Application of Porous Materials to Annular Plain Seals: Part 2—Dynamic Characteristics

1990 ◽  
Vol 112 (4) ◽  
pp. 624-630 ◽  
Author(s):  
S. Kaneko
Keyword(s):  
Laminar Flow ◽  
Porous Materials ◽  
Dynamic Performance ◽  
Reaction Force ◽  
Mass Effect ◽  
Porous Matrix ◽  
Solid Surfaces ◽  
Damping Coefficients ◽  
Whirling Motion ◽  
Stiffness And Damping

For improving the dynamic performance of the annular plain seals employed in pumps, porous materials are applied to the seal surface by insertion into the inlet part of the seal. The linear stiffness and damping coefficients of the seal film are calculated in the laminar-flow regime, assuming the mass effect of the fluid to be negligibly small. Numerical results show that the annular plain seals with the porous materials have larger main stiffness terms and smaller cross-coupled stiffness terms and main damping terms than the conventional ones with the solid surfaces. This tendency is more marked with increasing the axial length of the porous matrix applied to the seal surface. The larger main stiffness terms for “the porous seal” yield larger radial reaction force acting on a rotor as a consequence of small whirling motion of shaft about a centered position, which would contribute to rotor stability.

The Surface Roughness Effect on the Dynamic Stiffness and Damping Characteristics of the Hydrostatic Thrust Spherical Bearings: Part 5 of 5 — Clearance Type of Bearings

2007 ◽  
Author(s):  
Ahmad W. Yacout
Keyword(s):  
Surface Roughness ◽  
Capillary Tube ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Major Effect ◽  
Design Parameters ◽  
Compressibility Effect ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Fluid Compressibility

This study has theoretically analyzed the surface roughness, centripetal inertia and recess volume fluid compressibility effects on the dynamic behavior of a restrictor compensated hydrostatic thrust spherical clearance type of bearing. The stochastic Reynolds equation, with centripetal inertia effect, and the recess flow continuity equation with recess volume fluid compressibility effect have been derived to take into account the presence of roughness on the bearing surfaces. On the basis of a small perturbations method, the dynamic stiffness and damping coefficients have been evaluated. In addition to the usual bearing design parameters the results for the dynamic stiffness and damping coefficients have been calculated for various frequencies of vibrations or squeeze parameter (frequency parameter) and recess volume fluid compressibility parameter. The study shows that both of the surface roughness and the centripetal inertia have slight effects on the stiffness coefficient and remarkable effects on the damping coefficient while the recess volume fluid compressibility parameter has the major effect on the bearing dynamic characteristics. The cross dynamic stiffness showed the bearing self-aligning property and the ability to oppose whirl movements. The orifice restrictor showed better dynamic performance than that of the capillary tube.

Influence of Wear on the Performance of Multirecess Hydrostatic Journal Bearing Operating With Micropolar Lubricant

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
E. Rajasekhar Nicodemus ◽  
Satish C. Sharma
Keyword(s):  
Journal Bearing ◽  
Dynamic Performance ◽  
Flow Equation ◽  
Performance Characteristics ◽  
Wear Depth ◽  
Damping Coefficients ◽  
Load Line ◽  
Wide Range ◽  
Load Arrangement ◽  
Stiffness And Damping

The objective of the present work is to study theoretically the influence of wear on the performance of four-pocket capillary-compensated hydrostatic journal bearing operating with micropolar lubricant. In the present study, the lubricant containing additives and contaminants is modeled as micropolar fluid. The modified Reynolds equation for micropolar lubricant is solved using finite element method along with capillary restrictor flow equation as a constraint together with appropriate boundary conditions. The performance characteristics of a capillary-compensated four-pocket worn hydrostatic journal bearing operating with micropolar lubricant have been presented for a wide range of values of nondimensional external load, wear depth parameter, and micropolar parameters. The simulated results have also been presented for two different loading arrangements. In arrangement I, the load line acts through centers of the pockets, whereas in arrangement II, the load line bisects the land between two pockets. The simulated results suggest that a bearing lubricated with lubricant having higher micropolar effect has better static and dynamic performance characteristics as compared with Newtonian lubricant but the bearing lubricated with lubricant having higher micropolar effect is predominantly affected by the wear vis a vis static characteristics parameters as compared with Newtonian lubricant for both loading arrangements. However, in the case of stiffness and damping coefficients, loading arrangement II shows a significant higher enhancement in the value of direct stiffness and damping coefficients in z-direction due to micropolar effect as compared with load arrangement I. And also, the effect of wear on stiffness and damping coefficients in z-direction for bearing operating with micropolar lubricant is of same order as Newtonian lubricant for the loading arrangement II. A similar behavior is observed for the case of stiffness and damping coefficients in x-direction for loading arrangement I.

