Abstract
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 is presented. 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 analysed with a string theory. The boundary-layer analysis provides a description for the cohesive forces that hold the yarn windings in the package.
In most situations the motion of the unwind point forwards and backwards over the package is much longer than the rotational time of the balloon about the package axis, and a two-timing analysis is used to simulate this process as a series of quasi-stationary yarn balloons. The motion of the unwind point is shown to be asymmetrical with respect to its direction of motion on the package surface, which is in qualitative agreement with experimental measurements.
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Clark, J., Fraser, W. & Stump, D. Modelling of tension in yarn package unwinding. Journal of Engineering Mathematics 40, 59–75 (2001). https://doi.org/10.1023/A:1017525804392
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DOI: https://doi.org/10.1023/A:1017525804392