An analytical approach of filament bundle swinging dynamics, Part I: Modeling filament bundle by ANCF

A filament bundle is a kind of filament assembly with less twist or nontwist. It is a viscoelastic body and has a large aspect ratio. Its large deformation during motion over a wide range is a universal phenomenon in many textile processes. The dynamic viscoelasticity of the filament bundle, gravity, and air resistance are three important factors affecting the filament bundle's dynamic behavior. Taking account of these factors, a filament bundle dynamics analysis method is proposed in a series of three papers. This paper, the first in the series, presents an approach to model the dynamics of the flexible filament bundle with viscoelasticity and to analyze its dynamic behavior under the action of gravity and air resistance. The filament bundle element (FBE) is established based on absolute nodal coordinate formulation (ANCF), in which slope vectors and global coordinates are applied. The approach presented in this paper is well suited for the analysis of large deformation motions of filament bundles. As an example, a dynamic model was established to predict the filament bundle's trace during its swinging through large displacements under the action of gravity and air resistance, taking into account the filament bundle viscosity. The nonlinear differential equations of the filament bundle system were solved using MATLAB. Furthermore, the swing traces of the filament bundle in a closed Plexiglas box with different vacuum degrees were recorded using a high-speed camera to prove the validity of the established filament bundle model based on ANCF.