Experimental Identification of Linearized Oil Film Coefficients of Cylindrical and Tilting Pad Bearings

Abstract: In this paper, we present a review of the experimental identification of dynamic parameters of bearings in a rotating machine. Major emphasis is given to vibration-based identification methods and the review encompasses descriptions of experimental measurement techniques, mathematical modeling, parameter extraction algorithms and uncertainty in the estimates applied to a variety of bearings. The parameter extraction algorithms include the descriptions of governing equations of the rotor-bearing system and identification methods in both time and frequency domains. The identification techniques have been classified based on methods used to excite the system. The review includes a variety of bearings and similar components, which play an active link between the rotating and stationary parts of a machine. Based on the state of the art in bearing identification, conclusions are made and future directions are suggested.

Abstract: Fluid film journal bearings (FFBs) are used to support high-speed rotors in turbomachinery which often operate above the rotor first bending critical speed. The FFBs provide both lateral support and dynamic coefficients: stiffness, damping, and mass terms, related to machine vibrations. Detailed numerical values of the bearing dynamic characteristics are necessary for proper design and operation of rotating machinery. The methods of the identification of fluid film journal bearing static and dynamic characteristics, particularly the bearing stiffness, damping, and mass coefficients, from measured data, obtained from different measurement systems, is reviewed. Many bearing tests have been performed to validate a number of different theoretical models, including the classical Reynolds isoviscous model. More advanced bearing models include the thermohydrodynamic (THD), and thermoelastohydrodynamic (TEHD) approaches. The advanced models also include turbulence effects which are important as rotor speeds continue to increase. The range of measured bearing data no longer includes current operational conditions. The various approaches to the bearing identification problem are discussed, including the different force excitation methods of incremental loading, sinusoidal, pseudorandom, impulse, known/additional unbalance, and non-contact excitation. Also bearing excitation and rotor excitation approaches are discussed. Data processing methods in the time and frequency domains are presented. Methods of evaluating the effects of measurement uncertainty on overall bearing coefficient confidence levels are reviewed. In this review, the relative strengths and weaknesses of bearing identification methods are presented, and developments and trends in improving bearing measurements are documented. Future trends in journal bearing identification improvement are discussed.

Abstract: An identification algorithm for simultaneous estimation of residual unbalances and bearing dynamic parameters by using impulse response measurements is presented for multi-degree-of-freedom (mdofs) flexible rotor–bearing systems. The algorithm identifies speed-dependent bearing dynamic parameters for each bearing and residual unbalances at predefined balancing planes. Bearing dynamic parameters consist of four stiffness and four damping coefficients and residual unbalances contain the magnitude and phase information. Timoshenko beam with gyroscopic effects are included in the system finite element modelling. To overcome the practical difficulty of number of responses that can be measured, the standard condensation is used to reduce the number of degrees of freedom (dofs) of the model. For illustration, responses in time domain are simulated due to impulse forces in the presence of residual unbalances from a rotor–bearing model and transformed to frequency domain. The identification algorithm uses these responses to estimate bearing dynamic parameters along with residual unbalances. The proposed algorithm has the flexibility to incorporate any type and any number of bearings including seals. The identification algorithm has been tested with the measurement noise in the simulated response. Identified parameters match quite well with assumed parameters used for the simulation of responses. The response reproduction capability of identified parameters has been found to be excellent.

Abstract: The popularity of compressors utilizing foil bearings is increasing. Their mechanical design is challenging, and an accurate prediction of the bearing coefficients is important. A mathematical model taking into account the foil structure, and the detailed geometry of a three pad foil bearing are presented. The steady state solution and dynamic coefficients are obtained through zeroth and first order perturbed equations respectively. Analysis of the foil structure reveals the importance of distinguishing between a static foil stiffness for the zeroth order equation and a dynamic stiffness for the first order equation. Calculated bearing coefficients are compared to experimental results obtained from a dedicated test rig. Generally, good agreement is observed and minor discrepancies for the damping coefficients are discussed.

Abstract: In this paper an investigation has been made to evaluate experimentally the performance characteristics of a misaligned 3-lobe journal bearing. Various parameters which have been studied are: friction through coast down time analysis, vibration responses, minimum film thickness, stiffness and damping coefficients of the fluid film, system natural frequency and damping factor. The film thickness decreases, friction increases and system damping increases as the bearing misalignment increases. © 1997 Elsevier Science S.A.

Abstract: The dynamic behavior of a mechanical system generally are strongly affected by the properties of mechanical joints. An identification method which directly used the measured frequency response functions (FRFs) to identify the joint properties was introduced in this work. Because the measurement noise in the frequency response functions is unavoidable in practice and may lead to very faulty results, the proposed method has been developed especially to overcome this problem. The accuracy and feasibility of the proposed method were verified and demonstrated by theoretical simulation and experiments. The results show that the joint properties can be identified accurately from the FRFs even with noise effect.

Abstract: The vibration behaviour of a rotor system supported by hydrodynamic bearings is significantly influenced by the dynamic characteristics of the bearings. An identification procedure for estimating bearing oil-film coefficients is developed in this work. Eight linearized oil-film coefficients are identified by fitting the measured complex functions of frequency response to those calculated theoretically. The theoretical model and reliability are examined by computer simulation. From error analysis, some interesting conclusions are reached and a new identification method is suggested in order to reduce the influence of phase measurement errors on estimated results.

Abstract: The vibration behaviour of rotors with journal bearings is significantly influenced by the dynamic characteristics of the bearing oil-film. To validate analytical models of oil-film dynamics, numerous experimental investigations have been undertaken. The authors have previously carried out a project to improve the quality of the estimation of oil-film coefficients. In the companion paper (part I), a system model and an algorithm with simulation results have been presented for a flexible rotor-bearing system under operating conditions. This second paper gives details of an experimental investigation designed to demonstrate the feasibility of the method.