THREE DIMENSIONAL THEORY AND ANALYSIS OF TRAVELLING SAGGED CABLE DYNAMICS.

摘要

The purpose of this investigation is to predict the three dimensional response and stability of a single span travelling cable having arbitrary equilibrium sag and arbitrary support inclination. The investigation applies to common translating systems such as ski lifts, aerial tramways, towed marine cables, skyline logging cables, machine belts, translating fibers, and moving tapes.;The natural frequencies and modes shapes of stationary and travelling minimum catenaries are computed over wide ranges of cable axial stiffness, cable tension, support inclination, and cable speed. The model accurately predicts the cable natural frequencies measured using a travelling cable test stand. The travelling minimum catenary is stable under all finite cable transport speeds. The instability predicted by the idealized (straight) "moving threadline" model doesn't exist in any real (sagged) travelling cable system.;The vibration and stability of the travelling maximum catenary is investigated using analytical and experimental methods. The cable model predicts a stable travelling maximum catenary for cable transport speeds above a critical stabilization speed. The stable travelling maximum catenary is verified experimentally and exhibits a gradual transition from stability to instability.;A cable dynamics theory is presented. Three nonlinear equations describe the three dimensional motion of a single span elastic cable travelling between two fixed eyelets. The equations of motion are linearized about two cable equilibria: the minimum catenary and the maximum catenary. The maximum catenary, in which the cable stands as an arch, has been overlooked in the previous investigations of travelling sagged cables. The cable model permits arbitrary equilibrum cable sag and arbitrary support inclination. Cable natural frequencies, mode shapes, stability, and response are computed from the solution of a discretized cable model.