Numerical Analysis of Fiber Fleece Behavior in Roller Drafting in a Transient State

Abstract

Fiber bundle thickness irregularity from a roll draft mechanism was analyzed in the time domain on the basis of a theoretical model (Partial Differential Equation, PDE, system) for bundle flow. As the governing equations that consisted of continuity and motion equations turned out to be nonlinear, being coupled between variables, etc., a numerical method was established to solve the problem. In particular, the Forward-Time Central-Space (FTCS) difference formula with an explicit Euler scheme as the Finite Difference Method (FDM) was applied. Then the system of equations, which were in algebraic form, was solved according to given initial and boundary conditions in an iterative fashion. Results from this research confirmed that the theoretical response of the output linear density to the disturbance of drafting condition agreed very well with experiment. The transient state of the velocity profile faded out more quickly than that of the linear density profile. The response of the output bundle thickness to the step change perturbation depended on process conditions or material properties. With certain model parameters, the disturbed linear density of the output sliver converged to a fixed value or had an increasing variation magnitude. This indicated that the characteristics of the output bundle thickness could change according to the bundle properties or to the process conditions, which could induce unstable changes in thickness.