Academic literature on the topic 'Bearings (Machinery) – Vibration – Mathematical models'
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Journal articles on the topic "Bearings (Machinery) – Vibration – Mathematical models"
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Brito Junior, Geraldo Carvalho, Roberto Dalledone Machado, and Anselmo Chaves Neto. "Using Simplified Models to Assist Fault Detection and Diagnosis in Large Hydrogenerators." International Journal of Rotating Machinery 2017 (2017): 1–18. http://dx.doi.org/10.1155/2017/9258456.
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Based on experimental evidence collected in a set of twenty 700 MW hydrogenerators, this article shows that the operating conditions of large hydrogenerators journal bearings may have unpredictable and significant changes, without apparent reasons. These changes prevent the accurate determination of bearing dynamic coefficients and make the prediction of these machines dynamic behavior unfeasible, even using refined models. This makes it difficult to differentiate the normal changes in hydrogenerators dynamics from the changes created by a fault event. To overcome such difficulty, this article proposes a back-to-basics step, the using of simplified mathematical models to assist hydrogenerators vibration monitoring and exemplifies this proposal by modeling a 700 MW hydrogenerator. A first model estimates the influence of changes in bearing operating conditions in the bearing stiffnesses, considering only the hydrodynamic effects of an isoviscous oil film with linear thickness distribution. A second model simulates hydrogenerators dynamics using only 10 degrees of freedom, giving the monitored vibrations as outputs, under normal operating conditions or in the presence of a fault. This article shows that simplified models may give satisfactory results when bearing operating conditions are properly determined, results comparable to those obtained by more refined models or by measurements in the modeled hydrogenerator.
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Liu, Jing, Linfeng Wang, Zhifeng Shi, Wennian Yu, and Huifang Xiao. "A comparison investigation of the contact models for contact and vibration features of cylindrical roller bearings." Engineering Computations 36, no. 5 (June 10, 2019): 1656–75. http://dx.doi.org/10.1108/ec-11-2018-0516.
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Purpose The purpose of this study is to investigate the contact models for contact and vibration features of cylindrical roller bearings (CRBs). CRBs are important parts of rotating machinery. The contact deformation between the roller and the raceway is an essential research topic for the CRBs. The contact deformation between the roller and the raceway can greatly affect vibration characteristics and fatigue life of the CRBs. In this investigation, six different methods are adopted to calculate the contact deformation, contact area width and contact stress between the roller and raceways of a CRB. Design/methodology/approach In this paper, the contact deformations and the contact stiffnesses between the roller and the raceway of a CRB obtained by various well-known empirical methods (Lundberg’s, Palmgren’s, Houpert’s, Cheng’s and Hertzian methods) are directly compared with those by the finite element (FE) method. A two degree-of-freedom (2 DOF) dynamic model of the CRB is applied to investigate the effects of the contact stiffness obtained by different line contact deformation calculation methods on the vibration characteristics, such as the root mean square (RMS), the peak to peak (PTP), the crest factor and the kurtosis of the displacement, velocity and acceleration of the inner raceway. Findings The computational results show that different calculation methods for the contact deformations between rollers and raceways have significant effects on the vibrations of the CRB. It is found that that the differences of computational results obtained by Palmgren’s and Lundberg’s models with respect to the FE method are smaller than those by the other three methods, i.e. Houpert’s, Cheng’s and Hertzain models. The amplitude and peak frequency of the frequency response functions from Palmgren’s method are much more similar to those from the finite element method. The above results indicate that Palmgren’s method is a better calculation method for predicting the contact deformations and dynamics of the CRBs. Originality/value This work adopts six different methods to calculate the contact deformation, contact area width and contact stress between the roller and raceways of a CRB. Moreover, a vibration model of a CRB is used to investigate the effect of contact stiffness obtained by the above methods on the vibrations of the CRB. The works can give some guidance for the accurate analytical method for calculating the contact deformations between rollers and raceways and the vibrations of the CRB.
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Veselovska, Nataliya, Olha Yalina, and Vasyliy Yanishevskiy. "DEVELOPMENT OF AN ALGORITHM FOR DIAGNOSING DENTAL DEFECTS IN REDUCERS OF SELF-PROPELLED AGRICULTURAL MACHINES." ENGINEERING, ENERGY, TRANSPORT AIC, no. 3(110) (October 30, 2020): 16–23. http://dx.doi.org/10.37128/2520-6168-2020-3-2.
