On the strength calculation of the rotating parts

The existing solutions of differential equations of equilibrium of an infinitesimal element of the rotating parts of an isotropic elastic solid known as the Navier equilibrium equations are considered. Examples of the flat disk calculation by solving the differential equilibrium equations by the sweep method and the finite element method in the modern program "Autodesk Simulation Multiphysics" are represented; paradoxical changes of radial and hoop stresses are revealed. An original method of derivation formulas based only on the principle of d'Alembert to calculate radial and hoop stresses in parts that operate under centrifugal (inertial) forces is proposed. The solution for rotating disks of any profile that corrects unnatural classical solutions is obtained. Analysis of the obtained new formulas for calculating stresses shows that it is necessary to reject the concept of "equal-strength disk" because of the inability to provide the equality of the hoop and radial stress in all sections of the disk. A new method of the optimum strength disk profile calculation, which requires a restriction of outer radius disk, is suggested. In designing of optimum strength rotating parts is recommended to limit outer disk radius of 0,8 root[sigma]/(rho.omega(2)) were [sigma] - the allowable stress, rho - density of the disk material; omega - angular velocity of disk rotation. (C) 2014 The Authors. Published by Elsevier B.V.