Development of a Mathematical Model of an Un-coiling Idle Coiling Process Including an Effective Tension Model for Slip Behavior Among Contact Layers

Abstract

Mathematical model of an Un-Coiling Idle Coiling (UCIC) process has been used to estimate strip tension T and has combined with a controller to operate the UCIC system because T should be applied to a strip of the UCIC system to coil the strip uniformly. This paper suggests an advanced mathematical model of the UCIC process based on the previous model for winding a web to increase accuracy for estimating T. To conduct numerical integration of structural dynamics equations; the suggested model consists of equations of motion and state variable equations. Geometrical variations including radius of the coil r, eccentricity of the coil lecc, and effective strip tension Teff with slip behavior among contact layers are renewed automatically in numerical analysis. The suggested model contains real operating conditions and design variables, and is calculated by Newmark's method to get dynamics responses. Moreover, planar motions are defined in the equations of the motion to check how T and dynamics responses of the un-coiler, the pinch roller, and the coiler affect each other. The planar motions have translational motions by applying spring stiffness k x and k y on the center of the rotor that correspond to elastic deformation of a bearing and a shaft. Using the suggested model, T and unusual vibrations that are caused by improper coiling conditions are predicted quickly compared to a Finite Element (FE) model. Especially, Teff is similar to real T profile compared to the previous tension model when two tension models are validated with the FE model of the UCIC process.