Three-dimensional wrapping of stiff elastic belts around rollers

This research is concerned with quasi-static confgurations of axially moving materials helically wrapped onto cylindrical rollers. An elastic beam/rod model is built based on Antman's theory for a slender elastic body. The rod is subject to end forces and moments so that a central portion of it contacts a cylinder; the outer regions are free from external kinematic constraints. The location of the departure point (or contact point) and the configurations of both the contacting and non-contacting parts depend on the end loads.;Such systems arise in the material handling and processing operations in which axially moving continua are transported over pulleys. Most material processing occurs in a plane to which the guiding roller axes are perpendicular. The travel direction is only changed by altering the wrap angle around a roller. However, due to conditions such as space limitation, it is often necessary to have material move out of this process plane. This is accomplished by a device called a turn-bar. A turn-bar is a non-rotating roller whose axis is not perpendicular to the process plane and causes material wrapped around it to move out of the process plane.;Since the equilibrium equations governing the constrained and unconstrained parts are different, it is critical to find the departure point, across which matching conditions are satisfied. Numerical integration and a shooting method are used to solve this boundary value problem. Flexible materials with both circular and rectangular cross sections are investigated. Three-dimensional rod configurations subject to various system parameters are presented. The effect of anisotropy on the wrap angle, wrap length, reaction force and torque is also analyzed.;One-dimensional beam models can adequately describe the response in cases where the material does not have considerable thickness or width (e.g. thread, tape, rope, and cable). For an axially moving material whose width is much greater than the thickness, two-dimensional plate or shell theories have to be consulted. The equilibrium results obtained in this study can be used as a center-line location to build higher-order beam models which are expected to be able to capture some width dependant behaviors.