In the future landscape of electrical power generation, combined cycle power plants will play a major role in providing balancing power for fluctuating renewable energy sources due to their high availability and fast start-up times. This implies more frequent speed cycling with an increase in the number of starts and thus new challenges for plant design and operation.One of these challenges is a potential increase of last stage blade vibrations during start-up and coast-down. Blade vibrations might be induced by synchronous shaft vibrations when the blades fundamental mode shape interacts with the shaft vibrations. In this paper, we report measurements of shaft and blade vibrations observed at several units within the Siemens steam turbine fleet. Different phenomena can be observed including a distinctive dip of shaft vibrations at the low-pressure turbine bearings and a corresponding increase in blade vibrations when the double rotating speed crosses the blade resonance. We argue that this phenomenon is likely related to the interaction between blade and shaft vibrations and present a theoretical framework to describe this interaction and the observed effect.Modelling the interaction between blade vibrations and shaft vibrations is a challenging task in rotordynamics analysis. If individual blades are included in the rotor model, this breaks the rotational symmetry of the structure and its differential equation is thus no longer time-invariant in the inertial frame of reference. On the other hand, steam turbines have fluid film bearings with anisotropic stiffness and damping properties that are time-variant in the rotating frame. Thus, a time-invariant formulation of the coupled system cannot be defined neither in the inertial nor in the rotating frame of reference. This invalidates the traditional linear rotordynamics approach and calls for advanced numerical techniques that allow for coupling the inertial and rotating frames of reference and can deal with the explicit time-dependence of the resulting model. The approach we present here is based on the Samcef/Mecano solver package and employs an implicit Newmark scheme for direct time integration where the frame-coupling is achieved by time-dependent Lagrangian-multiplier constraints. This allows to solve the rotating and stationary subsystems separately within their respective reference frames. We show that the observed phenomena can be reproduced qualitatively with this approach.We believe that this work paves the way for a deeper theoretical understanding of rotor-blade coupling and will help to design rotors such that the transfer of vibration energy from shaft to blades during resonance drive-through is minimized. Moreover, a deeper understanding of this interaction might also allow for indirectly diagnosing blade vibrations, which are usually not measured, via shaft vibration data. In combination, these efforts will likely help to increase the permissible number of start-ups during the lifecycle of the plant without compromising on safety.

Rotor-Blade Interaction During Blade Resonance Drive-Through

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2021/volume/84898

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