A polyester filament winding spindle is the most complex winding rotor system, due to its high speed, heavy load, and frequency-dependent parameters; furthermore, the spindle's rotating speed constantly changes and it is continually crossing the critical speed points. This paper presents an approach to establish the finite element model of the winding spindle to predict its dynamic behavior characteristics during start-up. Firstly, three finite element models of the discrete single component were developed based on the Timoshenko beam theory. The bending, transverse shear effect, and gyroscopic moment were considered in these models. The flexible supporting system, which consists of a deep groove ball bearing and several rubber O-rings, is simplified by a nonlinear spring and damper. Its frequency-dependent dynamic supporting parameters are identified by experiment. Secondly, a fully dynamic model of the polyester winding spindle system, which consists of the cantilever supporting arm, shaft, and sleeve, as well as the flexible and rigid coupling elements, was established. Thirdly, the Newmark method was used to develop a program for solving the dynamic equations of the spindle system in MATLAB®. Based on the model of the spindle system and the computation program, the effects of the supporting stiffness, damping, and start-up time on the spindle's unbalanced response were investigated. The results indicate that the model of the spindle system presented in this paper is suitable for the prediction of the dynamic performance during its start-up.

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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.

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