Uncertainty Analysis of a Francis Hydropower Unit

This contribution is dedicated to the analysis of uncertainties affecting the vibration responses of a Francis hydropower unit. The system is composed by a vertical rotor and three hydrodynamic bearings: i) a combined tilting-pad guide/thrust bearing, located close to the generator; ii) an intermediate radial tilting-pad bearing; iii) and a cylindrical bearing located close to the Francis turbine. The bearings are represented by using linearized stiffness and damping coefficients. A fuzzy uncertainty analysis was applied aiming at determining the extreme vibration responses of the system. In this case, the bearings stiffness coefficients, generator mass, and Young’s modulus of the shaft were considered as uncertain information. The fuzzy analysis was carried out through the so-called α-level optimization approach due to its mathematical simplicity. Finally, a sensitivity analysis was performed based on the obtained results to determine the uncertain parameters that most affect the rotor responses. The obtained results demonstrate the representativeness of the conveyed methodology.