Stability of the High-Speed Journal Bearing Under Steady Load: 2—The Compressible Film

1963 ◽  
Vol 85 (3) ◽  
pp. 274-279 ◽  
Author(s):  
H. S. Cheng ◽  
P. R. Trumpler
Keyword(s):  
Equilibrium Position ◽  
High Speed ◽  
Equilibrium Solution ◽  
Journal Bearing ◽  
Analog Computer ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
Linearized Equations ◽  
Stability Chart ◽  
The Stability

The governing equations for the dynamical system of a self-acting gas-lubricated journal bearing are formulated. An approximate solution for the equilibrium position of the journal center is obtained by use of Galerkin’s method. The equilibrium solution shows close agreement with the exact numerical computer solution obtained by Elrod. The stability of the equilibrium solution is investigated by solving the linearized equations on an analog computer. The solution of the set of linearized equations shows that there exists a threshold speed of instability for each equilibrium position. The value of this threshold speed is presented in a stability chart. In addition, approximate particular solutions for the nonlinear dynamical equations are obtained by use of the analog computer. The results are shown as trajectories of the journal center when it is displaced arbitrarily from the equilibrium position.

Non-Linear Dynamic Stability of Shallow Reticulated Spherical Shells

2011 ◽  
Vol 142 ◽  
pp. 107-110
Author(s):  
Ming Jun Han ◽  
You Tang Li ◽  
Ping Qiu ◽  
Xin Zhi Wang
Keyword(s):  
Three Dimensional ◽  
Dynamical Equations ◽  
Third Order ◽  
Spherical Shells ◽  
Nonlinear Dynamical ◽  
Linear Dynamic ◽  
The Third ◽  
Displacement Mode ◽  
Nonlinear Forced Vibration ◽  
The Stability

The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom. Displacement mode that meets the boundary conditions of fixed edges is given by using the method of the separate variable, A nonlinear forced vibration equation containing the second and the third order is derived by using the method of Galerkin. The stability of the equilibrium point is studied by using the Floquet exponent.

Linear stability analysis of finite hydrodynamic journal bearing under turbulent lubrication with coupled-stress fluid

2016 ◽  
Vol 68 (3) ◽  
pp. 386-391 ◽  
Author(s):  
Abhishek Ghosh ◽  
Sisir Kumar Guha
Keyword(s):  
Stability Analysis ◽  
Newtonian Fluid ◽  
High Speed ◽  
Journal Bearing ◽  
Slenderness Ratio ◽  
Linear Perturbation ◽  
Content Type ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Coupled Stress

Purpose Several researchers have observed that to satisfy modern day’s need, it is essential to enhance the characteristics of journal bearing, which is used in numerous applications. Moreover, the use of Newtonian fluid as a lubricant is diminishing day by day, and the use of Non-Newtonian fluids is coming more into picture. Furthermore, if turbo-machinery applications are taken into account, then it can be seen that journal bearings are used for high speed applications as well. Thus, neglecting turbulent conditions may lead to erroneous results. Hence, this paper aims to present focuses on studying the stability characteristics of finite hydrodynamic journal bearing under turbulent coupled-stress lubrication. Design/methodology/approach First, the governing equation relevant to the problem is generated. Then, the dynamic analysis is carried out by linear perturbation technique, leading to three perturbed equations, which are again discretized by finite difference method. Finally, these discretized equations are solved with the help of Gauss-Seidel Iteration technique with successive over relaxation scheme. Consequently, the film response coefficients and the stability parameters are evaluated at different parametric conditions. Findings It has been concluded from the study that with increase in value of the coupled-stress parameter, the stability of the journal may increase. Whereas, with increase in Reynolds number, the stability of the journal decreases. On the other hand, stability increases with increasing values of slenderness ratio. Originality/value Researches have been performed to study the dynamic characteristics of journal bearing with non-Newtonian fluid as the lubricant. But in the class of non-Newtonian lubricants, the use of coupled-stress fluid has not yet been properly investigated. So, an attempt has been made to perform the stability analysis of bearings with coupled-stress fluid as the advanced lubricant.

