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In contrast to conventional rolling element and oil film bearings, magnetic bearings have had a relatively short history. The practical implementation of active magnetic bearings using electromagnets has been accelerated and driven recently by the development of digital control technology. Since 1988, the International Symposium on Magnetic Bearings (ISMB) series has been convened every two years and has been leading the studies in this field. In the industrial sector, the ISO TC108/SC2/WG7 “Working Group on Active Magnetic Bearings” started its activities in 1997 to develop standards to promote the adoption of rotating machinery with active magnetic bearings and to support the steady and smooth advancement of associated industries. The standards have been released as the ISO 14839 series. This chapter describes the basic specifications of magnetic bearings, along with the related vibration control technologies.

Oil-lubricated plain bearings used widely for large-sized rotating machinery can effectively suppress unbalance vibration amplitude of a rotor. This chapter outlines the nature of unbalance vibration amplitude of a rotor supported in plain bearings. The mathematical expression of unbalance vibration of a rotor is given in the rotating plane of the shaft. The two equations of motion given in the x–y-plane are converted into a single equation of motion derived with the complex expression of the displacement of the rotor. Then, the rotor is found to make an elliptical whirl orbit with major and minor axes around its equilibrium. The eight rotordynamic coefficients of a bearing oil film can be converted into the four effective coefficients expressed with the two coordinates of the major and minor axes. The vibration response and the whirl orbit are calculated and shown with varying shaft speed. The effects of bearing type and design variables on the unbalance vibration response are also calculated and compared. Furthermore, the effect of bearing pedestal characteristics on the unbalance vibration response is shown. Finally, it is shown how rotor-bearing systems can be designed to reduce the maximum amplitude of unbalance vibration when passing critical speeds.

This chapter is divided into three parts, which include our latest areas of interest. (1) Guyan reduction or mode synthesis: With respect to vibration analysis for actual machines, many types of codes, 3D-FEM and 1D-FEM (e.g., MyROT introduced in R1_Chap. 12), are available for engineering design based upon multi-DOF (degree of freedom) modeling. However, case studies of vibration problems show the benefits for understanding the vibration mechanisms and their practical and potential solutions using simplified models. In this book, Guyan reduction and the mode synthesis technique are strongly recommended for this purpose. (2) System instability in oil film bearing rotors: This model order reduction (MOR) is applied to a flexible rotor supported by oil film bearings to analyze system instability, often referred to as oil whip, oil whirl, and casing whirl. Stability analysis is generally performed by using complex eigenvalue codes in the 1D-FEM modeling. However, this chapter yields an alternative way without complex eigenvalue calculation, i.e., how to predict the limiting speed for stability and the resultant unstable frequency. (3) Blade modeling coupled with shaft vibration: The MOR by the mode synthesis technique is applied to a flexible blading system to analyze the vibration coupled with the rotating shafting system. Uncoupled eigen frequencies and modes may be analyzed initially for the rotating blading system only by a 3D-FEM code, based upon the rotating coordinates. As the result, the corresponding 2-DOF models for each eigen mode of blading are proposed by two methods depending upon the number of the nodal diameter, κ = 0 and κ = 1. The former is coupled with torsional and axial shaft vibration models and the latter with bending (lateral) shaft vibration models, respectively. These blade reduced models are combined into shaft vibration data by a 1D-FEM code for the evaluation of the coupling effect. The effectiveness of these procedures is confirmed by numerical examples.

The major problem in forced vibration response is resonance, where the frequencies of exciting forces coincide with the natural frequencies. Rotating machinery has different characteristics in resonance problems from general non-rotating structures. Therefore, the problems need be solved with this knowledge in mind, not only at the design stage, but also on-site. In the case of forced vibration, centrifugal forcing due to unbalance is a very typical example; however, various other external forces produced by different mechanisms may also become problematic and be experienced routinely. Examples include mechanically induced forces in gears, cross joints, and pulley belt systems; an electromagnetic force in a motor/generator; and rotating stall and impeller/blade interaction forces, which are induced by the fluid flow. Furthermore, torsional vibration is inevitable for rotating machinery and may become a large problem. In this chapter, these phenomena and appropriate countermeasures to implement are elucidated while referring to previously mentioned examples.

Rolling element bearings are used widely in rotating machinery. A significant variety of rolling element bearing types is available, and they are categorized by the shape of the ball or roller elements; the radial or axial loading direction; the ball type such as deep groove or angular contact; the roller type such as plain or tapered; etc. As most of them are standardized in ISO/JIS, interchangeability is guaranteed. This chapter introduces the dynamic properties of some rolling bearings, but does not make any reference to the static properties given in bearing manufacturers’ catalogues, such as load capacity, sizing, life estimation, and so on.

