Mathematical modeling and nonlinear vibration analysis of a coupled hydro-generator shaft-foundation system

Abstract

This paper presents a method to investigate the overall nonlinear dynamics of coupled hydro-generator shaft-foundation system. A novel coupled dynamic mathematical model is developed, which consists of mutual coupled foundation vibrations, external random excitation of foundation, besides classical dynamics of nonlinear hydro-generator shaft system. Previous coupled vibration analysis of water turbine generator unit and foundation (hydropower house) is based on finite element modeling of foundation system. But the too many discrete degrees of freedom in finite element model will result in difficulty of nonlinear dynamic calculation and infeasibility of the vibration controller design. In this study, a simplified equivalent lumped-mass model for foundation system is established using the natural vibration characteristics of hydropower house. The model of foundation random external excitation is proposed and simulated by a combination of bounded noise and harmonics. Then by calculating kinetic energy and potential energy of the coupled hydro-generator shaft-foundation system, a nonlinear dynamic differential equations of the coupled system based on Lagrangian equation are derived. After that Runge-Kutta algorithm is employed for the coupled system's nonlinear responses. The axis orbit diagram, poincaré map and bifurcation diagram are then used to investigate the effect of foundation system and some of the relevant parameters on the transverse vibration of the coupled system. The variable laws and its inner mechanism of the coupled system are revealed further. The advantage of this coupled mathematical model for hydro-generator shaft-foundation system is convenient to capture the key dynamic features of the coupled nonlinear system. The results of all these analyses have enriched the dynamical behaviors of a coupled hydro-generator shaft-foundation system.