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Intensive use of agricultural production technologies has recognized the intensive characteristics of agricultural producers, which allowed to present the need for frequent diagnostics, maintenance and repair. This transition is due to objective trends in the development of agricultural machinery. The solution to this problem involves the development and creation of effective tools for monitoring and diagnosing the state of the transmission elements of agricultural machinery; assessment of the value of the residual life of individual elements of the system and the study of energy conversion processes in these elements; construction of mathematical models on the basis of which it is possible to predict the occurrence of dangerous damage depending on the operating conditions of the equipment. Diagnostic means must ensure the assessment of the condition of the working surfaces of the interacting transmission elements, control of wear of their surfaces and assessment of the performance of the unit as a whole or the kinematic pair without their disassembly during operation. The time of collection of diagnostic information and allocation of informative signs and parameters of signals should be minimized. Control methods should be as simple as possible, and the means that implement them - compact, with built-in algorithms for information processing and decision-making. The most informative parameter that carries the maximum information about the state of the unit of a working machine or unit is mechanical oscillations (vibrations) - elastic waves propagating in continuous media. Measurement of vibroacoustic characteristics on bearing supports of mechanisms allows to recognize such defects and damages as imbalance and skew of shafts; damage to plain and rolling bearings; damage to gears in gears; damage to couplings; damage to electrical machines. With the systematic use of modern diagnostic methods it is possible to avoid serious damage to the transmission elements and reduce operating costs for maintenance of agricultural machinery due to the fact that the repair is carried out only when the measurement results indicate its need.
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Zarraga, Ondiz, Imanol Sarría, Jon García-Barruetabeña, and Fernando Cortés. "An Analysis of the Dynamical Behaviour of Systems with Fractional Damping for Mechanical Engineering Applications." Symmetry 11, no. 12 (December 11, 2019): 1499. http://dx.doi.org/10.3390/sym11121499.
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Fractional derivative models are widely used to easily characterise more complex damping behaviour than the viscous one, although the underlying properties are not trivial. Several studies about the mathematical properties can be found, but are usually far from the most daily applications. Thus, this paper studies the properties of structural systems whose damping is represented by a fractional model from the point of view of a mechanical engineer. First, a single-degree-of-freedom system with fractional damping is analysed. Specifically, the distribution of the poles and the dynamic response to several excitations is studied for different model parameter values highlighting dissimilarities from systems with conventional viscous damping. In fact, thanks to fractional models, particular behaviours are observed that cannot be reproduced by classical ones. Finally, the dynamics of a machine shaft supported by two bearings presenting fractional damping is analysed. The study is carried out by the Finite Element method, deriving in a system with symmetric matrices. Eigenvalues and eigenvectors are obtained by means of an iterative method, and the effect of damping is visualised on the mode shapes. In addition, the response to a perturbation is computed, revealing the influence of the model parameters on the resulting vibration.
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Amin, A. K. M. Nurul, Fawaz Mohsen Abdullah, Muammer Din Arif, and Israd H. Jaafar. "Mathematical Model for Chip Serration Frequency in Turning of Stainless Steel with Magnetic Damping from Bottom of Tool Shank." Applied Mechanics and Materials 393 (September 2013): 108–14. http://dx.doi.org/10.4028/www.scientific.net/amm.393.108.
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Chatter, a violent and often unpredictable relative oscillatory motion between the tool and work-piece, is a serious concern in turning operations. Its occurrence is usually associated with a loud monotonous sound and usually results in increased surface roughness, reduced material removal rates, shortened tool life, and damaged machine-tool bearings. The established theories for chatter are very limited in scope and are often contradicted by empirical evidences. Therefore, chatter avoidance in the past has relied on inefficient techniques like limiting material removal rates or expensive setups such as actuators and ultrasonic vibration damping systems. However, a deeper investigation into chatter formation reveals that chip morphology and segmentation play a significant role during the incidence of chatter. The novel Resonance theory of chatter combines the concept of mode coupling of the machining setup and serrated chip formation, to explain and predict chatter. To validate the postulates of this theory, models for chip serration frequency are essential. At the same time, a reliable and economical chatter control method is required. With this goal, the current research work has developed an empirical mathematical model of chip serration frequency in turning of stainless steel AISI 304 using Response Surface Methodology (RSM). Also, it investigated the influence of damping provided by magnetic field from a permanent ferrite magnet placed beneath the tool shank. The developed chip serration model is in good accord with the experimental data, demonstrating that the empirical model could be used for further chip morphology and chatter analyses.
