In order to analyze turbine blades vibration caused by flutter, it is necessary to understand both aerodynamic damping and structural damping of high vibration stress. Flutter Vibration mode occurring in rated speed is non-synchronous mode. For measuring non-synchronous mode damping ratio of turbine blades, AC-type electromagnet which can generate high frequency excitation force was developed. Damping ratio characteristics of non-synchronous mode of nodal diameter 12,4 was measured in rotational test. For comparison, synchronous mode of nodal diameter 4 was measured, too. It was concluded as follows. (1) It is possible to excite non-synchronous mode by high frequency excitation electromagnet and calculate damping ratio from measurement resonance curve. (2) Damping ratio of non-synchronous mode ND12,4 was increased by increasing the excitation force. Synchronous mode ND4 is also a similar trend. (3) Nodal diameter 4 damping ratio of non-synchronous mode (Resonant speed=100%) was lower than synchronous mode (Resonant speed=75%).
In a traditional turbine-generator set, rotor shaft designers and blade designers have their own models and design process which neglects the coupled effect. Since longer blade systems have recently been employed (Saito et al. 1998, “Development of a 3000 rpm 43-in. last stage blade with high efficiency and reliability,” International Joint Power Generation Conference, pp. 89–96.) for advanced turbine sets to get higher output and efficiency, additional consideration is required concerning rotor bending vibrations coupled with a one-nodal (k = 1) blade system. Rotor-blade coupled bending conditions generally include two types so that the parallel and tilting modes of the shaft vibrations are respectively coupled with in-plane and out-of-plane modes of blade vibrations with a one-nodal diameter (k = 1). This paper proposes a method to calculate the natural frequency of a shaft blade coupled system. According to this modeling technique, a certain blade mode is reduced to a single mass system, which is connected to the displacement and angle motions of the shaft. The former motion is modeled by the m-k system to be equivalent to the blade on the rotating coordinate. The latter motion is commonly modeled in discrete form using the beam FEM on an inertia coordinate. Eigenvalues of the hybrid system covering both coordinates provide the natural frequency of the coupled system. In order to solve the eigenfrequencies of the coupled system, a tracking solver method based on sliding mode control concept is used. An eight-blade system attached to a cantilever bar is used for an example to calculate a coupled vibration with a one-nodal diameter between the blade and shaft.
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