Structural Stiffness, Dry-Friction Coefficient and Equivalent Viscous Damping in a Bump-Type Foil Gas Bearing

2005 ◽  
Author(s):  
Dario Rubio ◽  
Luis San Andre´s
Keyword(s):  
Friction Coefficient ◽  
Dry Friction ◽  
Structural Parameters ◽  
Excitation Frequency ◽  
Single Frequency ◽  
Viscous Damping ◽  
Periodic Load ◽  
Stick Slip ◽  
Equivalent Viscous Damping ◽  
Frequency Domain Methods

High performance oil-free turbomachinery implements gas foil bearings (FBs) to improve mechanical efficiency in compact units. FB design, however, is still largely empirical due to their mechanical complexity. The paper provides test results for the structural parameters in a bump-type foil bearing. The stiffness and damping (Coulomb or viscous type) coefficients characterize the bearing compliant structure. The test bearing, 38.1 mm in diameter and length, consists of a thin top foil supported on bump-foil strips. A prior investigation identified the stiffness due to static loads. Presently, the test FB is mounted on a non-rotating stiff shaft and a shaker exerts single frequency loads on the bearing. The dynamic tests are conducted at shaft surface temperatures from 25 °C to 75°C. Time and frequency domain methods are implemented to determine the FB parameters from the recorded periodic load and bearing motions. Both methods deliver identical parameters. The dry friction coefficient ranges from 0.05 to 0.20, increasing as the amplitude of load increases. The recorded motions evidence a resonance at the system natural frequency, i.e. null damping. The test derived equivalent viscous damping is inversely proportional to the motion amplitude and excitation frequency. The characteristic stick-slip of dry friction is dominant at small amplitude dynamic loads leading to a hardening effect (stiffening) of the FB structure. The operating temperature produces shaft growth generating a bearing preload. However, the temperature does not affect significantly the identified FB parameters, albeit the experimental range was too small considering the bearings intended use in industry.

Structural Stiffness, Dry Friction Coefficient, and Equivalent Viscous Damping in a Bump-Type Foil Gas Bearing

2006 ◽  
Vol 129 (2) ◽  
pp. 494-502 ◽  
Author(s):  
Dario Rubio ◽  
Luis San Andres
Keyword(s):  
Friction Coefficient ◽  
Dry Friction ◽  
Structural Parameters ◽  
Excitation Frequency ◽  
Single Frequency ◽  
Viscous Damping ◽  
Periodic Load ◽  
Stick Slip ◽  
Equivalent Viscous Damping ◽  
Frequency Domain Methods

High performance oil-free turbomachinery implements gas foil bearings (FBs) to improve mechanical efficiency in compact units. FB design, however, is still largely empirical due to its mechanical complexity. The paper provides test results for the structural parameters in a bump-type foil bearing. The stiffness and damping (Coulomb or viscous type) coefficients characterize the bearing compliant structure. The test bearing, 38.1mm in diameter and length, consists of a thin top foil supported on bump-foil strips. A prior investigation identified the stiffness due to static loads. Presently, the test FB is mounted on a non-rotating stiff shaft and a shaker exerts single frequency loads on the bearing. The dynamic tests are conducted at shaft surface temperatures from 25to75°C. Time and frequency domain methods are implemented to determine the FB parameters from the recorded periodic load and bearing motions. Both methods deliver identical parameters. The dry friction coefficient ranges from 0.05 to 0.20, increasing as the amplitude of load increases. The recorded motions evidence a resonance at the system natural frequency, i.e., null damping. The test derived equivalent viscous damping is inversely proportional to the motion amplitude and excitation frequency. The characteristic stick-slip of dry friction is dominant at small amplitude dynamic loads leading to a hardening effect (stiffening) of the FB structure. The operating temperature produces shaft growth generating a bearing preload. However, the temperature does not significantly affect the identified FB parameters, albeit the experimental range was too small considering the bearings intended use in industry.

