A Simple Stability Analysis for Flexible Rotors in Tilting Pad Bearings

1978 ◽  
Vol 100 (1) ◽  
pp. 165-172 ◽  
Author(s):  
E. A. Bulanowski
Keyword(s):  
Stability Analysis ◽  
Free Vibrations ◽  
Damping Factor ◽  
Quick Method ◽  
Flexible Rotors ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Single Mass ◽  
Tilting Pad Bearings ◽  
Nonsynchronous Vibrations

A simplified stability analysis for flexible rotors in tilting pad bearings is developed which provides a convenient and practical approach for the consideration of nonsynchronous vibrations during the design phase of rotor bearing systems. It is known that the synchronous unbalance response of a single mass Jeffcott rotor in linear isotropic bearings is identical in form to the response of a simple spring-mass-damper system excited by a rotating unbalance. This paper demonstrates that the free vibrations, and hence the system damping factor, of a distributed mass flexible rotor in tilting pad bearings may be analyzed using a single mass, two tier spring-damper model. The relationship between the system damping factor and rotor stability is discussed. Non-synchronous tilting pad bearing characteristics are incorporated into the expression for the damping factor, and nondimensional curves are presented which establish values of the damping factor as a function of operating speed, critical speed, bearing clearance and Sommerfeld number. The subject curves provide a quick method for establishing stability guidelines during rotor design and for comparing existing rotor bearing systems.

Stability of Rotor-Bearing Systems With Generalized Support Flexibility and Damping and Aerodynamic Cross-Coupling

1975 ◽  
Vol 97 (3) ◽  
pp. 461-469 ◽  
Author(s):  
R. E. Warner ◽  
A. I. Soler
Keyword(s):  
Cross Coupling ◽  
Frequency Dependent ◽  
Oil Film ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Single Mass ◽  
Tilting Pad Bearings

This paper examines stability of the flexible single mass rotor, acted on by motion induced forces due to aero-dynamic cross-coupling and supported most generally by oil film tilting pad bearings which are in turn mounted on flexible, damped supports. Plotted results include the frequency dependent spring and damping coefficients for the 4-pad tilting pad bearing, damping coefficients for the 360-deg squeeze bearing and stability plots of rotor-bearing systems including aerodynamic cross-coupling, the 4-pad tilting pad bearing and the 150-deg partial arc bearing with various support arrangements.

Geometry Optimization of Hybrid Tilting-Pad Journal Bearings

2007 ◽  
Author(s):  
Ilmar Ferreira Santos ◽  
Bo Uldall Kristiansen
Keyword(s):  
Angular Velocity ◽  
Geometry Optimization ◽  
Injection Pressure ◽  
Hydrodynamic Condition ◽  
Damping Factor ◽  
Operational Conditions ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Run Up ◽  
Bearing System

Radial tilting-pad bearings under hybrid lubrication conditions are industrially used in heavy horizontal machines. One single orifice is normally designed and machined in the middle of the pad. Through such an orifice pressurized lubricant is injected and the rotor-bearing system is hydrostatically lubricated during start-up and run-up conditions. Nevertheless, at a pre-defined angular velocity the hydrostatic lubrication is turned-off and the rotor-bearing system operates under hydrodynamic condition. The main focus of the present work is to investigate the feasibility of using the hydrostatic lubrication as an auxiliary mechanism to improve rotor stability and increase damping reserve of rotor-bearing systems. The geometry of the bearing, namely number of orifices, their positioning over the pad surface and their diameters, are optimized using the damping factor of the rotor-bearing system as weighting functional. The dependency of the optimal parameters on the rotor angular velocity and injection pressure (operational conditions) is discussed and the limits of an increase in damping reserve via geometry optimization are elucidated.

Imbalance Response of a Rotor Supported on Flexure Pivot Tilting Pad Journal Bearings in Series With Integral Squeeze Film Dampers

2001 ◽  
Author(s):  
Luis San Andrés ◽  
Oscar De Santiago
Keyword(s):  
Peak Amplitude ◽  
Squeeze Film ◽  
Critical Speeds ◽  
Rotor Imbalance ◽  
Squeeze Film Dampers ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
In Series ◽  
Tilting Pad Bearings ◽  
Tilting Pad Journal Bearings

