scholarly journals Stability Analysis of an Externally Pressurized Gas-Lubricated Porous Thrust Bearing

1973 ◽  
Vol 95 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Dah-Chen Sun
Keyword(s):  
Stability Analysis ◽  
Thrust Bearing ◽  
Film Flow ◽  
Light Weight ◽  
Symmetric Mode ◽  
Axially Symmetric ◽  
Thin Film Flow ◽  
Pneumatic Hammer ◽  
Supply Pressure ◽  
The Stability

A linear stability analysis is carried out for a porous thrust bearing considering only the axially symmetric mode of oscillation. It is found that the stability characteristics of the bearing are determined by three competing mechanisms, namely, the compressibility of the lubricant, the mass of the bearing, and the viscous resistance to the thin film flow. To avoid pneumatic hammer, the bearing should be designed to be light weight and to operate at the smallest possible film thickness and supply pressure.

Characteristics evaluation of gas film in the aerostatic thrust bearing within rarefied effect

2016 ◽  
Vol 231 (2) ◽  
pp. 149-157 ◽  
Author(s):  
Dongju Chen ◽  
Shuai Zhou ◽  
Jihong Han ◽  
Jinwei Fan ◽  
Qiang Cheng
Keyword(s):  
Machine Tool ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Film Flow ◽  
Machining Accuracy ◽  
Aerostatic Bearing ◽  
Supply Pressure ◽  
Slip Regime ◽  
Key Factor ◽  
Gas Supply

The characteristic of gas film is a key factor in the performance of the aerostatic bearing. Because the gas film flow is in the slip regime, influence of the rarefied effect is significant. The modified Reynolds equation suitable for compressible gas in the rarefied effect is deduced through introducing the flow factor in the rarefied effect to the Reynolds equation. Pressure distribution, capacity, and stiffness of the gas film under the rarefied effect are analyzed. With the increase of gas pressure, the gas film capacity and stiffness of bearing would also increase. However, the greater the gas supply pressure, the more intense the gas film vibration, so it was important to select a reasonable gas supply pressure for achieving the optimal gas film characteristic. Finally, the gas rarefied effect is verified by the experiment indirectly, which agreed well with the analytical results and provided a theoretical guidance for the machining accuracy of the machine tool.

scholarly journals An Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lee Ken Yap ◽  
Fudziah Ismail ◽  
Norazak Senu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Film Flow ◽  
Direct Solution ◽  
Thin Film Flow ◽  
Block Method ◽  
Third Order ◽  
Block Form ◽  
The Stability

The block hybrid collocation method with two off-step points is proposed for the direct solution of general third order ordinary differential equations. Both the main and additional methods are derived via interpolation and collocation of the basic polynomial. These methods are applied in block form to provide the approximation at five points concurrently. The stability properties of the block method are investigated. Some numerical examples are tested to illustrate the efficiency of the method. The block hybrid collocation method is also implemented to solve the nonlinear Genesio equation and the problem in thin film flow.

Stability analysis of thin film flow along a heated porous wall

2009 ◽  
Vol 21 (1) ◽  
pp. 014103 ◽  
Author(s):  
Uwe Thiele ◽  
Benoît Goyeau ◽  
Manuel G. Velarde
Keyword(s):  
Thin Film ◽  
Stability Analysis ◽  
Film Flow ◽  
Porous Wall ◽  
Thin Film Flow

Stability of Gas-Lubricated, Externally Pressurized Porous Journal Bearings

1975 ◽  
Vol 97 (3) ◽  
pp. 494-505 ◽  
Author(s):  
Dah-chen Sun
Keyword(s):  
Approximate Solution ◽  
Linear Theory ◽  
Frequency Ratio ◽  
Stability Problem ◽  
Journal Bearings ◽  
Eccentricity Ratio ◽  
Pneumatic Hammer ◽  
Stability Parameters ◽  
Supply Pressure ◽  
The Stability

A linear theory of hybrid instability, due to a combination of both whirl and pneumatic hammer, in gas-lubricated porous journal bearings is presented. An approximate solution to the stability problem is obtained by the use of a Galerkin expansion. Results are presented in terms of the variation of stability parameters, such as the threshold mass, the whirl frequency ratio, etc., with the compressibility number and eccentricity ratio. In addition, the effects of permeability, supply pressure, and bearing length are investigated.