Characterization of a Foil Bearing Structure at Increasing Temperatures: Static Load and Dynamic Force Performance

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Tae Ho Kim ◽  
Anthony W. Breedlove ◽  
Luis San Andrés
Keyword(s):  
Friction Coefficient ◽  
Dynamic Load ◽  
Material Properties ◽  
Dry Friction ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Single Frequency ◽  
Viscous Damping ◽  
Structural Stiffness ◽  
Simple Physical Model

Oil-free turbomachinery relies on gas bearing supports for reduced power losses and enhanced rotordynamic stability. Gas foil bearings (GFBs) with bump-strip compliant layers can sustain large loads, both static and dynamic, and provide damping to reduce shaft vibrations. The ultimate load capacity of GFBs depends on the material properties and configuration of the underlying bump-strip structures. In high temperature applications, thermal effects, which change the operating clearances and material properties, can considerably affect the performance of the GFB structure. This paper presents experiments conducted to estimate the structural stiffness of a test GFB for increasing shaft temperatures. A 38.17 mm inner diameter GFB is mounted on a nonrotating hollow shaft affixed to a rigid structure. A cartridge heater inserted into the shaft provides a controllable heat source and thermocouples record the temperatures on the shaft and GFB housing. For increasing shaft temperatures (up to 188°C), increasing static loads (0–133 N) are applied to the bearing and its deflection recorded. In the test configuration, thermal expansion of the GFB housing, larger than that of the shaft, nets a significant increase in radial clearance, which produces a significant reduction in the bearing’s structural stiffness. A simple physical model, which assembles the individual bump stiffnesses, predicts well the measured GFB structural stiffness. Single frequency periodic loads (40–200 Hz) are exerted on the test bearing to identify its dynamic structural stiffness and equivalent viscous damping or a dry-friction coefficient. The GFB dynamic stiffness increases by as much as 50% with dynamic load amplitudes increasing from 13 N to 31 N. The stiffness nearly doubles from low to high frequencies, and most importantly, it decreases by a third as the shaft temperature rises to 188°C. In general, the GFB dynamic stiffness is lower than its static magnitude at low excitation frequencies, while it becomes larger with increasing excitation frequency due apparently to a bump slip-stick phenomenon. The GFB viscous damping is inversely proportional to the amplitude of the dynamic load, excitation frequency, and shaft temperature. The GFB dry-friction coefficient decreases with increasing amplitude of the applied load and shaft temperature, and increases with increasing excitation frequency.

Characterization of Foil Bearing Structure for Increasing Shaft Temperatures: Part II—Dynamic Force Performance

2008 ◽  
Author(s):  
Tae Ho Kim ◽  
Luis San Andre´s ◽  
Anthony W. Breedlove
Keyword(s):  
Friction Coefficient ◽  
Dry Friction ◽  
Excitation Frequency ◽  
Forced Response ◽  
Dynamic Loads ◽  
Dynamic Force ◽  
Viscous Damping ◽  
Structural Stiffness ◽  
Foil Bearing ◽  
Excitation Frequencies

The forced response of a gas foil bearing (GFB), a typical rotor support in oil-free microturbomachinery, relies heavily on its resilient bump-strip layers structure, which also offers dry-friction type damping to ameliorate rotor vibrations. Operation at high temperature not only changes the FB elastic support material properties, but also produces thermal growth of the rotor and bearing components which ultimately affect the bearing structural stiffness and energy dissipation characteristics. The paper presents dynamic shaker load versus foil bearing structural deflection measurements for increasing shaft temperatures, from ambient to 188°C. In the tests, a FB supported on a non-rotating shaft is excited with a shaker at three load amplitudes (13 N, 22 N, and 31 N) and frequencies ranging from 40 to 200 Hz. A mechanical impedance model identifies the frequency dependent FB structural stiffness and equivalent viscous damping coefficient or dry-friction coefficient. Surface plots show trends in test results across increasing dynamic loads, shaft temperatures, and excitation frequencies. The FB stiffness increases by as much as 50% with dynamic loads amplitudes increasing from 13 N to 31 N. The stiffness nearly doubles from low to high frequencies; and most importantly, it decreases by a third as the shaft temperature rises to 188°C. In general, the FB dynamic structural stiffness is lower than its static stiffness, reported in a companion paper, at low excitation frequencies, while it becomes larger with increasing excitation frequency due apparently to a bump slip-stick phenomenon. The bearing viscous damping is inversely proportional to the amplitude of dynamic load, excitation frequency, and shaft temperature. The FB structure dry-friction coefficient decreases with increasing amplitude of applied load and shaft temperature, and increases with increasing excitation frequency. The experimental results demonstrate the paramount effect of operating temperature on the structural parameters of a foil bearing.

