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.

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.

Study on the Performance of Gas Journal Bearings for Power MEMS

2011 ◽  
Vol 483 ◽  
pp. 635-639
Author(s):  
Hai Jun Zhang ◽  
Qin Yang
Keyword(s):  
Boundary Condition ◽  
Knudsen Number ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Journal Bearings ◽  
Slip Boundary ◽  
Attitude Angle ◽  
Pressure Profiles ◽  
Power Mems ◽  
Modified Reynolds Equation

Gas journal bearings, which are used to support radial loads in a rotating machine, have somewhat unusual requirements in Power MEMS deriving from the extremely shallow structures. With the reference Knudsen number being included, the modified Reynolds equation for gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The boundary condition for modified Reynolds equation is given. The numerical method is employed to solve the modified Reynolds equation to obtain the pressure profiles, load capacities and attitude angles of gas journal bearings for Power MEMS under different reference Knudsen numbers and eccentricity ratios. Numerical analysis shows that the pressure profiles and non-dimensional load capacities decrease obviously with the reference Knudsen number increasing, and the attitude angle changes conversely. Moreover, when the eccentricity ratio is smaller, the effect of gas rarefaction on the attitude angle is less.

scholarly journals Mathematical Model and Analysis of the Water-Lubricated Hydrostatic Journal Bearings considering the Translational and Tilting Motions

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hui-Hui Feng ◽  
Chun-Dong Xu ◽  
Jie Wan
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Journal Bearings ◽  
Linear Perturbation ◽  
Eccentricity Ratio ◽  
Dynamic Coefficients ◽  
Pressure Fields ◽  
Dynamic Performances ◽  
Rotary Speed

The water-lubricated bearings have been paid attention for their advantages to reduce the power loss and temperature rise and increase load capacity at high speed. To fully study the complete dynamic coefficients of two water-lubricated, hydrostatic journal bearings used to support a rigid rotor, a four-degree-of-freedom model considering the translational and tilting motion is presented. The effects of tilting ratio, rotary speed, and eccentricity ratio on the static and dynamic performances of the bearings are investigated. The bulk turbulent Reynolds equation is adopted. The finite difference method and a linear perturbation method are used to calculate the zeroth- and first-order pressure fields to obtain the static and dynamic coefficients. The results suggest that when the tilting ratio is smaller than 0.4 or the eccentricity ratio is smaller than 0.1, the static and dynamic characteristics are relatively insensitive to the tilting and eccentricity ratios; however, for larger tilting or eccentricity ratios, the tilting and eccentric effects should be fully considered. Meanwhile, the rotary speed significantly affects the performance of the hydrostatic, water-lubricated bearings.

Generalized Reynolds Equation for Micropolar Fluid With Microrotations Near Surface and Its Application to Journal Bearings

1994 ◽  
Vol 116 (3) ◽  
pp. 654-657 ◽  
Author(s):  
N. M. Bessonov
Keyword(s):  
Friction Surface ◽  
Effective Viscosity ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Journal Bearings ◽  
Thin Layers ◽  
Near Surface ◽  
Generalized Reynolds Equation ◽  
Micropolar Liquid

The theory of micropolar liquid lubrication (see Prakash and Sinha, 1975; Tipei, 1979; Singh and Sinha, 1982) takes into account only the increasing of effective viscosity in thin layers. Modern experiments (see Derjaguin et al., 1985) show that effective viscosity can increase or decrease and approaches to a certain limit (boundary viscosity), depending on the type of liquid and nature of the solid surface. A new generalized Reynolds equation that takes into account both these effects and also all possible situations in microrotation near the friction surface is derived in this work. An example using the equation for calculation of the journal bearing performance is given. It is shown that the friction coefficient can be sufficiently decreased without a noticeable change in the load capacity by regulation of interaction between micropolar lubricant and surfaces.

Hybrid Porous Gas Journal Bearings: Steady State Solution Incorporating the Effect of Velocity Slip

1984 ◽  
Vol 106 (3) ◽  
pp. 322-328 ◽  
Author(s):  
K. C. Singh ◽  
N. S. Rao ◽  
B. C. Majumdar
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Load Capacity ◽  
Velocity Slip ◽  
Steady State Solution ◽  
Static Characteristic ◽  
Journal Bearings ◽  
Mass Rate ◽  
Modified Reynolds Equation

A theoretical analysis is presented to predict the steady state performance characteristics of externally pressurized rotating gas journal bearings incorporating the effect of velocity slip at the porous interface. The governing equation for flow in the porous media and the modified Reynolds equation derived from the Navier-Stokes equations satisfying the velocity slip boundary condition, are solved simultaneously for film pressure distribution. Due to the nonlinearity of modified Reynolds equation the solution is obtained by perturbation method using finite difference technique. The dimensionless load capacity, attitude angle and mass rate of flow are computed numerically for different operating parameters. The effect of slip on the static characteristic is discussed. Comparison of the results with similar available solution for the no-slip case shows good agreement.

