Stretching and Slipping of Fibers in Isothermal Draw Processes

Abstract

We model the drawing of fibers and films on a roller with equations of motion in which centrifugal acceleration and acceleration due to stretching are retained in the momentum equations. An important distinction is that our new solution fundamentally couples fiber tension to fiber stretch, in contrast to all existing solutions, which either neglect stretching acceleration or neglect both centrifugal acceleration and stretching acceleration. We find that the tension and draw ratios between the point of exit to the point of attachment of fibers with the roller depend on three nondimensional parameters. For certain values of these parameters, the exact solution can be approximated either by the quasistatic solution. neglecting both acceleration terms in the momentum equation, or by the solution including only the centrifugal acceleration. The quasistatic approximation underpredicts the tension magnification and draw ratio when the stiffness k of the fibers is less than the initial tension T _o, and overpredicts when k is greater than T_o. The solution including only centrifugal acceleration always underpredicts tension magnification and the amount of draw.