Variance Tolerancing and Decomposition in Short-Staple Spinning Processes: Part I: Modeling Spun Yarn Strength Through Intrinsic Components

Abstract

A variance tolerancing method is developed as a means for separating and estimating random errors associated with raw materials and yarn structures from process-induced errors based on structural relationships governing the strength of a spun yarn. The method is successfully used to estimate the mean and variance of spun yarn strength by propagating the statistical parameters of fiber properties onto those of the resulting spun yarns. In developing the new estimation procedure, probabilistic models based on the distributions of fiber length and tensile properties are combined with geometric and structural models of fiber arrangements in spun yarns. For the first time, the concept of “effective gauge length” is used to model and simulate the breakage process of spun yarns. The new concept and specific methodology are aimed at better controlling process and product characteristics by quantifying the variances according to their sources.

Get full access to this article

View all access options for this article.

References

1. Casella, George , and Burger, Roger L. , “Statistical Inference,” 1st ed. Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1990, pp. 139–146, 153-160, 228-236.

2. Cui, X., Tensile Properties of Bundles and Their Constituent Fibers—An Application to HVI Cotton Testing, Doctoral thesis, College of Textiles, North Carolina State University, Raleigh, NC, 1995.

3. Evans, David H. , Statistical Tolerancing: The State of the Art, Part II—Methods for Estimating Moments, J. Qual. Technol. 7(1), 1–12 (1975).

4. Feller, W. , “An Introduction to Probability Theory and Its Applications,” 3rd ed., John Wiley & Sons, Inc., NY, 1967, pp. 146–171.

5. Peirce, F. T. , Tensile Tests for Cotton Yarns, Part V: The Weakest Link Theorems on the Strength of Long Composite Specimens, J. Textile Inst. 17, T335–T368 (1926).

6. Pitt, R. E. , and Phoenix, S. L. , On Modelling the Statistical Strength of Yarns and Cables under Localized Load-Sharing among Fibers, Textile Res. J. 51, 408–425 (1981).

7. Platt, M. M. , Klein, W. G. , and Hamburger, W. J. , Mechanics of Elastic Performance of Textile Materials, Part IX, Textile Res. J. 22, 641–667 (1952).

8. Suh, M. W. , Improving Textile Product and Process Qualities: Failure Mechanisms and New Directions for the Future, J. Textile Inst. 85, 476–483 (1994).

9. Suh, M. W. , Probabilistic Assessment of Irregularity in Random Fiber Arrays—Effect of Fiber Length Distribution on “Variance-Length Curve,” Textile Res. J. 46, 291 (1976).

10.

10. Suh, M. W. , Bhattacharyya, B. B. , and Gradage, A. A. , On the Distribution and Moments of the Strength of a Bundle of Filaments, J. Appl. Prob. 7, 712–720 (1970).

11.

11. Sullivan, R. R. , A Theoretical Approach to the Problem of Yarn Strength, J. Appl. Phys. 13, 157–167 (1941).

12.

12. Tukey, J. W., Propagation of Errors, Fluctuations and Tolerances, No. 1: Basic Generalized Formulas, Tech. Report No. 10, Stat. Tech. Res. Group, Princeton Univ., 1957.