Stability of Multirecess Hybrid-Operating Oil Journal Bearings

1985 ◽  
Vol 107 (1) ◽  
pp. 116-121 ◽  
Author(s):  
Y. S. Chen ◽  
H. Y. Wu ◽  
P. L. Xie
Keyword(s):  
Finite Difference Method ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Design Parameters ◽  
Stability Threshold ◽  
Damping Coefficients ◽  
Hybrid Bearing ◽  
The Stability ◽  
Stiffness And Damping ◽  
Bearing System

An analysis and a numerical solution using finite difference method to predict the dynamic performance of multirecess hybrid-operating oil journal bearings are presented. The linearized stiffness and damping coefficients of a typical capillary-compensated bearing with four recesses are computed for various design parameters. The corresponding stiffness and the stability threshold of the bearing are then obtained, and the opposite influences of the hydrodynamic action on them are demonstrated. The effect of rotor flexibility on the onset of self-excited whirl is discussed, and a method is given to determine the stability threshold of a rotor-hybrid bearing system.

Application of Porous Materials to Annular Plain Seals: Part 1—Static Characteristics

1989 ◽  
Vol 111 (4) ◽  
pp. 655-660 ◽  
Author(s):  
S. Kaneko
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Porous Materials ◽  
Continuity Equation ◽  
Reynolds Equation ◽  
Porous Matrix ◽  
Fluid Film ◽  
Force Component ◽  
Static Characteristics ◽  
Axial Acceleration

Porous materials are applied to the annular plain seals employed in pumps by insertion into the inlet part of the seal. The static characteristics of the seals with the porous materials are studied in the laminar-flow regime. The Reynolds equation for the fluid film in the seal clearance is modified to include a so-called filter term, and the pressure equation for the porous matrix is obtained from Darcy’s law and the continuity equation. These equations are applied to the system and are numerically solved with the pressure drop mainly due to the axial acceleration of liquid at the inlet end of the seal being taken into account. Results show that the annular plain seals with the porous materials have larger fluid film force component along the line of centers and smaller one perpendicular to the former than the ordinary solid seals.

Experimental Study on Static and Dynamic Characteristics of Liquid Annular Convergent-Tapered Damper Seals With Honeycomb Roughness Pattern

2003 ◽  
Vol 125 (3) ◽  
pp. 592-599 ◽  
Author(s):  
Satoru Kaneko ◽  
Takashi Ikeda ◽  
Takuro Saito ◽  
Shin Ito
Keyword(s):  
Dynamic Characteristics ◽  
Smooth Surface ◽  
Reaction Force ◽  
Static And Dynamic Characteristics ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Whirling Motion ◽  
Leakage Flow Rate ◽  
Annular Seal ◽  
Honeycomb Pattern

Honeycomb damper seals with convergent-tapered clearance have been proposed to improve static and dynamic characteristics of liquid annular seals employed in pumps. Their characteristics are experimentally investigated and compared to those for a conventional straight (no taper) annular seal with smooth surface and a straight damper seal with identical honeycomb pattern in seal stator. Three convergent-tapered honeycomb damper seals are used in the test, and have different inlet clearance (maximum clearance) and almost the same outlet clearance (minimum clearance). Their outlet clearance is almost the same as the clearance of the straight smooth seal and is slightly smaller than the clearance of the straight damper seal. Experimental results show that the convergent-tapered damper seals as well as the straight damper seal have lower leakage flow rate and cross-coupled stiffness coefficients, and larger main damping coefficients than the straight smooth seal, resulting in larger effective damping coefficients. These results are mainly due to surface roughness in the seal stator such as a honeycomb pattern used in the present analysis. The convergent-tapered damper seals also have larger main stiffness coefficients than the straight smooth and damper seals, which is mainly due to the convergent-tapered clearance and yields larger radial reaction force for a small concentric whirling motion. Consequently, the convergent-tapered damper seals have better seal characteristics than the conventional straight smooth seal and the straight damper seal with the same roughness pattern from the viewpoints of decreasing the leakage and improving the rotor stability capacity.