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Vania, A., and P. Pennacchi. "Effects of the Hot Alignment of a Power Unit on Oil-Whip Instability Phenomena." International Journal of Rotating Machinery 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/385947.
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This paper shows the results of the analysis of the dynamic behaviour of a power unit, whose shaft-train alignment was significantly influenced by the machine thermal state, that was affected in operating condition by high subsynchronous vibrations caused by oil-whip instability phenomena. The dynamic stiffness coefficients of the oil-film journal bearings of the generator were evaluated considering the critical average journal positions that caused the instability onsets. By including these bearing coefficients in a mathematical model of the fully assembled machine, the real part of the eigenvalue associated with the first balance resonance of the generator rotor became positive. This paper shows the successful results obtained by combining diagnostic techniques based on mathematical models of journal bearings and shaft train with detailed analyses of monitoring data aimed to investigate the effects of the hot alignment of rotating machines on the occurrence of oil-whip instability onsets.
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Ahmed, Elhaj A. I., and Li Shusen. "Optimization of Factors Affecting Vibration Characteristics of Unbalance Response for Machine Motorized Spindle Using Response Surface Method." Mathematical Problems in Engineering 2019 (February 10, 2019): 1–12. http://dx.doi.org/10.1155/2019/1845056.
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In this study, the response surface (RS) method and forced rotordynamic analyses together with Finite-Element-Analysis (FEA) have been established to optimize the factors affecting the vibration characteristics. The spindle specification, bearings locations, cutting force, and motor-rotor unbalance mass are proposed to represent the design factors and then they are utilized to develop Machine Motorized Spindle (MMS). The FEA-based Design of Experiment (DOE) is adopted to simulate the output responses with the input factors, wherein these DOE design points are used to carry out the RS models to visualize more obvious factors affecting the dynamic characteristics of MMS. The sensitivities of these factors and their contributions to the vibration of imbalance response have been evaluated by using the RS models. The simulation results show that the motor-rotor shaft inner diameter, the distance of the back bearing location, and the rotating unbalance-mass are highly sensitive to the vibration characteristics compared to the other factors. It is found that more than two-fifths of total vibration response amplitude has been conducted by induced rotating imbalance mass. The results also showed that the proposed factors optimization method is practicable and effective in improving the vibration response characteristics.
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Zmarzły, Paweł. "Mathematical model of the impact assessment of roughness and waviness deviations of races surfaces of rolling bearings on the level of generated vibration." Mechanik 92, no. 1 (January 14, 2019): 35–37. http://dx.doi.org/10.17814/mechanik.2019.1.5.
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The article presents mathematical models allowing to describe the level of vibration generated by ball bearings 6304-2z type depending on the value of roughness and waviness deviations of inner and outer bearings races. This models will allow to estimate what type of shape deviations have dominant influence on the vibration level generated in specific frequency ranges.
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Cole, Matthew O. T. "On stability of rotordynamic systems with rotor–stator contact interaction." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2100 (August 29, 2008): 3353–75. http://dx.doi.org/10.1098/rspa.2008.0237.
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In machine systems where a rotor spins within a finite clearance space supported by bearings, contact between the rotor and its surround can result in persistent coupled vibration of the rotor and stator. When the vibration response is driven predominantly by friction forces, rotordynamic stability becomes a serious issue. This paper introduces a theory for model-based verification of dynamic stability in rotor systems with stator contact and rub. Generalized multi-degree-of-freedom linear models of rotor and stator lateral vibration are considered, combined with contact models that account for finite clearance and Coulomb friction. State-space conditions for global stability as well as stability of contact-free synchronous whirl responses are derived using Lyapunov's direct method. This leads to feasibility problems involving matrix inequalities that can be quickly verified using numerical routines for convex optimization. Parametric studies involving flexible rotor models indicate that tight bounds on regions of stability can be obtained. A case study involving a realistic machine model illustrates how design optimization based on the theory might be used to overcome instability problems in real machines.