Dynamic stability of micropolar lubricated hydrodynamic offset-halves journal bearings

2020 ◽  
pp. 135065012093685
Author(s):  
Sanyam Sharma ◽  
Chimata M Krishna
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Critical Mass ◽  
Journal Bearings ◽  
Aspect Ratios ◽  
Input Parameters ◽  
Output Characteristics ◽  
The Stability ◽  
Offset Factor

The plain circular journal bearings are not found to be stable by researchers when used in high speed rotating machineries. Hence, extensive research in the study of stability characteristics of non-circular bearings or lobed bearings assumed importance, of late. Present article deals with the stability analysis of non-circular offset bearing by taking selected set of input and output parameters. Modified Reynolds equation for micropolar lubricated rigid journal bearing system is solved using finite element method. Two kinds of input parameters namely, offset factors (0.2, 0.4) and aspect ratios (1.6, 2.0) have been selected for the study. The important output characteristics such as load, critical mass, whirl frequency ratio, and threshold speed are computed and plotted for various set of values of input parameters. The results obtained indicate that micropolar lubricated circular offset bearing is highly stable for higher offset factor and higher aspect ratio.

Stability of the High-Speed Journal Bearing Under Steady Load: 1—The Incompressible Film

1962 ◽  
Vol 84 (3) ◽  
pp. 351-357 ◽  
Author(s):  
M. M. Reddi ◽  
P. R. Trumpler
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Orbital Motion ◽  
Hydrodynamic Force ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Static Equilibrium ◽  
The Stability ◽  
External Loads ◽  
Steady Load

The phenomenon of oil-film whirl in bearings subjected to steady external loads is analyzed. The journal, assumed to be a particle mass, is subjected to the action of two forces; namely, the external load acting on the bearing and the hydrodynamic force developed in the fluid film. The resulting equations of motion for a full-film bearing and a 180-deg partial-film bearing are developed as pairs of second-order nonlinear differential equations. In evaluating the hydrodynamic force, the contribution of the shear stress on the journal surface is found to be negligible for the full-film bearing, whereas for the partial-film bearing it is found to be significant at small attitude values. The equations of motion are linearized and the coefficients of the resulting characteristic equations are studied for the stability of the static-equilibrium positions. The full-film bearing is found to have no stable static-equilibrium position, whereas the 180-deg partial-film bearing is found to have stable static-equilibrium positions under certain parametric conditions. The equations of motion for the full-film bearing are integrated numerically on a digital computer. The results show that the journal center, depending on the parametric conditions, acquired either an orbital motion or a dynamical path of increasing attitude terminating in bearing failure.

The Influence of Internal Friction on the Stability of High Speed Rotors With Anisotropic Supports

1969 ◽  
Vol 91 (4) ◽  
pp. 1105-1113 ◽  
Author(s):  
E. J. Gunter ◽  
P. R. Trumpler
Keyword(s):  
Internal Friction ◽  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Analog Computer ◽  
Three Dimensional Model ◽  
Stiffness Properties ◽  
Stiffness Characteristics ◽  
The Stability ◽  
Internal Rotor

This paper evaluates the stability of the single mass rotor with internal friction on damped, anisotropic supports. The paper shows under what conditions the rotor stability may be improved by an undamped support with anisotropic stiffness properties. A three dimensional model is presented to show the influence of rotor and support stiffness characteristics on stability. Curves are also presented on how support damping may also improve or even reduce rotor stability. An analog computer solution of the governing equations of motion is presented showing the shaft transient motion for various speed ranges, and also plots of the rotor steady state motion are given for various speeds up to and including the stability threshold. The analysis is used to explain many of the experimental observations of B. L. Newkirk concerning stability due to internal rotor friction.

Development of Herringbon-Grooved Aerodynamic Journal Bearing Systems for Ultra-High-Speed Rotations

2015 ◽  
Vol 656-657 ◽  
pp. 652-657 ◽  
Author(s):  
Norifumi Miyanaga ◽  
Jun Tomioka
Keyword(s):  
Rotational Speed ◽  
High Speed ◽  
Journal Bearing ◽  
Damping Properties ◽  
Shaft Rotation ◽  
Ultra High Speed ◽  
The Difference ◽  
The Stability ◽  
Stiffness And Damping ◽  
Bearing System

It is absolutely important for ultra-compact rotational machineries to achieve sable shaft rotation at ultra-high-speed. This paper discussed herringbone-grooved aerodynamic journal bearing systems developed for the purpose. In this system, the bearings are supported by rubber-O-rings for accurate and stable operations. To grasp the possibility for stabilization, two types of O-rings with different stiffness and damping properties under bearing supporting were tested in the experiment. As the results, the bearing system demonstrated the maximum rotational speed over 460,000 rpm without unstable phenomenon called whirl. However, the difference in rubber O-rings definitely affected the stability of the bearing system.

