Akira Okabe

Reduced Modeling for Turbine Rotor-Blade Coupled Bending Vibration Analysis

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 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). In this paper, we propose a method to calculate the natural frequency of a shaft blade coupled system. According to our 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, we use a tracking solver based on sliding mode control. 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.

Resonance and Instability of Blade-Shaft Coupled Bending Vibrations with In-plane Blade Vibration

Abstract As a major component of a power plant, a turbine generator must have sufficient reliability. Longer blades have lower natural frequency, thereby requiring that the design of the shaft and blade takes into account the coupling of the blade vibration mode, nodal diameter k =0 and k =1 with vibration of the shaft. The present work analyzes the coupling of the translation motion of the shaft with in-plane vibration of the blades with k =1 modes. At a rotational speed Ω 1 =|ω s −ω b |, the resonance of the blades has a relatively large amplitude. A violent coupled resonance was observed at a rotational speed Ω 2 =ω s +ω b . Resonance in blade vibration at Ω 1 =|ω s −ω b | was experimentally confirmed. Keywords : Blade-Shaft coupled vibration, Bending vibration, Resonance, Instability, In-plane vibration, Turbine generator 1. Introduction As a major component of the power plant, a turbine generator must have sufficient reliability. The rotary shaft system is usually designed to give a low Q-factor and avoid resonance based on the rotor-dynamic analysis of the bending and torsional vibration of the shaft-bearing system, in which the blades are assumed to be a rigid disk. Meanwhile, the blade is designed to avoid resonance under the rated operation conditions based on analysis of a single blade under ideal conditions where the shaft is assumed to be fixed [1],[2]. The long blades used in turbine generators for nuclear power plants have low natural frequencies, thereby necessitating a design that takes into consideration blade-shaft coupled vibration. General conditions for coupling of blade and shaft vibrations are shown in Table 1. Blade

Rotor-Blade Coupled Vibration Analysis by Measuring Modal Parameters of Actual Rotor

The designers of rotor shafts and blades for a traditional turbine-generator set typically employed their own models and process by neglecting the coupled torsional effect. The torsional coupled umbrella mode of recent longer blades systems designed for higher output and efficiency tends to have nearly doubled the frequency of electric disturbance (i.e., 100 or 120 Hz). In order to precisely estimate the rotor-blade coupled vibration of rotating shafts, the analysis must include a process to identify the parameters of a mathematical model by using a real model. In this paper we propose the use of a unique quasi-modal technique based on a concept similar to that of the modal synthesis method, but which represents a unique method to provide a visually reduced model. An equivalent mass-spring system is produced for uncoupled umbrella mode and modal parameters are measured in an actual turbine rotor system. These parameters are used to estimate the rotor-blade coupled torsional frequencies of a 700-MW turbine-generator set, with the accuracy of estimation being verified through field testing.Copyright

Experimental Study of Torsional-Bending Coupled Vibration of a Rotor System With a Bladed Disk

An experimental investigation was conducted to confirm the bending-torsion coupled vibration of a rotor system with a bladed disk.For a rotor with relatively long blades such as in the latest low-pressure steam turbines, coupled vibration with shaft torsional vibration represents the bladed disk natural frequency of a nodal diameter (k) of zero (umbrella mode). Today this well-known behavior is reflected in the design of steam turbine rotor systems to prevent the blade vibration resonance due to torque excitation caused by the electric power grid, a standard for which is proposed by ISO 22266-1.The bending-torsion coupled resonance of rotor systems occurs, however, under specific conditions due to rotor unbalance. When the rotor’s rotational speed (Ω) is equal to the sum/difference of the bending natural frequency (ωb) and torsional natural frequency (ωθ), namely, Ω = ωθ ± ωb, there is coupled resonance, which was experimentally observed with a rotor with a relatively simplified shape.In this study, the test apparatus for a flexible rotor system equipped with a shrouded bladed disk driven by an electric motor was constructed to confirm the vibration characteristics, by envisioning the bending-torsion coupled resonance as applied to actual rotor systems of turbo machinery. A radial active magnetic bearing (AMB) was employed to support the rotor by controlling bearing stiffness and damping, and applying lateral directional excitation of forward and backward whirl to the rotor. A servomotor was also equipped at the end of the rotor system to excite the torsional vibration.The resonance of a bladed disk with nodal diameter (k) of zero, which was coupled with the rotor’s torsional vibration, was observed under the above condition (Ω = ωθ − ωb) through AMB excitation of the rotor’s bending natural frequency. Conversely, the torsional excitation caused by the servomotor was confirmed as causing the coupled resonance of rotor bending vibration.Copyright

DEVELOPMENT OF 40-INCH TURBINE BLADES USING TITANIUM ALLOYS

The Chubu Electric Power Co., Inc. and Hitachi, Ltd., jointly developed a 40-in long blade, capable of use at 3600rpm, to provide improved efficiency of the next-generation 700MW class steam turbines. The 40-in blade could improve the performance of steam turbines of the 700MW class about 1.6%. 12Cr-Ni-Mo-V steel, which is used in the previous longest 33.5-in blade and which cannot withstand the centrifugal force of a 40-in blade, was replaced with a titanium alloy of a small specific gravity to reduce the stress of the blade itself and the rotor to support it. Performance and reliability of the 40-in blade were evaluated by conducting demonstration runs using a full scale test turbine (2-stage) and a 1/2.5 scale model turbine (3-stage). The erosion resisting characteristics and the rupture strength of the blade root were determined by conducting basic tests.