W. B. Fraser

The Effect of Yarn Elasticity on an Unwinding Balloon

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.

Effect of Yarn Non-Uniformity on the Stability of the Ring-Spinning Balloon

This paper extends the results of W. B. Fraser and D. M. Stump on the stability of a ballooning yarn of uniform mass linear density to allow for non-uniformities in the yarn. A two-variable perturbation expansion procedure (two-timing ) is used to show that the effect of a slub (defined as a thick place or lump in a thread) on the stability of the ring-spinning balloon can be analysed as a sequence of quasistationary balloons for yarn of variable mass linear density as the slub travels slowly through the rapidly rotating balloon. The slub is modelled by the addition of a mass linear density term, in the shape of a gaussian or cosine distribution function, to the uniform mass linear density. Computational results are given for a ring spindle and yarn combination with representative geometry, air drag, and frictional parameters. These results show that even a slub that in practice would be considered quite small can have a significant effect on the stability of the yarn balloon. The results in this paper show how such effects can be quantified.

Air Drag and Friction in the Two-for-One Twister: Results from the Theory

A computational model of the two-for-one twister based on the mathematical model described in an earlier paper by the author is used to explore the effects of air-drag and balloon-limiter frictional drag on yarn tension in the balloon. As is to be expected, it is found that increasing the air drag or the frictional drag increases the yarn tension in both the free and the controlled balloon. However, the interaction between air drag and frictional drag is complex, and an increase in air drag may sometimes he compensated for by a decrease in frictional drag. The physics of free-balloon twister operation predicted by this model are highly non-linear, and concepts and terminology from bifurcation theory are introduced and explained in order to describe the behaviour of the free-balloon solutions concisely. The graph of dimensionless guide-eye tension against storage-cylinder radius exhibits a typical hysteresis bifurcation that unfolds as the air-drag parameter is increased. The effect of the balloon-limiter ...

Twist in Balanced-ply Structures

The theory of the bending and twisting of thin rods of uniform circular cross-section, and inextensible centre-line, is used to find an equation for the pretwist that must be inserted into the singles strands to create a balanced two-ply yarn of specified ply twist. In the final section, this result is extended to an N-ply structure.

The Effect of a Slub on the Stability of the Ring-spinning Balloon

In a recent paper, the authors have described a computational model for investigating the effect of a heavy slub passing through a ring-spinning balloon. In that paper, the additional mass in the slub was modeled by a gaussian-distribution function which allowed the total mass and length of the slub to be represented by two independent variables, Q and σ, respectively. Some limited results for a freely ballooning yarn were given. In this paper, the model of the previous paper is extended to allow for the effect of a control ring at the mid-balloon height, and a more extensive investigation of the solution space of the model is presented. It is shown that the effect of the control ring is greatly to extend the range of traveler-mass-parameter values over which the balloons are stable and, furthermore, the lower limit of these values is remarkably insensitive for a range of slubs with a total additional mass of up to 400%.

Torsional properties of staple fibre plied yarns

A mathematical analysis of the mechanical governing equations applying to the torsional behaviour of multi-ply yarns under tension has been carried out. This analysis clearly shows that there are two components, a geometric component that determines the slope or gradient of the torque due to tension and a component that determines the yarn torque at zero applied tension (intrinsic torque) that depends on the fibre number, fibre moduli and diameter as well as the strand structural geometry. The effect of the ratio of the ply twist to the spinning twist on the two components of yarn torque has been numerically analysed for two-, three- and four-ply yarns prepared from singles 31 yarns spun with different spinning twists and for two different fibre diameters. Other comparisons are made for two-ply yarns prepared from 40 and 80 tex singles yarn. The model allows the effects of the various yarn and fibre parameters to be assessed and compared with experimental data. Experimental torque data for a range of two-ply yarns plied at different percentages of the singles spinning twist and also with different yarn histories and test environments are consistent with the trends identified by the model.

Stationary solution of the ring-spinning balloon in zero air drag using a RBFN based mesh-free method

A technique for numerical analysis of the dynamics of the ring-spinning balloon based on radial basis function networks (RBFNs) is presented in this paper. This method uses a ‘universal approximator’ based on neural network methodology to solve the differential governing equations which are derived from the conditions of the dynamic equilibrium of the yarn to determine the shape of the yarn balloon. The method needs only a coarse finite number of collocation points without any finite element-type discretisation of the domain and its boundary for numerical solution of the governing differential equations. This paper will report a first assessment of the validity and efficiency of the present mesh-less method in predicting the balloon shape across a wide range of spinning conditions.

Ultrasound intensity calculations for a vessel with simulated wall lesion

Vascular disease alters the shape of the lumen of a blood vessel. The lumen is not circular from the early stages of the disease, where there is intimal thickening, through to advanced stages where a large plaque may protrude into the lumen. Using a mathematical model we investigated the ultrasound intensity distribution, both within the vessel wall and across the lumen, in the presence of a simulated wall lesion. Acoustic impedance interfaces due to wall lesions have dimensions (typically /spl sim/ 1 mm) only slightly greater than the wavelength (/spl sim/ 0.3 mm for 5 MHz ultrasound). Full wave solutions for the acoustic field are therefore required. Exact solutions in terms of Bessel functions are known for the case of a cylindrical vessel, and a collocation method based on this was developed for non-circular interfaces. By considering two such interfaces we developed a novel model representation of a vessel with a simulated wall lesion. The results of this study show how vessel wall properties may alter the ultrasound intensity distribution within the vessel wall and across the lumen. In the case of non-circular impedance interfaces there can be significant effects due to the local curvature and orientation of the interface.

The effect of yarn elasticity on the stability of the two‐for‐one twister balloon

The two‐for‐one twister balloon is a yarn‐twisting device widely used in the textile yarn manufacturing industry. Previous papers have investigated a mathematical dynamical model for the stability of the motion of an inextensible yarn in this machine. In this paper, we investigate the effect of yarn elasticity on this model. The unfolding of the inextensible yarn bifurcation curves as the elasticity of the yarn is increased exhibits some interesting behaviours.