A Model for Predicting Set in Helices

Abstract

A model is developed to calculate the residual set in a helical fiber axis after it has been wrapped around a mandrel, set into this shape, and released. The theory used is linear viscoelasticity in conjunction with the bending and twisting equations for thin rods. The model may be applied equally well to calculate the snarling behavior of twisted yams. An example of this is presented to confirm predictions made by the model. Two cases in the setting of helices are analyzed. In the first case the released helix is not in contact with the mandrel. In this case the bending and torsional set in the helical fiber axis follows quite simply from principles of linear viscoelasticity. In the second case, the released helix is constrained to lie on the surface of the mandrel. Results of this second case are more complex, but have been computed and presented in tabular form.

Get full access to this article

View all access options for this article.

References

Bennett, J.M. , The Mechanics of Yarn Structures in Torsion, doctoral thesis, University of New South Wales, 1977.

Bennett, J.M. , and Postle, R. , A Study of Torsional Stability in Plied Yams , J. Textile Inst. 68, 142-151 (1979).

de Jong, S. , A Study of Fabric Mechanics Using Energy Methods of Analysis, doctoral thesis , University of New South Wales, 1976 .

de Jong, S. , and Postle, R. , A General Energy Analysis of Fabric Mechanics Using Optimal Control Theory , Textile Res. J. 48, 127-135 (1978).

de Jong, S. , Linear Viscoelasticity Applied to Wool Setting Treatments, Textile Res. J. 55, 647-653 (1985).

de Jong, S. , An Analysis of the Viscoelastic Behaviour of Wool During Transient Moisture Changes, Textile Res. J. (submitted).

de Jong, S. , and Michie, N.A. , Linear Viscoelasticity Applied to Wool Fibre Setting, 3rd Japan-Australia Symposium on Objective Evaluation of Apparel Fabrics, Textile Marketing Society of Japan, Kyoto, September 1985.

de Jong, S., unpublished results.

Denby, E.F. , A Note on the Interconversion of Stress Relaxation, Creep and Recovery, Rheologica Acta 14, 591-593 (1975).

10.

Denby, E.F. , The Effect of Relaxation, Set and Hygral Expansion of Single Wool Fibres in Finishing Wool Fabrics, in "Proc. Second Australia-Japan Bilateral Science and Technology Symposium," Melbourne , October 24-November 4, 1983, pp. 421-431.

11.

Konopasek, M. , and Hearle, J.W.S. , The Mechanics of Twisted Continuous Filament Yarns, J. Textile Inst. 63, 217-221 (1974).

12.

Love, A.E.H. , A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press, Cambridge, 1952 , p. 414.

13.

Ly, N.G. , and Denby, E.F. , Bending Strains in a Sharp Fabric Crease, Textile Res. J. 53, 571-573 (1983).

14.

Mitchell, T.W. , and Feughelman, M. , Set in Bending of Single Wool Fibers, Textile Res. J. 35, 88-89 (1965).

15.

Robinson, M. S., private communication.

16.

Schapery, R.A. , Viscoelastic Behavior and Analysis of Composite Materials, in "Mechanics of Composite Materials," vol. 2, G. P. Sendeckyj , Ed., Academic Press, New York, 1974, pp. 85-168.