Analysis of Shafting System Vibration Characteristics for Mixed-Flow Hydropower Units Considering Sand Wear on Turbine Blades

Abstract

Addressing the issue of increased shaft-system vibration in high-altitude mixed-flow hydropower generating units due to sand wear on turbine blades, a three-dimensional model of a specific mixed-flow water turbine was constructed. CFD numerical simulations were employed to analyze the fluid exciting force acting on the turbine runner under varying degrees of blade wear. An approximate analytical model was then established for the variation of fluid exciting force in the turbine runner system using the Fourier harmonic analysis method. A multi-degree-of-freedom mathematical model of flexural and inclined coupling vibration of a hydropower unit’s shafting, considering blade wear, was constructed. The nonlinear dynamic model was numerically calculated by the Runge–Kutta method. The vibration responses of the shafting of hydropower units under different wear degrees were obtained by means of a time-domain diagram, frequency-domain diagram, axis-locus diagram, phase-locus diagram, and Poincare mapping. Based on the formula for calculating the wear amount of the blade material, the runner amplitude degradation trajectory model was established, and the pseudo-failure time of turbine blades was determined according to the allowable value of amplitude.