Identification of Bearing Force Coefficients From Measurements of Imbalance Response of a Flexible Rotor

2004 ◽  
Author(s):  
Luis San Andre´s ◽  
Oscar C. De Santiago
Keyword(s):  
High Performance ◽  
Fluid Film ◽  
Flexible Rotor ◽  
Simple Method ◽  
Force Coefficients ◽  
Fluid Film Bearings ◽  
Support Force ◽  
Bearing Force ◽  
Rotor Structure ◽  
Motion Amplitude

Field identification of fluid film bearing parameters is critical for adequate interpretation of rotating machinery performance and necessary to validate or calibrate predictions from restrictive computational fluid film bearing models. This paper presents a simple method for estimating bearing support force coefficients in flexible rotor-bearing systems. The method requires two independent tests with known mass imbalance distributions and the measurement of the rotor motion (amplitude and phase) at locations close to the supports. The procedure relies on the modeling of the rotor structure and finds the bearing transmitted forces as a function of observable quantities (rotor vibrations at bearing locations). Imbalance response measurements conducted with a two-disk flexible rotor supported on two-lobe fluid film bearings allow validation of the identification method estimations. Predicted (linearized) bearing force coefficients agree reasonably well with the parameters derived from the test data. The method advanced neither adds mathematical complexity nor requires additional instrumentation beyond that already available in most high performance turbomachinery.

Identification of Bearing Force Coefficients in Flexible Rotors: Extensions to a Field Method

2005 ◽  
Author(s):  
Luis San Andre´s ◽  
Oscar De Santiago
Keyword(s):  
Field Method ◽  
Mode Shapes ◽  
Flexible Rotor ◽  
Identification Procedure ◽  
Force Coefficients ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Support Force ◽  
Order Of Magnitude ◽  
Bearing Force

Rotor-bearing system characteristics, such as mode shapes and their associated natural frequencies and damping ratios are essential to diagnose and correct vibration problems during system operation. Of the above characteristics, reliable identification of fluid film bearing force parameters, i.e. stiffness and damping coefficients, is one of the most difficult to achieve, in particular during field operation. Results of an enhanced method to estimate support force coefficients in flexible rotor-bearing systems based on imbalance response measurements obtained near the bearing locations are presented herein. The procedure can be conducted on site with minimal instrumentation. A test flexible rotor mounted on two-lobe hydrodynamic bearings is used to validate the identification procedure. Imbalance response measurements for various imbalance magnitudes are obtained near the bearing locations and also at rotor mid-span. At shaft speeds around the bending critical speed, the displacements at rotor mid span are an order of magnitude larger than the shaft displacements at the bearings. The identification procedure renders reliable bearing force coefficients for shaft speeds between 1 krpm and 4 krpm. The sensitivity of the method and derived parameters to noise in the measurements is also quantified.

The Lower Bound of the Stability Threshold Speed of a Flexible Rotor System in Fluid-Film Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 351-353
Author(s):  
Wen Zhang
Keyword(s):  
Lower Bound ◽  
Theoretical Foundation ◽  
Simple Approach ◽  
Rotor System ◽  
Fluid Film ◽  
Flexible Rotor ◽  
Stability Threshold ◽  
Fluid Film Bearings ◽  
Single Disk ◽  
The Stability

The paper is devoted to the estimation of the lower bound of the stability threshold speed (STS) of a flexible rotor system supported in fluid-film bearings. It is proved theoretically that the STS of any multi-degree-of-freedom flexible rotor system is always higher than the STS of the corresponding equivalent single disk rotor. The conclusion offers us a simple approach to estimate the STS of any actual rotor system and provides a theoretical foundation for the approach.

The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Luis San Andrés ◽  
Yujiao Tao
Keyword(s):  
Experimental Data ◽  
Journal Bearings ◽  
Fluid Film ◽  
Virtual Mass ◽  
Force Coefficients ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Bearing Force ◽  
Film Stiffness ◽  
Tilting Pad Journal Bearings

