A nonlinear dynamic model for periodic motion of slender threadline structures

Moving slender threadline structures are widely used in various engineering fields. The dynamics of these systems is sometimes time dependent but in most cases follows a periodic pattern, and slender yarn motion in textile engineering is a typical problem of this category. In the present paper, we propose a nonlinear approach to model the dynamic behavior of slender threadline structures with a real example in the analysis of slender yarn motion in spinning. Moving boundary conditions of yarn are derived and a consequence of the perturbation analysis for the dimensionless governing equations provides the zero order approximate equation of motion to remove the time dependence. Consequently, the time dependent problem can be solved by approximate solutions of steady-state governing equations subject to the derived moving boundary conditions. The simulation results are more accurate than the results by earlier work and show good agreement with measurement data. The proposed modeling and perturbation approximation procedure is thus an accurate and practical way to deal with periodical motion of a category of slender threadline structures.