Method of Computation of Damped Resonance Frequencies for a System of Equal Masses, Equal Spring Constants, and Equal Viscous‐Damping Coefficients

1966 ◽  
Vol 39 (2) ◽  
pp. 269-271 ◽  
Author(s):  
S. Raynor ◽  
E. Frank
Keyword(s):  
Viscous Damping ◽  
Damping Coefficients ◽  
Resonance Frequencies ◽  
Spring Constants

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.

Rotordynamic Force Coefficients of a Hybrid Brush Seal: Measurements and Predictions

2009 ◽  
Author(s):  
Luis San Andre´s ◽  
Adolfo Delgado ◽  
Jose´ Baker
Keyword(s):  
Test System ◽  
Operating Conditions ◽  
Single Frequency ◽  
Viscous Damping ◽  
Domain Identification ◽  
Damping Coefficients ◽  
Brush Seal ◽  
Brush Seals ◽  
Lift Off ◽  
Stiffness And Damping

Brush seals effectively control leakage in air breathing engines, albeit only applied for relatively low-pressure differentials. Hybrid brush seals (HBS) are an alternative to resolve poor reliability resulting from bristle tip wear while also allowing for reverse shaft rotation operation. A HBS incorporates pads contacting the shaft on assembly; and which under rotor spinning, lift off due to the generation of a hydrodynamic pressure. The ensuing gas film prevents intermittent contact, reducing wear and thermal distortions. The paper presents rotordynamic measurements conducted on a test rig for evaluation of HBS technology. Single frequency shaker loads are exerted on a test rotor holding a hybrid brush seal and measurements of rotor displacements follow for operating conditions with increasing gas supply pressures and two rotor speeds. A frequency domain identification method delivers the test system stiffness and damping coefficients. The HBS stiffness coefficients are not affected by rotor speed though the seal viscous damping shows a strong frequency dependency. The identified HBS direct stiffness decreases ∼15% as the supply/discharge pressure increases Pr = 1.7 to 2.4. The HBS cross-coupled stiffnesses are insignificant, at least one order of magnitude smaller than the direct stiffnesses. A structural loss factor (γ) and dry friction coefficient (μ) represent the energy dissipated in a HBS by the bristle-to-bristle and bristle-to-pads interactions. Predictions of HBS stiffness and damping coefficients correlate well with the test derived parameters. Both model predictions and test results show the dramatic reduction of the seal equivalent viscous damping coefficients as the excitation whirl frequency increases.

Development of Vehicle Seat by Embedding Urethane Within Air Cell

2018 ◽  
Author(s):  
Shinichiro Ota ◽  
Yuji Nakamura
Keyword(s):  
Mechanical Properties ◽  
Resonance Frequency ◽  
Vibration Characteristics ◽  
Air Pressure ◽  
Damping Coefficients ◽  
Spring Constants ◽  
Vehicle Seat

This paper describes a new vehicle seat containing an air cell embedded with urethane. This air cell can be used to control mechanical properties such as spring constants and damping coefficients by varying the air pressure. When the air cell is retrofitted in a vehicle seat, it is essential for us to analyze its vibration characteristics, which is the aim of this study. Herein, after the air cell is retrofitted in a vehicle seat, its vibration characteristics are examined by performing excitation experiments using the prototype seat. From the results of this experiment, the resonance frequency of the human dummy (45.6 kg) was found to be 6.0 Hz when the pressure within the air cell was 2 kPa. However, the resonance frequency of the human dummy was found to be 5.3 Hz when the pressure within the air cell was 10 kPa. These results indicate that the vibration characteristics of the prototype seat can be varied by controlling the pressure within the air cell.

Numerical Simulation and Modelling Convention of Unsteady Fluidelastic Forces of Tube Arrays

2021 ◽  
Author(s):  
Mingjie Zhang ◽  
Xu Wang ◽  
Ole Øiseth
Keyword(s):  
Flow Velocity ◽  
Phase Error ◽  
Stability Boundary ◽  
Force Model ◽  
Viscous Damping ◽  
Damping Coefficients ◽  
Tube Arrays ◽  
Approach Zero ◽  
Flow Velocities ◽  
Reduced Flow