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Xiao, Long Xue, Guo Qing Wu, and Xu Dong Zhang. "Modal Analysis of Maglev Linear Feed Unit." Applied Mechanics and Materials 150 (January 2012): 205–10. http://dx.doi.org/10.4028/www.scientific.net/amm.150.205.
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The structural and working principle of a kind of maglev linear feed unit for CNC engraving and milling machine tools are presented, and its mathematical model is analyzed, then its model of vibration is established in this paper. The modal analysis is made, the natural frequency is calculated with its vibration models, and the influence on the natural frequency of electromagnetic levitation bearing unit, which is caused by stiffness and damping coefficients of electromagnetic levitation bearing, is analyzed respectively by means of ANSYS software. The calculation and analysis presented in this paper can help us design the structure of the maglev linear feed unit for CNC engraving and milling machine tools, and can also establish a solid foundation for further etailed dynamics analysis.
Dissertations / Theses on the topic "Bearings (Machinery) – Vibration – Mathematical models"
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Clark, William Walker. "Application of adaptive trusses to vibration isolation in flexible structures." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/38913.
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Sawalhi, Nader Mechanical & Manufacturing Engineering Faculty of Engineering UNSW. "Diagnostics, prognostics and fault simulation for rolling element bearings." 2007. http://handle.unsw.edu.au/1959.4/40544.
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Vibration signals generated from spalled elements in rolling element bearings (REBs) are investigated in this thesis. A novel signal-processing algorithm to diagnose localized faults in rolling element bearings has been developed and tested on a variety of signals. The algorithm is based on Spectral Kurtosis (SK), which has special qualities for detecting REBs faults. The algorithm includes three steps. It starts by pre-whitening the signal's power spectral density using an autoregressive (AR) model. The impulses, which are contained in the residual of the AR model, are then enhanced using the minimum entropy deconvolution (MED) technique, which effectively deconvolves the effect of the transmission path and clarifies the impulses. Finally the output of the MED filter is decomposed using complex Morlet wavelets and the SK is calculated to select the best filter for the envelope analysis. Results show the superiority of the developed algorithm and its effectiveness in extracting fault features from the raw vibration signal. The problem of modelling the vibration signals from a spalled bearing in a gearbox environment is discussed. This problem has been addressed through the incorporation of a time varying, non-linear stiffness bearing model into a previously developed gear model. It has the new capacity of modeling localized faults and extended faults in the different components of the bearing. The simulated signals were found to have the same basic characteristics as measured signals, and moreover were found to have a characteristic seen in the measured signals, and also referred to in the literature, of double pulses corresponding to entry into and exit from a localized fault, which could be made more evident by the MED technique. The simulation model is useful for producing typical fault signals from gearboxes to test new diagnostic algorithms, and also prognostic algorithms. The thesis provides two main tools (SK algorithm and the gear bearing simulation model), which could be effectively employed to develop a successful prognostic model.
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Lawrence, Tom Marquis. "Characterization and Measurement of Hybrid Gas Journal Bearings." 2012. http://hdl.handle.net/1805/2926.
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Indiana University-Purdue University Indianapolis (IUPUI)This thesis concentrates on the study of hybrid gas journal bearings (bearings with externally pressurized mass addition). It differs from most work in that it goes back to “basics” to explore the hydrodynamic phenomena in the bearing gap. The thesis compares geometrically identical bearings with 2 configurations of external pressurization, porous liners where mass-addition compensation is varied by varying the liner’s permeability, and bushings with 2 rows of 6 feedholes where the mass-addition compensation is varied by the feedhole diameter. Experimentally, prototype bearings with mass-addition compensation that spans 2 orders of magnitude with differing clearances are built and their aerostatic properties and mass addition characteristics are thoroughly tested. The fundamental equations for compressible, laminar, Poiseuille flow are used to suggest how the mass flow “compensation” should be mathematically modeled. This is back-checked against the experimental mass flow measurements and is used to determine a mass-addition compensation parameter (called Kmeas) for each prototype bushing. In so doing, the methodology of modeling and measuring the mass addition in a hybrid gas bearing is re-examined and an innovative, practical, and simple method is found that makes it possible to make an “apples-to-apples” comparison between different configurations of external pressurization. This mass addition model is