Modeling Polymeric Centrifugal-Pump Impeller Blades

Abstract

The paper describes a mathematical model and an algorithm to compute the stress–strain state of polymeric centrifugal-pump impeller blades. We explore the stress–strain state of a centrifugal-pump trapezoidal anisotropic blade constrained on both sides that are adjacent to plates (median-plane displacement is possible) while not constrained on the two other sides where the blade is exposed to the inertial forces of the blade eigen-weight. Differential equations of bending of a cylindrical anisotropic shell are obtained with respect to the deffection function and the stress function in the field of centrifugal inertia forces. To solve the boundary value problem described by the system of equations in partial derivatives and in boundary conditions, use the Dorodnitsyn’s method of integral ratios. Pursuant to the method, write the original equation system as a divergent system. Further apply the method of integral ratios to the original system of equations in partial derivatives to obtain a system of ordinary differential equations (order 8n) with variable coefficients, which are generally non-Euler. The boundary value problem is solved by the modified method of successive approximations, developed by Prof. V. A. Pukhliy and published by him in academic press. A numerical implementation has been programmed according to the analytical solution above. Computations were run for an orthotropic material of a blade where the principal elastic symmetry axes are turned by an angle φ against the blade axes x, y. The finding of the analysis is that it is necessary to take into account the anisotropy that occurs due to the main axes of the elastic orthotropic material not matching the computed axes of the blade.