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.

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.

Effect of journal cylindricity error with saddle or drum distribution on the performance of hydrodynamic journal bearing systems

2019 ◽  
Vol 234 (7) ◽  
pp. 1092-1105
Author(s):  
Bing Li ◽  
Dejian Zhou ◽  
Peter Ogrodnik ◽  
Wubin Xu
Keyword(s):  
Journal Bearing ◽  
System Stability ◽  
Analysis Method ◽  
Shape Distribution ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Cylindricity Error ◽  
Saddle Shape ◽  
Fourier Model ◽  
Bearing System

The present study investigates the effect of cylindricity error on the performance of hydrodynamic journal bearing systems. Two types of cylindricity errors of the journal, namely the drum shape distribution cylindricity error (DCE) and the saddle shape distribution cylindricity error (SCE), are considered. The Legendre–Fourier model is used to characterize the profile of each journal. Based on the nonlinear analysis method, the dynamic characteristics and stability of hydrodynamic journal bearing systems are analyzed. The results indicate that cylindricity error affects the system stability, and the effect is related to the type and level of the error. DCE used with a certain range of operating speed and load is not harmful and is even beneficial to the stability of hydrodynamic journal bearing systems; conversely, SCE decreases the system stability. When the Sommerfeld number is between 0.02 and 0.05, cylindricity errors have a minimal effect on the system stability. Additionally, the results indicate that the effect of cylindricity error on the bearing system is more significant than that of roundness error.

Analysis and Experimental Investigation of the Stability of Intershaft Squeeze Film Dampers—Part 2: Control of Instability

1978 ◽  
Vol 100 (3) ◽  
pp. 558-562 ◽  
Author(s):  
D. H. Hibner ◽  
P. N. Bansal ◽  
D. F. Buono
Keyword(s):  
Experimental Investigation ◽  
Stability Analysis ◽  
Shear Deformation ◽  
System Stability ◽  
Squeeze Film ◽  
Viscous Damper ◽  
Test Rig ◽  
Squeeze Film Dampers ◽  
Stability Maps ◽  
The Stability

The results of an analytical and experimental investigation showing the existence of an intershaft viscous damper instability were presented in reference [1]. In the present investigation, a more comprehensive stability analysis is used to study the stability of the test rig which incorporates a modified intershaft bearing support. The analysis is applicable to large multi-mass, rotor-bearing systems and includes the effects of gyroscopic moments, shear deformation, bearing support flexibility, and damping. The results of the stability analysis are presented in the form of system stability maps which clearly indicate the effectiveness of the modification in improving the instability onset speed of the system. Also presented are the results of an experimental investigation which substantiate the analytical predictions.

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.

Effect of Flexible Damped Bearing-Supports on the Dynamic Stability of High-Speed Turbochargers

2013 ◽  
Author(s):  
A. Alsaeed ◽  
G. Kirk ◽  
S. Bashmal
Keyword(s):  
Dynamic Stability ◽  
Dynamic Characteristics ◽  
High Speed ◽  
Element Model ◽  
Dynamic Coefficients ◽  
Speed Range ◽  
Rotor Bearing ◽  
The Stability ◽  
The Finite Element Model ◽  
Bearing System

The aim of this study is to analytically design flexible damped bearing-supports in order to improve the dynamic characteristics of the rotor-bearing system. The finite-element model of the turbocharger rotor with linearized bearing dynamic coefficients is used to solve for the logarithmic decrements and hence the stability map. The design process attempts to find the optimum dynamic characteristics of the flexible damped bearing-support that would give best dynamic stability of the rotor-bearing system. The method is successful in greatly improving the dynamic stability of the turbocharger and may also lead to a total linear stability throughout the entire speed range when used besides the enhanced-performance hydrodynamic bearings.

scholarly journals Hydrodynamic Instability of Solar Thermosyphon Water Heaters

1994 ◽  
Vol 116 (1) ◽  
pp. 53-62 ◽  
Author(s):  
S. C. Du ◽  
B. J. Huang ◽  
R. H. Yen
Keyword(s):  
Flow Instability ◽  
Hydrodynamic Instability ◽  
System Stability ◽  
Solar Irradiation ◽  
Linear Perturbation ◽  
Water Heater ◽  
Water Heaters ◽  
Stability Maps ◽  
The Stability ◽  
Solar Water Heaters

The flow instability of a solar thermosyphon water heater is studied analytically. A system dynamics model is derived by means of a one-dimensional approach and a linear perturbation method. The characteristic equation is obtained and the Nyquist criterion is used to examine the flow stability. The parameter M is a dimensionless parameter of system stability. The stability maps are plotted in terms of 14 parameters. The occurrence of hydrodynamic instability is determined by comparing the stability curves and the designed values of M. Flow instability is shown not to occur in most of solar water heaters commercially available, because the loop friction is relatively high in the design and because solar irradiation in field operation is still not high enough to cause flow instability.