used in conjunction with the Reynolds equation to perform theory-based numerical analysis of virtual hybrid gas journal bearings (CFD experiments). The first CFD experiments performed use virtual bearings modeled to be identical to the experimental prototypes and replicate the experimental work. The results are compared and the CFD model is validated. The ontological significance of appropriate dimensionless similitude parameters is re-examined and a, previously lacking, complete set of similitude factors is found for hybrid bearings. A new practical method is developed to study in unprecedented detail the aerostatic component of the hybrid bearings. It is used to definitively compare the feedhole bearings to the porous liner bearings. The hydrostatic bearing efficiency (HBE) is defined and it is determined that the maximum achievable hydrostatic bearing efficiency (MAHBE) is determined solely by the bearing’s mass addition configuration. The MAHBE of the porous liner bearings is determined to be over 5 times that of the feedhole bearings. The method also presents a means to tune the Kmeas to the clearance to achieve the MAHBE as well as giving a complete mapping of the hitherto misunderstood complex shapes of aerostatic load versus radial deflection curves. This method also rediscovers the obscure phenomenon of static instability which is called in this thesis the “near surface effect” and appears to be the first work to present a practical method to predict the range of static instability and quantify its resultant stiffness fall-off. It determines that porous liner type bearings are not subject to the phenomenon which appears for feedhole type bearings when the clearance exceeds a critical value relative to its mass-addition compensation. The standing pressure waves of hydrostatic and hybrid bearings with the 2 configurations of external pressurization as well as a geometrically identical hydrodynamic bearing are studied in detail under the methodology of the “CFD microscope”. This method is used to characterize and identify the development, growth, and movement of the pressure wave extrema with increased hydrodynamic action (either increasing speed or increasing eccentricity). This method is also used to determine the “cause” of the “near surface effect”. A gedanken experiment is performed based on these results which indicates that a bearing with a “stronger aerostatic strength” component should be more stable than one with a low aerostatic strength component. Numerical instability “speed limits” are found that are also related to the hydrostatic strength of the bearing. The local conditions in the standing waves are characterized in terms of their local Mach number, Knudsen number, Reynolds number, and Taylor Number. It is concluded that low eccentricity bearing whirl can be attributed to the off load-line orientation of the bearing load force caused by the overlay of the hydrodynamic bearing standing wave onto the hydrostatic bearing wave of the hybrid bearing, whereas it is hypothesized that aperiodic and random self-excited vibration which occurs at high eccentricity, as reported in the literature, is probably due to shock waves, turbulence, near surface effect, and slip at local areas of the standing wave.
Books on the topic "Bearings (Machinery) – Vibration – Mathematical models"
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Singh, Rajendra. Non-linear dynamic analysis of geared systems. [Columbus, Ohio]: The Ohio State University, Dept. of Mechanical Engineering, 1990.
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Singh, Rajendra. Non-linear dynamic analysis of geared systems. [Columbus, Ohio]: The Ohio State University, Dept. of Mechanical Engineering, 1990.
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Singh, Rajendra. Vibration transmission through rolling element bearings in geared rotor system.: Final report. [Columbus, Ohio ?]: Ohio State University, 1990.
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Fundamentals of mechanical vibrations. Hoboken: John Wiley & Sons, Inc., 2016.
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Mari͡uta, A. N. Teorii͡a modelirovanii͡a kolebaniĭ rabochikh organov mekhanizmov i ee prilozhenii͡a. Dnepropetrovsk: Izd-vo DGU, 1991.
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Gurskiĭ, N. N. Modelirovanie i optimizat︠s︡ii︠a︡ kolebaniĭ mnogoopornykh mashin: Monografii︠a︡. Minsk: BNTU, 2008.
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Singh, Rajendra. Vibration transmission through rolling element bearings in geared rotor systems. Washington, D.C: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1990.
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Vibration of structures and machines: Practical aspects. New York: Springer-Verlag, 1993.
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Vibration of structures and machines: Practical aspects. 2nd ed. New York: Springer-Verlag, 1995.
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Genta, G. Vibration of structures and machines: Practical aspects. 3rd ed. New York: Springer, 1999.
Find full textConference papers on the topic "Bearings (Machinery) – Vibration – Mathematical models"
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Santos, Ilmar F., and Alexandre Scalabrin. "Control System Design for Active Lubrication With Theoretical and Experimental Examples." In ASME Turbo Expo 2000: Power for Land, Sea, and Air. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/2000-gt-0643.
