NON-LINEAR ROTORDYNAMICS: COMPUTATIONAL STRATEGIES

Size: px
Start display at page:

Download "NON-LINEAR ROTORDYNAMICS: COMPUTATIONAL STRATEGIES"

Transcription

1 The 9th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery Honolulu, Hawaii, February 1-14, NON-LINEAR ROTORDNAMICS: COMPUTATIONAL STRATEGIES Tom J. Chalko Head of Rotordynamic Division, Scientific Eng. Research P/L, Melbourne, Australia, sci-e-research.com, ABSTRACT This article discusses strategies and algorithms for non-linear rotordynamic analysis from the point of view of their practical and effective engineering use. The algorithm implementation is demonstrated for the case of a cooling pump in a nuclear reactor. The pump has a vertical rotor supported in three hydrodynamic bearings, one contact seal and three other non-linear bearings, all in an elastic foundation. Unstable behavior of the machine and the development of limit cycle vibration following the loss of stability of the equilibrium position are demonstrated. Computational aspects as well as engineering results are discussed. INTRODUCTION Non-linear phenomena are quite common in rotating machinery. Among the most significant reasons for the non-linear phenomena in rotating machinery are: the fluid flow in hydrodynamic bearings (Fig 1), hydrostatic bearings, seals, impellers etc.. The fluid flow in the hydrodynamic suspension of the rotor provides not only a hydrodynamic force coupling between the rotor and foundation, but also facilitates a mechanism for the energy transfer from rotation to vibration. This mechanism of the energy transfer is the primary reason for the self-excited and limit cycle vibrations of rotors suspended hydrodynamically. non-linear elastic and energy dissipation properties of subsystems such as contact seals, rubber, polymer elements, elements with clearances such as partially worn ball bearings etc... linear, ordinary differential equations) that approximates the behavior of the non-linear system with sufficient accuracy in the vicinity of its equilibrium. This approach can be very effective, because it enables using all methods, techniques and algorithms of the well established linear vibration theory. The linearized approach has been successfully used to predict vibration performance of large turbine-generator sets (Chalko and Li [1]), analyze behavior of the system in terms of its alignment configuration (Li [], Krodkiewski and Sun [3]) and estimate alignment and the transverse static load in rotating machinery (Krodkiewski and Ding [4], Chalko and Li [5]). The main challenge of the linearization approach is determining the system equilibrium, especially for system with multiple non-linear bearings, where the system alignment effects are significant (Chalko and Li [1][6]). The main limitation of the linearization approach is that it has limited scope and applicability. In principle, this method can only be used if the Rotor-Bearing-Foundation (RBF) system equilibrium is stable and vibrations around such an equilibrium position are sufficiently small. Unfortunately these conditions are frequently not satisfied in certain classes of rotating machinery, such as in machines with vertical rotors supported in hydrodynamic bearings for example. TWO STRATEGIES There are essentially two strategies for vibration analysis of non-linear rotor-bearing-foundation systems that contain nonlinear sub-systems. 1. Linearization in the vicinity of a stable equilibrium position.. Direct solution of the non-linear differential equations of motion in the time domain. The essence of the linearization method is obtaining a reasonable linear system (a system that can be described by a set of Fig 1. Geometry of hydrodynamic bearing pad

2 Direct step by step solution of the non-linear differential equations of motion in the time domain is the alternative approach that doesn t impose limitations on the stability of the equilibrium position of the system or the magnitude of its dynamic deflections. In principle, this approach can be used for analysis of almost unlimited range of phenomena in rotating machinery, such as loss of stability of the static and dynamic equilibrium, self-excited fluid induced vibration and the development of limit cycles that are presented further on in this article. The main challenge in applying the direct step-by-step time domain solution approach in engineering practice arises due to high computational requirements of corresponding algorithms. The main computational load comes from the necessity of computing hydrodynamic forces (solving partial differential equations for the fluid flow) at every time step of integration. In addition, time domain solvers impose practical limits to the number of equations that can be simultaneously solved with satisfactory accuracy and hence impose practical limits on the number of degrees of freedom of the model. From the above, it becomes apparent that the practical implementation of the direct time domain approach in engineering practice depends on successful addressing of the two following issues: 1. Modelling. It is important to develop models in which the number of degrees of freedom is significantly reduced and that can satisfactorily represent the behavior of machinery in the given frequency range. Optimizing computations of hydrodynamic forces Application of the direct time domain approach will be demonstrated using a practical engineering example of a water pump used to circulate water coolant in nuclear reactors. MODELLING Every theoretical analysis and prediction is science and engineering relies of using sensible physical and mathematical models of Reality. Principles of modelling can be summarized in the following chart: REAL SSTEM Idealization PHSICAL MODEL Laws of physics OBSERVATION MATHEMATICAL MODEL Mathematics and computations RESULT? SOLUTION performance of the machine. If a simple model doesn t provide a satisfactory prediction of the machine performance, idealization process in the above chart is reviewed and the model is made more sophisticated. This section briefly describes the modelling strategy for the rotor-bearing-foundation (RBF) system of a centrifugal pump with a vertical shaft supported in 7 bearings: 3 of them hydrodynamic with 4 cylindrical pads each, 3 ball bearings and one contact seal. The presented model has been developed for the purpose of explaining the limit cycle development, predicting the transverse non-linear vibration response of the pump and establishing the influence of the pump parameters on its vibration levels. Models of the shaft and casing Elastic and inertia properties of the shaft and casing structures have been modelled using condensed [7] linear finite element models. The condensed model of the shaft contained 1 nodes and the condensed model of the casing contained 14 nodes. Each node of the reduced model had two degrees of freedom in the transverse directions x and y, so that the total 35 node shaftcasing model had 7 degrees of freedom Ball bearing Ball bearing Elastic coupling Ball bearing Contact seal 4-pad hydrodynamic bearing 4-pad hydrodynamic bearing 6 A good model of a non-linear rotor-bearing-foundation system should be capable of representing the range of phenomena of interest with satisfactory accuracy. It is important to stress that the complexity of the model depends on the range of phenomena to be represented and the accuracy requirements. The ultimate test for every model is a comparison of the predicted solution with a result of an experimental observation. In engineering practice it is sensible to aim for the simplest possible models that enable solving problems or predicting the pad hydrodynamic bearing Fig. Model of a pump with vertical rotor.