Energy Balancing Method to Identify Nonlinear Damping of Bolted-Joint Interface

2016 ◽  
Vol 693 ◽  
pp. 318-323 ◽  
Author(s):  
Xin Liao ◽  
Jian Run Zhang
Keyword(s):  
Dry Friction ◽  
Harmonic Excitation ◽  
Joint Interface ◽  
Damping Factor ◽  
Viscous Damping ◽  
Bolted Joint ◽  
Energy Balancing ◽  
Stick Slip ◽  
Non Linear ◽  
Linear Damping

The interface of bolted joint commonly focuses on the research of non-linear damping and stiffness, which affect structural response. In the article, the non-linear damping model of bolted-joint interface is built, consisting of viscous damping and Coulomb friction. Energy balancing method is developed to identify the dry-friction parameter and viscous damping factor. The corresponding estimation equations are acquired when the input is harmonic excitation. Then, the vibration experiments with different bolted preloads are conducted, from which amplitudes in various input levels are used to work out the interface parameters. Also, the fitting curves of dry-friction parameters are also obtained. Finally, the results illustrate that the most interface of bolted joint in lower excitation levels occurs stick-slip motion, and the feasibility of the identification approach is demonstrated.

Design and structural performance measurements of a novel multi-cantilever foil bearing

2014 ◽  
Vol 229 (10) ◽  
pp. 1830-1838 ◽  
Author(s):  
Kai Feng ◽  
Xueyuan Zhao ◽  
Zhiyang Guo
Keyword(s):  
Dynamic Characteristics ◽  
Dynamic Load ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Viscous Damping ◽  
Equivalent Viscous Damping ◽  
Foil Bearing ◽  
Load Tests ◽  
Stiffness And Damping ◽  
Motion Amplitude

With increasing need for high-speed, high-temperature, and oil-free turbomachinery, gas foil bearings (GFBs) have been considered to be the best substitutes for traditional oil-lubricated bearings. A multi-cantilever foil bearing (MCFB), a novel GFB with multi-cantilever foil strips serving as the compliant underlying structure, was designed, fabricated, and tested. A series of static and dynamic load tests were conducted to measure the structural stiffness and equivalent viscous damping of the prototype MCFB. Experiments of static load versus deflection showed that the proposed bearing has a large mechanical energy dissipation capability and a pronounced nonlinear static stiffness that can prevents overly large motion amplitude of journal. Dynamic load tests evaluated the influence of motion amplitude, loading orientation and misalignment on the dynamic stiffness and equivalent viscous damping with respect to excitation frequency. The test results demonstrated that the dynamic stiffness and damping are strongly dependent on the excitation frequency. Three motion amplitudes were applied to the bearing housing to investigate the effects of motion amplitude on the dynamic characteristics. It is noted that the bearing dynamic stiffness and damping decreases with incrementally increasing motion amplitudes. A high level of misalignment can lead to larger static and dynamic bearing stiffness as well as to larger equivalent viscous damping. With dynamic loads applied to two orientations in the bearing midplane separately, the dynamic stiffness increases rapidly and the equivalent viscous damping declines slightly. These results indicate that the loading orientation is a non-negligible factor on the dynamic characteristics of MCFBs.

Experimental Evaluation of the Structure Characterization of a Novel Hybrid Bump-Metal Mesh Foil Bearing

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Kai Feng ◽  
Yuman Liu ◽  
Xueyuan Zhao ◽  
Wanhui Liu
Keyword(s):  
Excitation Frequency ◽  
Structure Characterization ◽  
Viscous Damping ◽  
Metal Mesh ◽  
Equivalent Viscous Damping ◽  
Foil Bearings ◽  
Damping Characteristics ◽  
Foil Bearing ◽  
Mesh Density ◽  
Load Tests

Rotors supported by gas foil bearings (GFBs) experience stability problem caused by subsynchronous vibrations. To obtain a GFB with satisfactory damping characteristics, this study presented a novel hybrid bump-metal mesh foil bearing (HB-MMFB) that consists of a bump foil and metal mesh blocks in an underlying supporting structure, which takes advantage of both bump-type foil bearings (BFBs) and MMFBs. A test rig with a nonrotating shaft was designed to estimate structure characterization. Results from the static load tests show that the proposed HB-MFBs exhibit an excellent damping level compared with the BFBs with a similar size because of the countless microslips in the metal mesh blocks. In the dynamic load tests, the HB-MFB with a metal mesh density of 36% presents a viscous damping coefficient that is approximately twice that of the test BFB. The dynamics structural coefficients of HB-MFBs, including structural stiffness, equivalent viscous damping, and structural loss factor, are all dependent on excitation frequency and motion amplitude. Moreover, they exhibit an obvious decrease with the decline in metal mesh density.

