A Semi-Analytical Solution to the Dynamic Tracking of Non-contacting Gas Face Seals

2001 ◽  
Vol 124 (1) ◽  
pp. 196-202 ◽  
Author(s):  
Bo Ruan
Keyword(s):  
Dynamic Responses ◽  
Dynamic Force ◽  
Face Seal ◽  
Mass System ◽  
Dynamic Tracking ◽  
Conical Whirl ◽  
Tracking Motion ◽  
Gas Face Seal ◽  
Stiffness And Damping ◽  
Film Stiffness

The gas film stiffness and damping coefficients for a non-contacting gas face seal are obtained from the unsteady nonlinear Reynolds equation using the perturbation method. The seal assembly is converted to an equivalent spring-damper-mass system. The stator tracking motion is treated as a forced vibration caused by the rotor motion due to its runout and misalignment. The seal steady-state dynamic responses are solved semianalytically. Results for a typical spiral groove gas face seal agree well with that from a full numerical simulation. Stability of the seal axial pulsating and conical whirl are examined using the frequency dependent dynamic force and moment coefficients.

Numerical Analysis of Dry Gas Face Seals With Spiral Groove and Inner Annular Groove

2008 ◽  
Author(s):  
Xu-Dong Peng ◽  
Li-Li Tan ◽  
Ji-Yun Li ◽  
Song-En Sheng ◽  
Shao-Xian Bai
Keyword(s):  
Reynolds Equation ◽  
Geometric Parameters ◽  
Axial Stiffness ◽  
Face Seal ◽  
Optimization Principle ◽  
Face Seals ◽  
The Face ◽  
Gas Face Seal ◽  
Film Stiffness ◽  
Spiral Grooves

A two-dimensional Reynolds equation was established for isothermal compressible gas between the two faces of a dry gas face seal with both spiral grooves and an inner annular groove onto the hard face. The opening force, the leakage rate, the axial film stiffness and the film stiffness to leakage ratio were calculated by finite element method. The comparisons with the sealing performances of a typical gas face seal only with spiral grooves onto its hard face were made. The effects of the face geometric parameters on the static behavior of such a seal were analyzed. The optimization principle for geometric parameters of a dry gas face seals with spiral grooves and an inner annular groove was presented. The recommended geometric parameters of spiral grooves and circular groove presented by optimization can ensure larger axial stiffness while lower leakage rates.

scholarly journals A New Method to Calculate Water Film Stiffness and Damping for Water Lubricated Bearing with Multiple Axial Grooves

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Guojun Ren
Keyword(s):  
Analytical Procedure ◽  
Load Capacity ◽  
Water Film ◽  
New Method ◽  
Hard Materials ◽  
Stiffness And Damping ◽  
Film Stiffness ◽  
Hydro Turbines

Abstract Water lubricated guide bearings for hydro turbines and pumps are conventionally designed with multiple axial grooves to provide effectively cooling and flushing away abrasives. Due to the variety of groove configuration in terms of number and size, a predication of their performance is difficult. This paper deals with an analytical procedure to investigate groove effect on load capacity, stiffness and damping for this type of bearing where it is considered as an assembly of many inclined slide bearings. The result can be applied to bearings made of hard materials combined with low bearing pressure.

Experimental and Theoretical Rotordynamic Characteristics of a Hybrid Journal Bearing

1997 ◽  
Vol 119 (1) ◽  
pp. 132-141 ◽  
Author(s):  
J. T. Sawicki ◽  
R. J. Capaldi ◽  
M. L. Adams
Keyword(s):  
Journal Bearing ◽  
Operating Conditions ◽  
Dynamic Force ◽  
Test Results ◽  
Force Measurements ◽  
Lubrication Equation ◽  
Load Cells ◽  
Theoretical Predictions ◽  
Stiffness And Damping