3 Hydrodynamic bearings The pump had 3 water lubricated hydrodynamic bearings as indicated in Fig. Each of them was cylindrical and had 4 fixed pads. The fluid flow between a pad and journal in a hydrodynamic bearing is governed by the Reynolds equation of the following form: µ 1 h 3 p R + µ h 3 p =6Ω h ϕ µ ϕ z µ z ϕ +1 h (1) t where, the film thickness is obtained from the geometry of the journal bearing (Fig 1) h = r + e cos (ϕ α c ) so that h t = e t cos (ϕ α c)+e α c t sin (ϕ α c). Reynolds equation is solved using the Optimized Finite Difference Method (Li and Chalko [8]) for specific geometry for each pad in each bearing. For each non-fixed pad (tilting, rolling, pivoting) the algorithm finds its equilibrium using an iterative method. The total instantaneous hydrodynamic force F kh (e, α,e v, α v,t) in bearing k is a function of the relative position (e, α) and velocity (e v, α v ) of the shaft with respect to the casing of the bearing and is computed as the integral (sum) of all pressure forces that act on all pads of the bearing. The finite difference grid and the example of the relative pressure distribution in all bearing pads in a 4 pad pressurized hydrodynamic bearing are shown in Fig 3. Finite series of analytical functions bearings and contact seals: F j = K j r kj + C j r cj () K j and C j above are matrices of coefficients of the connecting element j, r kj = r cj = ³ r xj r xj n k 1,r yj r yj n k 1 T and ³ ṙ xj ṙ xj nc 1, ṙ yj ṙ yj nc 1 T. rxj = x Sj x Fj and r yj = y Sj y Fj define relative positions of the shaft with respect to foundation/casing at the connecting element j along x and y axes respectively. This method enables convenient and flexible modelling of linear elastic elements (where n k =1and n c =1) as well as nonlinear elements (where n k > 1 and/or n c > 1). Anisotropy of stiffness and damping is conveniently controlled by matrices of coefficients K j and C j. An example of approximating the characteristics of a ball bearing F x (r xj r xj n k 1,,, ) for n k =3 is presented in Fig x Fig 4. Approximation of the elastic properties of a ball bearing. Horizontal axis - relative position of the shaft in [µm]. Vertical axis - bearing force in [N]. A ball bearing has near zero stiffness for shaft displacements smaller than bearing clearance. Fig 3. Finite difference grid and the relative pressure distribution in a fixed 4 pad pressurized cylindrical bearing. Shown only a half of the pressure distribution along the axial direction. have been used to approximate certain aspects of the Computational Fluid Dynamics algorithms and their solutions. Axial and radial symmetry in each bearing has been taken advantage of whenever possible. These steps enabled an acceleration of the hydrodynamic force calculation many times, without compromising the accuracy of hydrodynamic force calculation more than 3% in comparison to the standard Finite Difference solution of the Reynolds equation. Modelling of elastic bearings and contact seals The pump had 3 ball bearings, and one contact seal as indicated in Fig. The following analytical function has been used to model elastic non-linear and anisotropic elements such as ball Equations of motion Equations of motion of the rotor-bearing-foundation system can be written in the following form: ½ ¾ ½ ¾ MS ηs CS ηs + + M F η F C F ηf ½ ¾ KS ηs + = K F η F ½ ¾ F (ηs, η = F, η S, η F,t)+F S (t) (3) F (η S, η F, η S, η F,t)+F F (t) where η S =[x S,y S ] and η F =[x F,y F ] are vector of displacement of the shaft and foundation/casing respectively in transverse directions x and y, M S,C S,K S are mass, damping and stiffness matrices of the shaft and M F,C F,K F are mass, damping and stiffness matrices of the foundation. F S (t) and F F (t) denote external excitation forces on the shaft and foundation respectively.

4 Equations (3) are coupled by non-linear forces F (η S, η F, η S, η F,t) and hence are non-linear. Transformed to state-space u =(η S, η F, η S, η F ) equations (3) have the following form: du = f (t, u) (4) dt which is suitable for the numerical step by step time domain solution. Numerical algorithm Fehlberg 4-5 order Runge-Kutta method [9] has been adopted to solve (4) because it provided a good compromise between the accuracy and numerical efficiency for non-stiff equations typically encountered in rotordynamics. Fortran 95 code compiled and executed using Pentium III 85 MHz processor in Win operating system enabled computation of about 5 time steps per second for a system with 7 degrees of freedom containing 7 bearings, 3 of them hydrodynamic. This performance allows the non-linear rotordynamic computations to gain a status of a practical engineering tool in rotordynamic design and analysis. The code has been named TURBINE-PAK non-linear because it complements the previously developed code for linearized analysis of turbomachinery (Chalko and Li [1][6]). RESULTS The code computed the rotor-bearing-foundation (RBF) system response as a function of the system configuration (static load and alignment) bearings (types, geometry, lubricant properties etc.) shaft (geometry, pre-bending, material properties, temperature distribution etc.) foundation and casings dynamic properties (general condensed FEM superelement model) rotor speed excitation forces and unbalance The time step was chosen to correspond to 3 degrees of the shaft rotation, so there were 1 time steps per each rotation of the shaft. About 46 rotations were analyzed which corresponded to about 1.8 seconds of the pump operation at 14 rpm. Initial conditions were set to zero. Calculations took about 18 minutes on Pentium III 85 MHz computer. The rotor had an elastic coupling that coupled the motor with the shaft of the pump (see Fig ). It has been established that this coupling introduced an unbalance excitation to the shaft. For this reason, the model was excited by the unbalance located at the coupling as shown in Fig 5. After about rotations, the motion of the system became quasi-periodic. As the vertical equilibrium position of the shaft is not stable in the hydrodynamic suspension, the motion of the shaft in all 3 hydrodynamic bearings became dominated by hydrodynamic forces. The quasi-periodic motion is depicted in Fig 6. Development of the quasi-periodic limit cycle is shown in subsequent figures. At the bottom section of the shaft, supported in hydrodynamic bearings 5,6,7 hydrodynamic force excitation dominates and vibrations of the shaft have frequency of less than half of the frequency of rotation. The motor, supported in ball bearings is dynamically isolated from the pump by the elastic coupling. Shaft nodes between the elastic coupling and the seal 4 vibrate with essentially frequencies: the frequency of rotation that corresponds to the unbalance excitation and the frequency of the hydrodynamic excitation, which is slightly less than half of the frequency of rotation. Since these frequencies do not have a common multiple, the motion of this section of the shaft is non-periodic (Fig 7). Although the motion of the bottom section of the shaft is also non-periodic, the dominant frequency component there corresponds to the near half-speed hydrodynamic excitation (Fig 8, Fig 9). The relative motion of the shaft with respect to casing in the contact seal 4 is shown in Fig 1. The corresponding reaction is shown in Fig 1. The relative motion of the shaft with respect to casing in hydrodynamic bearings 5,6 and 7 are shown in Fig 11, Fig 14 and Fig 15 respectively. The corresponding reactions are shown in Fig13,Fig16andFig17. CONCLUSIONS Practical application of a fully non-linear rotordynamic analysis of a rotor-bearing-fondation system has been demonstrated using an example of a pump with hydrodynamically supported vertical rotor. It has been demonstrated that the non-linear approach in rotordynamics is not only theoretically possible, but can be effectively applied in engineering practice to predict the performance and dynamic behavior of rotor-bearing-foundation systems. The practical applicability of the non-linear approach to rotordynamics demonstrated in this article has been achieved by reducing the number of degrees of freedom (by using condensed FEM models) for the shaft and the foundation substructures and by optimizing the hydrodynamic force calculations Unbalance Max=.3E-3 Fig 5. Instantaneous position of the shaft (blue) and foundation/casing (red) during the quasi-periodic limit cycle vibration. Digits indicate bearings. Bearing 4 is a contact seal. Unbalance is located at the shaft node that corresponds to the elastic coupling.

5 .5 Motion of the shaft node Z Fig 6. Quasi-periodic motion of the shaft (red), seen from the bottom of the pump. Shown are trajectories in bearings. Every shaft rotation is coded in different color. Note that there are more than rotations per quasi-periodic cycle, that confirms the hydrodynamic excitation. Fig 8. Motion of the shaft node 13. Hydrodynamically excited half-speed twirl dominates. 1.E-5 1.E-5 8.E-6 6.E-6 4.E-6.E-6 -.E-6-4.E-6-6.E-6-8.E-6-1.E-5-1.E-5 Motion of the shaft node Motion of the shaft node 1 Fig 7. Motion of the shaft at node 7 (located between the contact seal 4 and the hydrodynamic bearing 5) is composed from frequencies that are not multiples of one another. Fig 9. Motion of the shaft node 1. Hydrodynamically excited half-speed twirl dominates.