Experimental Study on Static and Dynamic Characteristics of Annular Plain Seals With Porous Materials

1998 ◽  
Vol 120 (2) ◽  
pp. 165-172 ◽  
Author(s):  
S. Kaneko ◽  
H. Kamei ◽  
Y. Yanagisawa ◽  
H. Kawahara
Keyword(s):  
Porous Materials ◽  
Flow Rate ◽  
Dynamic Characteristics ◽  
Reaction Force ◽  
Leakage Flow ◽  
Static And Dynamic Characteristics ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Leakage Flow Rate ◽  
Hydrostatic Force

Static and dynamic characteristics are experimentally investigated for annular plain seals with porous materials applied to the seal surface by insertion into the middle of the seal. Experimental results show that annular plain seals with porous materials have a higher leakage flow rate, larger main stiffness coefficients, and smaller cross-coupled stiffness coefficients and main damping coefficients than conventional annular plain seals with solid surfaces. In the porous seals, an increase of approximately 30 percent in the leakage flow rate and reduction of the same amount in the main damping coefficients are obtained, whereas the main stiffness coefficients for the porous seals are four to six times as much as those for the solid seals due to the increase in the hydrostatic force induced by a function of the hydrostatic porous bearing. This suggests that the quantitative effects of the porous materials on the main stiffness coefficients are much more significant than the effects on the leakage flow rate and the other dynamic coefficients. The larger main stiffness coefficients for the porous seals yield larger radial reaction force for a small concentric whirling motion, which would contribute to rotor stability from the viewpoint of increasing speed limits due to a stiffer rotor support.

Predicted Rotordynamic Behavior of a Labyrinth Seal as Rotor Surface Speed Approaches Mach 1

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Manish R. Thorat ◽  
Dara W. Childs
Keyword(s):  
Speed Of Sound ◽  
Reaction Force ◽  
Labyrinth Seal ◽  
Surface Velocity ◽  
Reduced Model ◽  
Running Speed ◽  
Frequency Dependent ◽  
Damping Coefficients ◽  
Rotor Surface ◽  
Stiffness And Damping

Prior one-control-volume (1CV) models for rotor-fluid interaction in labyrinth seals produce synchronously reduced (at running speed), frequency-independent stiffness and damping coefficients. The 1CV model, consisting of a leakage equation, a continuity equation, and a circumferential-momentum equation (for each cavity), was stated to be invalid for rotor surface speeds approaching the speed of sound. However, the present results show that while the 1CV fluid-mechanic model continues to be valid, the calculated rotordynamic coefficients become strongly dependent on the rotor’s precession frequency. A solution is developed for the reaction-force components for a range of precession frequencies, producing frequency-dependent stiffness and damping coefficients. They can be used to define a Laplace-domain transfer-function model for the reaction-force/rotor-motion components. Calculated results are presented for a simple Jeffcott rotor model acted on by a labyrinth seal. The model’s undamped natural frequency is 7.6 krpm. The fluid properties, seal radius Rs, and running speed ω cause the rotor surface velocity Rsω to equal the speed of sound c0 at ω=58 krpm. Calculated synchronous-response results due to imbalance coincide for the synchronously reduced and the frequency-dependent models. For an inlet preswirl ratio of 0.5, both models predict the same log-dec out to ω≈14.5 krpm. The synchronously reduced model predicts an onset speed of instability (OSI) at 10 krpm, but a return to stability at 48 krpm, with subsequent increases in log-dec out to 70 krpm. The frequency-dependent model predicts an OSI of 10 krpm and no return to stability out to 70 krpm. The frequency-dependent models predict small changes in the rotor’s damped natural frequencies. The synchronously reduced model predicts large changes. The stability-analysis results show that a frequency-dependent labyrinth seal model should be used if the rotor surface speed approaches a significant fraction of the speed of sound. For the present example, observable discrepancies arose when Rsω=0.26c0.

scholarly journals Journal Bearing Impedance Descriptions for Rotordynamic Applications

1977 ◽  
Vol 99 (2) ◽  
pp. 198-210 ◽  
Author(s):  
D. Childs ◽  
H. Moes ◽  
H. van Leeuwen
Keyword(s):  
Finite Length ◽  
Reaction Force ◽  
Squeeze Film ◽  
Damping Coefficients ◽  
Analytic Expressions ◽  
Complete Set ◽  
Impedance Vector ◽  
Force Components ◽  
Stiffness And Damping ◽  
Vector Magnitude

