scholarly journals Fluid Film Dynamic Coefficients in Mechanical Face Seals

1983 ◽  
Vol 105 (2) ◽  
pp. 297-302 ◽  
Author(s):  
I. Green ◽  
I. Etsion
Keyword(s):  
Small Perturbation ◽  
Equilibrium Position ◽  
Degrees Of Freedom ◽  
Fluid Film ◽  
Seal Ring ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Face Seals ◽  
Stiffness And Damping ◽  
Analytical Expressions

The stiffness and damping coefficients of the fluid film in mechanical face seals are calculated for the three major degrees of freedom of the primary seal ring. The calculation is based on small perturbation of the ring from its equilibrium position. Analytical expressions are presented for the various coefficients and a comparison is made with results of accurate but more complex analyses to establish the range of applicability.

scholarly journals A Nonlinear Model for Prediction of Dynamic Coefficients in a Hydrodynamic Journal Bearing

2004 ◽  
Vol 10 (6) ◽  
pp. 507-513 ◽  
Author(s):  
Jerzy T. Sawicki ◽  
T. V. V. L. N. Rao
Keyword(s):  
Equilibrium Position ◽  
Nonlinear Dynamic ◽  
Static Pressure ◽  
Journal Bearing ◽  
Dynamic Pressure ◽  
Higher Order ◽  
Pressure Gradients ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Stiffness And Damping

This paper investigates the variation of nonlinear stiffness and damping coefficients in a journal orbit with respect to equilibrium position. The journal orbit is obtained by the combined solution of equations of motion and Reynolds equation. In the linearized dynamic analysis, dynamic pressure is written as a perturbation of static pressure and pressure gradients at equilibrium position. However, in order to obtain nonlinear dynamic coefficients about equilibrium position, the dynamic pressure gradients in the orbit are also written as the first order perturbation of static pressure gradients and higher order pressure gradients for displacement and velocity perturbations. The dynamic coefficients are functions of bearing displacement and velocity perturbations. The higher order pressure gradients at equilibrium position are evaluated at various eccentricity ratios and L/D ratios of 0.5 and 1.0. The variation of nonlinear dynamic coefficients is analyzed for three Sommerfeld numbers of a two-axial groove journal bearing under the action of an external synchronous load along and perpendicular to the radial journal load. Results indicate that the oil film nonlinearities affect the journal motion at lower eccentricity ratios (higher Sommerfeld numbers) with wide variation in stiffness and damping coefficients.

A Method of Dual Number for the Aerodynamic Property Analysis of Gas-Lubricated Mechanism：Self-Pressurizing Thrust Bearings and Non-Contacting Face Seals

2011 ◽  
Vol 311-313 ◽  
pp. 360-369
Author(s):  
Wan Fu Xu ◽  
Xiu Hua Li ◽  
Gang Ma
Keyword(s):  
Small Perturbation ◽  
Dynamic Property ◽  
Motion Equations ◽  
Thrust Bearings ◽  
Dual Number ◽  
Damping Coefficients ◽  
Face Seals ◽  
Aerodynamic Property ◽  
Stiffness And Damping ◽  
Perturbation Approximation

By using dual number, the dynamic property of gas-lubricated thrust bearings or non-contacting face seals is analyzed in the small perturbation approximation, then an essential conclude, that the perturbation dynamic Reynolds’ equations independently of its whirl frequency, is advanced. According to this, the calculation of the stiffness and damping coefficients independently of system motion equations of bearings and seals is expedited.

Numerical Analysis of Dynamic Coefficients for Gas Film Face Seals

2002 ◽  
Vol 124 (4) ◽  
pp. 743-754 ◽  
Author(s):  
Yuchuan Liu ◽  
Xinmin Shen ◽  
Wanfu Xu
Keyword(s):  
Numerical Analysis ◽  
Degrees Of Freedom ◽  
Axial Direction ◽  
Spiral Groove ◽  
Gas Bearings ◽  
Damping Coefficients ◽  
Face Seals ◽  
Stiffness And Damping ◽  
Three Degrees Of Freedom ◽  
Perturbation Approximation

A numerical analysis of stiffness and damping coefficients for gas film face seals in three degrees of freedom is presented in this paper. By applying small perturbation approximation, the steady and perturbed Reynolds equations, taking account of both hydrodynamic and hydrostatic effects, are obtained and solved by finite element method. Several numerical samples, including externally pressurized annular thrust gas bearings and spiral groove thrust gas bearings, validate the model and numerical algorithm. The results show that the interactions between axial and angular perturbation are negligible. Hence, in the dynamic analysis of gas film face seals, the perturbation in three degrees of freedom can be simplified as two independent ones, an axial movement and an angular wobble around two orthogonal axes perpendicular to axial direction.

