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A Practicable Modification of The General Equation
for Estimating Combed-yarn CS at Near Optimum T.M. |
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In practice, at the time of taking the decision as to whether to buy the lot of cotton on offer or not, we will, obviously, not have fibre-tests on combed sliver. We should, therefore, be able to predict combed-yarn CSP from bale-cotton fibre-tests. In other words, what we need for combed-yarns is a prediction equation that has been so constructed that it will give estimates of combed yarn CSP on substitution of bale-cotton fibre-tests. Surprisingly, we have been able to derive such an equation. |
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The Modified Equation for combed yarns at near about optimum T. M. has been derived by taking advantage of some practical observations: |
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When the remaining processing machines are the same, the CS of combed yarn of any count from any cotton can be obtained by multiplying the CS of the counterpart carded yarn by a factor larger than unity; |
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This factor decreases with N, the average number of fibres in the yarn cross-section, and, therefore, at any count is less for a coarse cotton than for a fine cotton; the factor tends to one as N tends to zero; |
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The factor increases with initial increase in the noil percentage, and then levels off with further increase of noil extraction; |
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Spun from the same cotton, combed yarns have a steeper fall of CSP with count than carded yarns (15). |
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Furthermore, one would expect the factor, which gives the ratio of combed to carded yarn CSP, to be dependent upon the fibre-length distribution of the cotton. |
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In order to formulate the equation we should have data on carded and combed yarns spun from cottons of known fibre characteristics. The cottons should cover a wide range of fibre properties. We followed a short-cut to collect such data: we combed the card slivers from the experiment in which one long and fine cotton, and another short and coarse cotton were spun to yarns in isolation as well as in three mixings of differing proportions; we prepared combed slivers at 10% and 18% noil extractions; we spun each combed sliver to NE 30 at T.M. of 4.6, and NE 40 at T.M. of 4.2. |
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From these data we derived the Equation for the CSP of combed yarns keeping in mind the practical observations that we just listed: |
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In this equation the numerical values of l, m and Q are the same as those for carded yarns; and the three other fractions are evaluated from bale cotton fibre-data exactly in the same way as for carded yarns, and are, therefore, numerically equal to those for carded yarns; only the numerical values of p, r and s have to be determined for every noil-level by regression from combed yarn data. |
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Table II –6 -iii shows that this equation gives very accurate estimates of the CSP of combed yarns, at the two noil-extraction levels and for the two counts. This is so for both the long and fine cotton and for the short and coarse cotton; and also for the three mixings. |
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We must clarify a point here. The ratio of combed yarn CSP to carded yarn CSP, which can be calculated for any cotton from the equations, should tend to unity with increasing yarn count. This is found to be so in the case of VL cotton, but the ratio becomes less than unity for G11 cotton beyond NE = 90 or so. Obviously, this is because we have derived the equation for combed yarns from data on just two yarn-counts. More work is required to fine-tune this equation. |
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We can conclude that The General Equation can be modified to get estimates of CSP of combed yarns at near optimum T.M. from fibre-test data on bale-cotton. |
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