Abstract
A theory for the twist-induced localised snarling instability observed in whirling and transported yarn in textile manufacturing processes such as false-twisting is developed. The buckling of the yarn can occur in two modes. At a critical level of the tension the straight yarn path bifurcates to a whirling ballooning mode. The localised snarling bifurcation can be triggered either from the straight line path prior to whirling or from the post-whirling configuration depending on the transport speed of the yarn through the system. The yarn is modelled as a pre-tensioned elastic rod. A perturbation analysis is carried out in which the small parameter measures bending relative to dynamical forces. The whirling bifurcation is captured with a regular perturbation analysis and the snarling bifurcation is captured with an internal bending layer in a singular perturbation analysis. This localised snarling is a subcritical bifurcation that occurs at a critical combination of yarn torque and tension. Critical conditions, as well as the position along the yarn where the snarling instability occurs, are obtained by matching the internal layer to the outer solutions. To accomplish this matching yarn axial elasticity is essential.
Similar content being viewed by others
References
Hearle JWS, Hollick L, Wilson DK (2001) Yarn texturing technology. Woodhead Publishing Ltd., UK, and CRC Press LLC, USA
Thompson JMT, van der Heijden GHM, Neukirch S (2002). Supercoiling of DNA plasmids: mechanics of the generalized ply. Proc R Soc Lond A 458: 959–985
Neukirch S, van der Heijden GHM (2002). Geometry and mechanics of uniform n-plies: from engineering ropes to biological filaments. J Elasticity 69: 41–72
Kevorkian J and Cole JD (1981). Perturbation methods in applied mathematics. Springer-Verlag, NY
Krause HW, Soliman HA and Tian JL (1991). Untersuchung zur Festigkeit des Spinndreiecks beim Ringspinnen. Melliand Text ilberiche 72: 449–504
Thwaites JJ (1978). The dynamics of the false-twist process. Part I: the process surveyed. J Text Inst 69: 269–275
Fraser WB and Stump DM (1998). Yarn twist in the ring-spinning balloon. Proc R Soc Lond A 454: 707–723
Zhu F, Sharma R and Rahn CD (1997). Vibrations of ballooning elastic strings. J Appl Mech 64: 676–683
Miao M and Chen R (1993). Yarn twisting dynamics. Text Res J 63: 150–158
Coyne J (1990). Analysis of the formation and elimination of loops in twisted cable. IEEE J Oceanic Eng 15: 72–83
van der Heijden GHM, Thompson JMT (2000). Helical and localised buckling in twisted rods: A unified analysis of the symmetric case. Nonlinear Dynam 21: 71–99
Timoshenko S and Young DH (1962). Elements of strength of materials 4th edn. D. van Nostrand, Princeton, NJ
Bennett JM and Postle R (1979). A study of yarn torque and its dependence on the distribution of fibre tensile stress in the yarn Part II: experimental. J Text Inst 70: 133–141
Tandon SK, Sim SJ and Choi KF (1995). The torsional behaviour of singles yarns Part II: evaluation. J Text Inst 86: 200–217
Love AEH (1927) A treatise on the mathematical theory of elasticity, 4th edn. Cambridge University Press
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fraser, W.B., van der Heijden, G.H.M. On the theory of localised snarling instabilities in false-twist yarn processes. J Eng Math 61, 81–95 (2008). https://doi.org/10.1007/s10665-007-9180-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10665-007-9180-4