Recent comprehensive experimental data showcasing the force coefficients of commercial size tilting pad journal bearings has brought to rest the long standing issue on the adequacy of the [K,C,M] physical model to represent frequency independent bearing force coefficients, in particular viscous damping. Most experimental works test tilting pad journal bearings (TPJBs) with large preloads, operating over a large wide range of rotor speeds, and with null to beyond normal specific loads. Predictions from apparently simple fluid film bearing models stand poor against the test data which invariably signals to theory missing pivot and pad flexibility effects, and most importantly, ignoring significant differences in bearing and pad clearances due to actual operation, poor installation and test procedures, or simply errors in manufacturing and assembly. Presently, a conventional thermo hydrodynamic bulk flow model for prediction of the pressure and temperature fields in TPJBs is detailed. The model accounts for various pivot stiffness types, all load dependent and best when known empirically, and allows for dissimilar pad and bearing clearances. The algorithm, reliable even for very soft pad-pivots, predicts frequency reduced bearing impedance coefficients and over a certain frequency range delivers the bearing stiffness, damping and virtual mass force coefficients. Good correlation of predictions against a number of experimental results available in the literature bridges the gap between a theoretical model and the applications. Predicted pad reaction loads reveal large pivot deflections, in particular for a bearing with large preloaded pads, with significant differences in pivot stiffness as a function of specific load and operating speed. The question on how pivot stiffness acts to increase (or decrease) the bearing force coefficients, in particular the dynamic stiffness versus frequency, remains since the various experimental data show contradictory results. A predictive study with one of the test bearings varies its pivot stiffness from 10% of the fluid film stiffness to an almost rigid one, 100 times larger. With certainty, bearings with nearly rigid pivot stiffness show frequency independent force coefficients. However, for a range of pad pivot stiffness, 1/10 to ten times the fluid film stiffness, TPJB impedances vary dramatically with frequency, in particular as the excitation frequency grows above synchronous speed. The bearing virtual mass coefficients become negative, thus stiffening the bearing for most excitation frequencies.

Stability and Damped Critical Speeds of a Flexible Rotor in Fluid-Film Bearings

1974 ◽  
Vol 96 (2) ◽  
pp. 509-517 ◽  
Author(s):  
J. W. Lund
Keyword(s):  
Dynamic Properties ◽  
Fluid Film ◽  
Internal Damping ◽  
Flexible Rotor ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Fluid Film Bearings ◽  
Multistage Compressor ◽  
Stiffness And Damping ◽  
Rotor Model

A method is described for calculating the threshold speed of instability and the damped critical speeds of a general flexible rotor in fluid-film journal bearings. It is analogous to the Myklestad-Prohl method for calculating critical speeds and is readily programmed for numerical computation. The rotor model can simulate any practical shaft geometry and support configuration. The bearings are represented by their linearized dynamic properties, also known as the stiffness and damping coefficients of the bearing, and the calculation includes hysteretic internal damping in the shaft and destabilizing aerodynamic forces. To demonstrate the application of the method, results are shown for an industrial, multistage compressor.

The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings

2013 ◽  
Author(s):  
Luis San Andrés ◽  
Yujiao Tao
Keyword(s):  
Experimental Data ◽  
Journal Bearings ◽  
Fluid Film ◽  
Virtual Mass ◽  
Force Coefficients ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Bearing Force ◽  
Film Stiffness ◽  
Tilting Pad Journal Bearings

Recent comprehensive experimental data showcasing the force coefficients of commercial size tilting pad journal bearings has brought to rest the long standing issue on the adequacy of the [K,C,M] physical model to represent frequency independent bearing force coefficients, in particular viscous damping. Most experimental works test TPJBs with large preloads, operating over a large wide range of rotor speeds, and with null to beyond normal specific loads. Predictions from apparently simple fluid film bearing models stand poor against the test data which invariably signals to theory missing pivot and pad flexibility effects, and most importantly, ignoring significant differences in bearing and pad clearances due to actual operation, poor installation and test procedures, or simply errors in manufacturing and assembly. Presently, a conventional thermo hydrodynamic bulk flow model for prediction of the pressure and temperature fields in TPJBs is detailed. The model accounts for various pivot stiffness types, all load dependent and best when known empirically, and allows for dissimilar pad and bearing clearances. The algorithm, reliable even for very soft pad-pivots, predicts frequency reduced bearing impedance coefficients and, over a certain frequency range, delivers the bearing stiffness, damping and virtual mass force coefficients. Good correlation of predictions against a number of experimental results available in the literature bridges the gap between a theoretical model and the applications. Predicted pad reaction loads reveal large pivot deflections, in particular for a bearing with large preloaded pads, with significant differences in pivot stiffness as a function of specific load and operating speed. The question on how pivot stiffness acts to increase (or decrease) the bearing force coefficients, in particular the dynamic stiffness vs. frequency, remains since the various experimental data show contradictory results. A predictive study with one of the test bearings varies its pivot stiffness from 10% of the fluid film stiffness to an almost rigid one, 100 times larger. With certainty, bearings with nearly rigid pivot stiffness show frequency independent force coefficients. However, for a range of pad pivot stiffness, 1/10 to ten times the fluid film stiffness, TPJB impedances vary dramatically with frequency, in particular as the excitation frequency grows above synchronous speed. The bearing virtual mass coefficients become negative, thus stiffening the bearing for most excitation frequencies.