This chapter describes MyROT, a versatile software package for the rotor vibration analysis of rotating machinery. The calculation is based on a combination of beam elements according to finite element modeling , termed 1D-FEM, which is discretized by defining the mass, stiffness and damping matrices according to the actual geometry of the rotating shaft. These matrices are applied to calculations of natural frequencies, complex eigenvalues for stability analysis, unbalance vibration by frequency response analysis (FRA) and so on. Specifically, this chapter describes the theoretical background for formulation and presents outputs of typical rotor dynamic calculations in order to show how this program is convenient in analyzing rotordynamics. A trial version of the package is available at http://www.nda.ac.jp/cc/mech/member/osami.html. An input data manual and other documents related to the package may also be downloaded from the site.

Subsynchronous vibration of high-pressure steam turbine is one of the difficult problems to improve the reliability of power plant. Extensive work has been done to prevent the low frequency vibration of high-capacity steam turbine and most of the problems were practically solved (1). In the future, we must build up theoretical approach to design a new turbine operating under the steam condition of high-temperature and high-pressure. To design such an advanced steam turbine, it is necessary to solve the effect of partial admission on control stage of the steam turbine. This paper describes the experimental results from the scale model of the steam turbine and theoretical analysis of destabilizing forces. In theoretical analysis, destabilizing forces that take partial admission into consideration were analyzed. As a result, it was clarified that large destabilizing force was generated in partial admission condition and the destabilizing force varied periodically by the instant rotor position. In experimental study, we designed the new inlet seal for the prevention against the vibration. From the experimental result that increase of total flow rate leads the system stable, we showed the effectiveness of new inlet seal. And we paid attention to the step-up that is the step between blade and nozzle. As a result, it was experimentally proved that the step-up had a large influence on the rotor stability.

In the seismic design of nuclear power plant, it is recently considered to use probability method in addition to certainty method. The former method is called Seismic Probability Safety Assessment (Seismic PSA). In case of seismic PSA for some components of a nuclear power plant using a shaking table, it is necessary for some limited conditions with high level of accelerations such as actual conditions. However, it might be difficult to achieve the test conditions that a current shaking table based on hydraulic power system is intended for the test facility. Therefore, we have been planning out a test method in which both a current and another shaking table called a booster device are applied. This paper describes the verification test of a synchronized control between a current shaking table and a booster device.

The effectiveness of squeeze-film dampers in controlling vibrations in rotating machinery may be limited by the nonlinear interactions between large rotor imbalance forces with fluid-film forces induced by dampers operating in cavitated conditions. From a practical point of view, the occurrence of nonsynchronous and chaotic motion in rotating machinery is undesirable and should be avoided as they introduce cyclic stresses in the rotor, which in turn may rapidly induce fatigue failure. The bifurcations in the response of a rigid rotor supported by cavitated squeeze-film dampers resulting from such interactions are presented in this paper. The effects of design and operating parameters, namely the bearing parameter (B), gravity parameter (W), spring parameter (S) and unbalance parameter (U), on the bifurcations of the rotor response are investigated. Spring parameter (S) values between 0 and 1 are considered. A spring parameter value of S=0 represents the special case of dampers without centering springs. With the exception of the case S=1, jump phenomena appeared to be a common bifurcation that occurred at certain combinations of B, W and U irrespective of the value of S. Period-doubling and secondary Hopf bifurcations which occurred for low values of S (⩽0.3) were not observed for the higher values S⩾0.5. For very low stiffness values (S

This paper describes an active jiggle control of hung structure using a control moment gyro (CMG) which has two gimbals for one flywheel. The double gimbal CMG enables us to simultaneously control the vibrations for two different dirctions by only one flywheel. Due to the nonlinearlity and interference, it is however difficult to construct the control system for the double gimbal CMG. First, we propose a simple control system design method for the double gimbal CMG based on H2 optimal control theory. In order to improve the gimbal stability, which is necessary for avoiding the interference, we then propose an another design method based on H2/H∞ control using LMI optimization. The performance of all designed control system are evaluated by simulations and experiments.