Squeeze Effects in Radial Face Seals

1980 ◽  
Vol 102 (2) ◽  
pp. 145-151 ◽  
Author(s):  
I. Etsion
Keyword(s):  
Reynolds Equation ◽  
Radius Ratio ◽  
Fluid Film ◽  
Seal Ring ◽  
Face Seal ◽  
Angular Misalignment ◽  
Damping Coefficients ◽  
Wide Range ◽  
Face Seals ◽  
Hydrodynamic Effects

Squeeze effects in a liquid lubricated radial face seal are analyzed. The analysis considers face misalignment with both axial and angular vibrations of the primary seal ring. Translational, rotational, and cross-coupled damping coefficients of the fluid film are derived analytically from a solution of the Reynolds equation utilizing the narrow seal approximation. Results are given for a wide range of practical radius ratios. At each radius ratio, the complete range of angular misalignment—from parallel faces to touch down—is covered. It is shown that squeeze effects in face seals are usually larger than the more familiar hydrodynamic effects. These effects play an important role in the seal’s mechanism of operation and therefore have to be considered in any realistic seal model.

scholarly journals The Rotor Dynamic Coefficients of Coned-Face Mechanical Seals With Inward or Outward Flow

1987 ◽  
Vol 109 (1) ◽  
pp. 129-135 ◽  
Author(s):  
I. Green
Keyword(s):  
Fluid Film ◽  
Mechanical Seals ◽  
Dynamic Coefficients ◽  
Face Seals ◽  
Stiffness And Damping ◽  
Rotor Dynamic

The linearized fluid film dynamic coefficients, i.e., stiffness and damping, of flexibly-mounted rotor noncontacting mechanical face seals are found. The coefficients are derived from a previous study where the flexibly mounted element was the stator. The two cases of inward and outward flows, both having converging gaps in the direction of flow, are analyzed for the two mounting configurations, and it is found that the later case possesses higher angular stiffness.

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

Tilting Pad Journal Bearings: A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot Flexibility

2012 ◽  
Author(s):  
Jason C. Wilkes ◽  
Dara W. Childs
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Operating Temperature ◽  
Excitation Frequency ◽  
Full Model ◽  
Stability Calculation ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

For several years, researchers have presented predictions showing that using a full tilting-pad journal bearing (TPJB) model (retaining all of the pad degrees of freedom) is necessary to accurately perform stability calculations for a shaft operating on TPJBs. This paper will discuss this issue, discuss the importance of pad and pivot flexibility in predicting impedance coefficients for the tilting-pad journal bearing, present measured changes in bearing clearance with operating temperature, and summarize the differences between measured and predicted frequency dependence of dynamic impedance coefficients. The current work presents recent test data for a 100 mm (4 in) five-pad TPJB tested in load on pad (LOP) configuration. Measured results include bearing clearance as a function of operating temperature, pad clearance and radial displacement of the loaded pad (the pad having the static load vector directed through its pivot), and frequency dependent stiffness and damping. Measured hot bearing clearances are approximately 30% smaller than measured cold bearing clearances and are inversely proportional to pad surface temperature; predicting bearing impedances with a rigid pad and pivot model using these reduced clearances results in overpredicted stiffness and damping coefficients that are several times larger than previous comparisons. The effect of employing a full bearing model versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies. These predictions showed that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping, an outcome that is completely opposite from conclusions reached by comparing different prediction models. This contrasting outcome results from a predicted increase in damping with increasing excitation frequency at all speeds and loads; however, this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.

An Analytical Complete Model of Tilting-Pad Journal Bearing Considering Pivot Stiffness and Damping

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Zhiyong Yan ◽  
Yi Lu ◽  
Tiesheng Zheng
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Local Coordinate System ◽  
Dynamical Behavior ◽  
Complete Model ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Generalized Force ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Considering the freedom of pad tilting and pad translation along preload orientation, an analytical complete model, as well as mathematical method, which contains 2n+2 degrees of freedom, is presented for calculating the dynamical characteristics of tilting-pad journal bearing. Based on the motion relationship of shaft and pad, the local coordinate system, the generalized displacement, and the generalized force vector are chosen. The concise transformation of generalized displacement, generalized force, and its Jacobian matrix between the local and global coordinate systems are built up in matrix form. A fast algorithm using the Newton–Raphson method for calculating the equilibrium position of journal and pads is proposed. The eight reduced stiffness and damping coefficients can be obtained assuming that the journal and all pads are subject to harmonic vibration. Numerical results show that the reduced damping coefficients and the threshold speed can be effectively enhanced by giving suitable pad pivot stiffness and damping simultaneously, and this analytical method can be applied to analyze dynamical behavior of the tilting-pad journal bearing rotor system.

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.

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