An Application of Queuing Theory to Modeling of Melange Yarns Part I: A Queuing Model of Melange Yarn Structure

Abstract

Yarn structure is one of the important characteristics which define yarn mechanical properties and appearance. For example, it is known that the mechanical properties of a ring-spun and an open-end spun yarn of the same linear density and produced from the same fibers are different [1,2]. This is caused by the difference in their internal structure, which can be characterized by the cross-sectional and longitudinal distribution of fibers.A staple fiber yarn is composed of short-length fibers which are assembled and twisted together. Fibers start at different distances from the beginning of the yarn. The radial positions of fibers within the yarn body change randomly (with unknown probability distribution) along the yarn axis. 1 This behavior is known as fiber migration. Fiber migration is now a universally recognized phenomenon of yarn structure which provides necessary entanglement and cohesion between the fibers, thus creating a continuous structure devised from a discrete set of fibers. This dual nature of the structure of a staple fiber yarn makes it difficult to be modeled. Theoretical and experimental investigations of structure-properties relationship of yarns conducted over Abstract A queuing model of staple fiber yarn is presented that enables the modeling and a better understanding of fiber migration in a yarn. The model provides a fine yarn structure where the migrational behavior of fibers is associated with the behavior of customers traveling across an open network of queuing systems to get services. Based on this analogy, the underlying mathematical foundation of the queuing theory is used for the modeling of yarn structure and properties. The model uses yarn technical specifications including yarn linear density and twist level, fiber linear density and length distribution, together with specific parameters such as fiber packing density distribution and migration probabilities. The model can be used for modeling a wide range of structurally different yarns; examples include marl, mottle and melange yarns, yarns with different levels of hairiness, and yarns produced by various spinning systems. The model can be used for 3D simulation of yarns in computer-aided design systems for textile design and for the prediction of mechanical properties of yarns.

Predicting the number of fiber roots in lola drafting based on multi-field coupling

“…To establish the model of a strip when being pulled more intuitively, we introduce ring zones. 15,16 Assuming that the cross section of an undrafted cotton strip is a circle, we divided it into concentric circular areas, called ring zones, of different sizes. A schematic diagram of the ring zones is shown in Figure 1.…”

An extended virtual location method for yarn cross-section construction

“…It has been developed by Grishanov et al (1997), and has been applied to generate the structure of the yarn cross-section (Grishanov, Siewe, & Cassidy, 2011;Siewe, Grishanov, Cassidy, & Banyard, 2009;Sriprateep & Bohez, 2006). "VL" stands for a cell in a yarn cross-section which might be occupied by a fiber.…”

Advances in the CAD Simulation of Textile Yarns

“…Based on these probabilities, the dynamics of the network is modelled by a number of equations that are detailed in Baskett et al (1975). The following sections explain how this theory was used in Siewe et al (2009) to model the structure of melange yarns.…”

“…The yarn structure formed in this way is considered to be continuous so that there are infinitely many fibres involved. Using these assumptions, the staple fibre yarn structure was modelled as a Jackson open network of queuing systems where each queuing system represents one virtual location (Siewe et al, 2009). Figure 9 shows a simplified model for a yarn with three ring zones.…”