6 1.E-5 1.E-5 8.E-6 6.E-6 4.E-6.E-6 -.E-6-4.E-6-6.E-6-8.E-6-1.E-5-1.E-5 Relative motion at bearing Reaction at bearing 4 Fig 1. Relative motion of the shaft with respect to casing at the contact seal 4. Fig 1. Reaction at the contact seal 4. The seal was modelled to have almost no stiffness, but significant viscous damping. Relative motion at bearing 5 Reaction at bearing 5 4.E-5 3.E E E E E E E-5 - Fig 11. Relative motion of the shaft with respect to the casing at hydrodynamic bearing 5 Fig 13. Reaction at hydrodynamic bearing 5 reflects its 4-pad design.

7 .6.5 Relative motion at bearing 6 4 Reaction at bearing Fig 14. Relative motion of the shaft with respect to the casing at hydrodynamic bearing 6 Fig 16. Reaction at hydrodynamic bearing 6 reflects its 4-pad design..6.4 Relative motion at bearing Reaction at bearing Fig 15. Relative motion of the shaft with respect to the casing at hydrodynamic bearing 7 Fig 17. Reaction at hydrodynamic bearing 7 reflects its 4-pad design.

8 Non-linear rotordynamic modelling and analysis has provided invaluable insight into the pump dynamics, enabling us to gain fundamental understanding of its non-linear behavior. A very important aspect of obtained results cannot actually be shown in this article - it is impossible to show here the animation of the computed non-linear vibration of the pump. Animation of computed behavior of the pump using a computer screen provides a very effective way of communicating computational results and therefore greatly assists engineers in gaining the understanding of non-linear phenomena in rotating machinery. ACKNOWLEDGMENTS The author is grateful to staff of Toshiba Corporation and Tokyo Electric Power Company in Japan for providing the data and discussing results of computations. REFERENCES [1] Chalko T.J., Li D.., Modelling Turbine Vibration in Terms of its Load Variation, International Journal of Rotating Machinery, 1995, Vol 1, No 3-4, pp [] Li D.., Dynamic Optimization of Multi-Bearing Rotors in Terms of System Configuration Parameters, PhD thesis, Department of Mechanical Engineering, University of Melbourne, Australia, 199. [3] J.M. Krodkiewski, L. Sun, Modelling of multi- bearing rotor system incorporating an active journal bearing, Journal of Sound and Vibration, Vol. 1, No. 1, p. 15-9, [4] J.M. Krodkiewski,J. Ding, Theory and experiment on a method for on-side identification of configuration of multi-bearing rotor system, Journal of Sound and Vibration, Vol. 164, No., p , [5] Chalko T.J., Li D.., Bearing Alignment Estimation in Rotating Machinery, Proceedings of 6-th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC-6) Honolulu, Hawaii, USA, Feb 3-8, 1996 [6] Chalko T.J., Li D.., Estimation of Alignment and Transverse Load in Multi-Bearing Rotor Systems International Journal of Rotating Machinery, 1996, Vol. 1, No. 7-8, pp [7] Krodkiewski J.M., Rotordynamics Lecture notes, The University of Melbourne, Dept of Mech Eng,, [8] Li D.., Chalko T.J., Hydrodynamic Characteristics of Combination Pad Journal Bearing, Proceedings of 6-th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC-6) Honolulu, Hawaii, USA, Feb 3-8, 1996 [9] Fehlberg E., Low-order classical Runge Kutta formulas with step size control, NASA TR R-315

EFFECT OF HYDRODYNAMIC THRUST BEARINGS ON ROTORDYNAMICS

EFFECT OF HYDRODYNAMIC THRUST BEARINGS ON ROTORDYNAMICS The 12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery Honolulu, Hawaii, February 17-22, 2008 ISROMAC12-2008-20076 EFFECT OF HYDRODYNAMIC THRUST BEARINGS ON ROTORDYNAMICS

More information

SAMCEF For ROTORS. Chapter 1 : Physical Aspects of rotor dynamics. This document is the property of SAMTECH S.A. MEF A, Page 1

SAMCEF For ROTORS. Chapter 1 : Physical Aspects of rotor dynamics. This document is the property of SAMTECH S.A. MEF A, Page 1 SAMCEF For ROTORS Chapter 1 : Physical Aspects of rotor dynamics This document is the property of SAMTECH S.A. MEF 101-01-A, Page 1 Table of Contents rotor dynamics Introduction Rotating parts Gyroscopic

More information

Towards Rotordynamic Analysis with COMSOL Multiphysics

Towards Rotordynamic Analysis with COMSOL Multiphysics Towards Rotordynamic Analysis with COMSOL Multiphysics Martin Karlsson *1, and Jean-Claude Luneno 1 1 ÅF Sound & Vibration *Corresponding author: SE-169 99 Stockholm, martin.r.karlsson@afconsult.com Abstract:

More information

Nonlinear Rolling Element Bearings in MADYN 2000 Version 4.3

Nonlinear Rolling Element Bearings in MADYN 2000 Version 4.3 - 1 - Nonlinear Rolling Element Bearings in MADYN 2000 Version 4.3 In version 4.3 nonlinear rolling element bearings can be considered for transient analyses. The nonlinear forces are calculated with a

More information

Use of Full Spectrum Cascade for Rotor Rub Identification

Use of Full Spectrum Cascade for Rotor Rub Identification Use of Full Spectrum Cascade for Rotor Rub Identification T. H. Patel 1, A. K. Darpe 2 Department of Mechanical Engineering, Indian Institute of Technology, Delhi 110016, India. 1 Research scholar, 2 Assistant

More information

Effects of Structural Forces on the Dynamic Performance of High Speed Rotating Impellers.

Effects of Structural Forces on the Dynamic Performance of High Speed Rotating Impellers. Effects of Structural Forces on the Dynamic Performance of High Speed Rotating Impellers. G Shenoy 1, B S Shenoy 1 and Raj C Thiagarajan 2 * 1 Dept. of Mechanical & Mfg. Engineering, Manipal Institute

More information

1872. Dynamic effect of annular flow with finite axial length on the rotor

1872. Dynamic effect of annular flow with finite axial length on the rotor 1872. Dynamic effect of annular flow with finite axial length on the rotor De Cheng 1, Zhen-qiang Yao 2, Ya-bo Xue 3 1, 2 State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University,

More information

FEDSM99 S-291 AXIAL ROTOR OSCILLATIONS IN CRYOGENIC FLUID MACHINERY

FEDSM99 S-291 AXIAL ROTOR OSCILLATIONS IN CRYOGENIC FLUID MACHINERY Proceedings of the 3 rd ASME/JSME Joint Fluids Engineering Conference 1999 ASME Fluids Engineering Division Summer Meeting July 18-23 1999, San Francisco, California FEDSM99 S-291 AXIAL ROTOR OSCILLATIONS

More information

PROJECT 2 DYNAMICS OF MACHINES 41514

PROJECT 2 DYNAMICS OF MACHINES 41514 PROJECT 2 DYNAMICS OF MACHINES 41514 Dynamics of Rotor-Bearing System Lateral Vibrations and Stability Threshold of Rotors Supported On Hydrodynamic Bearing and Ball Bearing. Ilmar Ferreira Santos, Prof.

