Parametric Studies on Static and Dynamic Performance of Air Foil Bearings with Different Top Foil Geometries and Bump Stiffness Distributions

2006 ◽  
Vol 129 (2) ◽  
pp. 354-364 ◽  
Author(s):  
Daejong Kim
Keyword(s):  
Spatial Variation ◽  
Linear Stability ◽  
Load Capacity ◽  
Dynamic Performance ◽  
Dynamic Force ◽  
Stability Analyses ◽  
Foil Bearings ◽  
Analytical Studies ◽  
Different Types ◽  
Stiffness Distribution

Experimental and analytical studies on air foil bearings have been performed extensively over the past decades, and significant improvement in load capacity and rotor dynamics stability have been reported. Often, advanced air foil bearings are believed to have complicated bump foil structure to provide unique underlying support mechanism, which in turn make the bearing very stable and have high load capacity. However, all the analytical studies on air foil bearings so far assume a circular profile of top foil with uniform bump stiffness distribution because detailed information on bump stiffness distribution and overall bearing shape is not known to the public. This paper investigates load capacities and rotordynamic performances of two different types of air foil bearings, e.g., circular cylindrical bearings with single continuous top foil and noncircular preloaded bearings with three top foil pads. Within the two subcategories, stiffness variations along axial and circumferential directions were given to have a total of four types of air foil bearings with different overall bearing shapes and stiffness distributions. Overall static and dynamic performance of the four different types of air foil bearings are presented and compared via calculations of load capacities and dynamic force coefficients, modal stability analyses, and time domain orbit simulations. The major difference of load capacities comes from the overall bearing shape (circular continuous foil or preloaded three pad) rather than spatial variation of bump stiffness within the bump foils. Preloaded three-pad bearings have significantly reduced load capacity compared to the circular bearings because of small pad arc length. Rotordynamic performance is also much more sensitive to the overall bearing shape than spatial variation of bump stiffness and damping within the bump foils. The linear stability analyses predict modal natural frequencies very close to those from the orbit simulations. However, onset speeds of instability from these two approaches are quite different, manifesting the limitation of the linear stability analyses. The orbit simulations show the three-pad bearings have higher onset speeds of instability than circular bearing (47,000rpm versus 24,000rpm).

Foil Gas Bearing With Compression Springs: Analyses and Experiments

2007 ◽  
Vol 129 (3) ◽  
pp. 628-639 ◽  
Author(s):  
Ju-ho Song ◽  
Daejong Kim
Keyword(s):  
Loss Factor ◽  
Load Capacity ◽  
Underlying Structure ◽  
Equivalent Viscous Damping ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Different Types ◽  
Structural Loss ◽  
Compression Springs ◽  
Gas Bearing

A new foil gas bearing with spring bumps was constructed, analyzed, and tested. The new foil gas bearing uses a series of compression springs as compliant underlying structures instead of corrugated bump foils. Experiments on the stiffness of the spring bumps show an excellent agreement with an analytical model developed for the spring bumps. Load capacity, structural stiffness, and equivalent viscous damping (and structural loss factor) were measured to demonstrate the feasibility of the new foil bearing. Orbit and coast-down simulations using the calculated stiffness and measured structural loss factor indicate that the damping of underlying structure can suppress the maximum peak at the critical speed very effectively but not the onset of hydrodynamic rotor-bearing instability. However, the damping plays an important role in suppressing the subsynchronous vibrations under limit cycles. The observation is believed to be true with any air foil bearings with different types of elastic foundations.

A Comparison of the Steady-State and Dynamic Performance of First- and Second-Generation Foil Bearings

2010 ◽  
Author(s):  
M. J. Conlon ◽  
A. Dadouche ◽  
W. M. Dmochowski ◽  
R. Payette ◽  
J.-P. Be´dard
Keyword(s):  
Steady State ◽  
Experimental Evaluation ◽  
First Generation ◽  
Second Generation ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Stiffness And Damping

Oil-free foil bearing technology has advanced intermittently over the years, driven by research efforts to improve both steady-state and dynamic performance characteristics, namely: load capacity, stiffness, and damping. Bearing designs are thus classified according to “generation”, with first-generation bearings being the most primitive. This paper presents an experimental evaluation of a first- and a second-generation foil bearing, and aims to provide the high-fidelity data necessary for proper validation of theoretical predictive models of foil bearing performance. The aforementioned test bearings were fabricated in-house, and are both 70mm in diameter with an aspect ratio of 1; bearing manufacturing details are provided. The work makes use of a facility dedicated to measuring both the steady-state and dynamic properties of foil bearings under a variety of controlled operating conditions. The bearing under test is placed at the midspan of a horizontal, simply-supported, stepped shaft which rotates at up to 60krpm. Static and dynamic loads of up to 3500N and 450N (respectively) can be applied by means of a pneumatic cylinder and two electrodynamic shakers. The bearings’ structural (static) stiffnesses are highly nonlinear, and this affects the accuracy of the dynamic coefficient determination. Both dynamic stiffness and damping are found to vary nonlinearly with excitation frequency, and are over-predicted by a structural experimental evaluation — the film plays an important role in bearing dynamics. The second-generation bearing is found to have a higher load capacity, dynamic stiffness, and damping than the first-generation bearing.

