Vibration Analysis of Statically Indeterminate Rotors With Hydrodynamic Bearings

1998 ◽  
Vol 120 (4) ◽  
pp. 781-788 ◽  
Author(s):  
N. S. Feng ◽  
E. J. Hahn
Keyword(s):  
Vibration Analysis ◽  
Operating Conditions ◽  
System Stability ◽  
Hydrodynamic Bearings ◽  
Hydrodynamic Bearing ◽  
Unbalance Response ◽  
Tilting Pad ◽  
The Stability ◽  
Rotor Bearings ◽  
Stiffness And Damping

In statically indeterminate rotor bearings systems, where the rotor is supported by one or more hydrodynamic bearings, the reactions at each hydrodynamic bearing, and hence its stiffness and damping properties depend not only on the bearing type, the operating conditions and the bearing dimensions but also on the relative lateral alignment between the journal and the bearing housing; the alignment, therefore, has a significant influence on the system stability and unbalance response. Additional complications arise if nonsymmetric bearing types such as elliptic or tilting pad bearings are present. An iterative procedure is outlined which enables the bearing reactions to be determined at any speed, thereby enabling even large systems such as turbomachinery to be rapidly analyzed in conjunction with existing linear rotor bearing vibration analysis software. Sample numerical examples show how misalignment and bearing type can affect the natural frequencies, the stability threshold, and the unbalance response of such statically indeterminate systems.

Optimum Journal Bearing Parameters for Minimum Rotor Unbalance Response in Synchronous Whirl

1982 ◽  
Vol 104 (2) ◽  
pp. 339-344 ◽  
Author(s):  
R. B. Bhat ◽  
J. S. Rao ◽  
T. S. Sankar
Keyword(s):  
Optimal Design ◽  
Optimization Techniques ◽  
Oil Viscosity ◽  
Hydrodynamic Bearings ◽  
Unbalance Response ◽  
Design Variables ◽  
Tilting Pad ◽  
Bearing Design ◽  
Stiffness And Damping ◽  
Lower Limits

Optimization techniques are employed to design hydrodynamic bearings for minimum unbalance response of rotors in synchronous whirl. The analysis for the unbalance response considers the effects of direct and cross coupled coefficients of stiffness and damping in the bearings. A parametric study of the unbalance response is carried out to show the influence of bearing parameters on the response and to demonstrate the merits of applying optimization techniques in bearing design. The bearing parameters optimized are the diameter, clearance, and the oil viscosity. In addition to setting upper and lower limits on the foregoing design variables, the Sommerfeld number is also constrained to be within a certain range for the operational speeds of the rotor. The quantity minimized is the maximum unbalance response of the rotor in the operational speed range. Plain cylindrical, grooved, elliptical, and four shoe tilting pad type bearings are considered in the optimal design of the rotor bearing system. The results indicate that an optimal design of hydrodynamic bearings can reduce the unbalance response of rotors.

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Samuel F. Asokanthan ◽  
Soroush Arghavan ◽  
Mohamed Bognash
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Operating Conditions ◽  
System Stability ◽  
System Response ◽  
Ring Type ◽  
Mems Gyroscopes ◽  
The Stability

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

Rotor Damped Natural Frequencies and Stability Under Reduced Oil Supply Flow Rates to Tilting-Pad Journal Bearings

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Bradley R. Nichols ◽  
Roger L. Fittro ◽  
Christopher P. Goyne
Keyword(s):  
Experimental Data ◽  
Natural Frequencies ◽  
Dynamic Performance ◽  
Operating Conditions ◽  
System Stability ◽  
Flow Rates ◽  
Oil Supply ◽  
Pressure Profiles ◽  
Tilting Pad ◽  
Identification Technique

Reduced oil supply flow rates in fluid film bearings can cause cavitation, or lack of a fully developed film layer, over one or more of the pads due to starvation. Reduced oil flow has the well-documented effects of higher bearing operating temperatures and decreased power losses; however, little experimental data are available on its effects on system stability and dynamic performance. The study looks at the effects of oil supply flow rate on dynamic bearing performance by comparing experimentally identified damped natural frequencies and damping ratios to predictive models. A test rig consisting of a flexible rotor and supported by two tilting pad bearings in flooded housings is utilized in this study. Tests are conducted over a range of supercritical operating speeds and bearing loads while systematically reducing the oil supply flow rates provided to the bearings. Shaft response measured as a magnetic actuator is used to perform sine sweep excitations of the rotor. A single-input, multiple-output system identification technique is then used to obtain frequency response functions (FRFs) and modal parameters. All experimental results are compared to predicted results obtained from bearing models based on thermoelastohydrodynamic (TEHD) lubrication theory. Both flooded and starved model flow assumptions are considered and compared to the data. Differences in the predicted trends of the models and the experimental data across varying operating conditions are examined. Predicted pressure profiles and dynamic coefficients from the models are presented to help explain any differences in trends.

