The effect of stiffness of shoe brake elements on the distribution of contact pressures

Zabolotnyi, K.; Zhupiiev, O.; Molodchenko, A.

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. The Gaus's 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. 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 stress-strain 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. 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. The application of these recommendations will allow reducing the maximum contact pressure in the shoe brakes of mine hoisting machines.


	Наукова періодика України		Naukovyi visnyk Natsionalnoho Hirnychoho Universytetu