Identification of Structural Stiffness and Energy Dissipation Parameters in a Second Generation Foil Bearing: Effect of Shaft Temperature

2010 ◽  
Vol 133 (3) ◽  
Author(s):  
Luis San Andrés ◽  
Keun Ryu ◽  
Tae Ho Kim
Keyword(s):  
Energy Dissipation ◽  
Dynamic Load ◽  
Loss Factor ◽  
Static Load ◽  
Mechanical Energy ◽  
Excitation Frequency ◽  
Structural Stiffness ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Mechanical Energy Dissipation

Established high temperature operation of gas foil bearings (GFB) is of great interest for gas turbine applications. The effects of (high) shaft temperature on the structural stiffness and mechanical energy dissipation parameters of a foil bearing (FB) must be assessed experimentally. Presently, a hollow shaft warmed by an electric heater holds a floating second generation FB that is loaded dynamically by an electromagnetic shaker. In tests with the shaft temperature up to 184°C, the measurements of dynamic load and ensuing FB deflection render the bearing structural parameters, stiffness and damping, as a function of excitation frequency and amplitude of motion. The identified FB stiffness and viscous damping coefficients increase with shaft temperature due to an increase in the FB assembly interference or preload. The bearing material structural loss factor best representing mechanical energy dissipation decreases slightly with shaft temperature while increasing with excitation frequency. Separate static load measurements on the bearing also make evident the preload of the test bearing-shaft system at room temperature. The loss factor obtained from the area inside the hysteresis loop of the static load versus the deflection curve agrees remarkably with the loss factor obtained from the dynamic load measurements. The static procedure offers substantial savings in cost and time to determine the energy dissipation characteristics of foil bearings. Post-test inspection of the FB reveals sustained wear at the locations, where the bumps contact the top foil and the bearing sleeve inner surface, thus, evidences the bearing energy dissipation by dry friction.

Structural and Rotordynamic Force Coefficients of a Shimmed Bump Foil Bearing: An Assessment of a Simple Engineering Practice

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Luis San Andrés ◽  
Joshua Norsworthy
Keyword(s):  
Loss Factor ◽  
High Speed ◽  
Static Load ◽  
Low Cost ◽  
Mechanical Energy ◽  
Excitation Frequency ◽  
Engineering Practice ◽  
Force Coefficients ◽  
Damping Coefficients ◽  
Stiffness And Damping

High speed rotors supported on bump-type foil bearings (BFBs) often suffer from large subsynchronous whirl motions. Mechanically preloading BFBs through shimming is a common, low cost practice that shows improvements in rotordynamic stability. However, there is an absence of empirical information related to the force coefficients (structural and rotordynamic) of shimmed BFBs. This paper details a concerted study toward assessing the effect of shimming on a first generation BFB (L = 38.1 mm and D = 36.5 mm). Three metal shims, 120 deg apart, are glued to the inner surface of the bearing cartridge and facing the underside of the bump foil strip. The shim sets are of identical thickness, either 30 μm or 50 μm. In static load tests, a bearing with shims shows a (nonlinear) structural stiffness larger than for the bearing without shims. Torque measurements during shaft acceleration also demonstrate a shimmed BFB has a larger friction coefficient. For a static load of 14.3 kPa, dynamic loads with a frequency sweep from 250 Hz to 450 Hz are exerted on the BFB, without and with shims, to estimate its rotordynamic force coefficients while operating at ∼50 krpm (833 Hz). Similar measurements are conducted without shaft rotation. Results are presented for the original BFB (without shims) and the two shimmed BFB configurations. The direct stiffnesses of the BFB, shimmed or not, increase with excitation frequency, thus evidencing a mild hardening effect. The BFB stiffness and damping coefficients decrease slightly for operation with rotor speed as opposed to the coefficients when the shaft is stationary. For frequencies above 300 Hz, the direct damping coefficients of the BFB with 50 μm thick shims are ∼30% larger than the coefficients of the original bearing. The bearing structural loss factor, a measure of its ability to dissipate mechanical energy, is derived from the direct stiffness and damping coefficients. The BFB with 50 μm thick shims has a 25% larger loss factor—average from test data collected at 300 Hz to 400 Hz—than the original BFB. Further measurements of rotor motions while the shaft accelerates to ∼50 krpm demonstrate the shimmed BFB (thickest shim set) effectively removes subsynchronous whirl motions amplitudes that were conspicuous when operating with the original bearing.

