An analytical approach of filament bundle swinging dynamics, Part II: identifying equivalent dynamic constitutive parameters of filament bundles

Abstract

A filament bundle is a type of yarn, which is composed of nearly parallel and highly oriented polymer monofilaments. Due to its nonlinearity both in material constitutive properties and structure, the filament bundle possesses nonlinear viscoelastic properties. It is important to study the dynamic behavior of the filament bundle accurately during its high-speed movement. Therefore, an accurate expression of the constitutive relation of the filament bundle is an essential prerequisite for its dynamic simulation and analysis. Continued the previous study in Part I: modeling filament bundle method, in this paper, an approach was proposed to identify the equivalent dynamic constitutive parameters of the filament bundle considering frequency-dependent characteristics. Firstly, the identification formulas of the dynamic elastic modulus and viscoelastic coefficients were derived based on the Kelvin model. Then, a testing method of the cross-sectional parameters of the filament bundle under a certain tension was proposed, and the testing device was developed to obtain the area of the filament bundle; The dynamic loading test of the bundle filament was conducted in a DMA Q800 dynamic mechanical tester. Thirdly, the equivalent dynamic elastic modulus and viscoelastic coefficients were obtained through the experimental test. Finally, an analytical method was proposed to verify the correctness of experimental results through simulation. The results show that the excitation frequency has a significant influence on the dynamic elastic modulus and viscoelastic coefficient, and the curves of the equivalent dynamic elastic modulus and viscoelastic coefficient present nonlinear variation characteristics.

Active tension control of the conical winding system based on the neural network control algorithm of radial-basis functions

“…Yarn is a viscoelastic material with the elastic and damping characteristics of ordinary solids. The Kelvin model, 29 widely used in viscoelastic theory, is composed of Hook spring and Newton damping in parallel (see Figure 4). It can better describe the relationship between yarn deformations and tensions during rapid stretching.…”

Dynamic behavior analysis of the winding system during filament reversing pushed by the traverse mechanism

“…where A f is the cross-sectional area of the filament bundle, and A f ¼ pd 2 =4; J is the moment of inertia of the filament bundle; E l is the tensile modulus of the filament, and the value is obtained from the literature. 25 Here, U vis is the viscosity dissipated energy, and it can be written as…”

“…However, due to calculation errors and other factors during the numerical solution, the position and speed constraints of the system will be violated, leading to the divergence or instability of numerical calculations. Therefore, the numerical solutions violating constraint equations were corrected by Baumgarte’s modification approach during the integration procedure, which is to form a closed-loop system of the constraint equations 25 where α and β are feedback control coefficients.…”