Dynamics of lifting installation with weight and viscosity of the ropes

Abstract

The analysis of literature sources on the study of the dynamic approach to the theory of
calculation of lifting ropes is carried out. First, a rope with distributed mass in the form of a rod
with a load at the end was considered, then a transition to systems with a weightless rope occurred,
when 1/3 of the weight of the rope from the knot of oscillations should be added to discrete masses.
This entailed a transition to multi-mass mechanical systems with weightless elastic links and taking
into account the elastic-viscous properties of the rope.
Dynamic schemes of a one-end mine hoisting system are shown for a weightless rope and
taking into account linear-piece approximation.
A mathematical description of dynamical processes of oscillatory character in the elements
of a two-mass system with weightless rope is obtained in the process of inhibition in the form of an
analytical differential equation obtained on the basis of the Lagrange equation. The movements of
longitudinal oscillations of the rope with a load at the end are shown in the form of a linear-piece
approximation taking into account the viscosity of the rope.