Nonlinear Dynamic Characterization of Oil-Free Wire Mesh Dampers

2007 ◽  
Author(s):  
Bugra Ertas ◽  
Huageng Luo
Keyword(s):  
High Speed ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Forced Response ◽  
Wire Mesh ◽  
Dynamic Characterization ◽  
Transient Vibration ◽  
Force Coefficients ◽  
Stiffness And Damping

The present work focuses on the dynamic characterization of oil-free wire mesh dampers. The research was focused on determining nonlinear stiffness and damping coefficients while varying the excitation amplitude, excitation frequency, and static eccentricity. Force coefficients were extracted using a forced response method (FRM) and also a transient vibration method. Due to the nonlinearity of the dampers, controlled amplitude tests were required for the forced excitation method, whereas the transient response was analyzed using a Hilbert Transform procedure. The testing using both methods showed that eccentricity has minimal influence on force coefficients, whereas increasing excitation amplitude and frequency yield decreasing stiffness and damping trends. In addition to the parameter identification tests, a rotating test was performed demonstrating high-speed damping capability of the oil-free wire mesh dampers to 40,000 rpm, which was also simulated using an nonlinear rotordynamic response to imbalance analysis.

Nonlinear Dynamic Characterization of Oil-Free Wire Mesh Dampers

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Bugra H. Ertas ◽  
Huageng Luo
Keyword(s):  
High Speed ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Forced Response ◽  
Wire Mesh ◽  
Single Frequency ◽  
Dynamic Characterization ◽  
Force Coefficients ◽  
Stiffness And Damping

The present work focuses on the dynamic characterization of oil-free wire mesh dampers. The research was aimed at determining nonlinear stiffness and damping coefficients while varying the excitation amplitude, excitation frequency, and static eccentricity. Force coefficients were extracted using a forced response method and also a transient vibration method. Due to the nonlinearity of the dampers, controlled amplitude single frequency excitation tests were required for the forced excitation method, whereas the transient response was analyzed using a Hilbert transform procedure. The experimental results showed that eccentricity has minimal influence on force coefficients, whereas increasing excitation amplitude and frequency yields decreasing stiffness and damping trends. In addition to the parameter identification tests, a rotating test was performed demonstrating high-speed damping capability of the oil-free wire mesh dampers to 40,000 rpm, which was also simulated using a nonlinear rotordynamic response to imbalance analysis.

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.

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.

Identification of Rotordynamic Force Coefficients of a Metal Mesh Foil Bearing Using Impact Load Excitations

2010 ◽  
Author(s):  
Luis San Andre´s ◽  
Thomas Abraham Chirathadam
Keyword(s):  
High Speed ◽  
Impact Load ◽  
Mechanical Energy ◽  
Excitation Frequency ◽  
Forced Response ◽  
Dynamic Force ◽  
Rotating Shaft ◽  
Metal Mesh ◽  
Force Coefficients ◽  
Shaft Rotation

Metal mesh foil bearings (MMFB) are an inexpensive compliant gas bearing type that aims to enable high speed, high temperature operation of small turbomachinery. A MMFB with an inner diameter of 28.00 mm and length of 28.05 mm is constructed with low cost and common materials. The bearing incorporates a copper mesh ring, 20% in compactness and offering large material damping, beneath a 0.127mm thick preformed top foil. Prior experimentation (published papers) provide the bearing structure force coefficients and the break away torque for bearing lift off. Presently, the MMFB replaces a compressor in a small turbocharger driven test rig. Impact load tests aid to identify the direct and cross-coupled rotor dynamic force coefficients of the floating MMFB while operating at a speed of 50 krpm. Tests conducted with and without shaft rotation show the MMFB direct stiffness is less than its structural (static) stiffness, ∼25% lower at an excitation frequency of 200 Hz. The thin air film acting in series with the metal mesh support, and separating the rotating shaft and the bearing inner surface while airborne, reduces the bearing stiffness. The equivalent viscous damping is nearly identical with and without shaft rotation. The identified loss factor, best representing the hysteretic type damping from the metal mesh, is high at ∼0.50 in the frequency range 0–200 Hz. This magnitude reveals large mechanical energy dissipation ability from the MMFB. The measurements also show appreciable cross directional motions from the unidirectional impact loads, thus generating appreciable cross coupled force coefficients. Rotor speed coast down measurements reveal pronounced subsynchronous whirl motion amplitudes locked at distinct frequencies. The MMFB stiffness hardening nonlinearity produces the rich frequency forced response. The synchronous as well as subsynchronous motions peak while the shaft traverses its critical speeds. The measurements establish reliable operation of the test MMFB while airborne.