In this paper, the static characteristics of the four-nozzle pintle type servovalve are studies theoretically, under constant supply pressure and constant supply flow conditions.The study is on an eye to the effect of the valve improper configuration, the required pintle driving torque, and the effect of using unsymmetrical loads on the static characteristics.Errors in valve control gaps resulting from inaccurate initial adjustment, wear of else showed to affect slightly the load flow at each load pressure and input displacement.Units driven by unsymmetrical actuators showed to have lower valve flow forces and higher valve efficiency than symmetrical actuators.The minimum flow gain and flow pressure coefficient are obtained when the load is symmetric.The study showed that the flow forces have two instability sources, decentering nature and similar values at different input displacements.The study discussed the selection of the pintle centering spring to overcome the problems of instability.

Recently, according to the enlargement of rotating equipment such as turbines and pumps, the dynamic characteristics of bearings and seals tends to greatly affect the dynamic characteristics of the rotor system. Therefore, numerous researchers have been engaging in developing the hydrodynamically lubricated bearing theory and seal theory. However, it is still difficult to estimate the precise dynamic characteristics of bearings and seals analytically. On the other hand, there are many researcher who have been developing the experimental measurement technique of bearing and seal dynamic characteristics. This paper describes the measurement technique of bearing and seal dynamic characteristics using the random excitation technique.

In parallel mechanisms with redundant actuators, actuator forces are underspecified because of redundancy. In this paper, the method to minimize a maximum actuator force was proposed. At first, parallel mechanism with two redundant actuators and Stewart platform model using the linear shaft motor were developed. This redundant parallel mechanism was consists of Stewart platform and additional 2 redundant actuators. Inverse dynamics of each mechanisms were formulated. Secondly, effectiveness of dynamic control of Stewart platform was experimentally confirmed. Finally, the method to minimize a maximum actuator force using Linear Matrix Inequality (LMI) was proposed. And the effectiveness of the proposed method was confirmed by simulation.

Recently, the brake noise reduction is one of the most important environmental issues for not only passengers both inside and outside train but also people who live close to railway stations. In this paper, a friction-induced self-excited oscillation and accompanying noise of a tread brake system are experimentally investigated by using a brake dynamometer. The squeal phenomenon occurs in the frequency range over 2000Hz by the test stand and generates high intensity noise up to 120dBA. In order to suppress brake squeal successfully, a simple oil damper attaching to the system is proposed. Since the proposed oil damper is a kind of Houde damper, damping augmentation capability is obtained in broadband of frequencies. The experimental brake test results demonstrate the brake squeal elimination capability of the proposed damper.Copyright © 2006 by ASME

Subsynchronous vibration of high-pressure steam turbine is one of the difficult problems to improve the reliability of power plant. Extensive work has been done to prevent the low frequency vibration of high-capacity steam turbine and most of the problems were practically solved[1][2]. In the future, we must build up theoretical approach to design a new turbine operating under the steam condition of high-temperature and high-pressure. To design such an advanced steam turbine, it is necessary to solve the effect of partial admission on control stage of the steam turbine. This paper describes the experimental results from the scale model of the steam turbine and theoretical analysis of Alford force considered partial admission condition to solve the problem. (1) Subsynchronous vibration was reproduced in the scale model test. (2) Partial admission gave larger destabilizing force compared with full admission condition for same total flow rate. (3) Initial position of shaft center to the phase of admission arc on the partial admission had some effect on the stability of the rotor system. (4) Theoretical analysis of destabilizing force considered partial admission condition gave qualitative description of the experimental results from the scale model.Copyright © 2005 by ASME

Water (working fluid) lubricated bearings are used in various pump designs. This type of bearing has many characteristics different from usual oil lubricated bearings. This paper describes the following characteristics of the water lubricated bearings : (1) Turbulent flow (2) Full film due to high ambient pressure (3) Large additional mass effect Theoretical analysis by numerical calculation and model test using a special test system are performed for a cylindrical bearing. As a result, the characteristics of the water lubricated bearing are recognized and good agreement between theoretical and experimental results is confirmed.

This paper describes the vibration analysis technology of MW-701D Gas Turbine which was developed by Mitsubishi Heavy Industries, Ltd. for 50 Hz utilities. MW-701D is the highest performance gas turbine available with a firing temperature of 1,154°C for base load operation. It is employed by the 1,090 MW combined cycle plant, one of the largest of its kind in the world, and the plant began commercial operation at half of the total capacity of 1,090 MW in December, 1984. The plant was designed to supply base load electric power generation by burning imported liquefied natural gas (LNG) fuel. This paper describes the general description of the combined cycle plant and the vibration characteristics of MW-701D Gas Turbine.