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This work focuses on the theoretical and experimental behavior of rigid rotors controlled by tilting-pad journal bearings with active oil injection. Initially the mathematical model of the active bearing is presented: the equations that describe the dynamics of hydraulic actuators are introduced into the equations of the lubricant, resulting in a new form of Reynolds’ equation for active lubrication. The global model of the system is obtained by coupling the equation of motion of the rigid rotor with the stiffness and damping of the active oil film. This global model is then used to design the control system of the active bearing based on root locus curves. The active system stability is analyzed by calculating its eigen values and frequency response curves. The theoretical and experimental results show that this kind of bearing can significantly reduce the vibration level of rotating machinery.
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San Andre´s, Luis, and Oscar C. De Santiago. "Identification of Bearing Force Coefficients From Measurements of Imbalance Response of a Flexible Rotor." In ASME Turbo Expo 2004: Power for Land, Sea, and Air. ASMEDC, 2004. http://dx.doi.org/10.1115/gt2004-54160.
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Field identification of fluid film bearing parameters is critical for adequate interpretation of rotating machinery performance and necessary to validate or calibrate predictions from restrictive computational fluid film bearing models. This paper presents a simple method for estimating bearing support force coefficients in flexible rotor-bearing systems. The method requires two independent tests with known mass imbalance distributions and the measurement of the rotor motion (amplitude and phase) at locations close to the supports. The procedure relies on the modeling of the rotor structure and finds the bearing transmitted forces as a function of observable quantities (rotor vibrations at bearing locations). Imbalance response measurements conducted with a two-disk flexible rotor supported on two-lobe fluid film bearings allow validation of the identification method estimations. Predicted (linearized) bearing force coefficients agree reasonably well with the parameters derived from the test data. The method advanced neither adds mathematical complexity nor requires additional instrumentation beyond that already available in most high performance turbomachinery.
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Asadi, Saeed, Viktor Berbyuk, and Håkan Johansson. "Vibration Dynamics of a Wind Turbine Drive Train High Speed Subsystem: Modelling and Validation." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46016.
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Modern wind turbines are enormous large-scale electromechanical systems. They operate in complex conditions, determined by a turbulent wind field, by possible disturbances in the electricity grid and by the behavior of sea waves for offshore turbines. Guaranteeing the structural integrity of these machines during a lifetime of 20 years is an enormous challenge. In this paper the dynamics of a wind turbine drive train high speed subsystem is studied both by modeling and experiments with focus on system torsional and flexural vibrations and transient events which can reduce fatigue life of functional components (gearbox, bearings, shafts, couplings, others). A scaled down drive train high speed shaft test rig has been developed. Main components of the test rig are six-pole motor with variable frequency drive controller (up to 1000 rpm), shafts’ disk coupling and flexible mounting structure representing gearbox housing with output high speed bearing. The test rig is equipped with measurement system comprising a set of accelerometers and displacement sensors, data acquisition hardware and software (SKF WindCon3.0). Mathematical and computational models of the test rig have been developed and went through validation tests. The system kinematic and dynamic responses are studied for different operational scenarios and structural parameters (ratio of shaft bending stiffness and stiffness of mounting structures, unevenly inertia load distribution, others). The ultimate goal of the test rig is to get insight into interaction between internal dynamics of drive train functional components to be used the results obtained in developing novel methods to detect, predict and prevent faults and failures in wind turbine drive trains arising due to misalignments and transient external loads.
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Petrov, E. P. "Analytical Formulation of Friction Contact Elements for Frequency-Domain Analysis of Nonlinear Vibrations of Structures With High-Energy Rubs." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-90628.
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Abstract In gas-turbine engines and other rotating machinery structures rubbing contact interactions can occur when the contacting components have large relative motion between components: such as in rotating bladed disc-casing rubbing contacts, rubbing in rotor bearing and labyrinth seals, etc. The analysis of vibrations of structures with rubbing contacts requires the development of a mathematical model and special friction contact elements that would allow for the prescribed relative motion of rubbing surfaces in addition to the motion due to vibrations of the contacting components. In the proposed paper, the formulation of the friction contact elements is developed which includes the effects of the prescribed relative motion on the friction stick-slip transitions and, therefore, on the contact interaction forces. For a first time, the formulation is made for the frequency domain analysis of coupled rubbing and vibrational motion, using the multiharmonic representation of the vibration displacements. The formulation is made fully analytically to express the multiharmonic contact interaction forces and multiharmonic tangent stiffness matrix in an explicit analytical form allowing their calculation accurately and fast. The dependency of the friction and contact stiffness coefficients on the energy dissipated during high-energy rubbing contacts and, hence, on the corresponding increase of the contact interface temperature is included in the formulation. The efficiency of the developed friction elements is demonstrated on a set of test cases including simple models and a large-scale realistic blade.
