How Accurate Is The  General Equation In Estimating Cotton Yarn CSP?

Figure A – ii  Showing proximity of experimental points to smooth curve
given by algebraic expressions for F1, F2, F3 and F4 (Brown’s data)

Figure A - ii shows a plot of Brown’s experimental CSP (7) over which the smooth curves generated by the expressions for F1, F2, F3 and F4 are drawn. In most of the available 18 cases, the smooth curve passes through, or lies in close proximity to, the experimental points.

Figure A - iii shows a similar graph for the first ATIRA spinning. Again the smooth curves generated by the expressions for F1, F2, F3 and F4  are quite close to the corresponding experimental points.

Quantitatively, the %-age errors in the estimates of yarn tenacity from fibre characteristics are mostly within the acceptable limits in both the instances.

The proximity of the experimental points to the smooth curve generated by the expressions of the general equation in two independent sets of data proves that The General Equation fulfils the objective that we started with. The equation correctly quantifies the contributions of fibre-length and fibre-fineness to the translation of fibre tenacity into yarn tenacity. The relevance of  fibre-length and fibre-fineness to the translation of fibre tenacity into yarn tenacity is highlighted in Table A -v.

Table – A - v  Fibre Characteristics And Yarn Count And Twist
as Contributing Factors To F1, F2, F3 and F4

In the general Equation F₁  quantifies the distinctive contribution to yarn tenacity of yarn irregularity that is inevitable in roller drafting. F₁,F₂ and F₃ quantify the distinctive contribution of twist that has necessarily to be introduced into the drafted fleece to convert it into formed yarn.Obviously, these expressions have to be customized for use in any mill. In this context, there is an important point to note regarding these functions.

The algebraic expressions for  F₂ and F₃ derived from data from the first ATIRA spinning, as well as Bogdan’s expression for F₄, were found to be valid for use in the three other spinnings each on a different drafting system. This is a distinct merit of the General Equation that is of practical significance. The expressions for F2 and F3 are specific to the testing procedures in use for cotton and yarn. A mill has, therefore, to determine the numerical constants in these expressions once for its test set up. These expressions, however, are capable of dealing with a variety of drafting systems, and cottons with really disparate fibre-length distribution. A spinning mill that has ringframes with drafting systems that differ in age and other aspects can, therefore,  keep on using the same set of expressions for F₁,F₂ and F₃; only the numerical constants in F1 have to be determined afresh for each drafting system.

The procedure for deriving the set of constants in the expressions for F2 and F3  in any new set up is explained in part II, and that for evaluating only the numerical constants in F1 for any new drafting system in Part I.