Theoretical Study on Instability Boundary of Rotor-Hydrodynamic Bearing Systems: Part II — Rotor With External Flexible Damped Support

2001 ◽  
Author(s):  
Zenglin Guo ◽  
R. Gordon Kirk
Keyword(s):  
Analytical Study ◽  
Theoretical Study ◽  
System Stability ◽  
Hydrodynamic Bearing ◽  
System A ◽  
Vertical Rotor ◽  
Speed Range ◽  
Stability Maps ◽  
Alternative Means ◽  
The Stability

Abstract The situation of a rotor-hydrodynamic bearing system in external flexible damped support is more complicated than that discussed before in Part I but it can become an alternative means to improve the stability of the rotor system. A model for both vertical and horizontal analysis is built first. Then, the analytical study on the vertical rotor is conducted. The results show that there might be up to four threshold speeds in this configuration that form a consecutive regional pattern taken turns by stable or unstable regions. Furthermore, the numerical calculation by MATLAB is carried out to obtain the results of the horizontal system. The stability maps for various parametric configurations are presented. It has been shown that the value of support damping has a strong effect on the first several lower threshold speeds. But it has little effect on the last top threshold speed which is mainly determined by the portion of journal mass. Within a certain range of external damping value, the first several regions of instability can be reduced or eradicated. As far as the entire stability map is concerned, there is an optimum range of value for support damping that can make the rotor have only one top threshold speed over the entire running speed range. When the support stiffness is increased, the system stability map becomes narrow which means a small support stiffness is good for broadening the range of optimum external damping.

Stability Analysis of Two-Layered Finite Hydrodynamic Porous Journal Bearing Using Linear and Nonlinear Transient Method

2007 ◽  
Author(s):  
S. K. Kakoty ◽  
S. K. Laha ◽  
P. Mallik
Keyword(s):  
Journal Bearing ◽  
Journal Bearings ◽  
Operating Conditions ◽  
System Stability ◽  
Rigid Rotor ◽  
Transient Method ◽  
Porous Bearing ◽  
Nonlinear Transient ◽  
Linear And Nonlinear ◽  
The Stability

A theoretical analysis has been carried out to determine the stability of rigid rotor supported on two symmetrical finite two-layered porous oil journal bearings. The stability curves have been drawn for different eccentricity ratios and Sommerfeld numbers. The effect of bearing feeding parameter, L/D ratio on the stability is also investigated. This paper also deals with a theoretical investigation of stability using a non-linear transient method. This analysis gives the journal centre locus and from this the system stability can be determined. With the help of graphics, several trajectories of the journal centre have been obtained for different operating conditions. Finally a comparison between single-layered porous bearing and the two-layered porous bearing is presented here.

Investigation of the Hydrodynamic Behavior of New Construction Hydrodynamic Tilting-Pad Journal Bearing

2005 ◽  
Author(s):  
Vladas Vekteris ◽  
Vadim Mokshin
Keyword(s):  
High Stability ◽  
Journal Bearing ◽  
Complex Method ◽  
Hydrodynamic Behavior ◽  
Hydrodynamic Bearings ◽  
Hydrodynamic Bearing ◽  
Tilting Pad ◽  
New Construction ◽  
Tilting Pad Journal Bearing

The paper describes features of new construction pad-type (segmental) hydrodynamic bearing with mobile ring and results of investigations of this bearing. The researchers obtained complex method of interaction between the mobile ring and pads. Except the diagram of distribution of lubricant pressure on the surface of pad there are presented photos of the flowing lubricant in the bearing and graphs of trajectories of the rotor journal’s axis for various number of revolutions of the rotor. Presented results of investigations show high stability of new construction hydrodynamic bearings in case of big number of revolutions of the rotor. Researchers hope that new construction bearings can be successfully used in tribological systems at the mentioned condition.

Instability Boundary for Rotor-Hydrodynamic Bearing Systems, Part 2: Rotor With External Flexible Damped Support

2003 ◽  
Vol 125 (4) ◽  
pp. 423-426 ◽  
Author(s):  
Zenglin Guo ◽  
R. Gordon Kirk
Keyword(s):  
Analytical Study ◽  
System Stability ◽  
Regional Pattern ◽  
Hydrodynamic Bearing ◽  
System A ◽  
Vertical Rotor ◽  
Speed Range ◽  
Stability Maps ◽  
The Stability ◽  
Bearing System