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 Rotordynamic Force Coefficients of a Metal Mesh Foil Bearing Using Impact Load Excitations

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Luis San Andrés ◽  
Thomas Abraham Chirathadam
Keyword(s):  
High Speed ◽  
Impact Load ◽  
Mechanical Energy ◽  
Excitation Frequency ◽  
Forced Response ◽  
Dynamic Force ◽  
Rotating Shaft ◽  
Metal Mesh ◽  
Force Coefficients ◽  
Shaft Rotation

Metal mesh foil bearings (MMFBs) are inexpensive compliant gas bearing type that aim to enable high speed, high temperature operation of small turbomachinery. A MMFB with an inner diameter of 28.00 mm and length of 28.05 mm is constructed with low cost and common materials. The bearing incorporates a copper mesh ring, 20% in compactness, and offering large material damping beneath a 0.127 mm thick preformed top foil. Prior experimentations (published papers) provide the bearing structure force coefficients and the break away torque for bearing lift off. Presently, the MMFB replaces a compressor in a small turbocharger driven test rig. Impact load tests aid to identify the direct and cross-coupled rotor dynamic force coefficients of the floating MMFB while operating at a speed of 50 krpm. Tests conducted with and without shaft rotation show the MMFB direct stiffness is less than its structural (static) stiffness, ∼25% lower at an excitation frequency of 200 Hz. The thin air film acting in series with the metal mesh support and separating the rotating shaft and the bearing inner surface while airborne reduces the bearing stiffness. The equivalent viscous damping is nearly identical with and without shaft rotation. The identified loss factor, best representing the hysteretic type damping from the metal mesh, is high at ∼0.50 in the frequency range 0–200 Hz. This magnitude reveals large mechanical energy dissipation ability from the MMFB. The measurements also show appreciable cross directional motions from the unidirectional impact loads, thus generating appreciable cross-coupled force coefficients. Rotor speed coast down measurements reveal pronounced subsynchronous whirl motion amplitudes locked at distinct frequencies. The MMFB stiffness hardening nonlinearity produces the rich frequency forced response. The synchronous as well as subsynchronous motions peak while the shaft traverses its critical speeds. The measurements establish reliable operation of the test MMFB while airborne.

scholarly journals Dynamic Characterization of Rubber O-Rings: Squeeze and Size Effects

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Farid Al-Bender ◽  
Federico Colombo ◽  
Dominiek Reynaerts ◽  
Rodrigo Villavicencio ◽  
Tobias Waumans
Keyword(s):  
High Speed ◽  
Dynamic Characterization ◽  
Frequency Range ◽  
Damping Coefficients ◽  
Rubber Compounds ◽  
Frequency Independent ◽  
Stiffness And Damping ◽  
Gas Bearing ◽  
General Size

This paper concerns the dynamic characterization of rubber O-rings used to introduce damping in high speed gas bearing systems. O-shaped rubber rings composed of high temperature rubber compounds are characterized in terms of stiffness and damping coefficients in the frequency range 100–800 Hz. Simple formulas with frequency independent coefficients were identified to express the viscoelastic properties of the O-rings. The formulas proposed approximate the stiffness and damping coefficients of O-rings of general size.

Rotordynamic characterization of tilting-pad bearings with eight pads in vertical rotors

2021 ◽  
pp. 1-20
Author(s):  
David J Rondon ◽  
Gudeta Berhanu Benti ◽  
Jan-Olov Aidanpää ◽  
Rolf Gustavsson
Keyword(s):  
Stokes Equations ◽  
Forced Response ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Mean Values ◽  
Stationary Coordinate System ◽  
Tilting Pad ◽  
Tilting Pad Bearings ◽  
Stiffness And Damping

Abstract It has been documented that stiffness and damping for a four-pad bearing are dependent not only the magnitude of the load but also on the position of the rotor in the bearing. However, 8-pad bearings are not commonly employed on horizontal turbines, and the presence of several pads in the bearing will decisively affect the dynamics of the system. This paper evaluates the stiffness and damping coefficients of tilting-pad bearings with eight pads and explore the main frequencies acting on the forced response of a vertical rotor. The bearing properties were modeled as a function of eccentricity and position in the stationary coordinate system by Navier-Stokes equations whose results are taken from commercial software. The simulated unbalanced response is compared to experimental results; the changing position of the shaft produces a periodic stiffness and damping, which is dependent on the number of pads. Cross-coupled coefficients influence is discussed, showing that their absence makes an accurate model for the mean values. The results indicate that simulation of vertical rotors with 8-pad bearings can be simplified which allow more effective simulations and dynamic analysis.

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.

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