Previous investigators of the theory of balloon formation in over-end unwinding of yarn from cylindrical packages have made the simplifying assumption that the yarn is inextensible. In this paper, the balloon equations for a linear elastic yarn are derived, and numerical solutions of these equations for small values of the elastic parameter are presented. It is concluded that the inclusion of elasticity in the theoretical model leads to a decrease in the tension in the balloon and a decrease in the balloon radius. However, for the range of elastic parameters encountered in real yarns, this effect is very slight.
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W. B. Fraser (1992) studied this question.
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