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.

Measurements of Static and Dynamic Load Performance of a 102 MM Carbon-Graphite Porous Surface Tilting-Pad Gas Journal Bearing

2021 ◽  
Author(s):  
Luis San Andres ◽  
Jing Yang ◽  
Ryan McGowan
Keyword(s):  
Dynamic Load ◽  
Load Capacity ◽  
Stable Operation ◽  
Specific Load ◽  
Damping Coefficients ◽  
Supply Pressure ◽  
Air Supply ◽  
Frequency Independent ◽  
Stiffness And Damping ◽  
Gas Bearing

Abstract Aerostatic journal bearings with porous tilting pads enable shaft support with minute drag power losses. To date archival information on the static and dynamic load performance of this bearing type is scant. Thus, the paper presents measurements conducted with an air bearing with diameter 102 mm and comprising four tilting pads made of porous carbon-graphite, each with length = 76 mm. At ambient temperature of 21°C, as the air supply pressure into the bearing pads increases, so does the bearing aerostatic specific load that reaches 58% of the pressure difference. With a supply pressure of 7.8 bar(a), the test bearing static stiffness = 13.1 MN/m, is independent of both shaft speed and static load. While operating with shaft speeds = 6 krpm and 9 krpm and under specific loads to 115 kPa and 101 kPa respectively, dynamic load experiments with excitation frequencies up to 342 Hz show the test bearing supplied with air at 7.8 bar(a) has frequency independent stiffness and damping coefficients. For rotor speeds equaling 0, 6 and 9 krpm, the bearing direct stiffnesses range from 13.6 MN/m to 32.7 MN/m as the specific load increases from 0 kPa to 115 kPa. The direct damping coefficients are as large as 5.8 kN·s/m. The test porous gas bearing reached its intended load capacity, demonstrated a dynamically stable operation and produced force coefficients mainly affected by the pads' pivot supports and the magnitude of air supply pressurization.

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.

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.

Ball bearing turbocharger vibration management: application on high speed balancer

2020 ◽  
Vol 21 (6) ◽  
pp. 619
Author(s):  
Kostandin Gjika ◽  
Antoine Costeux ◽  
Gerry LaRue ◽  
John Wilson
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Internal Combustion Engines ◽  
Ball Bearing ◽  
Squeeze Film ◽  
Design And Technology ◽  
Squeeze Film Damper ◽  
Damping Coefficients ◽  
Bearing Loads ◽  
Stiffness And Damping

Today's modern internal combustion engines are increasingly focused on downsizing, high fuel efficiency and low emissions, which requires appropriate design and technology of turbocharger bearing systems. Automotive turbochargers operate faster and with strong engine excitation; vibration management is becoming a challenge and manufacturers are increasingly focusing on the design of low vibration and high-performance balancing technology. This paper discusses the synchronous vibration management of the ball bearing cartridge turbocharger on high-speed balancer and it is a continuation of papers [1–3]. In a first step, the synchronous rotordynamics behavior is identified. A prediction code is developed to calculate the static and dynamic performance of “ball bearing cartridge-squeeze film damper”. The dynamic behavior of balls is modeled by a spring with stiffness calculated from Tedric Harris formulas and the damping is considered null. The squeeze film damper model is derived from the Osborne Reynolds equation for incompressible and synchronous fluid loading; the stiffness and damping coefficients are calculated assuming that the bearing is infinitely short, and the oil film pressure is modeled as a cavitated π film model. The stiffness and damping coefficients are integrated on a rotordynamics code and the bearing loads are calculated by converging with the bearing eccentricity ratio. In a second step, a finite element structural dynamics model is built for the system “turbocharger housing-high speed balancer fixture” and validated by experimental frequency response functions. In the last step, the rotating dynamic bearing loads on the squeeze film damper are coupled with transfer functions and the vibration on the housings is predicted. The vibration response under single and multi-plane unbalances correlates very well with test data from turbocharger unbalance masters. The prediction model allows a thorough understanding of ball bearing turbocharger vibration on a high speed balancer, thus optimizing the dynamic behavior of the “turbocharger-high speed balancer” structural system for better rotordynamics performance identification and selection of the appropriate balancing process at the development stage of the turbocharger.