More information

Theory and Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati

Theory and Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Theory and Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Module - 7 Instability in rotor systems Lecture - 4 Steam Whirl and

More information

Influence of friction coefficient on rubbing behavior of oil bearing rotor system

Influence of friction coefficient on rubbing behavior of oil bearing rotor system Influence of friction coefficient on rubbing behavior of oil bearing rotor system Changliang Tang 1, Jinfu ang 2, Dongjiang Han 3, Huan Lei 4, Long Hao 5, Tianyu Zhang 6 1, 2, 3, 4, 5 Institute of Engineering

More information

WORK SHEET FOR MEP311

WORK SHEET FOR MEP311 EXPERIMENT II-1A STUDY OF PRESSURE DISTRIBUTIONS IN LUBRICATING OIL FILMS USING MICHELL TILTING PAD APPARATUS OBJECTIVE To study generation of pressure profile along and across the thick fluid film (converging,

More information

Study of coupling between bending and torsional vibration of cracked rotor system supported by radial active magnetic bearings

Study of coupling between bending and torsional vibration of cracked rotor system supported by radial active magnetic bearings Applied and Computational Mechanics 1 (2007) 427-436 Study of coupling between bending and torsional vibration of cracked rotor system supported by radial active magnetic bearings P. Ferfecki a, * a Center

More information

Journal-Bearing Databook

Journal-Bearing Databook Tsuneo Someya (Editor) Journal-Bearing Databook With Contributions by T. Someya, J. Mitsui, J. Esaki, S. Saito, Y Kanemitsu, T. Iwatsubo, M.Tanaka, S. Hisa, T. Fujikawa, H. Kanki With 60 Figures and 5

More information

Application of CFD analysis for static and dynamic characteristics of hydrodynamic journal bearing

Application of CFD analysis for static and dynamic characteristics of hydrodynamic journal bearing Application of CFD analysis for static and dynamic characteristics of hydrodynamic journal bearing Kenichiro Takenaka *, Tomoyuki Hayashi, Kazuyoshi Miyagawa Abstract ISROMAC 7 International Symposium

More information

Finite element analysis of rotating structures

Finite element analysis of rotating structures Finite element analysis of rotating structures Dr. Louis Komzsik Chief Numerical Analyst Siemens PLM Software Why do rotor dynamics with FEM? Very complex structures with millions of degrees of freedom

More information

Transient Vibration Prediction for Rotors on Ball Bearings Using Load-Dependent Nonlinear Bearing Stiffness

Transient Vibration Prediction for Rotors on Ball Bearings Using Load-Dependent Nonlinear Bearing Stiffness Rotating Machinery, 10(6): 489 494, 2004 Copyright c Taylor & Francis Inc. ISSN: 1023-621X print / 1542-3034 online DOI: 10.1080/10236210490504102 Transient Vibration Prediction for Rotors on Ball Bearings

More information

CHAPTER 1 INTRODUCTION Hydrodynamic journal bearings are considered to be a vital component of all the rotating machinery. These are used to support

CHAPTER 1 INTRODUCTION Hydrodynamic journal bearings are considered to be a vital component of all the rotating machinery. These are used to support CHAPTER 1 INTRODUCTION Hydrodynamic journal bearings are considered to be a vital component of all the rotating machinery. These are used to support radial loads under high speed operating conditions.

More information

ROTATING MACHINERY VIBRATION

ROTATING MACHINERY VIBRATION SECOND EDITION ROTATING MACHINERY VIBRATION From Analysis to Troubleshooting MAURICE L. ADAMS, JR Case Western Reserve University Cleveland, Ohio W^ C\ CRC Press У Taylor &. Francis Group Boca Raton London

More information

1 Introduction. Minho Lee 1 Jihoon Lee 1 Gunhee Jang 1

1 Introduction. Minho Lee 1 Jihoon Lee 1 Gunhee Jang 1 DOI 10.1007/s005-015-5-5 TECHNICAL PAPER Stability analysis of a whirling rigid rotor supported by stationary grooved FDBs considering the five degrees of freedom of a general rotor bearing system Minho

More information

Linear and Nonlinear Analysis of Plain Journal Bearings Lubricated With Couple Stress Fluid

Linear and Nonlinear Analysis of Plain Journal Bearings Lubricated With Couple Stress Fluid ISSN 2395-1621 Linear and Nonlinear Analysis of Plain Journal Bearings Lubricated With Couple Stress Fluid #1 Deepali Kangude 1 deepalikangude94@gmail.com 1 P.G. student Mechanical Department, DYPIET Pimpri,

More information

New Representation of Bearings in LS-DYNA

New Representation of Bearings in LS-DYNA 13 th International LS-DYNA Users Conference Session: Aerospace New Representation of Bearings in LS-DYNA Kelly S. Carney Samuel A. Howard NASA Glenn Research Center, Cleveland, OH 44135 Brad A. Miller

More information

Research Program Vibrations ENERGIFORSK Vibration Group

Research Program Vibrations ENERGIFORSK Vibration Group Vorlesungen Mechatronik im Wintersemester Research Program Vibrations ENERGIFORSK Vibration Group DIAM A Matrix Tool for Turbine and Generator Vibrations Detection, Investigation, Analysis, Mitigation

More information

Evaluation of Campbell diagrams for vertical hydropower machines supported by Tilting Pad Journal Bearings

Evaluation of Campbell diagrams for vertical hydropower machines supported by Tilting Pad Journal Bearings Evaluation of Campbell diagrams for vertical hydropower machines supported by Tilting Pad Journal Bearings Florian Thiery 1 *, Rolf Gustavsson, Jan-Olov Aidanpää 1 SYMPOSIA ON ROTATING MACHINERY ISROMAC

More information

A Novel Computational Model for Tilting Pad Journal Bearings with Soft Pivot Stiffness

A Novel Computational Model for Tilting Pad Journal Bearings with Soft Pivot Stiffness 32 nd Turbomachinery Research Consortium Meeting A Novel Computational Model for Tilting Pad Journal Bearings with Soft Pivot Stiffness May 212 Yujiao Tao Research Assistant Dr. Luis San Andrés Mast-Childs

More information

1820. Selection of torsional vibration damper based on the results of simulation

1820. Selection of torsional vibration damper based on the results of simulation 8. Selection of torsional vibration damper based on the results of simulation Tomasz Matyja, Bogusław Łazarz Silesian University of Technology, Faculty of Transport, Gliwice, Poland Corresponding author

More information

Dynamics of Rotor Systems with Clearance and Weak Pedestals in Full Contact

Dynamics of Rotor Systems with Clearance and Weak Pedestals in Full Contact Paper ID No: 23 Dynamics of Rotor Systems with Clearance and Weak Pedestals in Full Contact Dr. Magnus Karlberg 1, Dr. Martin Karlsson 2, Prof. Lennart Karlsson 3 and Ass. Prof. Mats Näsström 4 1 Department

More information

Nonlinear Dynamic Analysis of a Hydrodynamic Journal Bearing Considering the Effect of a Rotating or Stationary Herringbone Groove

Nonlinear Dynamic Analysis of a Hydrodynamic Journal Bearing Considering the Effect of a Rotating or Stationary Herringbone Groove G. H. Jang e-mail: ghjang@hanyang.ac.kr J. W. Yoon PREM, Department of Mechanical Engineering, Hanyang University, Seoul, 133-791, Korea Nonlinear Dynamic Analysis of a Hydrodynamic Journal Bearing Considering