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Patel, D. C., and D. P. Vakharia. "Analysis of Dynamically Loaded Floating Bush Bearing With Flexible Shaft in Flexible Anisotropic Bearing Used in Textile Application." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68401.
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A FLOATING bush bearing is a kind of bearing which has a thin bush floating freely between journal and fixed bush. In recent years considerable attention has been paid to the “vibration suppressing effect” of floating us bearing. It is reported that floating bush bearing are, if properly designed, effective in suppressing both resonant vibrations at the critical speed and self excited vibration call oil whip. This study deal with performance of dynamically loaded floating ring journal bearing and investigates their feasibility for two for one textile machine application. A mathematical model is developed and its analysis for performance of floating bush journal bearing with flexible shat in flexible anisotropic bearing is conducted. The potential contribution of the floating bush journal bearing design concept to reduce vibration is assessed and its compliance with current bearing durability criteria is evaluated. The result indicates that the adoption of floating bush design concept has potential for reducing power loss and vibration in two for one (TFO) textile machine bearing. It is shown that this can be accomplished without violating minimum film thickness constraints currently accepted as criteria for successful machine bearing operation.
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Hathout, J. P., and A. El-Shafei. "PI Control of HSFDs for Active Control of Rotor-Bearing Systems." In ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-gt-123.
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This paper describes the proportional integral (PI) control of hybrid squeeze film dampers (HSFDs) for active control of vibrations of rotors. Recently it was shown that the automatically controlled HSFD based on feedback of rotor speed can be a very efficient device for active control of rotor vibration when passing through critical speeds. Although considerable effort has been put into the study of steady state vibration control, there are few methods in the literature applicable to transient vibration control of rotor-bearing systems. Rotating machinery may experience dangerously high dynamic loading due to the sudden mass unbalance that could be associated with blade loss. Transient run-up and coast down through critical speeds when starting up or shutting down rotating machinery induces excessive bearing loads at criticals. In this paper, PI control is proposed as a regulator for the HSFD system to attenuate transient vibration for both sudden unbalance and transient run-up through critical speeds. A complete mathematical model of this closed-loop system is simulated on a digital computer. Results show an overall enhanced behavior for the closed-loop rotor system. Gain scheduling of both the integral gain and the reference input is incorporated to the closed-loop system with the PI regulator and results in an enhanced behavior of the controlled system.
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Yabui, Shota, Jotaro Chiba, Takafumi Suzuki, Shigeyuki Tomimatsu, and Tsuyoshi Inoue. "Transfer Function Modeling and Experimental Variation of Rotor System Considering Morton Effect Caused in Journal Bearing." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-91135.
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Abstract In recent years, a rotating machinery are required to operate at high rotational speed for high efficiency. However, the rotating machinery may become unstable due to the increase of rotational speed. One cause of unstable vibration is the Morton Effect generated in a journal bearing. To avoid unstable vibration due to the Morton Effect, construction of a mathematical model for predicting it becomes an important subject. Many researches on the Morton Effect have been conducted previously. Conventional researches are mostly divided into two types. The first one is a study based on detailed numerical simulation using computational fluid dynamics (CFD), thermoshydrodynamics (THD) and so on. It tries to find solution of a differential equation which indicates the Morton Effect induced vibration for a specific machine or a test rig. Therefore, this approach has led not comprehensive model. The other one is a study expressed by a simple mathematical formula. However, modeling in the time domain has been mainly focused and modeling in the frequency domain has not been investigated in detail. In this research, a model based on the frequency response that can quantitatively evaluate the Morton Effect induced vibration in the rotating machinery supported by the journal bearing is developed. First, experimental data was collected for modeling by using an experimental rig. Using these experimental data of journal position in the journal bearing and temperature of journal, a model of the Morton Effect was constructed based on frequency responses. In the proposed method, the characteristic of the journal bearing was considered as a proportional differential controller from control engineering point of view. In addition, the proposed model considers the Morton Effect induced vibration as a new bending mode of a rotating shaft caused by thermal difference. Then, the developed model of the Morton Effect was evaluated in the frequency domain. The characteristics of vibration calculated by the proposed model indicated good correlation with that of the experimental data. Finally, the behavior of the rotating shaft at another rotational speed was predicted by using the proposed model. It was confirmed that the experimental data well agreed with the predicted results. These results show the usefulness of the proposed method of this research for predicting the Morton Effect.
