Dynamic performance of foil bearings with a quadratic stiffness model

2016 ◽  
Vol 216 ◽  
pp. 666-671 ◽  
Author(s):  
Xu Fangcheng ◽  
Kim Daejong
Keyword(s):  
Dynamic Performance ◽  
Foil Bearings ◽  
Stiffness Model ◽  
Quadratic Stiffness

Effect of Mechanical Preloads on the Dynamic Performance of Gas Foil Bearings

2008 ◽  
Author(s):  
Tae Ho Kim ◽  
Luis San Andre´s
Keyword(s):  
Large Amplitude ◽  
High Speed ◽  
Low Cost ◽  
Dynamic Performance ◽  
Cycle Performance ◽  
High Power Density ◽  
Shaft Speed ◽  
Foil Bearings ◽  
Bearing Force ◽  
Good Agreement

Gas foil bearings (GFBs) enable efficient, reliable and maintenance free operation of high-power-density microturbomachinery (< 200 kW). High speed rotors supported on bump-type GFBs, however, are prone to show large-amplitude subsynchronous motions albeit reaching limit cycle performance. Presently, commercial GFBs are simply modified to introduce a mechanical preload that induces a hydrodynamic wedge to generate more load support and direct stiffnesses. Three metal shims inserted under the bump strip layers and in contact with the bearing housing create a multiple lobe clearance profile at a very low cost. Shaft speed coastdown measurements reveal the rotordynamic performance of a rotor supported on original GBFs and (modified) shimmed GFBs. The later GFBs determine a raise in the rotor-bearing system natural frequency, as expected, and also act to delay the onset speed of large-amplitude subsynchronous motions. Predictions of imbalance response implementing linearized bearing force coefficients are in good agreement with measured amplitudes of synchronous response for both GFB configurations, original and modified.

Effect of Side Feed Pressurization on the Dynamic Performance of Gas Foil Bearings: A Model Anchored to Test Data

2008 ◽  
Author(s):  
Tae Ho Kim ◽  
Luis San Andre´s
Keyword(s):  
Test Data ◽  
High Speed ◽  
Gas Flow ◽  
Dynamic Performance ◽  
Rotor Speed ◽  
Mass Distributions ◽  
Foil Bearings ◽  
Feed Pressure ◽  
Run Up ◽  
Forced Cooling

Comprehensive modeling of gas foil bearings (GFBs) anchored to reliable test data will enable the widespread usage of these bearings into novel high speed turbomachinery applications. GFBs often need a forced cooling gas flow, axially fed through one end of the bearing, for adequate thermal management. The paper presents rotordynamic response measurements on a rigid rotor supported on GFBs during rotor speed run-up and coastdown tests with the GFBs supplied with increasing feed gas pressures to 2.8 bar. Rotor speed run-up tests to 35 krpm show that bearing end side feed gas pressurization delays the onset speed of rotor subsynchronous whirl motions. The test data validate closely predictions of the threshold speed of instability and whirl frequency ratio derived from a GFB model that implements the axial evolution of gas circumferential flow velocity as a function of the imposed side feed pressure. Rotor speed coastdown tests from 25 krpm with a low feed pressure of 0.35 bar evidences a nearly linear synchronous rotor response for small and moderately large imbalance mass distributions. A structural FE rotordynamics model integrates linearized synchronous speed GFB force coefficients and predicts synchronous responses, amplitude and phase angle, agreeing with the test data. The analysis and measurements demonstrate the profound effect of end side, feed gas pressurization on the rotordynamic performance of GFBs.

scholarly journals Performance of Thrust Foil Bearings with Nonlinear Foil Stiffness Model

2020 ◽  
Vol 56 (15) ◽  
pp. 198
Author(s):  
XU Fangcheng ◽  
HOU Liukai ◽  
WU Bin
Keyword(s):  
Foil Bearings ◽  
Stiffness Model

Effect of taper error on the performance of gas foil conical bearing

2020 ◽  
Vol 72 (10) ◽  
pp. 1189-1197
Author(s):  
Hongyang Hu ◽  
Ming Feng ◽  
Tianming Ren
Keyword(s):  
Peer Review ◽  
Load Capacity ◽  
Dynamic Performance ◽  
Cone Angle ◽  
Nonlinear Structure ◽  
Content Type ◽  
Axial Load Capacity ◽  
Stiffness Model ◽  
Direct Stiffness ◽  
Conical Bearing