A rotor-hydrodynamic bearing system having external flexible damped bearing supports is more complicated than that discussed in Part 1 but it can provide a means to improve the stability of the rotor system. A model for both vertical and horizontal analysis is developed first. Then, the analytical study on the vertical rotor is conducted. The results show that there can be up to four threshold speeds in this configuration that form a consecutive regional pattern, taking turns by stable or unstable regions. Furthermore, the numerical calculation by MATLAB is carried out to obtain the results for the horizontal system. The stability maps for various parametric configurations are presented. It has been shown that the value of support damping has a strong effect on the first several lower threshold speeds. But it has little effect on the last top threshold speed which is mainly determined by the portion of journal mass. Within a certain range of external damping value, the first several regions of instability can be reduced or eradicated. As far as the entire stability map is concerned, there is an optimum range of support damping that can make the rotor have only one top threshold speed over the entire running speed range. When the support stiffness is increased, the system stability map becomes narrow which means a small support stiffness is good for broadening the range of optimum external damping.

Dynamic Properties of Tilting-Pad Journal Bearings: Experimental and Theoretical Investigation of Frequency Effects due to Pivot Flexibility

2006 ◽  
Vol 129 (3) ◽  
pp. 865-869 ◽  
Author(s):  
Waldemar Dmochowski
Keyword(s):  
High Speed ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Damping Properties ◽  
Frequency Effects ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearings

Tilting-pad journal bearings (TPJBs) dominate as rotor supports in high-speed rotating machinery. The paper analyzes frequency effects on the TPJB’s stiffness and damping characteristics based on experimental and theoretical investigations. The experimental investigation has been carried out on a five pad tilting-pad journal bearing of 98mm in diameter. Time domain and multifrequency excitation has been used to evaluate the dynamic coefficients. The calculated results have been obtained from a three-dimensional computer model of TPJB, which accounts for thermal effects, turbulent oil flow, and elastic effects, including that of pad flexibility. The analyzes of the TPJB’s stiffness and damping properties showed that the frequency effects on the bearing dynamic properties depend on the operating conditions and bearing design. It has been concluded that the pad inertia and pivot flexibility are behind the variations of the stiffness and damping properties with frequency of excitation.

Transient and Steady State Vibration Analysis of a Wavy Thrust Bearing

2005 ◽  
Vol 128 (1) ◽  
pp. 139-145 ◽  
Author(s):  
H. Zhao ◽  
F. K. Choy ◽  
M. J. Braun
Keyword(s):  
Steady State ◽  
Vibration Analysis ◽  
Thrust Bearing ◽  
Numerical Procedure ◽  
Operating Conditions ◽  
System Stability ◽  
Thrust Bearings ◽  
External Perturbations ◽  
Vibration Signature ◽  
Transient And Steady State

This paper describes a numerical procedure for analyzing the dynamics of transient and steady state vibrations in a wavy thrust bearing. The major effects of the wavy geometry and the operating parameters on the dynamic characteristics of the bearing had been discussed in a previous paper; the present paper thus concentrates on examining the relationships between the development of the transient and steady state vibrations when operating conditions are parametrically varied. Special attention is given to the development of steady state vibrations from initial transients with comparisons and consequences to the overall system stability. Numerical based vibration signature analysis procedures are then used to identify and quantify the transient vibrations. The conclusions provide general indicators for designing wavy thrust bearings that are less susceptible to transients induced by external perturbations.

Turbulent Flow, Flexure-Pivot Hybrid Bearings for Cryogenic Applications

1996 ◽  
Vol 118 (1) ◽  
pp. 190-200 ◽  
Author(s):  
Luis San Andres
Keyword(s):  
High Speed ◽  
Energy Transport ◽  
Load Capacity ◽  
Equations Of Motion ◽  
Liquid Oxygen ◽  
Hydrodynamic Bearings ◽  
Numerical Predictions ◽  
Tilting Pad ◽  
Direct Stiffness ◽  
Stiffness And Damping

The thermal analysis of flexure-pivot tilting-pad hybrid (combination hydrostatic-hydrodynamic) bearings for cryogenic turbopumps is presented. The advantages of this type of bearing for high speed operation are discussed. Turbulent bulk-flow, variable properties, momentum and energy transport equations of motion govern the flow in the bearing pads. Zeroth-order equations for the flow field at a journal equilibrium position render the bearing flow rate, load capacity, drag torque, and temperature rise. First-order equations for perturbed flow fields due to small amplitude journal motions provide rotordynamic force coefficients. A method to determine the tilting-pad moment coefficients from the force displacement coefficients is outlined. Numerical predictions correlate well with experimental measurements for tilting-pad hydrodynamic bearings. The design of a liquid oxygen, flexure-pad hybrid bearing shows a reduced whirl frequency ratio and without loss in load capacity or reduction in direct stiffness and damping coefficients.

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