On the Experimental Dynamic Force Performance of a Squeeze Film Damper Supplied Through a Check Valve and Sealed With O-Rings

2021 ◽  
Author(s):  
Luis San Andrés ◽  
Bryan Rodríguez
Keyword(s):  
Dynamic Pressure ◽  
Excitation Frequency ◽  
Check Valve ◽  
Forced Response ◽  
Single Frequency ◽  
Squeeze Film ◽  
Dynamic Force ◽  
Viscous Damping ◽  
Test Rig ◽  
Force Coefficients

Abstract In rotor-bearing systems, squeeze film dampers (SFDs) assist to reduce vibration amplitudes while traversing a critical speed and also offer a means to suppress rotor instabilities. Along with an elastic support element, SFDs are effective means to isolate a rotor from its casing. O-rings (ORs), piston rings (PRs) and side plates as end seals reduce leakage and air ingestion while amplifying the viscous damping in configurations with limited physical space. ORs also add a centering stiffness and damping to a SFD. The paper presents experiments to quantify the dynamic forced response of an O-rings sealed ends SFD (OR-SFD) lubricated with ISO VG2 oil supplied at a low pressure (0.7 bar(g)). The damper is 127 mm in diameter (D), short in axial length L = 0.2D, and the film clearance c = 0.279 mm. The lubricant flows into the film land through a mechanical check valve and exits through a single port. Upstream of the check valve, a large plenum filled with oil serves to attenuate dynamic pressure disturbances. Multiple sets of single-frequency dynamic loads, 10 Hz to 120 Hz, produce circular centered orbits with amplitudes r = 0.1c, 0.15c and 0.2c. The experimental results identify the test rig structure, ORs and SFD force coefficients; namely stiffness (K), mass (M) and viscous damping (C). The ORs coefficients are frequency independent and show a sizeable direct stiffness, KOR ∼ 50% of the test rig structure stiffness, along with a quadrature stiffness, K0∼0.26 KOR, demonstrative of material damping. The lubricated system damping coefficient equals CL = (CSFD + COR); the ORs contributing 10% to the total. The experimental SFD damping and inertia coefficients are large in physical magnitude; CSFD slightly grows with orbit size whereas MSFD is relatively constant. The added mass (MSFD) is approximately four-fold the bearing cartridge mass; hence, the test rig natural frequency drops by ∼50% once lubricated. A computational physics model predicts force coefficients that are just 10% lower than those estimated from experiments. The amplitude of measured dynamic pressures upstream of the plenum increases with excitation frequency. Unsuspectedly, during dynamic load operation, the check valve did allow for lubricant backflow into the plenum. Post-tests verification demonstrates that, under static pressure conditions, the check valve does work since it allows fluid flow in just one direction.

Measurement of Structural Stiffness and Damping Coefficients in a Metal Mesh Foil Bearing

2009 ◽  
Vol 132 (3) ◽  
Author(s):  
Luis San Andrés ◽  
Thomas Abraham Chirathadam ◽  
Tae-Ho Kim
Keyword(s):  
Loss Factor ◽  
Copper Wire ◽  
Mechanical Energy ◽  
Excitation Frequency ◽  
Viscous Damping ◽  
Structural Stiffness ◽  
Metal Mesh ◽  
Equivalent Viscous Damping ◽  
Damping Coefficients ◽  
Stiffness And Damping

Engineered metal mesh foil bearings (MMFBs) are a promising low cost bearing technology for oil-free microturbomachinery. In a MMFB, a ring shaped metal mesh provides a soft elastic support to a smooth arcuate foil wrapped around a rotating shaft. This paper details the construction of a MMFB and the static and dynamic load tests conducted on the bearing for estimation of its structural stiffness and equivalent viscous damping. The 28.00 mm diameter 28.05 mm long bearing, with a metal mesh ring made of 0.3 mm copper wire and compactness of 20%, is installed on a test shaft with a slight preload. Static load versus bearing deflection measurements display a cubic nonlinearity with large hysteresis. The bearing deflection varies linearly during loading, but nonlinearly during the unloading process. An electromagnetic shaker applies on the test bearing loads of controlled amplitude over a frequency range. In the frequency domain, the ratio of applied force to bearing deflection gives the bearing mechanical impedance, whose real part and imaginary part give the structural stiffness and damping coefficients, respectively. As with prior art published in the literature, the bearing stiffness decreases significantly with the amplitude of motion and shows a gradual increasing trend with frequency. The bearing equivalent viscous damping is inversely proportional to the excitation frequency and motion amplitude. Hence, it is best to describe the mechanical energy dissipation characteristics of the MMFB with a structural loss factor (material damping). The experimental results show a loss factor as high as 0.7 though dependent on the amplitude of motion. Empirically based formulas, originally developed for metal mesh rings, predict bearing structural stiffness and damping coefficients that agree well with the experimentally estimated parameters. Note, however, that the metal mesh ring, after continuous operation and various dismantling and re-assembly processes, showed significant creep or sag that resulted in a gradual decrease in its structural force coefficients.