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.

Metal Mesh Foil Bearing: Effect of Motion Amplitude, Rotor Speed, Static Load, and Excitation Frequency on Force Coefficients

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Luis San Andrés ◽  
Thomas Abraham Chirathadam
Keyword(s):  
Energy Dissipation ◽  
High Speed ◽  
Mechanical Energy ◽  
Excitation Frequency ◽  
Wire Mesh ◽  
Test Element ◽  
Metal Mesh ◽  
Force Coefficients ◽  
Damping Coefficients ◽  
Mechanical Energy Dissipation

Metal mesh foil bearings (MMFBs), simple to construct and inexpensive, are a promising bearing technology for oil-free microturbomachinery operating at high speed and high temperature. Prior research demonstrated the near friction-free operation of a MMFB operating to 60 krpm and showing substantial mechanical energy dissipation characteristics. This paper details further experimental work and reports MMFB rotordynamic force coefficients. The test rig comprises a turbocharger driven shaft and overhung journal onto which a MMFB is installed. A soft elastic support structure akin to a squirrel cage holds the bearing, aiding to its accurate positioning relative to the journal. Two orthogonally positioned shakers excite the test element via stingers. The test bearing comprises a cartridge holding a Copper wire mesh ring, 2.7 mm thick, and a top arcuate foil. The bearing length and inner diameter are 38 mm and 36.5 mm, respectively. Experiments were conducted with no rotation and with journal spinning at 40–50 krpm, with static loads of 22 N and 36 N acting on the bearing. Dynamic load tests spanning frequencies from 150 to 450 Hz were conducted while keeping the amplitude of bearing displacements at 20 µm, 25 µm, and 30 µm. With no journal spinning, the force coefficients represent the bearing elastic structure alone because the journal and bearing are in contact. The direct stiffnesses gradually increase with frequency while the direct damping coefficients drop quickly at low frequencies (< 200 Hz) and level off above this frequency. The damping combines both viscous and material types from the gas film and mesh structure. Journal rotation induces airborne operation with a hydrodynamic gas film separating the rotor from its bearing. Hence, cross-coupled stiffness coefficients appear although with magnitudes lower than those of the direct stiffnesses. The direct stiffnesses, 0.4 to 0.6 MN/m within 200–400 Hz, are slightly lower in magnitude as those obtained without journal rotation, suggesting the air film stiffness is quite high. Bearing direct stiffnesses are inversely proportional to the bearing motion amplitudes, whereas the direct equivalent viscous damping coefficients do not show any noticeable variation. All measurements evidence a test bearing system with material loss factor (γ) ∼ 1.0, indicating significant mechanical energy dissipation ability.

Experimental Structural Stiffness and Damping in a 2nd Generation Foil Bearing for Increasing Shaft Temperatures

2009 ◽  
Author(s):  
Luis San Andre´s ◽  
Keun Ryu
Keyword(s):  
Structural Parameters ◽  
Mechanical Energy ◽  
Excitation Frequency ◽  
Electric Heater ◽  
Structural Stiffness ◽  
Hollow Shaft ◽  
2Nd Generation ◽  
Foil Bearing ◽  
Structural Loss ◽  
Stiffness And Damping

Demonstrated gas foil bearing (GFB) operation at high temperature is of interest for gas turbine applications. The effects of (high) shaft temperature on the structural stiffness and damping parameters of a foil bearing must be assessed experimentally. Presently, a hollow shaft warmed by an electric heater holds a floating 2nd generation FB that is loaded dynamically by an electromagnetic shaker. In tests with the shaft temperature up to 184°C, the measurements of dynamic load and ensuing FB deflection render the bearing structural parameters, stiffness and damping, as a function of excitation frequency and amplitude of motion. The identified FB stiffness and viscous damping coefficients increase with shaft temperature due to a reduction in the FB clearance. The bearing material structural loss factor, best representing mechanical energy dissipation, decreases slightly with shaft temperature while increasing with excitation frequency.

