Development of a model of contact shoe brake-drum interaction in the context of a mine hoisting machine

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.