High Speed Stability of Coupled Band/Wheel Systems: Theory and Experiment

Abstract

A theoretical model is derived that describes the planar, non-linear response of a continuous band circulating about two rotating wheels. A closed form analysis of the non-linear steady response leads to elliptic integral solutions for the equilibrium band geometry and tension. These solutions, which are evaluated over a wide range of band/wheel designs, are also used to evaluate the extent of band/wheel contact and the effect of self-equilibriating wheel torques. The equations of motion are linearized about the equilibrium solution, and equilibrium stability and the free linear response are predicted from a discretized model. Results of a companion experimental study support theoretical predictions of steady and dynamic response. In particular, results indicate that band/wheel systems maintain stability at high translation speeds.