Purpose This paper aims to study the bearing performance with different cone angle errors, to study the effect law of manufacturing taper error on the properties of gas foil conical bearing (GFCB). Design/methodology/approach For the GFCB supported by separated bump foil strips, a nonlinear structure stiffness model considering Coulomb friction and arch characteristics was proposed. The finite element method and finite difference method were used to solve the Reynolds equation and the film thickness equation by coupling, and the properties of the GFCB were obtained. The effect of foil and bearing structure parameters on the static and dynamic performance under different taper error cases was analyzed. Moreover, a test on the air compressor supported by GFCBs was conducted to verify the practicability. Findings The taper error has a largely adverse effect on the load capacity of GFCB. When the taper error is −0.03°, the radial load capacity Fr and axial load capacity Fz decrease by 37.5 and 58.3%, respectively. The taper error decreases the direct stiffness and cross-coupled damping of GFCB, which will weaken the bearing stability. Moreover, the performance of GFCB is closely related to the foil and bearing parameters. Originality/value The taper error adversely affects the static and dynamic characteristics of GFCB, which should be concerned by bearing designers, researchers and academicians. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2020-0089/

On the characteristics of gas foil conical bearings considering misalignment

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hongyang Hu ◽  
Ming Feng ◽  
Tianming Ren
Keyword(s):  
Film Thickness ◽  
Peer Review ◽  
Load Capacity ◽  
Dynamic Performance ◽  
Critical Role ◽  
Friction Torque ◽  
Misalignment Angle ◽  
Content Type ◽  
Stiffness Model ◽  
Dynamic Performances

Purpose The purpose of this paper is to study the characteristics of gas foil conical bearings (GFCBs) considering the misalignment, the static and dynamic performances with different misalignment cases were studied. Design/methodology/approach A test rig on the air compressor supported by GFCBs has been developed to measure the practicability. A nonlinear bump stiffness model and one-dimensional beam top foil stiffness model were used as a basis for the calculation of static and dynamic performance. The finite element method and finite difference method are adopted to solve the Reynolds equation and the film thickness equation coupled, in which different misalignment cases were considered by changing the film thickness. Findings The supporting performance of GFCB is excellent, and the film clearance plays a critical role. The misalignment effects depend on the assembled angle and the misalignment angle. The load capacity, friction torque, temperature of GFCB decrease when the misalignment assembled angle is between 120° and 240°, while the dynamic bearing stability is improved. The static and dynamic performances show the opposite law for the other assembled angles, and the misalignment effect is more dramatic when there is a larger misalignment angle. Moreover, the bearing and running parameters largely affect the bearing performance. Originality/value The present study focuses on the static and dynamic characteristics of GFCB and investigates the effects of misalignment on the bearing performance. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-04-2020-0117

scholarly journals Design, Fabrication and Experiment of Double U-Beam MEMS Vibration Ring Gyroscope

Micromachines ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. 186 ◽  
Author(s):  
Huiliang Cao ◽  
Yu Liu ◽  
Zhiwei Kou ◽  
Yingjie Zhang ◽  
Xingling Shao ◽  
...  
Keyword(s):  
Finite Element ◽  
Resonant Frequency ◽  
Thin Shell ◽  
Dynamic Performance ◽  
Frequency Error ◽  
Element Analysis ◽  
Deep Reactive Ion Etching ◽  
System A ◽  
Stiffness Model ◽  
Bias Instability

This study presents a new microelectromechanical system, a vibration ring gyroscope with a double U-beam (DUVRG), which was designed using a combination of mathematical analysis and the finite element method. First, a ring vibration resonator with eight double U-beam structures was developed, and 24 capacitive electrodes were designed for drive and sense according to the advantageous characteristics of a thin-shell vibrating gyroscope. Then, based on the elastic mechanics and thin-shell theory, a mathematical stiffness model of the double U-beam was established. The maximum mode resonant frequency error calculated by the DUVRG stiffness model, finite element analysis (FEA) and experiments was 0.04%. DUVRG structures were manufactured by an efficient fabrication process using silicon-on-glass (SOG) and deep reactive ion etching (DRIE), and the FEA value and theoretical calculation had differences of 5.33% and 5.36% with the measured resonant frequency value, respectively. Finally, the static and dynamic performance of the fabricated DUVRG was tested, and the bias instability and angular random walk were less than 8.86 (°)/h and 0.776 (°)/√h, respectively.