Experimental Research of Characteristics of Fluid-Induced Force in Eccentric Seal

2011 ◽  
Vol 291-294 ◽  
pp. 2034-2040
Author(s):  
Wan Fu Zhang ◽  
Jian Gang Yang ◽  
Hao Cao ◽  
Rui Guo ◽  
Dan Sun
Keyword(s):  
Dynamic Analysis ◽  
Experimental Research ◽  
System Stability ◽  
Inlet Pressure ◽  
Analysis Model ◽  
Rotating Speed ◽  
Stiffness Coefficients ◽  
System A ◽  
The Difference ◽  
The Stability

This paper sets up a dynamic analysis model for cylinder-seal system. A new identification method for fluid-induced force and stiffness coefficients in eccentric seal is presented. The study shows that the system stability decreases with increasing cross-coupled stiffness in a certain range. Beyond this range, the system will be destabilized. Influences of rotating speed, inlet pressure, eccentricity and clearance on fluid-induced force were tested in the rig. It was found that a large tangential fluid-induced force was produced in the direction perpendicular to the eccentric displacement of rotor. The difference between the tangential and radial fluid-induced force became larger and larger with the increasing rotating speeds. Under the action of the seal force, the logarithmic decrement descended with increasing rotating speeds, and the stability of the system decreased. These effects became more and more serious for higher inlet pressure and tighter clearance.

Research of the Adaptation of Turbine Model Related to the Grid

2014 ◽  
Vol 960-961 ◽  
pp. 1437-1441
Author(s):  
Ge Jin ◽  
Shu Chang Liu ◽  
Yu Jia Ma
Keyword(s):  
Power System ◽  
Rapid Development ◽  
System Stability ◽  
System A ◽  
The Stability ◽  
Turbine Speed ◽  
The Impact ◽  
Safety And Stability ◽  
Important Basis ◽  
Turbine Model

With the rapid development of China's interconnected power grid, power system operation environment has become increasingly complex. The safety and stability of the power system requirements are also increasing. Turbine is an important basis for the analysis of power system stability. This paper studied the influence of turbine parameters related to network on the stability of the grid from the perspective of the frequency domain, and obtained the impact properties of turbine speed control system parameters related to different oscillation frequency of the power system. The conclusions are validated from time domain. So that when analyzing the stability of the power system, a more targeted turbine model according to different research purposes can be chosen because the parameters’ importance can show the necessity of the modules.

scholarly journals Analysis of Vibration Characteristics for a Rotor-Bearing System Using Distributed Spring and Damper Model

1995 ◽  
Vol 1 (3-4) ◽  
pp. 277-284 ◽  
Author(s):  
D. C. Han ◽  
S. H. Choi ◽  
Y. H. Lee
Keyword(s):  
Shape Function ◽  
Quadratic Function ◽  
Journal Bearings ◽  
Vibration Characteristics ◽  
Distributed Model ◽  
System A ◽  
Rotor Bearing ◽  
The Stability ◽  
Stability Limits ◽  
Bearing System

In this paper, we modelled the journal beatings as distributed springs and dampers to investigate the influence of beating width on the vibration characteristics of a rotor-beating system. A quadratic function is used as a shape function for hydrodynamic journal bearings. And a trapezoidally or a quadratically distributed model is used as a shape function for hydrostatic journal bearings. A finite element method is applied for analyzing the vibration characteristics of a rotor-bearing system.Dimensionless governing equations are derived for a uniform rotor supported by two journal bearings, which are modelled as point supported or distributed springs and dampers. For these models, natural frequencies for various beating length ratios and stiffness ratios between the bearing and the shaft are calculated and compared with each other. Then the stability limits of a rotor supported by two cylindrical journal beatings are calculated for the point supported or distributed springs and dampers.

NPLs — The Solution Recipe for Albania

2015 ◽  
Vol 3 (1) ◽  
pp. 48
Author(s):  
Elona Shehu ◽  
Elona Meka
Keyword(s):  
Interest Rate ◽  
Negative Relationship ◽  
Banking System ◽  
Gdp Growth ◽  
System A ◽  
Analysis Technique ◽  
Recent Financial Crisis ◽  
The Stability ◽  
Asset Quality ◽  
Macroeconomic Determinants

The quality of the loan portfolio in Albanian banking system is facing many obstacles during the last decade. In this paper we look at possible determinants of assets quality. During the recent financial crisis commercial banks were confronted with deteriorating asset quality that threatened not only the banking industry, but also the stability of the entire financial system. This study aims to examine the correlation between non-performing loans and the macroeconomic determinants in Albania during the last decade. NPLs are considered to be of a high importance as they represent the high risk exposure of banking system. A solid bank with healthy assets increases the market efficiency. Our approach is based on a panel data regression analysis technique from 2005-2015. Within this methodology this study finds robust evidence on the existing relationship between lending interest rate, real GDP growth and NPLs. We expect to find a negative relationship between lending interest rate and asset quality. Further we assume an inverse relationship between GDP growth and non-performing loans, suggesting that NPLs decrease if the economy is growing. Furthermore this study proposes a solution platform, which looks deeper into the possibility of creating a secondary active market for troubled loans, restructuring the banking system or implementing the Podgorica model. This research paper opens a new lieu of discussion in terms of academic debates and decision-making policies.

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