This paper describes an experimental and theoretical investigation of a four-pocket, oil-fed, orifice-compensated hydrostatic bearing including the hybrid effects of journal rotation. The test apparatus incorporates a double-spool-shaft spindle which permits independent control over the journal spin speed and the frequency of an adjustable-magnitude circular orbit, for both forward and backward whirling. This configuration yields data that enables determination of the full linear anisotropic rotordynamic model. The dynamic force measurements were made simultaneously with two independent systems, one with piezoelectric load cells and the other with strain gage load cells. Theoretical predictions are made for the same configuration and operating conditions as the test matrix using a finite-difference solver of Reynolds lubrication equation. The computational results agree well with test results, theoretical predictions of stiffness and damping coefficients are typically within thirty percent of the experimental results.

Calculation and Measurement of the Stiffness and Damping Coefficients for a Low Impedance Hydrodynamic Bearing

1997 ◽  
Vol 119 (1) ◽  
pp. 57-63 ◽  
Author(s):  
M. J. Goodwin ◽  
P. J. Ogrodnik ◽  
M. P. Roach ◽  
Y. Fang
Keyword(s):  
Experimental Data ◽  
Dynamic Stiffness ◽  
Perturbation Technique ◽  
The Novel ◽  
Oil Film ◽  
Hydrodynamic Bearing ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Film Stiffness ◽  
Novel Design

This paper describes a combined theoretical and experimental investigation of the eight oil film stiffness and damping coefficients for a novel low impedance hydrodynamic bearing. The novel design incorporates a recess in the bearing surface which is connected to a standard commercial gas bag accumulator; this arrangement reduces the oil film dynamic stiffness and leads to improved machine response and stability. A finite difference method was used to solve Reynolds equation and yield the pressure distribution in the bearing oil film. Integration of the pressure profile then enabled the fluid film forces to be evaluated. A perturbation technique was used to determine the dynamic pressure components, and hence to determine the eight oil film stiffness and damping coefficients. Experimental data was obtained from a laboratory test rig in which a test bearing, floating on a rotating shaft, was excited by a multi-frequency force signal. Measurements of the resulting relative movement between bearing and journal enabled the oil film coefficients to be measured. The results of the work show good agreement between theoretical and experimental data, and indicate that the oil film impedance of the novel design is considerably lower than that of a conventional bearing.

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.

scholarly journals Dynamic Analysis of a Planar Hydraulic Rock-Breaker Mechanism with Multiple Clearance Joints

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Ke Chen ◽  
Guojun Zhang ◽  
Rui Wu ◽  
Li Wang ◽  
Hongmei Zheng ◽  
...  
Keyword(s):  
Hydraulic Cylinder ◽  
Dynamic Responses ◽  
Force Model ◽  
Engineering Applications ◽  
Mass System ◽  
Clearance Joints ◽  
Cylinder Model ◽  
Practical Engineering ◽  
Manufacturing Tolerances ◽  
Joint Clearances

Clearance exists in the joint of a mechanism because of the assemblage, manufacturing tolerances, wear, and other conditions, and it is a focus of research in the field of multibody dynamics. This study built a planar hydraulic rock-breaker model with multiple joint clearances by combining the hydraulic cylinder model, the clearance joints based on the Lankarani–Nikravesh contact force model, and the Lagrange multiplier method. Dynamic simulation results indicated that multiple clearance joints can degrade the dynamic responses of a rock-breaker model, which can be decomposed to rapid vibrations and slow movements. The rapid vibrations are excited by coupling the spring-mass system of hydraulic cylinder and clearances. The effects of the clearance size, input force, damping coefficient, and friction on the dynamic behaviour of the rock-breaker mechanism are also investigated. The friction could reduce the rapid vibration state significantly, which is feasible for practical engineering applications. As compared with the traditional models without clearances, the present model provides not only better predictions for the theoretical study of the hydraulic rock-breaker but also useful guidance for reducing the vibrations of the hydraulic rock-breaker in practical engineering applications.

