A Model for Predicting Set in Helices

Abstract

A model is developed to calculate the residual set in a helical fiber axis after it has been wrapped around a mandrel, set into this shape, and released. The theory used is linear viscoelasticity in conjunction with the bending and twisting equations for thin rods. The model may be applied equally well to calculate the snarling behavior of twisted yams. An example of this is presented to confirm predictions made by the model. Two cases in the setting of helices are analyzed. In the first case the released helix is not in contact with the mandrel. In this case the bending and torsional set in the helical fiber axis follows quite simply from principles of linear viscoelasticity. In the second case, the released helix is constrained to lie on the surface of the mandrel. Results of this second case are more complex, but have been computed and presented in tabular form.