Transverse vibrations of elevator chain excited by borders motion

Abstract The paper contains an analysis of transverse vibrations of an elevator chain excited by the movement of the chain ends. The equation of motion of the system was derived using a model of a moving string taking into account the tension force component resulting from axial acceleration. The equation of motion is written in a non-inertial system related to the moving ends of the chain. Using Galerkin's method, a system of ordinary differential equations containing periodic, dynamic and parametric excitations (resulting from inertial forces) was obtained, being a generalization of the scalar Hill equation. Sample calculations were performed for parameters describing the laboratory model of an elevator and an industrial bucket elevator operating in an aggregate processing plant. The numerical analysis made it possible to determine the conditions under which resonance occurs in the system. The determined amplitude-frequency characteristics enabled selection of the operating parameters that ensure avoidance of the negative effects of vibrations of the elevator chain.