Air-drag on a ballooning yarn and balloon shape affect the yarn tension and ends-down (yarn breakage), which in turn affects energy consumption and yarn productivity in ring spinning. In this article, a mathematical model of yarn ballooning motion in ring spinning is established. The model can be used to generate balloon shape and predict tension in the ballooning yarn under given spinning conditions. Yarn tension was measured using a computer data acquisition system and the balloon shapes were captured using a digital camera with video capability during the experiments using cotton and wool yarns at various balloon-heights and with varying yarn-length in the balloon. The air-drag coefficients on ballooning cotton and wool yarns in ring spinning were estimated by making a "best fit" between the theoretical and experimental turning points. The theoretical results were verified with experimental data. The effects of air-drag and balloon shape on yarn tension are discussed.

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An orthogonality relation for the Rayleigh-Lamb modes of vibration of an isotropic, homogeneous, elastic plate is derived. Subject Classification: [43]40.24.

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The large deflection theory of circular cross-section elastic rods is used to consider the writhing of long straight rods subjected to tension and torque, such as undersea cables, and to closed loops with inserted twist, such as DNA supercoils.The writhed shape of the long straight rod under tension and torque is easily generated by twisting a piece of string with the fingers and consists of three separate parts: a balanced-ply region, a free end loop, and two tail regions. The solution for the rod shape in each of the regions is found. The results are then joined together to ensure continuity of the position and tangent vectors of the strand centreline through the introduction of point forces and moments at the points where the strands enter and exit the balanced ply. The results of the model are consistent with simple experiments on long braided rope.The writhed shape of the closed loop with twist inserted between the ends prior to closure is modelled as a balanced ply joined to two end loops. The analysis combines the mechanics solution with the conservation of topological link to provide a simple formula which quantitatively predicts the approximate shape and helix angle of the supercoil. The results are in good agreement with simple experiments on rope and with available data on DNA supercoils.

The over-end unwinding of yarn from a stationary helically wound cylindrical package is considered. The motion of the yarn between the unwind point (where it first starts to slip across the package surface before flying into the unwinding balloon) and the guide eye located on the package axis is analysed. The motion is periodic as the unwind point moves backwards and forwards along the length of the package surface. In 1958 D. G. Padfield argued that, provided the helix angle is small, the time derivative terms in the equations of motion can be neglected and the problem can be reduced to a stationary (relative to rotating axes) balloon problem subject to a modified boundary condition at the unwind point. The problem of yarn slipping across the package surface has also been investigated by D. G. Padfield and by H. V. Booth. In the present paper a regular perturbation expansion is used to provide a theoretical framework for Padfield’s ideas and to remove the time dependence from the zero order equations of motion. To this order of approximation the time dependence appears in the ‘moving’ boundary condition at the unwind point. A new derivation of this boundary condition is given and a set of continuity conditions between the yarn slipping on the package and the yarn in the balloon is used to splice the two solutions together so that the package can be unwound through a complete period of the unwinding cycle.

Rotating yarn loops, which are called yarn balloons in the textile industry, play an important role in establishing yarn tension in textile yarn-manufacturing processes such as ring spinning and two-for-one twisting. Recent theoretical work has brought the computational simulation of these processes to a high degree of refinement.In this paper, a simple experimental system, consisting of a loop of yarn rotating about a fixed axis, without twist insertion, is described. This system exhibits a rich variety of bifurcation behaviours as the length of yarn in the loop is varied.It is shown that the theoretical bifurcation curves (which plot guide-eye tension versus the unstretched yarn length in the rotating loop) can be fitted to the experimentally obtained curves by an appropriate choice for the value of the air-drag parameter. For the almost inextensible yarns considered here, the value of the elasticity parameter has only a very slight effect on the theoretical results.In particular it is shown that the 'fluttering' oscillations of the experimental balloons, corresponding to certain sections of the experimental bifurcation curve, can be identified with the limit-cycle behaviour of the theoretical balloons between Hopf bifurcation points on the theoretical bifurcation curve.