An analytical model for the drum-rope interaction in hoisting mechanisms and cable-driven systems

Abstract

This study introduces a new analytical model for the drum-rope interaction in mechanical systems actuated through ropes or cables. The model consists of a set of analytical force–displacement relations that capture the extensibility of the rope and the drum-rope contact interaction, assuming linear elastic behavior and Coulomb friction. It is derived from a detailed analysis of the tension distribution along the rope when subjected to a dynamic pulling force, distinguishing between stick and slip regions. The response of the rope is found to be linear under gross slip conditions, becoming significantly nonlinear under partial slip. In practical terms, the proposed drum-rope model can be applied to the dynamic simulation of hoisting mechanisms and cable driven systems. This is achieved by introducing a nonlinear spring, defined by specific force–displacement relations, to represent each cable wound on a reeling drum within the overall model. The presented approach is numerically validated using a finite element model, with remarkable agreement between both solutions. It is also compared with a conventional modeling approach that assumes no slippage between drum and rope, demonstrating 39% higher accuracy in a representative scenario.