Dynamic Stability Analysis of High Speed Axially Moving Bands With End Curvatures

Measurements of vibration on continuous bands driven by rotating wheels show that the end curvature of the spans can greatly affect the system dynamic characteristics [1,2]. Significant error in the predicted response of a span can occur if the end curvature is neglected. To understand the global dynamic behavior of such systems under high speed operating conditions, a nonlinear model of axially moving bands with finite end curvatures is developed and analyzed in this paper. It is shown that a pitch-fork bifurcation from the trivial equilibrium state will occur at the critical speed of a perfectly straight, axially moving band and the original trivial equilibrium configuration will become unstable. However, for bands with finite end curvatures, the classical critical speed theory does not apply. The equilibrium configuration will continuously change with increasing band speed, but will remain stable. Multiple equilibrium states will occur at sufficiently high band speed, and the minimum speed for this phenomenon to happen increases with the end curvature of the band. Large oscillation coupling the multiple equilibrium states will be induced by large enough initial disturbance. The disturbance required for this to occur varies with the band end curvature and transport speed. The study provides us with new insight and guidelines toward optimizing this class of high speed mechanical systems.