Measurement of Structural Stiffness and Damping Coefficients in a Metal Mesh Foil Bearing

2009 ◽  
Author(s):  
Luis San Andre´s ◽  
Thomas Abraham Chirathadam ◽  
Tae-Ho Kim
Keyword(s):  
Loss Factor ◽  
Copper Wire ◽  
Mechanical Energy ◽  
Excitation Frequency ◽  
Viscous Damping ◽  
Structural Stiffness ◽  
Metal Mesh ◽  
Equivalent Viscous Damping ◽  
Damping Coefficients ◽  
Stiffness And Damping

Engineered Metal Mesh Foil Bearings (MMFB) are a promising low cost bearing technology for oil-free microturbomachinery. In a MMFB, a ring shaped metal mesh (MM) provides a soft elastic support to a smooth arcuate foil wrapped around a rotating shaft. The paper details the construction of a MMFB and the static and dynamic load tests conducted on the bearing for estimation of its structural stiffness and equivalent viscous damping. The 28.00 mm diameter, 28.05 mm long bearing, with a metal mesh ring made of 0.3 mm Copper wire and compactness of 20%, is installed on a test shaft with a slight preload. Static load versus bearing deflection measurements display a cubic nonlinearity with large hysteresis. The bearing deflection varies linearly during loading, but nonlinearly during the unloading process. An electromagnetic shaker applies on the test bearing loads of controlled amplitude over a frequency range. In the frequency domain, the ratio of applied force to bearing deflection gives the bearing mechanical impedance, whose real part and imaginary part give the structural stiffness and damping coefficients, respectively. As with prior art published in the literature, the bearing stiffness decreases significantly with the amplitude of motion and shows a gradual increasing trend with frequency. The bearing equivalent viscous damping is inversely proportional to the excitation frequency and motion amplitude. Hence, it is best to describe the mechanical energy dissipation characteristics of the MMFB with a structural loss factor (material damping). The experimental results show a loss factor as high as 0.7 though dependent on the amplitude of motion. Empirically based formulas, originally developed for metal mesh rings, predict bearing structural stiffness and damping coefficients agreeing well with the experimentally estimated parameters. Note, however, that the metal mesh ring, after continuous operation and various dismantling and reassembly processes, showed significant creep or sag that resulted in a gradual decrease of its structural force coefficients.

Influence of Tensioner Dry Friction on the Vibration of Belt Drives With Belt Bending Stiffness

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Farong Zhu ◽  
Robert G. Parker
Keyword(s):  
Dry Friction ◽  
Harmonic Balance ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Friction Torque ◽  
Stick Slip ◽  
Pulley System ◽  
Coulomb Damping ◽  
Belt Drives ◽  
Linear Subsystem

A model of dry friction tensioner in a belt-pulley system considering transverse belt vibration is developed, and the influence of the dry friction on the system dynamics is examined. The discretized formulation is divided into a linear subsystem including linear coordinates and a nonlinear subsystem addressing tensioner arm vibration, which reduces the dimension of the iteration matrices when employing the harmonic balance method. The Coulomb damping at the tensioner arm pivot mitigates the tensioner arm vibration but not necessarily the vibrations of other system components. The extent of the mitigation varies for different excitation frequency ranges. The critical amplitude of the dry friction torque beyond which the system operates with a locked arm is determined analytically. Superharmonic resonances are observed in the responses of the generalized span coordinates, but their amplitudes are small. The energy dissipation at the tensioner arm hub is discussed, and the stick-slip phenomena of the arm are reflected in the velocity reversals near the arm extreme location. Dependence of the span tension fluctuations on Coulomb torque is explored.

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