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Nicoletti, Rodrigo, and Ilmar Ferreira Santos. "Frequency Response Analysis of an Actively Lubricated Rotor/Tilting-Pad Bearing System." In ASME Turbo Expo 2004: Power for Land, Sea, and Air. ASMEDC, 2004. http://dx.doi.org/10.1115/gt2004-54034.
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In the present paper, the dynamic response of a rotor supported by an active lubricated tilting-pad bearing is investigated in the frequency domain. The theoretical part of the investigation is based on a mathematical model obtained by means of rigid body dynamics. The oil film forces are inserted into the model by using two different approaches: (a) linearized active oil film forces and the assumption that the hydrodynamic forces and the active hydraulic forces can be decoupled; (b) equivalent dynamic coefficients of the active oil film and the solution of the modified Reynolds equation for the active lubrication. The second approach based on the equivalent dynamic coefficients leads to more accurate results since it includes the frequency dependence of the active hydraulic forces. Theoretical and experimental results reveal the feasibility of reducing resonance peaks by using the active lubricated tilting-pad bearing. By applying a simple proportional controller, it is possible to reach 30% reduction of the resonance peak associated with the first rigid body mode shape of the system. One of the most important consequences of such a vibration reduction in rotating machines is the feasibility of increasing their operational range by attenuating resonance peaks and reducing vibration problems.
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Ericson, Tristan M., and Robert G. Parker. "Planetary Gear Modal Vibration Properties Torque Sensitivity." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13678.
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The effect of preload torque on planetary gear behavior is investigated with experiments and mathematical models. Natural frequencies, mode shapes, and damping are influenced by mean torque levels. Natural frequencies increase with greater torque. Damping increases in some modes and decreases in others. The mode shapes undergo various changes as torque increases as demonstrated in the trajectory of a planet gear in a high frequency mode. A finite element bearing model is used to obtain the load dependent stiffness of the planet bearings, and these values greatly increase the accuracy of a lumped parameter model in predicting the natural frequencies measured in experiments.
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Maslen, Eric H., Christopher K. Sortore, José A. Vázquez, and Carl R. Knospe. "Synchronous Response Estimation in Rotating Machinery." In ASME Turbo Expo 2000: Power for Land, Sea, and Air. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/2000-gt-0397.
Full textAbstract:
Synchronous response estimation attempts to determine the forced response (displacement) of a rotor at critical points which cannot be measured directly. This type of prediction, if accurate and reliable, has broad potential use in the rotating machinery industry. Many machines have close clearance points on their shafts, such as seals, which can easily be damaged by excess vibration. Accurate estimates of the actual level of vibration at these points could usefully assist machine operators in troubleshooting and in protecting the equipment from expensive damage. This type of response information can be used both to generate less conservative alarm limits and, if magnetic bearings are available, to directly guide the bearing controllers in restricting the rotor motion at these critical points. It is assumed that the disturbance forces acting upon the rotor are predominantly synchronous. The response estimate is constructed using the measurable response in conjunction with an estimator gain matrix derived from a model of the transmissibilites of the rotor system. A fundamental performance bound is established based on the single-speed set of measurements by bounding the response to the unmeasurable component of the disturbance force. Acknowledging that some model uncertainty will always exist, a robust performance analysis is developed using structured singular value (μ) analysis techniques. Assuming some reasonable levels of uncertainty for the model parameters (natural frequencies, modal dampings, mode shapes, bearing stiffnesses and dampings) the results of the estimator construction and analysis establish feasibility of the proposed estimation. Two reference rotor models that are representative of industrially sized machines are used to demonstrate and evaluate the estimation. The unmeasurable response estimation errors consistently lie below 25 μm for the examples examined.