Mechanical Properties of a Migrating Fiber

A mathematical model of a helix with variable radius is developed to analyze geo metric and mechanical properties of a migrating fiber. The factors concerned include the frequency and amplitude of fiber migration as well as the equivalent radial position and equivalent helix height of the fiber. This treatment permits the application of experimentally 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 functions of the length of the helix axis. A critical migration amplitude is identified where the axial component of the couple and trans verse component of the force change their direction. The implication of these behaviors for yam properties such as total yam torque and local pressure distribution is also revealed. Cylindrical and sinuous helices are compared, with the effects of the amplitude and frequency of fiber migration quantitatively determined.