On the Coupling of Foil Bearing Supported Rotors: Part 1 — Analysis

2007 ◽  
Author(s):  
Hooshang Heshmat ◽  
James F. Walton ◽  
Crystal A. Heshmat
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Ball Bearing ◽  
Dynamic Performance ◽  
Rotor Systems ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Flexible Rotors ◽  
Coupling Dynamic ◽  
Bearing System

The expanded application of high-speed rotor systems operating on compliant foil bearings will be greatly enhanced with the ability to adequately couple multiple shaft systems with differing bearing systems and dynamic performance. In this paper the results of an analytical tradeoff study assessing coupling dynamic characteristics and their impact on coupled rotor-bearing system dynamics are presented. This analysis effort was completed in an effort to establish the form of characteristics needed to couple foil bearing supported rotors to ball bearing supported rotors, other foil bearing supported rotors as well as coupling rigid and flexible rotors both supported on foil bearings. The conclusions from this study indicate that with appropriate coupling design, a wide array of foil bearing supported rotor systems may be successfully coupled.

Effect of Side Feed Pressurization on the Dynamic Performance of Gas Foil Bearings

2007 ◽  
Author(s):  
Luis San Andre´s ◽  
Tae Ho Kim
Keyword(s):  
Gas Turbines ◽  
Gas Flow ◽  
Dynamic Performance ◽  
Mechanical Efficiency ◽  
System Stability ◽  
Remarkable Effect ◽  
Foil Bearings ◽  
Feed Pressure ◽  
Side Pressure ◽  
The Difference

Oil-free micro turbomachinery implementing gas foil bearings (GFBs) has improved mechanical efficiency and reliability. Adequate thermal management for operation in high temperature environments is an issue of importance in applications such as in gas turbines and turbochargers. GFBs often need a cooling gas flow, axially fed through one end of the bearing, to transport the heat conducted from a hot turbine, for example. Side gas pressurization, however, has a paramount effect on reducing amplitudes of motion, synchronous and subsynchronous. Presently, shaft motion measurements in a test rotor supported on GFBs show this remarkable effect. A computational gas film model implementing the evolution of gas circumferential flow velocity as a function of the imposed side pressure is advanced. Predicted direct stiffnesses and damping coefficients for the test GFB increase as the magnitude of feed pressure raises, while the difference in cross-coupled stiffnesses, directly related to rotor-bearing system stability, decreases. Predictions of threshold speed of instability and whirl frequency ratio are in close agreement with the measurements.

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.

Thermo-elastohydrodynamic analysis of the inhomogeneous foil bearing with misalignment

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hao Li ◽  
Haipeng Geng ◽  
Hao Lin
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Dynamic Performance ◽  
Gas Temperature ◽  
Content Type ◽  
Rotor Systems ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Deformation Equation ◽  
Small Perturbation Method

Purpose The misalignment is generally inevitable in the process of machining and assembly of rotor systems with gas foil bearings, but the exploration on this phenomenon is relatively less. Therefore, the purpose of this paper is to carry out the thermo-elastohydrodynamic analysis of the foil bearing with misalignment, especially the inhomogeneous foil bearing. Design/methodology/approach The rotor is allowed to misalign in two non-rotating directions. Then the static and dynamic performance of the inhomogeneous foil bearing is studied. The thermal-elastohydrodynamic analysis is realized by combining the Reynolds equation, foil deformation equation and energy equation. The small perturbation method is used to calculate the dynamic coefficients, then the critical whirl ratio is obtained. Findings The gas pressure, film thickness and temperature distribution distort when the misalignment appears. The rotor misalignment can improve the loading capacity but rise the gas temperature at the same time. Furthermore, the rotor misalignment can affect the critical whirl ratio which demonstrates that it is necessary to analyze the misalignment before the rotordynamic design. Originality/value The value of this paper is the exploration of the thermo-elastohydrodynamic performance of the inhomogeneous foil bearing with misalignment, the analysis procedure and the corresponding results are valuable for the design of turbo system with gas foil bearings.

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