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.

Numerical Analysis for Galloping of Iced Quad Bundle Conductors

2012 ◽  
Vol 226-228 ◽  
pp. 30-34
Author(s):  
Jun Yan Cai ◽  
Xi Jun Liu ◽  
Su Xia Zhang
Keyword(s):  
Numerical Analysis ◽  
Degrees Of Freedom ◽  
Damping Ratio ◽  
Simplified Model ◽  
Fluid Density ◽  
Spring Stiffness ◽  
Critical Wind Velocity ◽  
Line Path ◽  
Stiffness And Damping ◽  
Three Degrees Of Freedom

In order to attain the purpose of anti-galloping, a simplified model for iced quad bundle conductors of three degrees of freedom in vertical, horizontal and torsional directions is established by means of the Hamilton principle, in which the effect of spacers stiffness and damping is considered. Based on the model, the influence of related parameters such as fluid density, damping ratio on conductor galloping amplitude and critical wind velocity is analyzed. Simultaneously, the relation curve between elastic property of spacers and conductor galloping is obtained. The results indicate that the conductor galloping can be weakened to some degree with the proper enlargement of damping ratio, the reasonable setting of spring stiffness on spacers and the avoidance of areas such as the wind outlet and windward as much as possible when choosing the line path and so on.

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.

The Rotordynamic Coefficients of Mechanical Seals Having Two Flexibly Mounted Rotors

1991 ◽  
Vol 113 (4) ◽  
pp. 795-804 ◽  
Author(s):  
J. Wileman ◽  
I. Green
Keyword(s):  
Degrees Of Freedom ◽  
Reynolds Equation ◽  
Mechanical Seal ◽  
Mechanical Seals ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Rotating Shafts ◽  
Stiffness And Damping ◽  
Three Degrees Of Freedom ◽  
Degenerate Cases

The Reynolds equation is derived for a mechanical seal in which both elements are flexibly mounted to rotating shafts. Stiffness and damping coefficients for the fluid film are calculated for the three degrees of freedom of each element based upon a small perturbation analysis. The analogous coefficients for simpler configurations (e.g., flexibly mounted rotor, flexibly mounted stator) contained in the literature are shown to be obtainable as degenerate cases of the more general results presented in this work.

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.

Dynamic Stability Prediction of Spherical Spiral Groove Hybrid Gas Bearings Rotor System

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Chenhui Jia ◽  
Huanjie Pang ◽  
Wensuo Ma ◽  
Ming Qiu
Keyword(s):  
Dynamic Stiffness ◽  
Three Dimensional ◽  
Pressure Control ◽  
Spiral Groove ◽  
Gas Bearings ◽  
Hurwitz Stability ◽  
Damping Coefficients ◽  
Control Equation ◽  
Perturbation Pressure ◽  
Stiffness And Damping

Taking the hemisphere spiral groove hybrid gas bearings (HSGHGB) as the research object, the nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established with the axis instantaneous position and instantaneous displacement speed as the parameters. The perturbation pressure control equation is solved by means of the finite difference method in generalized coordinate system. The calculation program is prepared based on VC++6.0, and the transient perturbation pressure distribution of three-dimensional (3D) gas film, nonlinear gas film force, and dynamic stiffness and damping coefficients are numerically calculated. The influences of different speeds, eccentricity ratios, and gas supply pressures on the dynamic characteristic coefficients of gas film are studied. The results show that the influence of bearing's supply pressure, speed, and eccentricity on the dynamic characteristics of gas film is significant. The dynamic equations of rotor-bearing system containing the gas film dynamic stiffness and the damping coefficients are established, and the stability of the gas film is predicted based on the Routh–Hurwitz stability criterion. The research provides the theoretical foundation for actively controlling the bearing running stiffness and damping and stemming the instability of gas film.

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.

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.

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