Metal Mesh Foil Bearing: Effect of Motion Amplitude, Rotor Speed, Static Load, and Excitation Frequency on Force Coefficients

2011 ◽  
Author(s):  
Luis San Andre´s ◽  
Thomas Abraham Chirathadam
Keyword(s):  
Energy Dissipation ◽  
High Speed ◽  
Mechanical Energy ◽  
Excitation Frequency ◽  
Wire Mesh ◽  
Test Element ◽  
Metal Mesh ◽  
Force Coefficients ◽  
Damping Coefficients ◽  
Mechanical Energy Dissipation

Metal mesh foil bearings (MMFBs), simple to construct and inexpensive, are a promising bearing technology for oil-free microturbomachinery operating at high speed and high temperature. Prior research demonstrated the near friction-free operation of a MMFB operating to 60 krpm and showing substantial mechanical energy dissipation characteristics. This paper details further experimental work and reports MMFB rotordynamic force coefficients. The test rig comprises of a turbocharger driven shaft and overhung journal onto which a MMFB is installed. A soft elastic support structure akin to a squirrel cage holds the bearing, aiding to its accurate positioning relative to the journal. Two orthogonally positioned shakers excite the test element via stingers. The test bearing comprises of a cartridge holding a Copper wire mesh ring, 2.7 mm thick, and a top arcuate foil. The bearing length and inner diameter are 38 mm and 36.5 mm, respectively. Experiments were conducted with no rotation and with journal spinning at 40–50 krpm, with static loads of 22 N and 36 N acting on the bearing. Dynamic load tests spanning frequencies from 150 to 450 Hz were conducted while keeping the amplitude of bearing displacements at 20 μm, 25 μm, and 30 μm. With no journal spinning, the force coefficients represent the bearing elastic structure alone since the journal and bearing are in contact. The direct stiffnesses gradually increase with frequency while the direct damping coefficients drop quickly at low frequencies (< 200 Hz) and level off above this frequency. The damping combines both viscous and material types from the gas film and mesh structure. Journal rotation induces airborne operation with a hydrodynamic gas film separating the rotor from its bearing. Hence, cross-coupled stiffness coefficients appear though with magnitudes lower than those of the direct stiffnesses. The direct stiffnesses, 0.4 to 0.6 MN/m within 200–400 Hz, are slightly lower in magnitude as those obtained without journal rotation suggesting the air film stiffness is quite high. Bearing direct stiffnesses are inversely proportional to the bearing motion amplitudes, whereas the direct equivalent viscous damping coefficients do not show any noticeable variation. All measurements evidence a test bearing system with material loss factor (γ) ∼ 1.0, indicating significant mechanical energy dissipation ability.

Structural and Rotordynamic Force Coefficients of a Shimmed Bump Foil Bearing: An Assessment of a Simple Engineering Practice

2015 ◽  
Author(s):  
Luis San Andrés ◽  
Joshua Norsworthy
Keyword(s):  
Loss Factor ◽  
High Speed ◽  
Static Load ◽  
Low Cost ◽  
Mechanical Energy ◽  
Excitation Frequency ◽  
Engineering Practice ◽  
Force Coefficients ◽  
Damping Coefficients ◽  
Stiffness And Damping

High speed rotors supported on bump-type foil bearings (BFBs) often suffer from large sub synchronous whirl motions. Mechanically preloading BFBs through shimming is a common, low cost practice that shows improvements in rotordynamic stability. However, there is absence of empirical information related to the force coefficients (structural and rotordynamic) of shimmed BFBs. This paper details a concerted study towards assessing the effect of shimming on a first generation BFB (L=38.1 mm, D =36.5 mm). Three metal shims, 120° apart, are glued to the inner surface of the bearing cartridge and facing the underside of the bump foil strip. The shim sets are of identical thickness, either 30 μm or 50 μm. Static load tests show that shimming produces nonlinear static load vs. deflection curves leading to a larger structural stiffness than for the bearing without shims. Torque measurements during shaft acceleration also demonstrate a shimmed BFB has a larger friction coefficient. For a static load of 14.3 kPa, dynamic loads with a frequency sweep from 250 Hz to 450 Hz are exerted on the BFB, without and with shims, to estimate its rotordynamic force coefficients while operating at ∼50 krpm (833 Hz). Similar measurements are conducted without shaft rotation. Results are presented for the original BFB (without shims) and the two shimmed BFB configurations. The direct stiffnesses of the BFB, shimmed or not, increase with excitation frequency thus evidencing a mild hardening effect. The BFB stiffness and damping coefficients decrease slightly for operation with rotor speed as opposed to the coefficients when the shaft is stationary. For frequencies above 300 Hz, the direct damping coefficients of the BFB with 50 μm thick shims are ∼ 30% larger than the coefficients of the original bearing. The bearing structural loss factor, a measure of its ability to dissipate mechanical energy, is derived from the direct stiffness and damping coefficients. The BFB with 50 μm thick shims has a 25% larger loss factor — average from test data collected at 300 Hz to 400 Hz — than the original BFB. Further measurements of rotor motions while the shaft accelerates to ∼50 krpm demonstrate the shimmed BFB (thickest shim set) effectively removes sub synchronous whirl motions amplitudes that were conspicuous when operating with the original bearing.