Stability Analysis of A Thin Micropolar Fluid Flowing on A Rotating Circular Disk

2011 ◽  
Vol 27 (1) ◽  
pp. 95-105 ◽  
Author(s):  
C. K. Chen ◽  
M. C. Lin ◽  
C. I. Chen
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Micropolar Fluid ◽  
Film Flow ◽  
Multiple Scales ◽  
Landau Equation ◽  
Kinematic Model ◽  
Circular Disk ◽  
Necessary Condition ◽  
Thin Film Flow

ABSTRACTThe stability analysis of a thin micropolar fluid flowing on a rotating circular disk is investigated numerically. The target is restricted to some neighborhood of critical value in the linear stability analysis. First, a generalized nonlinear kinematic model is derived by the long wave perturbation method. The method of normal mode is applied to the linear stability. After the weakly nonlinear dynamics of a film flow is studied by using the method of multiple scales, the Ginzburg-Landau equation is determined to discuss the necessary condition in terms of the various states of subcritical stability, subcritical instability, supercritical stability, and supercritical explosion for the existence of such flow pattern. The modeling results indicate that the rotation number and the radius of circular disk play the significant roles in destabilizing the flow. Furthermore, the micropolar parameter K serves as the stabilizing factor in the thin film flow.

Pneumatic stability analysis of single-pad aerostatic thrust bearing with pocketed orifice

2019 ◽  
Vol 234 (12) ◽  
pp. 1857-1866
Author(s):  
Yueqing Zheng ◽  
Guangwei Yang ◽  
Hailong Cui ◽  
Yu Hou
Keyword(s):  
Stability Analysis ◽  
Film Thickness ◽  
Thrust Bearing ◽  
Pressure Change ◽  
Volume Effect ◽  
Aerostatic Bearing ◽  
Pneumatic Hammer ◽  
Delay Effect ◽  
Bearing Force ◽  
Negative Damping

The pneumatic hammer phenomenon and pneumatic stability of a single-pad aerostatic thrust bearing with pocked orifice were investigated numerically. A time-dependent dynamic model for pneumatic stability analysis of the bearing was established with taking the pocket volume and the mass flow difference between the pocket inlet and outlet into account. The numerical prediction indicates that the delay effect is an important reason for the pneumatic hammer phenomenon. With considering the delay effect, an in-depth explanation for the pneumatic hammer phenomenon is proposed in this paper. The air compressibility combined with the volume effect in the aerostatic bearing could lead to the delay of pocket pressure change, then resulting in the delay of bearing force change at larger film thickness region. The delay of the bearing force change at larger film thickness region causes the bearing damping to become negative at larger film thickness. The negative damping provides some energy into the aerostatic bearing system at larger film thickness and maintains vibration, which leads to the pneumatic hammer phenomenon.

A Study of the Stability of an Externally-Pressurized Gas-Lubricated Thrust Bearing With a Flexible Damped Support

1978 ◽  
Vol 100 (3) ◽  
pp. 364-368 ◽  
Author(s):  
D. A. Boffey
Keyword(s):  
Feasibility Study ◽  
Equilibrium Position ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Dynamic Instability ◽  
Pneumatic Hammer ◽  
Gas Bearings ◽  
Dynamic Coefficients ◽  
The Stability ◽  
Improve Stability

Externally-pressurized gas bearings are prone to a dynamic instability known as pneumatic hammer. This paper examines the possibility of using a flexible damped bearing support to suppress the instability. A circular thrust bearing having a central feed hole and pocket is employed in the feasibility study. The linearized gas film dynamic coefficients are derived using an adaptation of an existing solution to Reynolds equation for a long rectangular bearing. Only stability of the equilibrium position is considered. Results obtained for a support having a stiffness comparable to the stiffness of the gas film show that damping in the support can substantially improve stability.

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