MECHANICAL-PROPERTIES OF A MIGRATING FIBER

A mathematical model of a helix with variable radius is developed to a nalyze geometric and mechanical properties of a migrating fiber. The f actors concerned include the frequency and amplitude of fiber migratio n as well as the equivalent radial position and equivalent helix heigh t of the fiber. This treatment permits the application of experimental ly determined migration patterns defined by those factors. The derived properties are the curvature and torsion components of the migrating fibers, bending moments, torque, strain energy distribution, and total strain energy. The terminal force and couple are calculated as functi ons of the length of the helix axis. A critical migration amplitude is identified where the axial component of the couple and transverse com ponent of the force change their direction. The implication of these b ehaviors for yarn properties such as total yarn torque and local press ure distribution is also revealed. Cylindrical and sinuous helices are compared, with the effects of the amplitude and frequency of fiber mi gration quantitatively determined.