scholarly journals The Effect of the Pivot Stiffness on the Performances of Five-Pad Tilting Pad Bearings

Lubricants ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 61 ◽  
Author(s):  
Phuoc Vinh Dang ◽  
Steven Chatterton ◽  
Paolo Pennacchi
Keyword(s):  
Excitation Frequency ◽  
Experimental Results ◽  
Dynamic Force ◽  
Dynamic Coefficients ◽  
Pivot Bearing ◽  
Tilting Pad ◽  
In Series ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearings

The role of the pivot flexibility in tilting-pad journal bearings (TPJBs) has become essential, particularly for bearings working at high applied load and relatively high rotor speeds. Predictions from a simple bearing model with rigid pivots show incorrect estimation of the dynamic coefficients in comparison with the experimental results. Normally, the more flexible the pad pivot, the lower the dynamic coefficients because the stiffness of the pivot takes in series with the stiffness and damping of the oil film. This paper investigates the influence of pivot stiffness on the dynamic force coefficients of two different five-pad TPJBs as a function of the applied static load and excitation frequency: rocker-backed pivot and spherical pivot bearings. In order to highlight the effect of the pivot stiffness in the spherical pivot bearing, displacement restriction components and elastic copper made shims have been used. Firstly, a thermo-elasto-hydrodynamic model for the static and dynamic characteristics of the two bearings is described. This model takes into account the flexibility of both pad and pivot. The pivot stiffnesses calculated by means of the Hertz theory and those obtained by experiments have been introduced and compared in the model. The clearance profiles of two tested bearing and the shaft center loci obtained by measurement and prediction are also shown. The dynamic coefficients of the two bearings obtained from the numerical simulation were compared with the experimental results. By the analysis it can be concluded that the effect of the pivot flexibility on the clearance profile, the shaft locus and on the dynamic coefficients is very significant. More important, it is important to estimate the pivot stiffness of each single pad using experimental measurements.

Investigation of nonlinear landing gear behavior and dynamic responses on high performance aircraft

2019 ◽  
Vol 233 (15) ◽  
pp. 5674-5688
Author(s):  
PS Suresh ◽  
Niranjan K Sura ◽  
K Shankar
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Landing Gear ◽  
Flight Mechanics ◽  
Dynamic Responses ◽  
Nonlinear Stiffness ◽  
Response Model ◽  
Nonlinear Dynamic Response ◽  
Vertical Descent ◽  
Stiffness And Damping

The dynamic responses simulation of aircraft as rigid body considering heave, pitch, and roll motions, coupled onto a tricycle landing gear arrangement is presented. Equation of motion for each landing gear consists of un-sprung mass vertical and longitudinal motions considering strut nonlinear stiffness and damping combined with strut bending flexibility. Initially, the nonlinear dynamic response model is subjected to an input of riding over staggered bump and the responses are compared with linear landing gear model. It is observed that aircraft dynamics and important landing gear events such as vertical, spin-up and spring-back are truly represented with nonlinear stiffness and damping model considering strut bending flexibility. Later, landing response analysis is performed, with the input from nonlinear flight mechanics model for several vertical descent rate cases. The aircraft and landing gear dynamic responses such as displacement, velocity, acceleration, and reaction forces are obtained. The vertical and longitudinal drag forces from the nonlinear dynamic response model is compared with “Book-case method” outlined in landing gear design technical specifications. From the reaction force ratio calculation, it is shown that for lower vertical descent rate case the predicted loads are lesser using nonlinear dynamic response model. The same model for higher vertical descent rate cases predicts higher ratios on vertical reaction for main landing gear and longitudinal reaction for nose landing gear, respectively. The scope for increase in fatigue life for low vertical descent rate landing covering major design spectrum and the concern for static strength and structural integrity consideration for higher vertical descent rate cases are discussed in the context of event monitoring on aircraft in services.

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