More information

Dynamics of Machinery

Dynamics of Machinery Dynamics of Machinery Two Mark Questions & Answers Varun B Page 1 Force Analysis 1. Define inertia force. Inertia force is an imaginary force, which when acts upon a rigid body, brings it to an equilibrium

More information

Breathing mechanism of a cracked rotor subject to non-trivial mass unbalance

Breathing mechanism of a cracked rotor subject to non-trivial mass unbalance Breathing mechanism of a cracked rotor subject to non-trivial mass unbalance Joseph Patrick SPAGNOL 1 ; Helen WU 2 1, 2 University of Western Sydney, Australia ABSTRACT The effects of dynamic loading on

More information

Effect of an hourglass shaped sleeve on the performance of the fluid dynamic bearings of a HDD spindle motor

Effect of an hourglass shaped sleeve on the performance of the fluid dynamic bearings of a HDD spindle motor DOI 10.1007/s00542-014-2136-5 Technical Paper Effect of an hourglass shaped sleeve on the performance of the fluid dynamic bearings of a HDD spindle motor Jihoon Lee Minho Lee Gunhee Jang Received: 14

More information

Research Article Stability Analysis of Journal Bearing: Dynamic Characteristics

Research Article Stability Analysis of Journal Bearing: Dynamic Characteristics Research Journal of Applied Sciences, Engineering and Technology 9(1): 47-52, 2015 DOI:10.19026/rjaset.9.1375 ISSN: 2040-7459; e-issn: 2040-7467 2015 Maxwell Scientific Publication Corp. Submitted: July

More information

Modal Analysis: What it is and is not Gerrit Visser

Modal Analysis: What it is and is not Gerrit Visser Modal Analysis: What it is and is not Gerrit Visser What is a Modal Analysis? What answers do we get out of it? How is it useful? What does it not tell us? In this article, we ll discuss where a modal

More information

ANALYSIS AND IDENTIFICATION IN ROTOR-BEARING SYSTEMS

ANALYSIS AND IDENTIFICATION IN ROTOR-BEARING SYSTEMS ANALYSIS AND IDENTIFICATION IN ROTOR-BEARING SYSTEMS A Lecture Notes Developed under the Curriculum Development Scheme of Quality Improvement Programme at IIT Guwahati Sponsored by All India Council of

More information

The Phenomena of Oil Whirl and Oil Whip

The Phenomena of Oil Whirl and Oil Whip Ali M. Al-Shurafa, Vibration Engineer Saudi Electricity Company- Ghazlan Power Plant Saudi Arabia ashurafa@hotmail.com The Phenomena of Oil Whirl and Oil Whip 1. Introduction Large machines mounted on

More information

Implementation of a Thermo- Hydrodynamic Model to Predict Morton Effect

Implementation of a Thermo- Hydrodynamic Model to Predict Morton Effect Implementation of a Thermo- Hydrodynamic Model to Predict Morton Effect Antonini *, Fausti and Mor Polibrixia srl, Via A. Tadini 49, 25125 Brescia. *orresponding author: Via Branze 45, 25123 Brescia, massimo.antonini@polibrixia.it

More information

This equation of motion may be solved either by differential equation method or by graphical method as discussed below:

This equation of motion may be solved either by differential equation method or by graphical method as discussed below: 2.15. Frequency of Under Damped Forced Vibrations Consider a system consisting of spring, mass and damper as shown in Fig. 22. Let the system is acted upon by an external periodic (i.e. simple harmonic)

More information

Finite Element Analysis Lecture 1. Dr./ Ahmed Nagib

Finite Element Analysis Lecture 1. Dr./ Ahmed Nagib Finite Element Analysis Lecture 1 Dr./ Ahmed Nagib April 30, 2016 Research and Development Mathematical Model Mathematical Model Mathematical Model Finite Element Analysis The linear equation of motion

More information

Stability Analysis of a Hydrodynamic Journal Bearing With Rotating Herringbone Grooves

Stability Analysis of a Hydrodynamic Journal Bearing With Rotating Herringbone Grooves G. H. Jang e-mail: ghjang@hanyang.ac.kr J. W. Yoon PREM, Department of Mechanical Engineering, Hanyang University, Seoul, 33-79, Korea Stability Analysis of a Hydrodynamic Journal Bearing With Rotating

More information

Dynamic analysis of a HDD spindle system with FDBs due to the bearing width and asymmetric grooves of journal bearing

Dynamic analysis of a HDD spindle system with FDBs due to the bearing width and asymmetric grooves of journal bearing Microsystem Technologies Micro- and Nanosystems Information Storage and Pro Springer-Verlag 2005 10.1007/s00542-005-0606-5 Technical paper Dynamic analysis of a HDD spindle system with FDBs due to the

More information

Robust shaft design to compensate deformation in the hub press fitting and disk clamping process of 2.5 HDDs

Robust shaft design to compensate deformation in the hub press fitting and disk clamping process of 2.5 HDDs DOI 10.1007/s00542-016-2850-2 TECHNICAL PAPER Robust shaft design to compensate deformation in the hub press fitting and disk clamping process of 2.5 HDDs Bumcho Kim 1,2 Minho Lee 3 Gunhee Jang 3 Received:

More information

Dynamics of assembled structures of rotor systems of aviation gas turbine engines of type two-rotor

Dynamics of assembled structures of rotor systems of aviation gas turbine engines of type two-rotor Dynamics of assembled structures of rotor systems of aviation gas turbine engines of type two-rotor Anatoly А. Pykhalov 1, Mikhail А. Dudaev 2, Mikhail Ye. Kolotnikov 3, Paul V. Makarov 4 1 Irkutsk State

More information

Finite element analysis of misaligned rotors on oil-film bearings

Finite element analysis of misaligned rotors on oil-film bearings Sādhanā Vol. 35, Part 1, February 2010, pp. 45 61. Indian Academy of Sciences Finite element analysis of misaligned rotors on oil-film bearings S SARKAR 1, A NANDI 1, S NEOGY 1, J K DUTT 2 and T K KUNDRA

More information

Sliding Bearings. Fig.(1) (a) Full-journal bearing and (b) partial-journal bearing

Sliding Bearings. Fig.(1) (a) Full-journal bearing and (b) partial-journal bearing Sliding Bearings The goal of a bearing is to provide relative positioning and rotational freedom while transmitting a load between two parts, commonly a shaft and its housing. The object of lubrication

More information

VIBRATION ANALYSIS OF TIE-ROD/TIE-BOLT ROTORS USING FEM

VIBRATION ANALYSIS OF TIE-ROD/TIE-BOLT ROTORS USING FEM VIBRATION ANALYSIS OF TIE-ROD/TIE-BOLT ROTORS USING FEM J. E. Jam, F. Meisami Composite Materials and Technology Center Tehran, IRAN jejaam@gmail.com N. G. Nia Iran Polymer & Petrochemical Institute, Tehran,

More information

THE INFLUENCE OF SWIRL BRAKES ON THE ROTORDYNAMIC FORCES GENERATED BY DISCHARGE-TO-SUCTION LEAKAGE FLOWS 1N CENTRIFUGAL PUMPS

