Purpose. Development of a mathematical model of the stress-strain state of the body of the winding of the bobbin hoisting machine with rubber-rope cable. Methodology. Methods of mathematical and computational experiment based on the finite element analysis are used. Findings. To solve the problem of defining the torsional stiffness of the body of the winding of the rubber-rope cable (RRC), the physical model of the body of the winding was represented in the form of a composite in which the reinforcement is an infinitely thin spiral having stiffness characteristics of a metal rope and the matrix is a rubber sheath. After processing the results of the computational experiment using the computer finite element modeling method, an analytical expression for determining the torsional stiffness coefficient of the body of the winding of the RRC was obtained, the analysis of which shows that the stiffness of the body of the winding depends quadratically on its outer diameter, and the local stiffness depends little on the diameter. The danger of dynamic effects occurring in the bobbin hoist can take place at a large number of turns in the winding. Originality. The regularities of the influence of the rubber-rope cable parameters on the torsional stiffness of the body of the winding have been established. The nonlinear character of changing the given stiffness characteristics of the RRC packet layers is caused by the peculiarity of interaction of the first packet layer with the bobbin surface. This interaction can be taken into account by applying the coefficient of a torsional stiffness hardening, for which an analytical expression was obtained by processing the results of the computational experiment. Practical value. The developed mathematical model of determining the stiffness of the rubber-rope cable winding allows finding the parameters of the bobbin hoist, at which the danger of dynamic effects during the emergency and service braking caused by the torsional stiffness of the body of the winding is excepted.

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