Zero-Load Stability of Rotating Externally Pressurized Gas-Lubricated Journal Bearings

1970 ◽  
Vol 92 (2) ◽  
pp. 325-334 ◽  
Author(s):  
David P. Fleming ◽  
R. E. Cunningham ◽  
W. J. Anderson
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Digital Computer ◽  
Pressure Ratio ◽  
Journal Bearings ◽  
Small Eccentricity ◽  
Attitude Angle ◽  
Stability Data ◽  
Bearing Number ◽  
Load Stability

A small eccentricity analysis was performed for a bearing having two feeding planes, each of which is assumed to be a line source. Numerical results were obtained for a range of bearing number, pressure ratio, feeding parameter, and orifice recess volume by means of a digital computer. Steady-state load and attitude angle were obtained, as well as stability data. Stability decreased markedly with increasing recess volume; moreover, for large recess volume and low bearing number, an increase in pressure ratio decreased stability. There was no correlation between stability and steady-state attitude angle for any of the cases studied. Fair agreement was obtained with available experimental data.

scholarly journals Experiments on an Ultrastable Gas Journal Bearing

1967 ◽  
Vol 89 (4) ◽  
pp. 433-438 ◽  
Author(s):  
S. B. Malanoski
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Design Data ◽  
Attitude Angle ◽  
Angle Data ◽  
The Stability ◽  
Data Design ◽  
Gas Journal Bearing

Shallow grooving in a herringbone pattern has been proposed to enhance the stability of both gas and liquid-lubricated journal bearings. It has been shown theoretically that this possibility is particularly advantageous for unloaded journal bearings. This paper describes corroborating experiments. The experiments included the running of an unloaded bearing up to speeds of 60,000 rpm and the collection of steady-state load-displacement, attitude angle data at intermediate speeds up to and including 60,000 rpm. No sign of bearing whirl instability was detected. There was good correlation between theoretical and experimental data. Design data for the partially grooved journal bearing is included for future designs.

Analysis and Modeling of the Vortex Amplifier

1969 ◽  
Vol 91 (4) ◽  
pp. 755-763 ◽  
Author(s):  
R. T. Bichara ◽  
P. A. Orner
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Computer Program ◽  
Flow Regime ◽  
Incompressible Flow ◽  
Digital Computer ◽  
Input Output ◽  
Critical Dimensions ◽  
Fluid Properties ◽  
Output Characteristics

A model has been derived to predict the steady-state input-output characteristics of vortex amplifiers operating in the incompressible flow regime. The model was correlated with experimental data to affect prediction of the influence of the operating fluid properties and the vortex valve critical dimensions on the valve characteristics. The model has been implemented in a digital computer program which includes procedures for the design of vortex valves with specified flow and pressure turndown ratios and the design of vortex amplifiers with proportional (single-valued) characteristics.

Dynamic stability analysis of noncircular two-lobe journal bearings with couple stress lubricant regime

2020 ◽  
pp. 135065012094551
Author(s):  
Mahdi Zare Mehrjardi
Keyword(s):  
Steady State ◽  
Carrying Capacity ◽  
Couple Stress ◽  
Journal Bearings ◽  
Lubricating Oil ◽  
Couple Stress Fluid ◽  
Load Carrying Capacity ◽  
Stress Parameter ◽  
Attitude Angle ◽  
Load Carrying

In this research, the steady state and dynamic performances of two-lobe noncircular journal bearings with couple stress lubricant are presented. The lubricating oil, containing additives and contaminants, is modeled as the couple stress fluid. The modified Reynolds equation is obtained using the couple stress lubrication theory and is then solved by finite element method as an efficient numerical technique. The steady-state characteristics of bearings, including the load carrying capacity and attitude angle, are determined for various values of the couple stress parameter. The results show that applying the couple stress fluid improves the efficiency of two-lobe bearings in terms of an increased load carrying capacity and reduced attitude angle. Also, the stability performance of the investigated bearings is studied using rotor motion equations based on linear and nonlinear dynamic methods. The results indicate that any increase in the lubricant couple stress parameter enhances the bearing ability to damp the rotor perturbations. In other words, by varying the lubricant from Newtonian oil to the couple stress type and upgrading its properties, the curves of the critical mass parameter and whirl frequency ratio have an increasing and decreasing trend, respectively. Based on the fourth-order Runge–Kutta method results, the dynamic trajectory of the rotor center in the bearing space changes with increasing the couple stress parameter from diverging disturbances and limits the cycle perturbations around the bearing center to converging oscillations to the static equilibrium point. Moreover, the effect of changing lubricant properties on the two-lobe bearing’s performance is more pronounced at higher values of the couple stress parameter, especially with an increase in the noncircularity of bearings’ geometry.