Bearing impedance vectors are introduced for plain journal bearings which define the bearing reaction force components as a function of the bearing motion. Impedance descriptions are developed directly for the approximate Ocvirk (short) and Sommerfeld (long) bearing solutions. The impedance vector magnitude and the mobility vector magnitude of Booker are shown to be reciprocals. The transformation relationships between mobilities and impedance are derived and used to define impedance vectors for a number of existing mobility vectors including the finite-length mobility vectors developed by Moes. The attractiveness and utility of the impedance-vector formulation for transient simulation work is demonstrated by numerical examples for the Ocvirk “π”, and “2π” bearing impedances and the cavitating finite-length-bearing impedance. The examples presented demonstrate both bearing and squeeze-film damper application. A direct analytic method for deriving a complete set of (analytic) stiffness and damping coefficients from impedance descriptions is developed and demonstrated for the cavitating finite-length-bearing impedances. Analytic expressions are provided for all direct and cross-coupled stiffness and damping coefficients, and compared to previously developed numerical results. These coefficients are used for stability analysis of a rotor, supported in finite-length cavitating bearings. Onset-speed-of-instability results are presented as a function of the L/D ratio for a range of bearing numbers. Damping coefficients are also presented for finite-length squeeze-film dampers.

Rotordynamic-Coefficients and Static (Equilibrium Loci and Leakage) Characteristics for Short, Laminar-flow Annular Seals

2005 ◽  
Vol 128 (2) ◽  
pp. 378-387 ◽  
Author(s):  
Dara W. Childs ◽  
Luis E. Rodriguez ◽  
Vito Cullotta ◽  
Adnan Al-Ghasem ◽  
Matthew Graviss
Keyword(s):  
Laminar Flow ◽  
Groove Depth ◽  
Test Results ◽  
Clearance Ratio ◽  
Industrial Practice ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Static Data ◽  
Deep Groove ◽  
Stiffness And Damping

Test results are presented for laminar-flow seals that are representative of buffered-flow oil seals in centrifugal compressors. The seals are short (L∕D≅0.21), with a diameter of 117mm and a clearance-to-radius ratio 0.0007. A smooth seal, a seal with one central groove, and a seal with three grooves were tested. Groove geometries employed are representative of industrial practice for compressors with a groove-depth to clearance ratio on the order of 6. Tests were conducted at 4000, 7000, and 10,000rpm shaft speed with delta pressures across the seals of 21, 45, and 69bars. For all cases, the flow was laminar. The seals were tested from a centered position out to an eccentricity ratio of 0.7. Static data included leakage and equilibrium loci for a range of loads. Direct and cross-coupled stiffness and damping coefficients and direct mass coefficients were determined from dynamic tests. For the smooth seal, comparisons between measurements and predictions were reasonable for the direct and cross-coupled stiffness and damping coefficients; however, measured added mass coefficients were roughly ten times larger than predicted. Predictions for the grooved seals from a “deep-groove” model that assumed zero pressure oscillations in the grooves greatly over predicted the influence of the grooves. In a centered position, smooth and grooved seals had comparable leakage performance. At higher eccentricity ratios, the grooved seals leaked modestly more. For eccentricity ratios less than approximately 0.3, the grooved seals and the smooth seal had qualitatively similar static and dynamic characteristics. In terms of cross-coupled stiffness coefficients, the grooved seals were less stable than the smooth seal at eccentricity ratios greater than approximately 0.5 but had significantly lower cross-coupled coefficients at reduced eccentricity ratios between zero and 0.3. A grooved centered seal is more stable than a smooth centered seal. The smooth seal had higher damping than the grooved seals and had moderately better centering capabilities.

Influences of journal with 3D form errors on dynamic coefficients of hydrodynamic bearings yielded to JFO boundary conditions

2018 ◽  
Vol 233 (2) ◽  
pp. 289-302 ◽  
Author(s):  
Xun Ma ◽  
Wubin Xu ◽  
Xueping Zhang ◽  
Siyi Ding
Keyword(s):  
Boundary Conditions ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Form Error ◽  
Form Errors ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Stiffness And Damping

The dynamic characteristics of the journal with form error are analyzed, including normalized stiffness and damping coefficients. A new expression for journal surface with form error is presented, which is capable of formulating any types of form errors on the journal, and the dimensionless Reynolds equation is renewed and solved suffering from the Jakobsson, Floberg, and Olsson boundary conditions. The results show that form errors do have a significant influence on the dynamic performance of journal bearings and that the uncertainty attribute of form error could result in variations of dynamic properties so significantly that the system might operate in an entirely different way. Therefore, it is necessary to take more operating information into account, such as the elaborate state of the journal surface, in order to predict the bearing performance more accurately.

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