John D. Tallant

The Changes in Fiber-Number Length Distribution Under Various Breakage Models

Two basic models for the breakage of uniform rods or fibers are discussed—the lost ends in which one of the pieces of each broken rod is discarded from the system and the saved ends under which all fragments are retained. Random breakage is considered as a process with an input length distribution F(x), a breakage function π( x), and an output distribution G(x). General solutions are given so that, from any two functions, the third may be obtained. Cases under which departures from random breakage occur are discussed, and a solution is given for each. Simplifications of the general solutions are show n for the two important cases of breakage independent of and proportional to length, i.e., π( x) = α and #( x) = βx, respectively. Practical application to the length distributions of cotton fibers which had been subjected to varying degrees of damage are given.

The Effect of the Short Fibers in a Cotton on its Processing Efficiency and Product Quality Part I. Affecting the Short Fiber Content by the Addition of Cut Cotton Fibers

The effect of the short fiber content of a cotton on yarn and fabric properties and processing efficiency, long a speculative and controversial subject, is investigated to a limited extent in this paper by the technique of cutting sliver into and ¼- and ½-in. segments and adding the resulting short fibers to the parent cotton. The results indicate that increases in short fibers are detrimental to virtually all yarn and fabric properties and require increased roving twist for efficient drafting during spinning. A 1% increase in fibers shorter than 3/8 in. causes a strength loss in yarns of somewhat more than 1%. The quantities of cotton processed for this paper were insufficient to draw conclusions on neps, waste, or processing efficiency. The effect of short fibers on these properties will be considered in subsequent papers.

Breakage Models and Measuring Techniques for Fiber. Weight-Length Distributions

Previously developed number-frequency equations are translated into their weight- frequency counterparts. A solution is developed for the problem of fiber-length distri bution to be expected when a sliver or similar textile structure, with straight fibers, is cut systematically. A double-clamping technique is described which permits the determina tion of the weight-frequency distribution and weight-mean length of the fiber population in the sliver, with the same assumption that the fibers are straight and parallel to the structure axis. It is shown that, if the fibers are not straight and parallel, the same technique measures the projection of the fibers along the structure axis. Simple methods for measuring the projected length are described and data are represented showing the change in projected length as a typical cotton proceeds from card sliver through roving. The basic mathematical equations for the Lindsley combing ratio are derived, and it is shown that a modification of the Lindsley technique can also yield the projected mean length.

Mathematical Aspects of Cotton Fiber Length Distribution under Various Breakage Models

Mathematical models of cotton fiber length distribution under various breakage models are discussed. Theoretical analyses are given, including the demonstration of certain factors, capable of measurement. which afford the possibility for numerical con firmation of the respective models. For example, the model for random fiber breakage independent of length shows that where μ F and μ G are the means and γ F and γ G are the absolute second moments about the origin of the parent and daughter populations, respectively. In addition, mathematical models, somewhat more complicated, are given when breakage is proportional to length and for the case where the fibers are held and then subjected to breakage.

The Effect of Short Fibers in a Cotton on its Processing Efficiency and Product Quality: Part II: Yarns Made by Miniature Spinning Techniques from Differentially Ginned Cotton

The conclusions reached by means of miniature spinning techniques with very small samples of cotton were similar to those obtained in Part I : changes in short fiber con tent do not affect the twist required for maximum strength hut do lower strength some what more than 1% for each 1% increase in short fiber content. These samples covered an exceptionally wide range of short fiber contents, from less than 1% to almost 20% by weight of fibers 3 in. and shorter. The very low short fiber content cottons were produced hy careful hand ginning techniques while the re mainder were obtained by differential ginning techniques.

Random-Fiber Breakage Models

Letters to the Editor are brief communications intended to provide prompt publication of significant research results and to permit an exchange of views on papers previously published in the Journal. Letters are subject to review, but the authors assume full responsibility for information or opinion expressed.

Investigation of the Minimum Length of Cotton Fiber Effective in Single Yarn Tenacity

A systematic investigation of the translation of cotton fiber length distribution and fiber bundle tenacity into single yarn tenacity is reported. The mathematical model proposed is: Y = af (l, x) × S + b where Y is single yarn tenacity, a and b are constants, S is fiber bundle tenacity, l is length distribution of the cotton, x is critical length, and f(l, x) is a numerical value termed “effective weight” which is dependent upon the entire fiber length distribution. The investigation was carried out over a wide range of twists and yarn numbers, the latter ranging from 15/1 (40 tex) to 80/1 (7.2 tex). The optimum f(l, x) was selected, and it was found that fibers shorter than about 1/8 in. do not contribute to yarn tenacity. Similarly, a 1/8-in. portion of each longer fiber is ineffective. This may be viewed as implying physically that, on the average, the 1/8-in. tip at each end of each fiber does not contribute to the yarn tenacity. Hence, the degree of translation of fiber bundle tenacity to yarn tenacity is a function of the entire length distribution. An interesting finding of this investigation is that the “zero”-gauge fiber bundle test is superior to the ⅛-in.-gauge length test as a criterion for relating bundle to yarn tenacity if the zero-gauge value is modified by the effective weight, i.e. f(l, x) above.

The Effect of the Short Fibers in a Cotton on Its Processing Efficiency and Product Quality Part III: Pilot-Scale Processing of Yarns

By differentially ginning a single lot of Acala 44 cotton, various short fiber content levels were obtained. Yarns produced from these cottons showed the effects of increases in short fiber content; namely, reduced strength, elongation, and appearance grade. The twist required for maximum strength was found to be largely unaffected by changes in short fiber content, except for a medium yarn number for which a relationship was demonstrated. A graph showing the close relationship between the percentage of fibers less than 3/8 in. and those less than 1/2 in., calculated for a wide number of cottons, is included. Spinning efficiency is shown to be adversely affected by changes in short fiber content.

A Statistical Procedure for Determining End Breakage Rate in Spinning

Standard deviations of yarn break data, taken by uniform increments of spindle hours, increased linearly with average rate of breakage and were larger than expected for a Poisson distribution. Transforming the numbers of breaks to log10 (1 + number of breaks) stabilized the variance. In a specific case, analysis of data for 720 spindle hours per yarn taken by 12 increments of 60 hours yielded 95% confidence limits describing the average number of breaks per yarn as within 30% of the observed number of breaks.

Progress Reports on Use and Application of the Nepotometer: Some Factors that Affect Test Results 1

The Nepotometer is in many respects a miniature card designed to simulate on laboratory samples of cotton the effects of actions encountered during the carding opera tion which are largely responsible for nep formation. It was developed at the North Carolina State College School of Textiles. under a contract with the U. S. Department of Agriculture, to predict the nepping potential of cottons. The use of a standard-weight test specimen does not necessarily produce a standard weight web. There may be considerable differences in this respect among different cot tons. For each of eight cottons tested, the web weight and log of neps per grain increased with increase in specimen weight in the region tested between 17.5 and 27.5 grains in clusive, the increases being linear with no indication of curvilinearity. Since evaluations are based on comparison of the webs with appearance standards, the production of a constant weight web in the test is believed to be necessary. The possibility of controlling web weight by consideration of some readily determined property such as Micronaire reading or Fibrograph upper half mean length, or a combination of these, appears promising. Two simple equations have been derived for determining the specimen weight to use for a fixed web weight—one based on Micronaire reading and the other on upper half mean length. Good correlation was found between the log of neps per grain and the photographic standards when the web weights were approximately constant. The regression curve above Grade 1 was essentially a straight line. Neppiness stindards following a regular progression can be obtained from the present photographic grades by adding another grade between the present Grades 1 and 2.