A Theoretical Analysis of Whirl Instability and Pneumatic Hammer for a Rigid Rotor in Pressurized Gas Journal Bearings

1967 ◽  
Vol 89 (2) ◽  
pp. 154-165 ◽  
Author(s):  
J. W. Lund
Keyword(s):  
Theoretical Analysis ◽  
Time Constant ◽  
Pressure Ratio ◽  
Journal Bearings ◽  
Restricted Feeding ◽  
Rigid Rotor ◽  
Eccentricity Ratio ◽  
Pneumatic Hammer ◽  
Small Eccentricity ◽  
First Order

A theoretical analysis is presented for the threshold of instability for a rigid rotor supported in hydrostatic gas journal bearings. Both rotationally induced instability (hybrid instability) and pneumatic hammer are considered. The analysis is based on a first-order perturbation with respect to the eccentricity ratio (i.e., the results are limited to small eccentricity ratios) and makes use of the linearized Ph-method [2, 5, 8]. The pressurized gas is supplied to the bearing through restricted feeding holes in the center plane of the bearing and the analysis takes into account the discreteness of the feeding holes, the feeder hole time constant, and inherent compensation effects. Numerical results are given in form of 16 graphs, showing the threshold of instability as a function of supply pressure ratio, feeding parameter and eccentricity ratio. Also, the effect of the feeder hole time constant is investigated with respect to pneumatic hammer.

Rarefaction Effect on the Characteristics of Micro Gas Journal Bearings

2009 ◽  
Author(s):  
Haijun Zhang ◽  
Qin Yang
Keyword(s):  
Knudsen Number ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Slip Boundary Condition ◽  
Journal Bearings ◽  
Radial Clearance ◽  
Clearance Ratio ◽  
Attitude Angle ◽  
Modified Reynolds Equation ◽  
Bearing Number

Journal bearings, which are used to support radial loads in a rotating machine, have somewhat unusual requirements in MEMS deriving from the extremely shallow structures. Thus, the micro gas journal bearings are characterized by a very small length-diameter ratio, defined as the ratio of the bearing length to its diameter and a paradoxically large bearing clearance ratio, defined as the ratio of the average radial clearance to the bearing radius. Given the definition of the reference Knudsen number for micro gas journal bearings, the range of the reference Knudsen number is illustrated according to the viscosity values of air under different temperatures. With the reference Knudsen number being included, the modified Reynolds equation for micro gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The finite difference method (FDM) is employed to solve the modified Reynolds equation to obtain the pressure distribution, load capacities and attitude angles for micro gas journal bearings under different reference Knudsen numbers, bearing numbers and eccentricity ratios. Numerical analysis shows that the pressure profiles and non-dimensional load capacities decrease obviously with gas rarefaction strengthened, and the attitude angle changes conversely. Moreover, when the bearing number is smaller, the effect of gas rarefaction on the non-dimensional load capacity and attitude angle is less.