On the vibration and control of a flexible rotor mounted on fluid film bearings

1997 ◽  
Vol 65 (6) ◽  
pp. 849-856 ◽  
Author(s):  
Z. Abduljabbar ◽  
M.M. ElMadany ◽  
E. Al-Bahkali
Keyword(s):  
Fluid Film ◽  
Flexible Rotor ◽  
Fluid Film Bearings ◽  
And Control

Field Identification of Stiffness and Damping Characteristics of Fluid Film Bearings

2008 ◽  
Author(s):  
Sameh H. Tawfick ◽  
Aly El-Shafei ◽  
M. O. A. Mokhtar
Keyword(s):  
Journal Bearings ◽  
Fluid Film ◽  
Flexible Rotor ◽  
Test Rig ◽  
Vibration Data ◽  
Damping Characteristics ◽  
Fluid Film Bearings ◽  
Field Identification ◽  
Modal Mass ◽  
Stiffness And Damping

A method for field identification of stiffness and damping characteristics of fluid film bearings FFB is derived. The method relies on measuring both the shaft and the housing’s vibration response. Two independent unbalance runs are performed and the synchronous response is recorded. Using the housing vibration data, the amount of unbalance acting on the bearing, as well as the flexible shafts’ “modal mass” can be experimentally determined. Thus, with this method, field engineers can identify the bearings impedance in flexible rotor-bearing systems. A test rig comprising a flexible shaft supported on two cylindrical journal bearings is used to verify the proposed method. The amount of uncertainty in the derived coefficients is calculated.

Jorgen W. Lund: Theories Versus Tests

2001 ◽  
Author(s):  
Jorgen Tonnesen
Keyword(s):  
Thermal Properties ◽  
Experimental Work ◽  
Rotor Dynamics ◽  
Fluid Film ◽  
Flexible Rotor ◽  
Late Professor ◽  
Fluid Film Bearings ◽  
Condensed Form ◽  
Flexible Rotors ◽  
Rotor Balancing

Abstract The contribution of the late Professor Jorgen W. Lund in the field of rotor dynamics and fluid film bearings is presented in a condensed form with the emphasis on the experimental work and results that confirm and support many of Dr. Lund’s theories and analyses. Included are subjects of rotor balancing by the influence method, unbalance response of a flexible rotor, damped critical speeds of flexible rotors and fluid film bearing’s static, dynamic and thermal properties.

Orbit-Model Force Coefficients for Fluid Film Bearings: A Step Beyond Linearization

2015 ◽  
Author(s):  
Luis San Andrés ◽  
Sung-Hwa Jeung
Keyword(s):  
Equilibrium Position ◽  
Large Amplitude ◽  
Operating Conditions ◽  
Fluid Film ◽  
System Response ◽  
Force Coefficients ◽  
Fluid Film Bearings ◽  
Rotor Bearing ◽  
Orbit Analysis ◽  
Reaction Forces

High performance turbomachinery demands high shaft speeds, increased rotor flexibility, tighter clearances in the flow passages, advanced materials, and increased tolerance to imbalances. Operation at high speeds induces severe dynamic loading with large amplitude shaft motions at the bearing supports. Typical rotordynamic models rely on linearized force coefficients (stiffness K, damping C, and inertia M) to model the reaction forces from fluid film bearings and seal elements. These true linear force coefficients are derived from infinitesimally small amplitude motions about an equilibrium position. Often, however, a rotor-bearing system does not reach an equilibrium position and displaces with motions amounting to a sizable portion of the film clearance; the most notable example being a squeeze film damper (SFD). Clearly, linearized force coefficients cannot be used in situations exceeding its basic formulation. Conversely, the current speed of computing permits to evaluate fluid film element reaction forces in real time for ready numerical integration of the transient response of complex rotor-bearing systems. This approach albeit fast does not help to gauge the importance of individual effects on system response. Presently, an orbit analysis method estimates force coefficients from numerical simulations of specified journal motions and predicted fluid film reaction forces. For identical operating conditions in static eccentricity and whirl amplitude and frequency as those in measurements, the computational physics model calculates instantaneous damper reaction forces during one full period of motion and performs a Fourier analysis to characterize the fundamental components of the dynamic forces. The procedure is repeated over a range of frequencies to accumulate sets of forces and displacements building mechanical transfer functions from which force coefficients are identified. These coefficients thus represent best fits to the motion over a frequency range and dissipate the same mechanical energy as the nonlinear mechanical element. More accurate than the true linearized coefficients, force coefficients from the orbit analysis correlate best with SFD test data, in particular for large amplitude motions, statically off-centered. The comparisons also reveal the fallacy in representing nonlinear systems as simple K-C-M models impervious to the kinematics of motion.

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