Design of Multi-Recess Hydrostatic Journal Bearings for Minimum Total Power Loss

1974 ◽  
Vol 96 (1) ◽  
pp. 226-232 ◽  
Author(s):  
C. Cusano ◽  
T. F. Conry
Keyword(s):  
Rotational Speed ◽  
Power Loss ◽  
Load Capacity ◽  
Maximum Load ◽  
Journal Bearings ◽  
Design Criterion ◽  
Total Power ◽  
Eccentricity Ratio ◽  
Constant Ratio ◽  
Design Charts

The design problem is formulated for multi-recess hydrostatic journal bearings with a design criterion of minimum total power loss. The design is subject to the constraints of constant ratio of the recess area to the total bearing area and maximum load capacity for a given recess geometry. The L/D ratio, eccentricity ratio, ratio of recess area to total bearing area, and shaft rotational speed are considered as parameters. The analysis is based on the bearing model of Raimondi and Boyd [1]. This model is generally valid for low-to-moderate speeds and a ratio of recess area-to-total bearing area of approximately 0.5 or greater. Design charts are presented for bearings having a ratio of recess area-to-total bearing area of 0.6 and employing capillary and orifice restrictors, these being the most common types of compensating elements. A design example is given to illustrate the use of the design charts.

Lubrication of Porous Journal Bearings

1972 ◽  
Vol 94 (1) ◽  
pp. 69-73 ◽  
Author(s):  
C. Cusano
Keyword(s):  
Analytical Solution ◽  
Coefficient Of Friction ◽  
Load Capacity ◽  
Journal Bearings ◽  
Performance Characteristics ◽  
Eccentricity Ratio ◽  
Design Variables

An analytical solution for the performance characteristics of finite porous journal bearings is obtained. Results are presented which relate the eccentricity ratio and coefficient of friction as functions of load number for design variables of 0.0001, 0.001, 0.01, and 0.1. The load capacity obtained by using the finite bearing theory is compared to the load capacity obtained by using the short-bearing approximation and the infinite-bearing approximation.

Rayleigh Step Journal Bearing: Part 1—Compressible Fluid

1968 ◽  
Vol 90 (1) ◽  
pp. 271-280 ◽  
Author(s):  
B. J. Hamrock
Keyword(s):  
Compressible Fluid ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Maximum Load ◽  
Pressure Profile ◽  
Clearance Ratio ◽  
Attitude Angle ◽  
Step Parameters ◽  
Bearing Part

A linearized PH solution to the Reynolds equation was obtained while neglecting side leakage. The analysis was divided into two parts—the step and ridge regions. The pressure profile across the step and ridge region of the various pads which are placed around the journal was obtained from the linearized PH Reynolds equation. Knowing the pressure, the load components and attitude angle were calculated. The resulting equations were found to be a function of the bearing parameters (the eccentricity and compressibility number) and the step parameters (ratio of the stepped clearance to the ridge clearance, ratio of the angle extended by the ridge to the angle extended by the pad, and number of pads placed around the journal). The maximum load capacity can be determined by numerically differentiating the load with respect to the step bearing parameters while finding where the slope is zero. A series of data was run while varying the bearing parameters. The attitude angle was calculated for the various cases which were run.

Empirical Treatment of Hydrodynamic Journal Bearing Performance in the Superlaminar Regime

1970 ◽  
Vol 12 (2) ◽  
pp. 116-122 ◽  
Author(s):  
H. F. Black
Keyword(s):  
Reynolds Number ◽  
Field Equation ◽  
Experimental Work ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Journal Bearing ◽  
Load Capacity ◽  
Journal Bearings ◽  
Theoretical Treatment ◽  
Hydrodynamic Journal Bearing

The application of a perturbation in terms of simple correlations for friction in turbulent Couette and ‘screw’ flows, together with a further empirical assumption consonant with the experimental work of Smith and Fuller (1), leads to a pressure field equation identical in form with the Reynolds equation. The load capacity of journal bearings throughout most of the superlaminar range may be represented by a single curve, and existing laminar solutions may be applied with the parameters modified by Reynolds number. The theory is compared with published experimental results, and with the most successful theoretical treatment (4). The correlations obtained confirm the adequacy of the theory to predict performance in the superlaminar régime.

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