THE INFLUENCE OF SWIRL BRAKES ON THE ROTORDYNAMIC FORCES GENERATED BY DISCHARGE-TO-SUCTION LEAKAGE FLOWS 1N CENTRIFUGAL PUMPS FED-Vol. 154, Pumping Machinery ASME 1993 THE INFLUENCE OF SWIRL BRAKES ON THE ROTORDYNAMIC FORCES GENERATED BY DISCHARGE-TO-SUCTION LEAKAGE FLOWS 1N CENTRIFUGAL PUMPS Joseph M. Sivo, Allan J. Acosta,

More information

Theory and Practice of Rotor Dynamics Prof. Dr. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati

Theory and Practice of Rotor Dynamics Prof. Dr. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Theory and Practice of Rotor Dynamics Prof. Dr. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Module - 2 Simpul Rotors Lecture - 2 Jeffcott Rotor Model In the

More information

Application of Nonlinear Dynamics Tools for Diagnosis of Cracked Rotor Vibration Signatures

Application of Nonlinear Dynamics Tools for Diagnosis of Cracked Rotor Vibration Signatures Application of Nonlinear Dynamics Tools for Diagnosis of Cracked Rotor Vibration Signatures Jery T. Sawicki *, Xi Wu *, Andrew L. Gyekenyesi **, George Y. Baaklini * Cleveland State University, Dept. of

More information

Analysis of Fluid Film Stiffness and Damping coefficient for A Circular Journal Bearing with Micropolar Fluid

Analysis of Fluid Film Stiffness and Damping coefficient for A Circular Journal Bearing with Micropolar Fluid et International Journal on Emerging Technologies 5(1): 206-211(2014) ISSN No. (Print) : 0975-8364 ISSN No. (Online) : 2249-3255 Analysis of Fluid Film Stiffness Damping coefficient for A Circular Journal

More information

Stability of Water-Lubricated, Hydrostatic, Conical Bearings With Spiral Grooves for High-Speed Spindles

Stability of Water-Lubricated, Hydrostatic, Conical Bearings With Spiral Grooves for High-Speed Spindles S. Yoshimoto Professor Science University of Tokyo, Department of Mechanical Engineering, 1-3 Kagurazaka Shinjuku-ku, Tokyo 16-8601 Japan S. Oshima Graduate Student Science University of Tokyo, Department

More information

Vibration Dynamics and Control

Vibration Dynamics and Control Giancarlo Genta Vibration Dynamics and Control Spri ringer Contents Series Preface Preface Symbols vii ix xxi Introduction 1 I Dynamics of Linear, Time Invariant, Systems 23 1 Conservative Discrete Vibrating

More information

SYNTHESIS OF A FLUID JOURNAL BEARING USING A GENETIC ALGORITHM

SYNTHESIS OF A FLUID JOURNAL BEARING USING A GENETIC ALGORITHM SYNTHESIS OF A FLUID JOURNAL BEARING USING A GENETIC ALGORITHM A. MANFREDINI and P. VIGNI Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione (DIMNP) - University of Pisa Via Diotisalvi,

More information

41514 Dynamics of Machinery

41514 Dynamics of Machinery 41514 Dynamics of Machinery Theory, Experiment, Phenomenology and Industrial Applications Ilmar (Iumár) Ferreira Santos 1. Course Structure 2. Objectives 3. Theoretical and Experimental Example 4. Industrial

More information

Some Aspects Regarding the Modeling of Highly Pressurized Squeeze Film Dampers

Some Aspects Regarding the Modeling of Highly Pressurized Squeeze Film Dampers Some Aspects Regarding the Modeling of ighly Pressurized Squeeze Film Dampers Laurenţiu MORARU* *Corresponding author Department of Aerospace Sciences, The POLITENICA University of Bucharest Splaiul Independenţei

More information

STABILITY CONSIDERATIONS A SIMPLIFIED APPROACH

STABILITY CONSIDERATIONS A SIMPLIFIED APPROACH Proceedings of the First Middle East Turbomachinery Symposium February 13-16, 2011, Doha, Qatar STABILITY CONSIDERATIONS A SIMPLIFIED APPROACH Urs Baumann Head of Calculation and Development MAN Diesel

More information

1544. Synchronous and subsynchronous vibration under the combined effect of bearings and seals: numerical simulation and its experimental validation

1544. Synchronous and subsynchronous vibration under the combined effect of bearings and seals: numerical simulation and its experimental validation 1544. Synchronous and subsynchronous vibration under the combined effect of bearings and seals: numerical simulation and its experimental validation Wanfu Zhang 1, Jiangang Yang 2, Chun Li 3, Ren Dai 4,

More information

Model of the gas journal bearing dynamics with a flexibly supported foil

Model of the gas journal bearing dynamics with a flexibly supported foil Model of the gas journal bearing dynamics with a flexibly supported foil (NUM209-15) Eliza Tkacz, Zbigniew Kozanecki, Dorota Kozanecka, Jakub Lagodziski Abstract: The work is devoted to an analysis of

More information

Step 1: Mathematical Modeling

Step 1: Mathematical Modeling 083 Mechanical Vibrations Lesson Vibration Analysis Procedure The analysis of a vibrating system usually involves four steps: mathematical modeling derivation of the governing uations solution of the uations

More information

Dynamic Responses of Composite Marine Propeller in Spatially Wake

Dynamic Responses of Composite Marine Propeller in Spatially Wake Dynamic Responses of Composite Marine Propeller in Spatially Wake Dynamic Responses of Composite Marine Propeller in Spatially Wake Y. Hong a, X.D. He a,*, R.G. Wang a, Y.B. Li a, J.Z. Zhang a, H.M. Zhang

More information

Dynamic Analysis of Rotor-Ball Bearing System of Air Conditioning Motor of Electric Vehicle

Dynamic Analysis of Rotor-Ball Bearing System of Air Conditioning Motor of Electric Vehicle International Journal of Mechanical Engineering and Applications 2015; 3(3-1): 22-28 Published online February 13, 2015 (http://www.sciencepublishinggroup.com/j/ijmea) doi: 10.11648/j.ijmea.s.2015030301.14

More information

Research Article Response of a Warped Flexible Rotor with a Fluid Bearing

Research Article Response of a Warped Flexible Rotor with a Fluid Bearing Hindawi Publishing Corporation International Journal of Rotating Machinery Volume 8, Article ID 753, 9 pages doi:.55/8/753 Research Article Response of a Warped Flexible Rotor with a Fluid Bearing Jim

More information

A SIMULATION STUDY OF THE ROTOR VIBRATION IN A JOURNAL BEARING

A SIMULATION STUDY OF THE ROTOR VIBRATION IN A JOURNAL BEARING Engineering MECHANICS, Vol. 15, 2008, No. 6, p. 461 470 461 A SIMULATION STUDY OF THE ROTOR VIBRATION IN A JOURNAL BEARING JiříTůma*, Alena Bilošová**, Jiří Šimek***, Rudolf Svoboda*** The paper deals

More information

Dynamic behavior of turbine foundation considering full interaction among facility, structure and soil

Dynamic behavior of turbine foundation considering full interaction among facility, structure and soil Dynamic behavior of turbine foundation considering full interaction among facility, structure and soil Fang Ming Scholl of Civil Engineering, Harbin Institute of Technology, China Wang Tao Institute of

More information

Bearing Technologies: An Overview

Bearing Technologies: An Overview Bearing Technologies: An Overview Dr. H. Hirani Assistant Professor, Mechanical Engineering INDIAN INSTITUTE OF TECHNOLOGY BOMBAY I.I.T. Bombay 1 I.I.T. Bombay Computer Hard disk with read/write head Tribo-Pair

