The field of tensions of a rotating anisotropic disc of a variable thickness loaded with undistracted forces on the outer contour

V. V. Korolevich

Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2019), pp. 40-51.

Résumé

The work gives a solution of the plane elasticity problem for rotating polar-orthotropic annular disks of a variable thickness. The disk is loaded with a system of equal focused forces on the outer contour applied evenly along the rim and symmetric concerning the diameter. The disk is seated with an interference fit on the flexible shaft so that a constant contact pressure acts on the interior contour. The stresses and deformations arising in such a rotating anisotropic annular disk will be non-axisymmetric. A conclusion of a fourth-order partial differential equation for the effort function is drawn. Its general solution is searched out in the form of a Fourier series of cosines with even numbers. As a result, an infinite system of ordinary differential equations is solved for the coefficients of the series. These differential equations correspond to the linear Volterra integral equations of the 2nd kind, which are solved using resolvents. Constants of integration are determined from the border conditions. Expressions for the stress components are written through the effort function by the well-known formulas. We find the components of the displacement vector in the disk by the integration of the Hooke’s law equations for the polar-orthotropic plate. We calculate the deformation components in a ring anisotropic disk by Cauchy differential relations if we know the displacements. The solved formulas for stresses, deformations and displacements completely describe the stress-deformed state in a rotating polar-orthotropic disc of variable thickness with a system of focused forces on the outer contour. The results of the work can be used in the design of working disks of turbomachines and turbo compressors, as well as rotors of centrifugal stands.

Détail

Keywords: polar-orthotropic disk of variable thickness; focused force; differential equations; integral equations; resolvent; stresses in the disc; deformations in the disc; displacements in the disc.