Damping force of air acting on vibrating elevator rope

Abstract

This paper describes the vibration damping characteristics of elevator ropes acted on by air. High-rise buildings sometimes resonate during earthquakes, and the elevator ropes in the building may swing significantly as a result. The vibration analysis of the elevator ropes is required because the swing of the ropes may interfere with the subsequent operation. However, there is no sufficient study on the damping force of air acting on the elevator rope, which is necessary for vibration analysis. We established a damping theory to estimate the damping force and loss factor of air acting on a vibrating rope, and conducted principle experiments using silicon rope and piano wire. Theoretically, the vibrating rope was considered as a cylindrical object placed in a flow field, and the drag force derived in the field of fluid mechanics was considered as the damping force exerted by the air on the rope. In particular, the vibration damping of ropes by air can be classified into two major types: viscous damping—proportional to the 1.5^th-power of the vibration velocity—and vortex damping—proportional to the square of the velocity. Additionally, the loss factor of the vibrating rope was evaluated from the displacement transfer function of the excitation amplitude and the rope vibration amplitude. As the loss factor exhibited large values for large-amplitude vibrations of the rope, the loss factor was influenced by the vibration velocity of the rope. Moreover, the damping theory presented in this paper can be applied to nonlinear rope vibrations as well.