scholarly journals Study on dynamic characteristics of gas films of spherical spiral groove hybrid gas bearings

2019 ◽  
Vol 233 (8) ◽  
pp. 1169-1181
Author(s):  
Chenhui Jia ◽  
Haijiang Zhang ◽  
Shijun Guo ◽  
Ming Qiu ◽  
Wensuo Ma ◽  
...  
Keyword(s):  
Pressure Effect ◽  
Dynamic Pressure ◽  
Iteration Algorithm ◽  
Unstable State ◽  
Gas Bearings ◽  
Damping Coefficients ◽  
The Stability ◽  
Stiffness And Damping ◽  
Film Stiffness ◽  
Gas Bearing

According to the gas film force variation law, when the bearing axis is slightly displaced from the static equilibrium position, displacement and velocity disturbance relation expressions for the gas film force increment are constructed. Moreover, combined with the bearing rotor system motion equation, calculation model equations for the gas film stiffness and damping coefficients are established. The axial and radial vibration and velocity of the gas bearings during operation are collected. The instantaneous stiffness and damping coefficients of the gas film are calculated by the rolling iteration algorithm using MATLAB. The dynamic changes in the gas film stiffness and damping under different motion states are analyzed, and the mechanism of the gas film vortex and oscillation is studied. The results demonstrate the following: (1) When the gas bearing is running in the linear steady state in cycle 1, the dynamic pressure effect is enhanced and the stability is improved by increasing the eccentricity; when the gas supply pressure is increased, the static pressure effect is enhanced and the gas film vortex is reduced, but the oscillation is strengthened. (2) With the increase in rotational speed, the gas film vortex force gradually exceeds the gas film damping force, and the stability gradually worsens, causing a fluctuation in the gas film stiffness and damping, following which singularity occurs and a half-speed vortex is formed. Meanwhile, the gas film oscillation is intensified, and the rotor enters the nonlinear stable cycle 2 state operation. (3) As the fluctuation of the film force increases, the instantaneous stiffness and damping oscillation of the film intensifies, most of the stiffness and damping coefficients exhibit distortion, and the rotor operation will enter a chaotic or unstable state. Therefore, the gas bearing stiffness and damping variation characteristics can be used to study and predict the gas bearing operating state. Finally, measures for reducing the vortex and oscillation of the gas film and improving the stability of the gas bearing operation are proposed.

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness and Different Pad Preloads

2010 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul E. Allaire ◽  
John C. Nicholas
Keyword(s):  
Frequency Response ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Theoretical Calculations ◽  
Leading Edge ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
The Subject ◽  
Stiffness And Damping

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to non-synchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are considered using a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced non-synchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

Dynamic characterization of a mechanical coupling for a rotating shaft

2010 ◽  
Vol 225 (3) ◽  
pp. 604-616 ◽  
Author(s):  
A T Tadeo ◽  
K L Cavalca ◽  
M J Brennan
Keyword(s):  
Frequency Response ◽  
Response Functions ◽  
Dynamic Characterization ◽  
Rotating Shaft ◽  
Frequency Response Functions ◽  
Mechanical Coupling ◽  
Lumped Parameter ◽  
Parameter Coupling ◽  
Stiffness And Damping

This article concerns the dynamic characterization of a flexible coupling that connects two co-axial shafts. Four different lumped parameter coupling models from the literature are investigated to see which model could best predict the dynamic behaviour of the coupling. The finite-element method was used to model the rotor dynamic system incorporating the coupling. Frequency response functions from this model were compared with measured frequency response functions from the rotor test rig with the shaft and coupling rotating at a specific speed. Parameters from the model were adjusted to minimize an objective function involving the measured and predicted frequency response functions. It was found that the simplest model of the coupling that could reasonably represent the coupling involves rotational (bending) stiffness and damping.

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.

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