Abstract This paper presents a numerical investigation on the unsteady fluidelastic forces of tube arrays. The key focus is on the consistency between the unsteady fluidelastic force model and the quasi-steady model for tube arrays at large reduced flow velocities, as well as comparing two well-known conventions for the unsteady model. Two-dimensional unsteady Reynolds-averaged Navier-Stokes (URANS) simulations are used to prove that the viscous damping coefficients of Tanaka's convention (Tanaka and Takahara, 1981) approach their quasi-steady values as the reduced flow velocity approaches infinity, whereas the hysteretic damping coefficients of Chen's modified convention (Chen et al., 1983) always approach zero and hence result in low-resolution data plots as the reduced flow velocity becomes large. The non-constant viscous damping coefficients of Tanaka's experimental data at high reduced flow velocities (which motivated the introduction of Chen's modified convention) might be induced by a systematic identification error in the phase of the fluidelastic force. A row of three flexible cylinders is used as a numerical example to analyse the effect of systematic phase error on the predicted stability boundary of the fluidelastic instability. Although identical fluidelastic forces are simulated by using the two conventions, Tanaka's convention is recommended due to its compatibility with the quasi-steady theory and optimal resolutions of data plots over any range of reduced flow velocities.

Using CFD to Assess Low Frequency Damping

2012 ◽  
Author(s):  
Alessio Pistidda ◽  
Harald Ottens ◽  
Richard Zoontjes
Keyword(s):  
Standard Procedure ◽  
Low Frequency ◽  
Added Mass ◽  
Model Tests ◽  
Viscous Damping ◽  
Viscous Effects ◽  
Floating Bodies ◽  
Time Step ◽  
Damping Coefficients ◽  
Quadratic Component

During offshore installation operations, floating bodies are often moored using soft mooring which are designed to withstand the environmental forces. Large amplitude motions often occur due to excitation by slowly varying wind and wave drift forces. To analyze these motions the dynamic system has to be accurately described, which includes an estimation of the added mass and damping coefficients. In general, the added mass can be accurately calculated with traditional potential theory. However for the damping this method is not adequate because viscous effects play an important role. Generally these data are obtained using model tests. This paper validates the CFD methodology as an alternative to model tests to evaluate the viscous damping. The aim is to define a standard procedure to derive viscous damping coefficients for surge, sway and yaw motion of floating bodies. To estimate viscous damping in CFD, a 3D model of the launch and float-over barge H-851 was used. For this barge, model test data is available which could be compared with the results of the CFD analysis. For the simulations, the commercial package STAR-CCM+ with the implicit unsteady solver for Reynolds-Averaged Navier-Stokes (RANS) equations was used. The turbulence model implemented was the k-Omega-SST. Numerical errors have been assessed performing sensitivity analysis on time step and grid size. Damping has been investigated by performing decay simulations as in the model tests, taking the effect of coupling among all motions into account. The P-Q fitting method has been used to determine the linear and quadratic component of the damping. Numerical results are validated with those obtained from the towing tank. Results show that CFD is an adequate tool to estimate the low frequency damping in terms of equivalent damping. More investigations are required to determine the linear and quadratic component.

Hermetically Sealed Squeeze Film Damper for Operation in Oil-Free Environments

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Bugra Ertas ◽  
Adolfo Delgado
Keyword(s):  
Excitation Frequency ◽  
Squeeze Film ◽  
Force Density ◽  
Viscous Damping ◽  
Squeeze Film Damper ◽  
Open Flow ◽  
Damping Coefficients ◽  
End Plate ◽  
Stiffness And Damping ◽  
Gas Bearing

The following work advances a new concept for a hermetically sealed squeeze film damper (HSFD), which does not require an open-flow lubrication system. The hermetically sealed concept utilizes a submersed plunger within a contained fluidic cavity filled with incompressible fluid and carefully controlled end plate clearances to generate high levels of viscous damping. Although the application space for a hermetic damper can be envisioned to be quite broad, the context here will target the use of this device as a rotordynamic bearing support damper in flexibly mounted gas bearing systems. The effort focused on identifying the stiffness and damping behavior of the damper while varying test parameters such as excitation frequency, vibration amplitude, and end plate clearance. To gain further insight to the damper behavior, key dynamic pressure measurements in the damper land were used for identifying the onset conditions for squeeze film cavitation. The HSFD performance is compared to existing gas bearing support dampers and a conventional open-flow squeeze film dampers (SFD) used in turbomachinery. The damper concept yields high viscous damping coefficients an order of magnitude larger than existing oil-free gas bearing supports dampers and shows comparable damping levels to current state of the art open-flow SFD. The force coefficients were shown to contribute frequency-dependent stiffness and damping coefficients while exhibiting amplitude independent behavior within operating regimes without cavitation. Finally, using experimentally based force density calculations, the data revealed threshold cavitation velocities, approximated for the three end seal clearance cases. To complement the experimental work, a Reynolds-based fluid flow model was developed and is compared to the HSFD damping and stiffness results.