A Study of the Effect of Various Recess Shapes on Hybrid Journal Bearing Using CFD and Response Surface Method

2016 ◽  
Author(s):  
Gen Fu ◽  
Alexandrina Untaroiu
Keyword(s):  
Response Surface ◽  
Equilibrium Position ◽  
High Speed ◽  
Journal Bearing ◽  
Accurate Solution ◽  
Response Surface Model ◽  
Dominant Factor ◽  
Surface Model ◽  
Cfd Model ◽  
Geometrical Shapes

Hybrid bearings are mostly used in high speed and load situations due to their better stability and loading capacity. They are typically designed with recess grooves to enhance both static and dynamic performance of the bearing. Previous theoretical studies on the influence of the recess geometrical shapes often utilize the Reynolds equation method and most of the research focuses on thrust bearings. The aims of this paper is to analytically study the influence of various recess geometrical shapes on hybrid journal bearings. A 3-D CFD model of a hybrid journal bearing is built and a new method of response surface model is employed to determine the equilibrium position of the rotor. Based the response surface model, an optimization scheme is used to search around the equilibrium position to get a more accurate solution. The current analysis includes the recess geometry of rectangular, circular, triangular, elliptical and annular shapes. All these different shapes are studied assuming the same operating and loading conditions and bearing static properties are used as the indices of the bearing performance. The flow rate, fluid film thickness and recess flow pattern are analyzed for various recess shapes. The CFD model for the baseline bearing is validated against experimental data. The results show that the response surface model method is fast and robust in determining the rotor equilibrium position even though a 3-D CFD model is utilized. The results suggest that recess shape is a dominant factor in hybrid bearing design. This study proposed a new design process for a 3-D CFD bearing model with the ability of calculating equilibrium position and is expected to be useful to bearing designers.

Effects of Synchronous Vibration of Bearing on Stability of Externally Pressurized Air Journal Bearings

1999 ◽  
Vol 121 (4) ◽  
pp. 830-835 ◽  
Author(s):  
Jeong-Bae Lee ◽  
Kyung-Woong Kim
Keyword(s):  
Steady State ◽  
Phase Difference ◽  
High Speed ◽  
Control Algorithm ◽  
Journal Bearing ◽  
Stability Limit ◽  
Air Bearing ◽  
Synchronous Motion ◽  
Maximum Stability ◽  
The Stability

An active control of bearing is proposed as a new method to improve the stability characteristics of the externally pressurized air journal bearing and the results of numerical investigations of the stability characteristics of the actively controlled air journal bearing are presented. The synchronous control, where the bearing center whirls with the same frequency as the journal center with respect to the position in the steady state, is proposed as a control algorithm of the active air bearing. The step jump method is used to calculate the locus of the journal center which whirls or vibrates relative to the whirling bearing. The stability characteristics of the high speed rotor supported by actively controlled bearing system for zero steady-state eccentricity are investigated for various phase difference between the bearing and journal. It is shown that the stability of the air bearing can be greatly increased by the controlled synchronous motion of the bearing, and there is an optimum phase difference, which gives the maximum stability limit of the system.

Stability Boundaries of High-Speed Milling Corresponding to Period Doubling Are Essentially Closed Curves

Manufacturing ◽  
2003 ◽  
Author(s):  
Ro´bert Szalai ◽  
Ga´bor Ste´pa´n
Keyword(s):  
Characteristic Function ◽  
High Speed ◽  
Period Doubling ◽  
Stability Boundaries ◽  
Closed Curves ◽  
High Speed Milling ◽  
Complex Roots ◽  
Stability Chart ◽  
The Stability ◽  
Special Case

In this paper a new method for the stability analysis of high-speed milling processes is introduced. The approach is based on the construction of a characteristic function whose complex roots determine the stability of the system. By using the argument principle, the number of roots causing instability can be counted, and thus, an exact stability chart can be drawn. In the special case of period doubling bifurcation, the corresponding multiplier −1 is substituted into the characteristic function leading to an implicit formula of the stability boundaries. Further investigations show that all the period doubling boundaries are closed curves, except the first lobe at the highest cutting speeds. Together with the stability boundaries of Neimark-Sacker (or secondary Hopf) bifurcations, the unstable parameter domains are formed from the union of lobes and lenses.

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