More information

USING ROTOR KIT BENTLY NEVADA FOR EXPERIMENTS WITH AEROSTATIC BEARINGS

USING ROTOR KIT BENTLY NEVADA FOR EXPERIMENTS WITH AEROSTATIC BEARINGS USING ROTOR KIT BENTLY NEVADA FOR EXPERIMENTS WITH AEROSTATIC BEARINGS ŠIMEK, J. 1, KOZÁNEK, J., STEINBAUER, P., NEUSSER, Z. 3 1 TECHLAB Ltd., Prague, Institute of Thermomechanics AS CR 3 CTU in Prague,

More information

DAMPING AND INERTIA COEFFICIENTS FOR TWO END SEALED SUEEZE FILM DAMPERS WITH A CENTRAL GROOVE: MEASUREMENTS AND PREDICTIONS

DAMPING AND INERTIA COEFFICIENTS FOR TWO END SEALED SUEEZE FILM DAMPERS WITH A CENTRAL GROOVE: MEASUREMENTS AND PREDICTIONS 2013 ASME Turbo Expo Conference, June 3-7 2013, San Antonio, TX, USA DAMPING AND INERTIA COEFFICIENTS FOR TWO END SEALED SUEEZE FILM DAMPERS WITH A CENTRAL GROOVE: MEASUREMENTS AND PREDICTIONS Luis San

More information

Table of Contents. Preface... 13

Table of Contents. Preface... 13 Table of Contents Preface... 13 Chapter 1. Vibrations of Continuous Elastic Solid Media... 17 1.1. Objective of the chapter... 17 1.2. Equations of motion and boundary conditions of continuous media...

More information

Modelling of lateral-torsional vibrations of the crank system with a damper of vibrations

Modelling of lateral-torsional vibrations of the crank system with a damper of vibrations Modelling of lateral-torsional vibrations of the crank system with a damper of vibrations Bogumil Chiliński 1, Maciej Zawisza 2 Warsaw University of Technology, Institute of Machine Design Fundamentals,

More information

STATIC AND DYNAMIC CHARACTERISTICS OF HYDRODYNAMIC FOUR- LOBE JOURNAL BEARING WITH COUPLE STRESS LUBRICANTS

STATIC AND DYNAMIC CHARACTERISTICS OF HYDRODYNAMIC FOUR- LOBE JOURNAL BEARING WITH COUPLE STRESS LUBRICANTS STATIC AND DYNAMIC CHARACTERISTICS OF HYDRODYNAMIC FOUR- LOBE JOURNAL BEARING WITH COUPLE STRESS LUBRICANTS B. Chetti, b.chetti@gmail.com, Institute of sciences and Technology, Center University of Khemis

More information

Experimental test of static and dynamic characteristics of tilting-pad thrust bearings

Experimental test of static and dynamic characteristics of tilting-pad thrust bearings Special Issue Article Experimental test of static and dynamic characteristics of tilting-pad thrust bearings Advances in Mechanical Engineering 2015, Vol. 7(7) 1 8 Ó The Author(s) 2015 DOI: 10.1177/1687814015593878

More information

Response of an Open Ends Squeeze Film Damper to Large Amplitude Impact Loads

Response of an Open Ends Squeeze Film Damper to Large Amplitude Impact Loads 2015 STLE Annual Meeting & Exhibition, May 17-21, 2015, Dallas, TX Response of an Open Ends Squeeze Film Damper to Large Amplitude Impact Loads Luis San Andrés Mast-Childs Chair Professor Fellow STLE Sung-Hwa

More information

Experimental Identification of Bearing Stiffness in a Rotor Bearing System

Experimental Identification of Bearing Stiffness in a Rotor Bearing System Experimental Identification of Bearing Stiffness in a Rotor Bearing System Sharad Shekhar Palariya, M. Rajasekhar and J. Srinivas Department of Mechanical Engineering, National Institute of Technology

More information

Numerical Simulation of Impacts involving a Collapsible Nonlinear Multilayer Structure

Numerical Simulation of Impacts involving a Collapsible Nonlinear Multilayer Structure Numerical Simulation of Impacts involving a Collapsible Nonlinear Multilayer Structure Michael A. Sek Abstract A numerical model for the simulation of dynamic compression of a nonlinear multilayer structure

More information

Chapter 2: Rigid Bar Supported by Two Buckled Struts under Axial, Harmonic, Displacement Excitation..14

Chapter 2: Rigid Bar Supported by Two Buckled Struts under Axial, Harmonic, Displacement Excitation..14 Table of Contents Chapter 1: Research Objectives and Literature Review..1 1.1 Introduction...1 1.2 Literature Review......3 1.2.1 Describing Vibration......3 1.2.2 Vibration Isolation.....6 1.2.2.1 Overview.

More information

THE KIMMEL EQUATION FOR HYDRAULICALLY DAMPED AXIAL ROTOR OSCILLATIONS

THE KIMMEL EQUATION FOR HYDRAULICALLY DAMPED AXIAL ROTOR OSCILLATIONS The 9th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery Honolulu, Hawaii, February -4, THE KIMMEL EQUATION FOR HYDRAULICALLY DAMPED AXIAL ROTOR OSCILLATIONS Philip R.

More information

STATIC AND DYNAMIC ANALYSIS OF A PUMP IMPELLER WITH A BALANCING DEVICE PART I: STATIC ANALYSIS

STATIC AND DYNAMIC ANALYSIS OF A PUMP IMPELLER WITH A BALANCING DEVICE PART I: STATIC ANALYSIS Int. J. of Applied Mechanics and Engineering, 04, vol.9, No.3, pp.609-69 DOI: 0.478/ijame-04-004 STATIC AND DYNAMIC ANALYSIS OF A PUMP IMPELLER WITH A BALANCING DEVICE PART I: STATIC ANALYSIS C. KUNDERA

More information

Chapter 23: Principles of Passive Vibration Control: Design of absorber

Chapter 23: Principles of Passive Vibration Control: Design of absorber Chapter 23: Principles of Passive Vibration Control: Design of absorber INTRODUCTION The term 'vibration absorber' is used for passive devices attached to the vibrating structure. Such devices are made

More information

557. Radial correction controllers of gyroscopic stabilizer

557. Radial correction controllers of gyroscopic stabilizer 557. Radial correction controllers of gyroscopic stabilizer M. Sivčák 1, J. Škoda, Technical University in Liberec, Studentská, Liberec, Czech Republic e-mail: 1 michal.sivcak@tul.cz; jan.skoda@pevnosti.cz

More information

Effects of Residual Imbalance on the Rotordynamic Performance of Variable-Speed Turbo Blower

Effects of Residual Imbalance on the Rotordynamic Performance of Variable-Speed Turbo Blower Effects of Residual Imbalance on the Rotordynamic Performance of Variable-Speed urbo Blower Sena Jeong 1,3, Eojin Kim 1,4, Kyungho Jeong 2, Doyoung Jeon 3, Yong Bok Lee 1 * ISROMAC 2016 International Symposium

More information

Dept.of Mechanical Engg, Defence Institute of Advanced Technology, Pune. India

Dept.of Mechanical Engg, Defence Institute of Advanced Technology, Pune. India Applied Mechanics and Materials Submitted: 2014-04-23 ISSN: 1662-7482, Vols. 592-594, pp 1084-1088 Revised: 2014-05-16 doi:10.4028/www.scientific.net/amm.592-594.1084 Accepted: 2014-05-19 2014 Trans Tech