Identification of Dynamic Characteristics of Gas Foil Thrust Bearings Using Base Excitation

2016 ◽  
Author(s):  
Tae Ho Kim ◽  
Moon Sung Park ◽  
Jongsung Lee ◽  
Young Min Kim ◽  
Kyoung-Ku Ha ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Dynamic Load ◽  
Loss Factor ◽  
Load Capacity ◽  
Excitation Frequency ◽  
Vibrational Amplitude ◽  
Test Rig ◽  
Thrust Bearings ◽  
Bearing Plate ◽  
Bearing Stiffness

Gas foil bearings (GFBs) have clear advantages over oil-lubricated and rolling element bearings, by virtue of low power loss, oil-free operation in compact units, and rotordynamic stability at high speeds. However, because of the inherent low gas viscosity, GFBs have lower load capacity than the other bearings. In particular, accurate measurement of load capacity and dynamic characteristics of gas foil thrust bearings (GFTBs) is utmost important to widening their applications to high performance turbomachinery. In this study, a series of excitation tests were performed on a small oil-free turbomachinery with base excitations in the rotor axial direction to measure the dynamic load characteristics of a pair of six-pad, bump-type GFTBs, which support the thrust collar. An electromagnetic shaker provided dynamic sine sweep loads to the test bench (shaking table), which held rigidly the turbomachinery test rig for increasing excitation frequency from 10 Hz to 200 Hz. The magnitude of the shaker dynamic load, represented as an acceleration measured on the test rig, was increased up to 9 G (gravity). An eddy current sensor installed on the test rig housing measured the axial displacement (or vibrational amplitude) of the rotor thrust collar during the excitation tests. The axial acceleration of the rotor relative to the test rig was calculated using the measured displacement. A single degree-of-freedom base excitation model identified the frequency-dependent dynamic load capacity, stiffness, damping, and loss factor of the test GFTB for increasing shaker dynamic loads and increasing bearing clearances. The test results show that, for a constant shaker force and the test GFTB with a clearance of 155 μm, an increasing excitation frequency increases the dynamic load carried by the test GFTB, i.e., bearing reaction force, until a certain value of the frequency where it jumps down suddenly because of the influence from Duffing’s vibrations of the rotor. The bearing stiffness increases and the damping decreases dramatically as the excitation frequency increases. Generally, the bearing loss factor ranges from 0.5 to 1.5 independent of the frequency. As the shaker force increases, the bearing dynamic load, stiffness, damping, and loss factor increase depending on the excitation frequency. Interestingly, the agreements between the measured GFTB dynamic load versus the thrust runner displacement, the measured GFTB static load versus the structural deflection, and the predicted static load versus the thrust runner displacement are remarkable. Further tests with increasing GFTB clearances of 155, 180, 205, and 225 μm revealed that the vibrational amplitude increases and the jump-down frequency decreases with increasing clearances. The bearing load increases, but the bearing stiffness, damping, and loss factor decrease slightly as the clearance increases. The test results after a modification of the GFTB by rotating one side bearing plate by 30° relative to the other side bearing plate revealed insignificant changes in the dynamic characteristics. The present dynamic performance measurements provide a useful database of GFTBs for use in microturbomachinery.

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.

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