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.Keywords: bobbin hoisting machine, rubber-rope cable, multilayer winding, the body of the winding, torsional stiffness of the winding introduction. The multilayer winding of the rubberrope cable is one of the insufficiently explored elements of the bobbin hoisting machines, which has a high compliance and influences the dynamic processes in the hoisting installation. Because of the high compliance of the cable wound on the bobbin in a short branch, considerable oscillations of the lifting vessel can arise, which are dangerous for the possibility of its offset from the discharge curves. It follows from the foregoing that the evaluation of stiffness is an important problem, the solution of which is necessary for the research on dynamics of the hoisting installation. Analysis of the recent research and publications. The works of V. P. Franchuk and K. A. Ziborov [1] are devoted to the elaboration of mathematical models of the mechanical systems with distributed and lumped parameters during stationary and non-stationary rec...

For new designs of mine hoisting machines, the development of scientifically-based solutions to increase the rope capacity and reduce the size of the machines is relevant. Based on the theory of laying the rope on a lined cylindrical drum developed by the authors, it is shown that when choosing a groove profile and winding pitch for a non-lined drum, it is necessary to use a geometric rope laying model, and for taking into account the elastic lining, it is necessary to use a physical model of static interaction of a rope with a scallop of the groove. It is recommended to use the U-tilda-groove profile, which will allow a 4.5 % increase in the drum capacity while maintaining the rope’s curvature radius that is permissible under safety rules during its installation.

Purpose. To develop models of contact brake shoe-drum interaction of a mine hoisting machine while braking, taking into account final bending stiffness of a beam and the effect of friction forces on the distribution of a contact pressure in it to make recommendations as for the rational design of a brake beam.Methods. Laws of contact force distribution, forces within a vertical post, and braking moment arising in the braking process have been formulated with the help of exclusion method and Euler's method. Findings.Areas to apply the hypotheses on absolute stiffness of a beam and the non-effect of friction forces on the distribution of contact pressure in it while calculating force of brakes of mine hoisting machines have been analyzed. Physical and mathematical models of contact interaction between a brake beam of a mine hoisting machine and a drum in the braking process have been developed. Originality.For the first time, physical model of a brake lining in the form of a group of elastic non-interacting bodies of Winkler foundation has been developed. The bodies resist compression and transfer through themselves distributed friction forces arising between brake drum and brake shoe; the friction forces are meant for limiting balance state in accordance with Coulomb's law; physical model of a brake beam in the shape of uniform-section circular bar mounted on a vertical post and interacting with a brake drum through brake lining loaded with distributed normal and tangential load modeling contact brake shoe-drum interaction, and a vertical post has been modeled as a movable pivot point located in the medial part of the circular bar. For the first time, mathematical model to determine both tangential and normal forces acting on a brake beam has been formulated. Practical implications.The developed recommendations concerning the use of different models of the braking process make it possible to generate the most rational model for force calculation of a brake beam using finite-element method. Keywords: physical and mathematical models of beam and lining, mine hoisting machine shoe brake, Euler's method, Coulomb's law

When calculating the stress-strain state of a cylindrical drum of a mine hoisting machine loaded with a metal rope, the stiffness parameters of the elastic lining and frontal surface are taken into account. It is defined that, depending on the values of the radial and bending stiffness of the frontal surface, two zones can be distinguished. If the parameters of the frontal surface fall into the first of them, the stresses in the shell slightly differ from the stresses in the hinged supported shell. The second zone is characterized by a sharp (up to 70%) increase in stresses. An algorithm has been developed for selecting rational parameters of a lined drum, which allows to reduce the stresses in the metal shell by up to 20%.

Existing methods for the mine hoisting machines shoe brakes calculating are unreasonably based on the hypothesis in which the brake rim and the brake beam are assumed to be absolutely rigid. Purpose. To develop recommendations for reducing the maximum contact stresses when the brake lining interacts with the drum of a mine hoisting machine. The tasks of this paper are to determine the applicability of the hypothesis on the absolute rigidity of the brake beam and to determine the dependence of the contact pressures distribution nature on the ratio of the brake lining transverse rigidity to the brake beam bending stiffness. methodology. The Gauss method for the sequential elimination of unknown variables; Euler's method for solving systems of differential equations; Newton's method for determining the numerical values of the roots of a differential equation; the finite element method for optimizing the design of the brake beam. findings. An analytical model of the brake beam as a circular beam of a constant section on the Winkler base is developed, whose rigidity depends on the stiffness properties of the composite lining. From the analysis of the stressstrain state, a dimensionless factor determining the nature of the contact pressure distribution is revealed, namely, the relative rigidity. To clarify the effect of this factor, computational experiments for a beam of constant section and a real brake pad for various design solutions for varying the relative rigidity were carried out in the SolidWorks Simulation software. A method for determining the distribution of contact pressures depending on the ratio of the brake lining transverse rigidity to the brake beam bending stiffness is developed. A comparison of the results of various design approaches to achieve an even distribution of the contact pressure along the brake beam is presented. originality. For the first time it has been analytically proved that the nature of the distribution of the contact pressure in the shoe brake of mine hoisting machines depends on the ratio of the brake lining transverse rigidity to the brake beam bending stiffness, and with its decrease the character of the distribution tends to be sinusoidal. Practical value. The application of these recommendations will allow reducing the maximum contact pressure in the shoe brakes of mine hoisting machines.