Parametric Study of Bump Foil Gas Bearings for Industrial Applications

2011 ◽  
Author(s):  
Oscar De Santiago ◽  
Luis San Andres
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Dynamic Performance ◽  
Scaling Up ◽  
Industrial Applications ◽  
Working Fluid ◽  
Metal Foil ◽  
Gas Bearings ◽  
Foil Bearings ◽  
Process Gas

Gas bearings are an appealing technology for rotor support due to their inherent characteristic of oil-free operation. Elimination of lubricant brings also the possibility of designing the bearings for operation within the flow path of thermal machines and even using the process gas as working fluid for the bearing. Among several gas bearing technologies, foil bearings are the most common ones currently found in applications such as small compressors for aircraft pressurization, microturbines, and other small turbomachinery. Broad application of foil gas bearings to date is precluded due to their limited load capacity. Presently, scaling up of foil bearings requires expensive testing due to limitation of validated computational models of the fluid flow in the bearing coupled to the mechanical behavior of the metal foil and underlying corrugated structure. Recent work in this area shows that calibrated models are now available in the open literature and it is possible to predict more accurately the performance of the bearings at non-conventional sizes. The objective of this work is to present a study of the most relevant parameters of foil bearings affecting their static and dynamic performance and aimed at scaling them up for industrial applications currently not considered for them. The paper presents a calibration of the computational model to previous tests by independent researchers and discusses simple rules for scaling up the bearing components. Finally, the paper presents a feasibility study of application of foil gas bearings to a generic centrifugal compressor for industrial use.

Heavily Loaded Gas Foil Bearings: A Model Anchored to Test Data

2005 ◽  
Author(s):  
Tae Ho Kim ◽  
Luis San Andre´s
Keyword(s):  
Test Data ◽  
Load Capacity ◽  
Stable Operation ◽  
Dynamic Force ◽  
Damping Force ◽  
Force Coefficients ◽  
Foil Bearings ◽  
Foundation Model ◽  
Accurate Performance ◽  
Force Characteristics

Widespread usage of gas foil bearings (FBs) into micro turbomachinery to midsize gas turbine engines requires accurate performance predictions anchored to reliable test data. The paper presents a simple yet accurate model predicting the static and dynamic force characteristics of gas FBs. The analysis couples the Reynolds equation for a thin gas film to a simple elastic foundation model for the top foil and bump strip layer. An exact flow advection model is adopted to solve the partial differential equations for the zeroth- and first- order pressure fields that render the FB load capacity and frequency dependent force coefficients. As the static load imposed on the foil bearing increases, predictions show the journal center displaces to eccentricities exceeding the bearing nominal clearance. A nearly constant FB static stiffness, independent of journal speed, is estimated for operation with large loads; and approaching closely the structural stiffness derived from contact operation at null rotor speed. Predicted minimum film thickness and journal attitude angle demonstrate good agreement with archival test data for a first-generation gas FB. The bump-foil strip structural loss factor, exemplifying a dry-friction dissipation mechanism, aids to largely enhance the bearing direct damping force coefficients. At high loads, the bump-foil structure influences most the stiffness and damping coefficients. The FB whirl frequency ratio (WFR) is examined to ensure its dynamically stable operation. The predictions demonstrate that FBs have greatly different static and dynamic force characteristics when operating at journal eccentricities in excess of the bearing clearance from those obtained for operation at low loads, i.e. small journal eccentricities.

Heavily Loaded Gas Foil Bearings: A Model Anchored to Test Data

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Tae Ho Kim ◽  
Luis San Andrés
Keyword(s):  
Test Data ◽  
Load Capacity ◽  
Dynamic Force ◽  
Damping Force ◽  
Rotor Spinning ◽  
Force Coefficients ◽  
Foil Bearings ◽  
Foundation Model ◽  
Accurate Performance ◽  
Force Characteristics

Widespread usage of gas foil bearings (FBs) into microturbomachinery to midsize gas turbine engines requires accurate performance predictions anchored to reliable test data. This paper presents a simple yet accurate model predicting the static and dynamic force characteristics of gas FBs. The analysis couples the Reynolds equation for a thin gas film to a simple elastic foundation model for the top foil and bump strip layer. An exact flow advection model is adopted to solve the partial differential equations for the zeroth- and first-order pressure fields that render the FB load capacity and frequency-dependent force coefficients. As the static load imposed on the foil bearing increases, predictions show that the journal center displaces to eccentricities exceeding the bearing nominal clearance. A nearly constant FB static stiffness, independent of journal speed, is estimated for operation with large loads, and approaching closely the bearing structural stiffness derived from contact operation without rotor spinning. Predicted minimum film thickness and journal attitude angle demonstrate good agreement with archival test data for a first-generation gas FB. The bump-foil-strip structural loss factor, exemplifying a dry-friction dissipation mechanism, aids to largely enhance the bearing direct damping force coefficients. At high loads, the bump-foil structure influences most the stiffness and damping coefficients. The predictions demonstrate that FBs have greatly different static and dynamic force characteristics when operating at journal eccentricities in excess of the bearing clearance from those obtained for operation at low loads, i.e., small journal eccentricity.

