Development of a model of contact shoe brake-drum interaction in the context of a mine hoisting machine
K. Zabolotnyi1, O. Zhupiiev1, A. Molodchenko1
1Mining Machines and Engineering Department, National Mining University, Dnipro, Ukraine
Min. miner. depos. 2017, 11(4):38-45
Full text (PDF)
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
Barecki, Z., & Scieszka, S.F. (1989). Some Factors Influencing Friction Brake Performance: Part 2-A Mathematical Model of the Brake Shoe and the Brake Path System. Journal of Mechanisms Transmissions and Automation in Design, 111(1), 8-12.
Barkand, T.D., & Helfrich, W.J. (1988). Application of Dynamic Braking to Mine Hoisting Systems. IEEE Transactions on Industry Applications, 24(5), 884-896.
Cummings, S. (2009). Brake Shoe Force Variation. In ASME 2009 Rail Transportation Division Fall Technical Conference (pp. 71-78). Fort Worth, Texas, USA: Rail Transportation Division.
Cummings, S., McCabe, T., Guelde, G., & Gosselin, D. (2009). Brake Shoe Coefficient of Friction Variation. In ASME 2009 Rail Transportation Division Fall Technical Conference (pp. 79-87). Fort Worth, Texas, USA: Rail Transportation Division.
Davydov, B.L. (1959). Raschet i konstruirovanie shakhtnykh pod’’emnykh mashin. Moskva: Ugletekhizdat.
Day, A.J., Harding, P.J., & Newcomb, T.P. (1979). A Finite Element Approach to Drum Brake Analysis. Proceedings of the Institution of Mechanical Engineers, (193), 400-406.
Fedorova, Z.M. (1961). Sbornik primerov i zadach po rudnichnym pod’’emnym ustanovkam. Moskva: Gosudarstvennoe nauchno-tekhnicheskoe izdatel’stvo literatury po gornomu delu.
Huang, Y.M., & Shyr, J.S. (2002). On Pressure Distributions of Drum Brakes. Journal of Mechanical Design, 124(1), 115-120.
Karpyshev, N.S. (1968). Tormoznye ustroystva shakhtnykh pod’’emnykh mashin. Moskva: Nedra.
Nosko, A.L. (2017). A Method of Estimating Changes in the Braking Torque as Applied to Brakes of Hoisting Machines. Proceedings of Higher Educational Institutions. Маchine Building, 5(686), 37-44.
Zabolotny, K.S., Zhupiev, O.L., & Molodchenko, A.V. (2015). Analysis of Current Trends Development of Mining Hoist Design Engineering. New Developments in Mining Engineering 2015: Theoretical and Practical Solutions of Mineral Resources Mining, 175-178.
Zabolotnyi, K., Panchenko, O., & Zhupiev, O. (2017). Substantiation of Parameters for the Tunnel Erector with Two Manipulators. Advanced Engineering Forum, (25), 43-53.