for use in industry today than in the eighties. This is so because of two developments: the availability today of instruments for the rapid measurement of cotton fibre characteristics like fibre-fineness and fibre-length distribution; the ubiquitous presence of the computer that has literally put numerical evaluation of the most complex algebraic formulae at the finger-tips on the computer key-board.

This work is just the toddler’s first step. I have a vision: Indian Cotton Selectors traveling across cotton-growing regions in air-conditioned caravans with testing equipment interlinked to lap-tops.