The Impact of Modified Corrugated Bump Structures on the Rotor Dynamic Performance of Gas Foil Bearings

2014 ◽  
Author(s):  
Robert Hoffmann ◽  
Tomasz Pronobis ◽  
Robert Liebich
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Stability Range ◽  
Numerical Investigations ◽  
Foil Bearings ◽  
The Stability ◽  
Stiffness And Damping ◽  
The Impact ◽  
Rotor Dynamic ◽  
Stiffness Distribution

Gas foil bearings (GFBs) have been successfully introduced in the field of high speed turbo machineries. Low drag friction, high speed operation and the omission of an oil system are some advantages of bump type foil bearings. However, experimental and numerical investigations have shown sub synchronous vibrations, which affect the rotor dynamic behavior. Several methods and devices have been introduced to decrease these vibrations (e.g. viscoelastic foil bearings, shims and side feed pressurization). This current paper examines the effect of different bump foil configurations on the rotor dynamic performance. Different bump stiffness distributions in axial and circumferential direction are considered for a set of loadings (5, 15, 30 and 60 N) and rotor speeds (6,000–70,000 rpm). To evaluate the onset speed of sub synchronous vibration a linear stability analysis is applied. It uses the linearized bearing parameters stiffness and damping. The results show, that a variation of stiffness distributions may enlarge the stability range. Simulations indicate that a non-uniform circumferential stiffness distribution is very effective to avoid sub synchronous vibrations, due to smaller cross coupling effects.

A fuzzy evaluation method of road vehicle automatic weighing instrument in dynamic force metrological performance

2020 ◽  
Vol 64 (1-4) ◽  
pp. 1365-1372
Author(s):  
Xiaohui Mao ◽  
Liping Fei ◽  
Xianping Shang ◽  
Jie Chen ◽  
Zhihao Zhao
Keyword(s):  
Evaluation Method ◽  
Comprehensive Evaluation ◽  
Evaluation Model ◽  
Dynamic Performance ◽  
Dynamic Force ◽  
Fuzzy Evaluation ◽  
Road Vehicle ◽  
Evaluation Standard ◽  
The Road ◽  
Metrological Performance

The measurement performance of road vehicle automatic weighing instrument installed on highways is directly related to the safety of roads and bridges. The fuzzy number indicates that the uncertain quantization problem has obvious advantages. By analyzing the factors affecting the metrological performance of the road vehicle automatic weighing instrument, combined with the fuzzy mathematics theory, the weight evaluation model of the dynamic performance evaluation of the road vehicle automatic weighing instrument is proposed. The factors of measurement performance are summarized and calculated, and the comprehensive evaluation standard of the metering performance of the weighing equipment is obtained, so as to realize the quantifiable analysis and evaluation of the metering performance of the dynamic road vehicle automatic weighing instrument in use, and provide data reference for adopting a more scientific measurement supervision method.

Rotordynamic Performance of a Rotor Supported on Bump Type Foil Gas Bearings: Experiments and Predictions

2006 ◽  
Vol 129 (3) ◽  
pp. 850-857 ◽  
Author(s):  
Luis San Andrés ◽  
Dario Rubio ◽  
Tae Ho Kim
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Load Capacity ◽  
Test System ◽  
Foil Bearings ◽  
Rotor Imbalance ◽  
Synchronous Motion ◽  
Damping Characteristics ◽  
Rotor Surface ◽  
Stiffness And Damping

Gas foil bearings (GFBs) satisfy the requirements for oil-free turbomachinery, i.e., simple construction and ensuring low drag friction and reliable high speed operation. However, GFBs have a limited load capacity and minimal damping, as well as frequency and amplitude dependent stiffness and damping characteristics. This paper provides experimental results of the rotordynamic performance of a small rotor supported on two bump-type GFBs of length and diameter equal to 38.10mm. Coast down rotor responses from 25krpm to rest are recorded for various imbalance conditions and increasing air feed pressures. The peak amplitudes of rotor synchronous motion at the system critical speed are not proportional to the imbalance introduced. Furthermore, for the largest imbalance, the test system shows subsynchronous motions from 20.5krpm to 15krpm with a whirl frequency at ∼50% of shaft speed. Rotor imbalance exacerbates the severity of subsynchronous motions, thus denoting a forced nonlinearity in the GFBs. The rotor dynamic analysis with calculated GFB force coefficients predicts a critical speed at 8.5krpm, as in the experiments; and importantly enough, unstable operation in the same speed range as the test results for the largest imbalance. Predicted imbalance responses do not agree with the rotor measurements while crossing the critical speed, except for the lowest imbalance case. Gas pressurization through the bearings’ side ameliorates rotor subsynchronous motions and reduces the peak amplitudes at the critical speed. Posttest inspection reveal wear spots on the top foils and rotor surface.

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