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.

Optimization of Journal Bearing Profile for Higher Dynamic Stability Limits

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Rodrigo Nicoletti
Keyword(s):  
Journal Bearing ◽  
Optimization Procedure ◽  
Control Points ◽  
Time Domain Simulation ◽  
Rotating System ◽  
Stability Margins ◽  
Dynamic Coefficients ◽  
The Stability ◽  
Stability Limits ◽  
Improve Stability

This work presents an optimization procedure to find bearing profiles that improve stability margins of rotor-bearing systems. The profile is defined by control points and cubic splines. Stability margins are estimated using bearing dynamic coefficients, and obtained solutions are analyzed as a function of the number of control points and of the Sommerfeld number at optimization. Results show the feasibility of finding shapes for the bearing that significantly improve the stability margins. Some of the obtained solutions overcome the stability margins of conventional bearings, such as the journal bearing and preloaded bearings with 0.5 and 0.67 preload. A time domain simulation of a flexible shaft rotating system supported by such bearings corroborates the results.

Dynamic analysis of water-lubricated motorized spindle considering tilting effect of thrust bearing

2016 ◽  
Vol 231 (20) ◽  
pp. 3780-3790 ◽  
Author(s):  
Huihui Feng ◽  
Shuyun Jiang
Keyword(s):  
Reynolds Equation ◽  
Thrust Bearing ◽  
Dynamic Performance ◽  
Large Diameter ◽  
Machining Process ◽  
Motorized Spindle ◽  
Thrust Bearings ◽  
Dynamic Coefficients ◽  
Key Issues ◽  
Dynamic Performances

The dynamic modeling for the rotor with large diameter thrust bearings is one of the key issues in the design and operation of water-lubricated motorized spindle. In the machining process, the spindle not only translates along the x, y, z directions, but also tilts about the x and y axes under the cutting forces. As a result, the tilting effect of the thrust bearing on the dynamic performances of the motorized spindle should be considered. A five degree-of-freedom dynamic model for the spindle is established based on the Newton’s Laws and the principle of Angular Momentum. The translational and tilting dynamic coefficients for both the journal and thrust water-lubricated bearings were obtained by using Reynolds equation. The computed results show that the tilting effect of the thrust bearing on the dynamic performance of the motorized spindle should be considered when a large diameter thrust bearing is employed.

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.

Derivation of Hydrodynamic Bearing Coefficients Using the Minimum Square Method

1997 ◽  
Vol 119 (4) ◽  
pp. 802-807 ◽  
Author(s):  
Carmen M. Mu¨ller-Karger ◽  
Andre´s L. Granados
Keyword(s):  
Transient Response ◽  
Equilibrium Position ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Linear Analysis ◽  
Frequency Domain Method ◽  
Transient Solution ◽  
Nonlinear Simulation ◽  
Hydrodynamic Bearing ◽  
Dynamic Coefficients

A linear analysis of the parameters for the orbital transient response of journal-bearing systems is made with the purpose of computing the bearing dynamic coefficients using the minimum square method. The journal-bearing response is obtained from a nonlinear simulation that includes a transient solution of the Reynolds equation. The minimum square method permits the adjustment of coefficients with only one orbit and does not need prior linearization of the response. Therefore it was found to be advantageous compared with the more traditional experimental method of using a frequency domain method with two orbital responses. Three different Sommerfeld numbers were analyzed. Comparisons between the eight adjusted coefficients and the linear coefficients obtained from perturbations of the Reynolds equation about the equilibrium position permit the establishment of the ranges where the bearings behave linearly.

scholarly journals Run-Up Simulation of a Semi-Floating Ring Supported Turbocharger Rotor Considering Thrust Bearing and Mass-Conserving Cavitation

Lubricants ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 44
Author(s):  
Christian Ziese ◽  
Cornelius Irmscher ◽  
Steffen Nitzschke ◽  
Christian Daniel ◽  
Elmar Woschke
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Thrust Bearing ◽  
Three Dimensional ◽  
Reliable Prediction ◽  
Two Phase ◽  
Hydrodynamic Bearings ◽  
Thrust Bearings ◽  
Run Up ◽  
The Impact

The vibration behaviour of turbocharger rotors is influenced by the acting loads as well as by the type and arrangement of the hydrodynamic bearings and their operating condition. Due to the highly non-linear bearing behaviour, lubricant film-induced excitations can occur, which lead to sub-synchronous rotor vibrations. A significant impact on the oscillation behaviour is attributed to the pressure distribution in the hydrodynamic bearings, which is influenced by the thermo-hydrodynamic conditions and the occurrence of outgassing processes. This contribution investigates the vibration behaviour of a floating ring supported turbocharger rotor. For detailed modelling of the bearings, the Reynolds equation with mass-conserving cavitation, the three-dimensional energy equation and the heat conduction equation are solved. To examine the impact of outgassing processes and thrust bearing on the occurrence of sub-synchronous rotor vibrations separately, a variation of the bearing model is made. This includes run-up simulations considering or neglecting thrust bearings and two-phase flow in the lubrication gap. It is shown that, for a reliable prediction of sub-synchronous vibrations, both the modelling of outgassing processes in hydrodynamic bearings and the consideration of thrust bearing are necessary.