Characteristics of Micro Gas Journal Bearings Based on Effective Viscosity

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Haijun Zhang ◽  
Changsheng Zhu ◽  
Qin Yang
Keyword(s):  
Knudsen Number ◽  
Effective Viscosity ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Journal Bearings ◽  
Eccentricity Ratio ◽  
Rarefied Flow ◽  
Attitude Angle ◽  
Modified Reynolds Equation ◽  
Bearing Number

According to the first order slip velocity boundary, a modified Reynolds equation for micro gas journal bearings is presented with consideration of effective viscosity under a rarefied flow condition. A modified Reynolds equation is attained and solved using the finite difference method. The nondimensional pressure, load capacity, and attitude angle for micro gas journal bearings under different reference Knudsen numbers (the ratio of ambient molecular mean free path to the average radial clearance), bearing numbers, and eccentricity ratios are obtained. The numerical analysis demonstrates that the slip model with effective viscosity is in a better agreement with the FK model derived by Fukui and Kaneko than that without effective viscosity. When the bearing number is constant, the pressure and load capacity decrease, and the attitude angle changes inversely with the increasing reference Knudsen number. The larger the eccentricity ratio, the larger change in attitude angle from effective viscosity. When eccentricity ratio is less than 0.6, the attitude angle changes softly, and the effect of effective viscosity is unobvious. When the eccentricity ratio is constant, the influence of effective viscosity on nondimensional load capacity and attitude angle becomes larger with the increasing bearing number, and the influence is more prominent with a larger reference Knudsen number.

Numerical Analysis of Herringbone-Grooved Gas-Lubricated Journal Bearings Using a Multigrid Technique

1999 ◽  
Vol 121 (1) ◽  
pp. 148-156 ◽  
Author(s):  
Takuji Kobayashi
Keyword(s):  
Steady State ◽  
Numerical Analysis ◽  
Reasonable Agreement ◽  
Reynolds Equation ◽  
Journal Bearings ◽  
Static And Dynamic Characteristics ◽  
Slow Convergence ◽  
Relaxation Scheme ◽  
Bearing Number ◽  
Successive Over Relaxation

In this paper, a multigrid technique is applied to the compressible Reynolds equation discretized by the divergence formulation in order to analyze both static and dynamic characteristics of herringbone-grooved gas-lubricated journal bearings. The developed code demonstrates quicker convergence than an optimized successive over-relaxation scheme, and the dominance in numerical efficiency is especially remarkable at higher values of bearing number where slow convergence is generally observed. Comparisons between the present nonlinear orbit solutions and previously published experimental results show reasonable agreement in both steady-state and dynamic stability performances.

Analysis of the Steady State Characteristics of Gas-Lubricated, Porous Journal Bearings

1975 ◽  
Vol 97 (1) ◽  
pp. 44-51 ◽  
Author(s):  
Dah-chen Sun
Keyword(s):  
Steady State ◽  
Iterative Method ◽  
Ambient Pressure ◽  
Pressure Ratio ◽  
Journal Bearings ◽  
Diameter Ratio ◽  
Operational Performance ◽  
Eccentricity Ratio ◽  
Length To Diameter Ratio

The steady state operational performance of gas-lubricated porous journal bearings is analyzed by using a numerical iterative method. Results are obtained, and presented in charts and tables, for the length-to-diameter ratio values of 1, 2, and 3; the eccentricity ratio values of 0.2, 0.4, 0.6, and 0.8; the compressibility number from 0 to 10; and several values of the feeding parameter and the supply-to-ambient pressure ratio commonly found in applications.

Predicting the Effect of Tire Tread Pattern Design on Thick Film Wet Traction

1977 ◽  
Vol 5 (1) ◽  
pp. 6-28 ◽  
Author(s):  
A. L. Browne
Keyword(s):  
Experimental Data ◽  
Network Design ◽  
Thick Film ◽  
Digital Computer ◽  
Analytical Tool ◽  
Design Practice ◽  
Pattern Design ◽  
Performance Results ◽  
Good Agreement

Abstract An analytical tool is presented for the prediction of the effects of changes in tread pattern design on thick film wet traction performance. Results are reported for studies in which the analysis, implemented on a digital computer, was used to determine the effect of different tread geometry features, among these being the number, width, and lateral spacing of longitudinal grooves and the angle of zigzags in longitudinal grooves, on thick film wet traction. These results are shown to be in good agreement with experimental data appearing in the literature and are used to formulate guidelines for tread groove network design practice.

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