Measurements of the imbalance responses of a massive 45 kg rotor supported on series (flexure pivot) tilting pad bearings and integral squeeze film dampers (SFDs) are presented. The rotor-bearing configuration is of interest in compressor applications where often oil lubricated dampers are introduced in series with fluid film bearings to relocate critical speeds, enhance the overall system damping, and reduce the risks of rotordynamic instabilities due to seals and impellers, for example. Coast-down experiments from 9,000 rpm are conducted for increasing levels of rotor imbalance, and equivalent system damping coefficients identified from the peak amplitude of rotor response while traversing cylindrical mode critical speeds. The tests performed with locked (inactive) and active SFDs demonstrate the effectiveness of the flexible damped support in reducing the system critical speed and improving the overall rotor response with reduced transmitted forces to ground. The SFDs allow safe rotor operation with values of imbalance twice as large as the maximum sustained by the rotor supported on tilting pad bearings alone. The experiments reveal a linear relationship between the peak amplitude of vibration at the critical speeds and the imbalance displacement, even for rotor motions larger than 50% of the tilting pad bearing and damper clearances. The tests also show little cross-coupling effects with the shaft centerline moving along a nearly vertical path. The rotor-bearing system remained stable in the entire range of operation and without the appearance of subsynchronous vibration or non-linear damper jump response.

Imbalance Response of a Rotor Supported on Flexure Pivot Tilting Pad Journal Bearings in Series With Integral Squeeze Film Dampers

2003 ◽  
Vol 125 (4) ◽  
pp. 1026-1032 ◽  
Author(s):  
L. San Andre´s ◽  
O. De Santiago
Keyword(s):  
Peak Amplitude ◽  
Squeeze Film ◽  
Critical Speeds ◽  
Rotor Imbalance ◽  
Squeeze Film Dampers ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
In Series ◽  
Tilting Pad Bearings ◽  
Tilting Pad Journal Bearings

Measurements of the imbalance responses of a massive 45 kg rotor supported on series (flexure pivot) tilting pad bearings and integral squeeze film dampers (SFDs) are presented. The rotor-bearing configuration is of interest in compressor applications where often oil lubricated dampers are introduced in series with fluid film bearings to relocate critical speeds, enhance the overall system damping, and reduce the risks of rotordynamic instabilities due to seals and impellers, for example. Coast-down experiments from 9000 rpm are conducted for increasing levels of rotor imbalance, and equivalent system damping coefficients identified from the peak amplitude of rotor response while traversing cylindrical mode critical speeds. The tests performed with locked (inactive) and active SFDs demonstrate the effectiveness of the flexible damped support in reducing the system critical speed and improving the overall rotor response with reduced transmitted forces to ground. The SFDs allow safe rotor operation with values of imbalance twice as large as the maximum sustained by the rotor supported on tilting pad bearings alone. The experiments reveal a linear relationship between the peak amplitude of vibration at the critical speeds and the imbalance displacement, even for rotor motions larger than 50% of the tilting pad bearing and damper clearances. The tests also show little cross-coupling effects with the shaft centerline moving along a nearly vertical path. The rotor-bearing system remained stable in the entire range of operation and without the appearance of subsynchronous vibration or nonlinear damper jump response.

Constrained Design Optimization of Rotor-Tilting Pad Bearing Systems

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Costin D. Untaroiu ◽  
Alexandrina Untaroiu
Keyword(s):  
Design Optimization ◽  
Power Loss ◽  
Optimization Design ◽  
Optimization Approach ◽  
Design Variables ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Automatic Optimization ◽  
Tilting Pad Bearings ◽  
Bearing System

Design of a rotor-bearing system is a challenging task due to various conflicting design requirements, which should be fulfilled. This study considers an automatic optimization approach for the design of a rotor supported on tilting-pad bearings. A numerical example of a rotor-bearing system is employed to demonstrate the merits of the proposed design approach. The finite element method is used to model the rotor-bearing system, and the dynamic speed-dependent coefficients of the bearing are calculated using a bulk flow code. A number of geometrical characteristics of the rotor simultaneously with the parameters defining the configuration of tilting pad bearings are considered as design variables into the automatic optimization process. The power loss in bearings, stability criteria, and unbalance responses are defined as a set of objective functions and constraints. The complex design optimization problem is solved using heuristic optimization algorithms, such as genetic, and particle-swarm optimization. Whereas both algorithms found better design solutions than the initial design, the genetic algorithms exhibited the fastest convergence. A statistical approach was used to identify the influence of the design variables on the objective function and constraint measures. The bearing clearances, preloads and lengths showed to have the highest influence on the power loss in the chosen design space. The high performance of the best solution obtained in the optimization design suggests that the proposed approach has good potential for improving design of rotor-bearing systems encountered in industrial applications.

scholarly journals Nonlinear stability analysis of rotor-bearing systems

PAMM ◽  
2009 ◽  
Vol 9 (1) ◽  
pp. 279-280 ◽  
Author(s):  
Aydin Boyaci ◽  
Wolfgang Seemann ◽  
Carsten Proppe
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Nonlinear Stability Analysis ◽  
Rotor Bearing
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