5.7.2 Sources of vibration excitation
Vibration excitation can arise from a variety of sources but principally involves the following categories:
(a) Non-uniform pressures, velocity or changes in the angle of steam flow resulting in a periodic fluctuating force on the rotating blades. This may be caused by:
- Steam entering the rotating row over only a portion of its circular path (partial admission). This may exist in the control stage of some HP turbines but not in LP stages.
- A change in the direction of flow, particularly from axial to radial at exit from moving blades. Good aerodynamic design should minimise the magnitude of this non-uniformity and ensure that multiple harmonics of the synchronous speed are not produced.
- Flow distortions produced by the presence of steam extraction passages for feedheater tappings.
(b) Periodic effects due to manufacturing constraints or structural features. These can include:
- Inexact matching of stationary blade geometry at horizontal joints. Blade-pitching at diaphragm horizontal joints may not be uniform and this can give rise to excitation at even multiples of rotational frequency.
- Leakage through gaps in stationary blade shrouds and diaphragm discs at horizontal joints. The current arrangement of diaphragm support precludes this effect.
- Eccentricity of diaphragms and other stationary elements with respect to the rotating blade assembly. Again, current design practice should minimise this.
- Ellipticity of stationary parts, such as end walls, seals, etc.
- Non-uniformity in the gauge or thickness of stationary blades. Modern quality control and manufacturing normally obviates this effect
- Moisture removal slots.
All the above sources give rise to excitation frequencies at the rotational frequency or low multiples (harmonics) of that frequency.
(c) Nozzle wake excitation caused by the aerodynamic force-fluctuations seen by the rotating blade as it passes each stationary blade or traverses each stationary blade pitch. This is seen by the rotating blades as excitation at the nozzle passing frequency (rotational frequency x number of stationary blades) and its multiples.
A number of sources can also give rise to excitation having no direct relationship to rotational speed. In the stationary flow passages, these can include:
- Acoustic resonances in inlet passages, extraction lines or other cavities, excited by the flow past them.
- Vortex-shedding from stay bars, etc.
- Unsteady flow separation from stationary blades, etc.
- Unsteady shocks in choked stationary blade passages.
- Surface pressure fluctuations, due to impingement of turbulent flow onto rotating blade shrouds, discs, etc.
In the rotating blades themselves, flow instability, and hence excitation, can arise from:
- Boundary layer pressure fluctuations.
- Vortex-shedding from blade trailing edges, causing unsteady aerodynamic force.
- Recirculating flow, particularly in last-stage LP blades.
- Unsteady condensation shocks, caused by supersaturation in supersonic diverging passages.
A necessary condition for high resonant vibratory stresses is the coincidence between the frequency of a harmonic component (of significantly high magnitude) and the natural frequency of a mode of vibration of a blade, or a blade group, or bladed disc assembly. With a continuously-connected blade row, a resonance condition is associated with a multinodal standing wave pattern around the circumference. This, however, is not always a sufficient condition. It is also necessary that the distribution of vibratory deformations and the distribution of exciting forces have a relationship that permits a net input of energy into the vibration.
For example, consider a long blade vibrating in a mode with one displacement node (point of zero displacement). The upper portion of the blade deflects in one direction when the lower portion deflects in the opposite direction. If the distribution of exciting force along the height of the blade is essentially uniform, then the upper portion of the blade wants to respond at a phase angle 180° different from that of the lower portion. The net response of the blade to this exciting force would therefore be very low.