Simple models for rope substructure mechanics: Application to electro-mechanical lifts

Mechanical systems modelled as rigid mass elements connected by tensioned slender structural members such as ropes and cables represent quite common substructures used in lift engineering and hoisting applications. Special interest is devoted by engineers and researchers to the vibratory response of such systems for optimum performance and durability. This paper presents simplified models that can be employed to determine the natural frequencies of systems having substructures of two rigid masses constrained by tensioned rope/cable elements. The exact solution for free un-damped longitudinal displacement response is discussed in the context of simple two-degree-of-freedom models. The results are compared and the influence of characteristics parameters such as the ratio of the average mass of the two rigid masses with respect to the rope mass and the deviation ratio of the two rigid masses with respect to the average mass is analyzed. This analysis gives criteria for the application of such simplified models in complex elevator and hoisting system configurations.