Rotordynamic Force Coefficients of a Hybrid Brush Seal: Measurements and Predictions

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Luis San Andrés ◽  
José Baker ◽  
Adolfo Delgado
Keyword(s):  
Test System ◽  
Operating Conditions ◽  
Single Frequency ◽  
Viscous Damping ◽  
Domain Identification ◽  
Damping Coefficients ◽  
Brush Seal ◽  
Brush Seals ◽  
Lift Off ◽  
Stiffness And Damping

Brush seals effectively control leakage in air breathing engines, albeit only applied for relatively low-pressure differentials. Hybrid brush seals (HBS) are an alternative to resolve poor reliability resulting from bristle tip wear while also allowing for reverse shaft rotation operations. A HBS incorporates pads contacting the shaft on assembly; and which under rotor spinning, lift off due to the generation of a hydrodynamic pressure. The ensuing gas film prevents intermittent contact, reducing wear, and thermal distortions. This paper presents rotordynamic measurements conducted on a test rig for evaluation of HBS technology. Single frequency shaker loads are exerted on a test rotor holding a hybrid brush seal, and measurements of rotor displacements follow for operating conditions with increasing gas supply pressures and two rotor speeds. A frequency domain identification method delivers the test system stiffness and damping coefficients. The HBS stiffness coefficients are not affected by rotor speed though the seal viscous damping shows a strong frequency dependency. The identified HBS direct stiffness decreases ∼15% as the supply/discharge pressure increases Pr=1.7–2.4. The HBS cross-coupled stiffnesses are insignificant, at least one order of magnitude smaller than the direct stiffnesses. A structural loss factor (γ) and dry-friction coefficient (μ) represent the energy dissipated in a HBS by the bristle-to-bristle and bristle-to-pad interactions. Predictions of HBS stiffness and damping coefficients correlate well with the test derived parameters. Both model predictions and test results show the dramatic reduction in the seal equivalent viscous damping coefficients as the excitation whirl frequency increases.

PWR Fuel Assembly Damping Characteristics

2006 ◽  
Author(s):  
Roger Y. Lu ◽  
David D. Steel
Keyword(s):  
Fuel Assembly ◽  
Temperature Effect ◽  
Damping Ratio ◽  
Damping Coefficient ◽  
Low Flow ◽  
Published Data ◽  
Viscous Damping ◽  
Flowing Water ◽  
Damping Coefficients ◽  
Flow Velocities

PWR fuel assembly damping is a key parameter in seismic/LOCA safety analysis. The damping coefficients of a fuel assembly in air, still water and flowing water are significantly different. Several researchers and engineers have published their results and methods in the past. With this paper, PWR fuel assembly damping was studied and tested in air, still water, and flowing water (including flowrate and temperature variation). The damping coefficients were obtained by the initial displacement and first response method. The coefficients are also compared with published data. Several conclusions are obtained. • The damping obtained from the tests in air gives the damping component of assembly structure damping. From the comparison of the damping in air with still water the amount of viscous damping can be determined. The viscous damping component is the effect of still water on damping. The amount of viscous damping is represented by the increase in the damping ratio from air to still water at room temperature. The results show that damping in still water is approximately two times the damping in air. • The temperature effect on damping in still water is minimal. In flowing water, the results show a very slight effect of temperature, as the damping slightly decreases with an increase in temperature. This temperature effect is much smaller than the data scatter observed in most damping measurement tests under the same test conditions. • The damping is significantly affected by flowing water. For relatively low flow velocities, compared to in-core conditions, the damping coefficient is around two times the damping in still water. For intermediate to high flow velocities, all damping coefficients are 2.5 times higher than that in still water. For high velocities and large displacement, the damping coefficient can be over 3 times higher than that in still water. The flow velocity appears to be acting on the system by suppressing the motion of the assembly. Additional damping due to flowing water is called hydraulic damping, which is generated by hydraulic force. When a fuel assembly vibrates in flowing water, the assembly is trying to change the flow direction and momentum, but the flow mass wants to retain its pure axial direction which suppresses the motion of the assembly.

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.

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