The nonlinear dynamic characteristics analysis and vibration reduction control of the shafting system of a hydropower unit

Abstract

The shafting system of a hydropower unit is accompanied by radial, axial, and torsional multi-dimensional coupled vibrations that are a serious threat to the reliability and security of the unit. However, the nonlinear dynamic characteristics and vibration reduction control of these vibrations are rarely studied. Therefore, in this study, a nonlinear model of the multi-dimensional coupled vibrations of a shafting system of conventional and pumped storage units that are excited by multi-coupled vibration sources is first established. Subsequently, the Sobol method is introduced to analyze the global sensitivity of the parameters corresponding to the mean amplitude of these vibrations. Additionally, the nonlinear dynamic behaviors of the most sensitive parameters are determined using bifurcation diagrams. Furthermore, a state feedback controller, the design principle of which is based on the Euler–Lagrange error equation and Lyapunov theory, is designed for these vibrations, and the nonlinear dynamic behaviors of the controller parameters are obtained using bifurcation diagrams. Finally, the nonlinear dynamic response characteristics of these vibrations with and without control are revealed using phase-space trajectories, Poincare cross-sections, time-domain diagrams, and frequency domain diagrams. Notably, the guide bearing stiffness coefficients have the greatest influence on these vibrations and the state feedback controller can significantly reduce the amplitude of the shafting vibrations. More importantly, the proposed dynamic models and analysis results reveal that the generator and hydro-turbine vibrations are quasi-periodic and composed of several frequency components in a three-dimensional space and the torsional vibration of the shaft is stable with a small torsional angle. These results can serve as a guideline for the safe and stable design and operation of hydropower units.