More information

Nonlinear effects on the rotor driven by a motor with limited power

Nonlinear effects on the rotor driven by a motor with limited power Applied and Computational Mechanics 1 (007) 603-61 Nonlinear effects on the rotor driven by a motor with limited power L. Pst Institute of Thermomechanics, Academy of Sciences of CR, Dolejškova 5,18 00

More information

Shared on QualifyGate.com

Shared on QualifyGate.com GTE 014 Brief nalysis (Based on student test experiences in the stream of ME on 16th February, 014 - Second Session) Section wise analysis of the paper 1 Mark Marks Total No of Questions Engineering Mathematics

More information

Stability analysis of a whirling disk-spindle system supported by FDBs with rotating grooves

Stability analysis of a whirling disk-spindle system supported by FDBs with rotating grooves Microsyst Technol (011) 17:787 797 DOI 10.1007/s0054-010-111-9 TECHNICAL PAPER Stability analysis of a whirling disk-spindle system supported by FDBs with rotating grooves Jihoon Lee Gunhee Jang Kyungmoon

More information

Investigation of Coupled Lateral and Torsional Vibrations of a Cracked Rotor Under Radial Load

Investigation of Coupled Lateral and Torsional Vibrations of a Cracked Rotor Under Radial Load NOMENCLATURE Investigation of Coupled Lateral and Torsional Vibrations of a Cracked Rotor Under Radial Load Xi Wu, Assistant Professor Jim Meagher, Professor Clinton Judd, Graduate Student Department of

More information

Vibrations in Mechanical Systems

Vibrations in Mechanical Systems Maurice Roseau Vibrations in Mechanical Systems Analytical Methods and Applications With 112 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Contents Chapter I. Forced Vibrations

More information

In this lecture you will learn the following

In this lecture you will learn the following Module 9 : Forced Vibration with Harmonic Excitation; Undamped Systems and resonance; Viscously Damped Systems; Frequency Response Characteristics and Phase Lag; Systems with Base Excitation; Transmissibility

More information

Thermohydrodynamic Lubrication Characteristics of High-Speed Tilting Pad Journal Bearings

Thermohydrodynamic Lubrication Characteristics of High-Speed Tilting Pad Journal Bearings Thermohydrodynamic Lubrication Characteristics of High-Speed Tilting Pad Journal Bearings OGATA Hideki : Manager, Vibration Engineering & Tribology Department, Research Laboratory, Corporate Research &

More information

Lubrication and Journal Bearings

Lubrication and Journal Bearings UNIVERSITY OF HAIL College of Engineering Department of Mechanical Engineering Chapter 12 Lubrication and Journal Bearings Text Book : Mechanical Engineering Design, 9th Edition Dr. Badreddine AYADI 2016

More information

An Analysis Technique for Vibration Reduction of Motor Pump

An Analysis Technique for Vibration Reduction of Motor Pump An Analysis Technique for Vibration Reduction of Motor Pump Young Kuen Cho, Seong Guk Kim, Dae Won Lee, Paul Han and Han Sung Kim Abstract The purpose of this study was to examine the efficiency of the

More information

International Journal of Advance Engineering and Research Development

International Journal of Advance Engineering and Research Development Scientific Journal of Impact Factor (SJIF): 4.14 International Journal of Advance Engineering and Research Development Volume 3, Issue 3, March -2016 e-issn (O): 2348-4470 p-issn (P): 2348-6406 BIFURCATION

More information

Study on Nonlinear Dynamic Response of an Unbalanced Rotor Supported on Ball Bearing

Study on Nonlinear Dynamic Response of an Unbalanced Rotor Supported on Ball Bearing G. Chen College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P.R.C. e-mail: cgzyx@263.net Study on Nonlinear Dynamic Response of an Unbalanced Rotor Supported

More information

WEEKS 8-9 Dynamics of Machinery

WEEKS 8-9 Dynamics of Machinery WEEKS 8-9 Dynamics of Machinery References Theory of Machines and Mechanisms, J.J.Uicker, G.R.Pennock ve J.E. Shigley, 2011 Mechanical Vibrations, Singiresu S. Rao, 2010 Mechanical Vibrations: Theory and

More information

Contact problems in rotor systems

Contact problems in rotor systems Contact problems in rotor systems Liudmila Banakh Mechanical Engineering Research Institute of RAS, Moscow, Russia E-mail: banl@inbox.ru (Received 18 July 2016; accepted 24 August 2016) Abstract. We consider

More information

Rotordynamic Forces from Dischargeto-Suction Leakage Flows in Centrifugal Pumps : Effects of Geometry*

Rotordynamic Forces from Dischargeto-Suction Leakage Flows in Centrifugal Pumps : Effects of Geometry* Rotordynamic Forces from Dischargeto-Suction Leakage Flows in Centrifugal Pumps : Effects of Geometry* Robert V. UY**, Brian L. BIRCUMSHAW** and Christopher E. BRENNEN* * The rotordynamic forces generated

More information

Simulation and Experimental Research on Dynamics of Low-Pressure Rotor System in Turbofan Engine

Simulation and Experimental Research on Dynamics of Low-Pressure Rotor System in Turbofan Engine Simulation and Experimental Research on Dynamics of Low-Pressure Rotor System in Turbofan Engine Shengxiang Li 1, Chengxue Jin 2, Guang Zhao 1*, Zhiliang Xiong 1, Baopeng Xu 1 1. Collaborative Innovation

More information

Dynamic Analysis of An 1150 MW Turbine Generator

Dynamic Analysis of An 1150 MW Turbine Generator Dyrobes Rotordynamics Software https://dyrobes.com 1 PWR2005-50142 Abract Dynamic Analysis of An 1150 MW Turbine Generator Edgar J. Gunter Fellow ASME RODYN Vibration Inc Charlottesville, Va. 22903 DrGunter@aol.com

More information

Basics of rotordynamics 2

Basics of rotordynamics 2 Basics of rotordynamics Jeffcott rotor 3 M A O a rigid rotor disk rotates at angular frequency W massless shaft acts as a spring restoring displacements disk can move only in the plane defined by axes

More information

Seminar Energiforsk Vibrations in Nuclear Applications Stockholm, Sweden ( )

Seminar Energiforsk Vibrations in Nuclear Applications Stockholm, Sweden ( ) Vorlesungen Mechatronik im Wintersemester Seminar Energiforsk Vibrations in Nuclear Applications Stockholm, Sweden (13.11.2018) Numerical Analysis of Influence Coefficients for On-Site Balancing of Flexible

More information

COMPARISON OF RESPONSE TO UNBALANCE OF OVERHUNG ROTOR SYSTEM FOR DIFFERENT SUPPORTS

COMPARISON OF RESPONSE TO UNBALANCE OF OVERHUNG ROTOR SYSTEM FOR DIFFERENT SUPPORTS International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 3, March 017, pp. 56 65 Article ID: IJMET_08_03_007 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=8&itype=3

More information

Centrifugal pumps (Agriculture) unbalance and shaft Dynamic analysis from the experimental data in a rotor system

Centrifugal pumps (Agriculture) unbalance and shaft Dynamic analysis from the experimental data in a rotor system Research Article International Journal of Current Engineering and Technology E-ISSN 77 416, P-ISSN 347-5161 14 INPRESSCO, All Rights Reserved Available at http://inpressco.com/category/ijcet Centrifugal

More information