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Modelling of tension in yarn package unwinding. (English) Zbl 0998.74043

From the summary: We present an improved theory for the variation of yarn tension during high speed over-end unwinding from cylindrical yarn packages based upon the theory of bent and twisted elastic rods. A singular perturbation analysis is used to show that the effects of bending and twisting stiffnesses are confined to a boundary layer in the neighbourhood of the unwind point while, over most of the yarn path, the yarn motion can be analyzed with a string theory. The boundary-layer analysis provides a description for the cohesive forces that hold the yarn windings in the package.

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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