Deflection curves of an elastic strip under tension and friction forces

Abstract

The purpose of this thesis is to develop the deflection curves resulting when a succession of forces and moments are applied to a semi-infinite beam which is under tension, and where displacement is resisted by distributed friction loads. The problem applies to the study of web guidance, which is concerned with accurately passing long strips over a series of rollers. The area studied in this thesis can be interpreted as the region of contact between the strip and a roller. The exact, general solution to the problem consists of an infinite number of waves, but a closed form solution is impossible. A method is described for calculating a solution accurate to any given number of waves. This method is demonstrated, the two wave and one wave approximations being developed as examples. A Fortran program is provided, which uses the one wave approximation to generate deflection curves in tabular form. This program may be incorporated as a subroutine into a larger program to provide a precise computer simulation of an entire rolling strip system.