A typical continuous web-processing machine consists of hundreds of idle rollers and web spans. A web span is formed by tensioning a thin film (the web) over at least two idle rollers. Machine drive controls, bearing friction, and air impingement on the web surface represent some of the factors that can influence web tension and web speed. A significant effort is devoted to maintaining uniform web tension and web speed in these machines. The uniformity of these parameters is a requirement to consistently manufacture web products within rigorous quality specifications. In support of this effort to control web tension and web speed, reports have been published to investigate the vibration response of the web-idle roller system. The machine is modeled as a multidegree-of-freedom system consisting of numerous springs and masses connected in series. The equivalent spring and mass elements are represented by the web span and roller inertia respectively. The scope of this investigation is limited to the analysis of the axial vibration of a single web span and idle roller interface. The two main objectives of this work are to characterize the axial vibration response of a single web span and numerically determine axial displacements of the web. A correlation is made between the axial displacement (less than 0.05 inch) of the web relative to the surface of an idle roller and small scratches (0.005-0.010 inch long) formed on the surface of the web. The web is assumed to be an elastic member subject to tensile forces only. The one-dimensional wave equation is shown to be the governing equation of motion for the web-idle roller system. Boundary conditions are developed to accommodate the web-idle roller interface at one end of the web and the input tension force at the opposite end. A simplifying assumption of the model is that the average web speed is zero. The effect of zero average web speed is assumed to be small because the wave speed is nearly 1000 times greater than the typical average web conveyance speed of 250 feet per minute. Three solution methods have been presented for the wave equation (Separation of Variables, Laplace Transform combined with Inverse Fast Fourier Transform, and Galerkin Finite Element). The Finite Element method, written in a spreadsheet software format, was found to be the best method of solution for this partial differential equation.
Library of Congress Subject Headings
Rolling contact--Mathematical models; Vibration--Control--Mathematical models; Automatic control--Mathematical models
Department, Program, or Center
Mechanical Engineering (KGCOE)
Bomba, Richard, "On axial vibration of a web-idle roller system" (1990). Thesis. Rochester Institute of Technology. Accessed from
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