Vibration induced High Cycle Fatigue (HCF) is a major consideration in designing gas turbines. Indeed, the Gas Turbine manufacturer must demonstrate that the vibration level of the turbomachinery blading is acceptably low, usually by using an engine strain gauge test. If the test shows unacceptable vibration levels then a redesign is required which adds cost and time to the engine development programme. It is highly desirable, therefore to develop a capability which can predict the vibration level of the blade to ensure that it will be robust.
The High-Pressure Turbine is of particular interest because of the harshness of the environment in which it operates (high mechanical speed and high air temperatures and pressures) so friction dampers are routinely introduced to control the vibration level. The friction dampers can introduce a degree of non-linearity into the structure which affects not only the vibration amplitude, but also the resonant frequency. The resonant frequency, amplitude, damper behaviour and aerodynamic forcing are all inter-related such that they must be considered as a single system.
This thesis describes the development of two new approaches to predict the vibration behaviour of a High-Pressure Turbine blade including the effect of friction dampers. The first utilises existing prediction tools for modelling of the fluid, the structure and the friction behaviour, but uses a novel method for coupling the various aspects together. This approach is based on modelling an ‘engine acceleration’ across a wide speed range and prescribing the variation of all the relevant parameters with shaft speed. For example, both the excitation force on the blade and the centrifugal load of the damper vary strongly with rotor speed so these effects must be included in the analysis. The second approach extends the first approach by using a new iterative ‘resonance tracking’ methodology in which the aerodynamic boundary conditions are adjusted based on the shaft speed at resonance until convergence is reached. Both methodologies calculate the resonant frequency, amplitude and operating condition of each mode of interest as an output of the analysis.
The engine acceleration methodology has been investigated in detail and has been validated against several High-Pressure Turbine cases. It has been found to be reliable: the amplitude predictions were in broad agreement with the available engine strain gauge results and the frequency shift introduced by the damper was in very good agreement. The methodology captures some important features of the physical system such as (a) the amplitude dependence of the damper, (b) the sudden drop in frequency when approaching the second flap resonance because the damper starts to slide, and (c) the effect of the damper on the ratio between stress and tip displacement. One rather surprising result was that in certain cases, where the forcing level was low, the damper increased the blade response because it moved the resonance to a higher shaft speed where the forcing level was larger. The main advantage of the method is its speed, which allows optimisation of key parameters within design timescales.
The resonance tracking methodology has been compared directly with the engine acceleration approach on one of the test cases and it produced very similar results. Convergence was achieved quickly, in two or three iterations for the chosen test case, mainly because the blade surface pressure distribution was consistent across a broad speed range. The method showed that the first torsion resonance was more sensitive to aerodynamic conditions than the second flap mode, and may offer an explanation for the scatter seen in engine test results. The approach offers the advantage that it is more generally applicable, because it can deal with cases where the pressure distribution is sensitive to shaft speed, but it can only converge to a single mode and requires significantly more computational effort.
The methodologies have been used to explore vibration reduction strategies such as wake shaping, damper optimisation and defining acceptance limits for the orientation of the single crystal material used in turbine manufacture. Overall these provided almost an order of magnitude reduction in blade response.
Stockholm: KTH , 2006. , 94 p.