This dissertation addresses several open problems in the modeling of industrial polymeric fiber manufacturing processes. In melt spinning, the molten polymer is extruded through a spinneret, from which it emerges as many molten fibers. Then the molten fibers are then exposed to quench air, which cools and solidifies the polymer. After spinning, the solidified polymer fiber is called an "undrawn" or "as-spun" fiber. Undrawn fibers exhibit unsatisfactory mechanical characteristics for use in textiles and as structural reinforcement. To remove this unsatisfactory mechanical characteristic, the as-spun fiber undergoes an additional process in which it is drawn.
With the help of empirical studies, polymer fibers have been manufactured for many years without a deep investigation of the underlying physical nature of the spinning and drawing processes. As the requirements placed on polymer fibers have increased and quality control has become more important, the necessity of studying the theoretical fundamentals of polymer fiber spinning and drawing has grown. My Ph.D. research has sought to improve the modeling capability in both the spinning and drawing processes of polymer fiber manufacture.
This dissertation creates a fiber-air interaction model incorporating the influence of temperature change in the density of quench air, a feature which has not been modeled in previous research. Neglecting the temperature change of quench air and the resulting density change in the quench air results in an underestimation the variation of fiber behavior through the fiber bundle. In addition, the fiber-air interaction model of this dissertation for the first time incorporates momentum conservation, which enables the model to deduce the boundary layer volume flow rate entrained by each fiber from first principles rather than an empirical formula. This removal of empiricism means fewer experiments are needed to model the fiber-air interaction. A single fiber spinning model incorporating the temperature-dependent density is presented in this dissertation. In addition, the model incorporates the radial variation of temperature and pressure throughout the entire model. The new melt-spinning model predicts delayed cooling and stretching of the fiber, and a lower maximum tensile stress than does the conventional theory. As a preliminary modeling of the drawing process, this dissertation developed the fundamental governing equations for a fiber moving and wrapped on a pulley. The conservation of momentum gives a generalized capstan formula, which takes the inertia of the fiber into account. The model is applied to solve the torque transmission problem of a belt connection two pulleys.