Osami Matsushita

Aseismic Vibration Control of Flexible Rotors Using Active Magnetic Bearing

The wide application of active magnetic bearing (AMB) requires an aseismic evaluation with respect to AMB rotor vibrations caused by actual earthquakes. A flexible rotor supported by AMB is selected for this purpose. A shaking simulation obtained using the quasi-modal model and the actual Kobe earthquake was completed. A corresponding test rotor was excited by seismic waves and the resulting vibration was measured for the vibration evaluation. In order to reduce the response severity against earthquakes, we propose an additional feed forward control method which is proportional to the signal detected by the accelerometers attached to the bearing housings. Since this additional control can cancel rotor vibration generated by the earthquakes, AMB rotor vibrations are successfully suppressed at a low level.

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.

Vibration Criteria Considered from Case Studies of Active Magnetic Bearing Equipped Rotating Machines

The main part of turbo machinery is conventionally supported by oil film lubricated bearings. The rotor vibrations can be suppressed within low levels as to satisfy vibration criteria, e.g., ISO standards for general rotors and API 617 for process compressors. Recently, the sophisticated advantages of the active magnetic bearing (AMB) have been increasing the number of applications to industrial rotors. The AMB vibration control design requires the weak support which induces inevitably large vibration amplitude, though it is normal for AMB itself. Vibration criteria indicated by present standards are thus too strict for AMB equipped rotors. The difference of the bearing dynamic characteristics between the oil film lubricated bearing and the AMB compels us to prepare a new ISO standard which recommends the acceptance of higher vibration levels for AMB operation.

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

Blade-Shaft Coupled Resonance Vibration by Using Active Magnetic Bearing Excitation

The turbine generator requires sufficient reliability as a major component of the power plant. The rotor dynamics calculates the critical speed of the shaft-bearing system for design to avoid appearance of the critical speed, while the blade dynamics calculates the natural frequency of the blade to avoid nX resonance. For longer blades, however, the lower natural frequency requires that the design of the shaft and blade takes into account the coupling of the blade vibration mode with nodal diameter k = 0 and k = 1 with the vibration of the shaft. The present work analyzes the coupling of the parallel motion of the shaft with the in-plane vibration of the blade within k = 1 modes. More specifically, the existence of an unstable region due to coupling and the coupled resonance in an eight-blade (N = 8) where each blade is assumed to be a 1-DOF mass-spring system were analyzed in detail. Analysis was also made on the forced vibration of a stable damped system. At a rotational speed Ω = |ωs − ωb |, the vibration of the shaft was limited to a relatively small amplitude due to anti-resonance points resulting from the dynamic vibration absorber effect, while the resonance of the blades was relatively big amplitude. A violent coupled resonance resulting from the dynamic absorber effect of the blades and shaft was observed at a rotational speed Ω = ωs + ωb . The resonance in blade vibration at Ω = |ωb − ωs | was experimentally confirmed.Copyright

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

A Q-value measurement for damping evaluation of AMB rotors

The sensitivity function of feedback control systems is recommended for AMB (active magnetic bearing) equipped rotors to evaluate the stability margin. Alternatively before rotor operation, we need to predict the resonance severity called Q-value. In this paper, the sensitivity and the Q-value are discussed and the difference is made clear. How to obtain the Q-value from the open loop transfer function is also discussed. Our proposed Q-value function is numerically and experimentally demonstrated so well for several AMB rotors. This obtained Q-value peak agrees with exact values calculated by eigenvalues and/or measured by the half power point method

Modeling for Flexible Mechanical Systems

An alternative modelling technique is proposed in place of the well known modal reduction method for mechanical system modelling. The method, called quasi-modal reduction, belongs to the category of mode synthesis methods and represents a special way of substructuring.

Basics for a Single-Degree-of-Freedom Rotor

This chapter specifies the definitions, calculation and measurement of basic vibration properties: natural frequency, modal damping, resonance and Q-value ( Q-factor).

Vibration Analysis of Blade and Impeller Systems

This chapter discusses vibrations of rotating structures such as blades in turbines and impellers in pumps or compressors. The natural frequencies of a rotating structure may be analyzed using the 3-D finite element method and classified by the number of the nodal diameters or circular nodal modes. These results are represented in the rotational coordinate system. The difference between the inertial coordinate system fixed to the stationary side and the rotational coordinate system fixed with the rotor must be taken into account in analysis of: (1) resonance caused by any static load distributed in the circumference direction of the stationary side facing blades or impellers, and (2) resonance caused by harmonic excitation at a certain point in the stationary side facing blades or impellers.