Contrasting the Predictions for Coulomb and Creep-Rate-Dependent Friction in the Modeling of Fiber-Draw Processes

Abstract

One of the most important features in industrial fiber-drawing processes is the friction between filament tow and draw rollers, because it is what creates the tension in the fiber that performs the draw. To understand fiber draw, therefore, it would be valuable to examine the sensitivity of model predictions to the choice of the idealization of the friction incorporated in the model. This paper begins the comparative study by deriving and solving models for fiber draw, which for the first time study the friction between filament tow and draw rollers as something other than Coulomb friction, namely creep-rate-dependent friction. Sensitivity of the draw model to the choice of friction idealization is investigated by contrasting process simulations employing the usual Coulomb model for friction with simulations of the same processes employing the creep-rate-dependent friction model. It is demonstrated that the draw-model predictions of fiber behavior depend both qualitatively and quantitatively on the specific idealization of the friction between filament and rollers. For example, whereas the Coulomb friction model predicts adhesion zones on the rollers, in which the fibers and roller move together with no slip, there are strictly no adhesion zones with the creep-rate-dependent friction model, although with a choice of processing parameters the predicted relative velocity between fiber and roller can be made arbitrarily small. With the creep-rate-dependent friction model the fiber speed at the point of attachment to the draw roller must be greater than the roller surface speed for the equations of momentum to be satisfied. This small, but finite, abrupt change in speed profile can be interpreted as the formation of a neck in the fiber just upstream of the point of attachment to the roller.