An Energy-Equivalent Simplified Model for Lateral Nonlinear Vibrations of Coupled Water Turbine Generator Set Shaft-Foundation System

Abstract

\n The traditional whole finite element method (WFEM[1]) has several shortcomings, including that it has too many degrees of freedom so the execution is not efficient and is difficult to solve in nonlinear dynamic analysis. In this paper, a novel simplified modeling approach is proposed to investigate the lateral nonlinear vibration characteristics of coupled water turbine generator set shaft-foundation system (CSFS[2]). The simplified coupled model is generated in two stages. First, a more reasonable simplified model for foundation subsystem considering coupling with each other is constructed to simulate the lateral vibrations of guide bearing foundations in hydropower house. Based on the response spectra of WFEM of hydropower house and a constructed energy error objective function, the optimal equivalent parameters of the simplified foundation model are then determined by using the genetic algorithm. Second, considering actions of various nonlinear factors and the pulsating water pressure acting on turbine runner, a nonlinear dynamic differential equations of CSFS based on Lagrange equation are derived. The nonlinear dynamic responses of CSFS using the optimal equivalent model are also compared with the field test data. It is demonstrated that the method proposed to develop the equivalent model is more efficient and more convenient in capturing the nonlinear dynamic behavior of CSFS. In addition, this energy-equivalent model is more adaptable to the stochastic uncertainty and frequency band variation in hydropower station system. Some novel dynamic laws and inner mechanism of the coupled system are also revealed further based on the proposed model. Footnotes: [1] WFEM: whole finite element method[2] CSFS: coupled water turbine generator set shaft-foundation system