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

Dynamic Instability in Quartering Seas—Part III: Nonlinear Effects on Periodic Motions

1997 ◽  
Vol 41 (03) ◽  
pp. 210-223 ◽  
Author(s):  
K. J. Spyrou
Keyword(s):  
Periodic Motion ◽  
Horizontal Plane ◽  
Dynamic Instability ◽  
Parametric Instability ◽  
Nonlinear Effects ◽  
Ship Motions ◽  
Nonlinear Phenomena ◽  
Specific Sequence ◽  
The Stability ◽  
Two Stages

The loss of stability of the horizontal-plane periodic motion of a steered ship in waves is investigated. In earlier reports we referred to the possibility of a broaching mechanism that will be intrinsic to the periodic mode, whereby there will exist no need for the ship to go through the surf-riding stage. However, about this point the discussion was essentially conjectural. In order to provide substance we present here a theoretical approach that is organized in two stages: Initially, we demonstrate the existence of a mechanism of parametric instability of yaw on the basis of a rudimentary, single-degree model of maneuvering motion in waves. Then, with a more elaborate model, we identify the underlying nonlinear phenomena that govern the large-amplitude horizontal ship motions, considering the ship as a multi-degree, nonlinear oscillator. Our analysis brings to light a very specific sequence of phenomena leading to cumulative broaching that involves a change in the stability of the ordinary periodic motion on the horizontal plane, a transition towards subharmonic response and, ultimately, a sudden jump to resonance. Possible means for controlling the onset of such undesirable behavior are also investigated.

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.

A Theoretical Analysis of Floating Bush Journal Bearing With Axial Oil Film Rupture Being Considered

2002 ◽  
Vol 124 (3) ◽  
pp. 494-505 ◽  
Author(s):  
Kiyoshi Hatakenaka ◽  
Masato Tanaka ◽  
Kenji Suzuki
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Speed Ratio ◽  
Shaft Speed ◽  
Film Rupture ◽  
State Behavior ◽  
Oil Film ◽  
Rotordynamic Coefficients ◽  
The Stability ◽  
Very High

A new modified Reynolds equation is derived with centrifugal force acting on the hydrodynamic oil film being considered. This equation, together with a cavitation model, is used to obtain the steady-state equilibrium and calculate the rotordynamic coefficients of lightly loaded floating bush journal bearings operating at very high shaft speeds. The bush-to-shaft speed ratio and the linear cross-coupling spring coefficients of the inner oil film is found to decrease with the increase in shaft speed as the axial oil film rupture develops in the inner oil film. The present model can give reasonable explanation to the steady-state behavior and the stability behavior of the bearing observed in actual machines.

Stability Analysis of a Hydrodynamic Journal Bearing With Rotating Herringbone Grooves

2003 ◽  
Vol 125 (2) ◽  
pp. 291-300 ◽  
Author(s):  
G. H. Jang ◽  
J. W. Yoon
Keyword(s):  
Journal Bearing ◽  
Equations Of Motion ◽  
Fourier Series Expansion ◽  
Algebraic Equations ◽  
High Rotational Speed ◽  
Dynamic Coefficients ◽  
Stiffness Coefficients ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Herringbone Grooves

This paper presents an analytical method to investigate the stability of a hydrodynamic journal bearing with rotating herringbone grooves. The dynamic coefficients of the hydrodynamic journal bearing are calculated using the FEM and the perturbation method. The linear equations of motion can be represented as a parametrically excited system because the dynamic coefficients have time-varying components due to the rotating grooves, even in the steady state. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill’s infinite determinant of these algebraic equations. The validity of this research is proved by the comparison of the stability chart with the time response of the whirl radius obtained from the equations of motion. This research shows that the instability of the hydrodynamic journal bearing with rotating herringbone grooves increases with increasing eccentricity and with decreasing groove number, which play the major roles in increasing the average and variation of stiffness coefficients, respectively. It also shows that a high rotational speed is another source of instability by increasing the stiffness coefficients without changing the damping coefficients.

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