Variance tolerancing and decomposition in textile products and processes

This research developed a procedure for quantifying and decomposing the variabilities of textile products and processes in accordance with such sources as raw material properties and processing conditions by introducing a new variance tolerancing technique that employs geometrical, probabilistic and structural models depicting tensile strengths of spun yarns and the fabrics woven from them. The decomposition of variances of yarn and fabric tensile strengths were accomplished in two ways; by direct estimation and quantification and by subtraction. In the course of the development, a new concept of intrinsic components was introduced and applied.; A large amount of test data from a 3-year production experiment was collected for this research in order to test the concept and validate the theoretical models. In addition, the model validation included over 70,000 single fiber tensile test data from MANTIS{dollar}spcircler.{dollar}; A spun yarn was modeled as a chain of twisted bundles with a known distribution of the number of "continuous" fibers within an arbitrary interval within the yarn. The mean and variance of yarn tensile strength were derived as a function of fiber length, strength, fineness and the effective gauge length "L" as intrinsic components of the model developed. While the effects of fiber length were shown to be large for the mean yarn tensile strength, that of fiber strength were found to be highly significant in determining the variance of yarn tensile strength.; The variance of the actual yarn tensile strength was decomposed into between-package variances resulting from the spinning processes and within-package variances which, in turn, were due to random components of the fiber properties and nonrandom components that were process dependent. The effects of nonrandom components (6.17 {dollar}sim{dollar} 11.59%) were shown to be greater than that of the random components (3.17 {dollar}sim{dollar} 7.78%).; On the basis of a classical parallel fiber bundle model, the mean and variance were derived for the tensile strength of 3/1 twill fabrics as a function of the yarn tensile strength distribution and the number of yarns in the test direction. The variance of the fabric tensile strength was estimated by two different methods; one based on an intrinsic model by tolerancing the actual variance of the yarn tensile strength and the other by tolerancing the variances of the fiber properties. The latter was found to be quite small, implying that most of the variations observed in fabric properties were due to process factors unrelated to raw materials. Thus, importance of process control in textiles manufacturing was exemplified quantitatively.; The combined effects of actual yarn tensile strength distribution and presence of interference factors relating to fabric structures were found significant in explaining the variabilities of fabric tensile strength. The tighter the filling density was, the stronger the fabric warp tensile strength and the smaller its variance.; The new variance tolerancing techniques and the intrinsic component models developed were proven to be highly effective for decomposing and quantifying the magnitudes of variances in the tensile properties of spun yarns and woven fabrics obtained from the 3-year production experiment and the large amount of single fiber tensile data. The methods and concepts developed, however, are considered equally applicable to all other textile products and processes.