Roughness Effects on the Dynamic Coefficients of Ultra-Thin Gas Film in Magnetic Recording

1996 ◽  
Vol 118 (4) ◽  
pp. 774-782 ◽  
Author(s):  
Wang-Long Li ◽  
Cheng-I Weng ◽  
Chi-Chuan Hwang
Keyword(s):  
Knudsen Number ◽  
Surface Characteristics ◽  
Mean Free Path ◽  
Roughness Effects ◽  
Roughness Effect ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Induced Flow ◽  
Bearing Number ◽  
Stiffness And Damping

The stiffness and damping coefficients of a slider gas bearing operating under arbitrary Knudsen number are calculated. A perfect gas is used as the lubricant, and its behavior is described by the modified average Reynolds equation proposed by Makino et al. (1993). The effects of molecular mean free-path on the roughness-induced flow factors are included. The effects of the nondimensional film thickness, Hs0, the surface characteristics, (γ1, γ2). the inverse Knudsen number, D0, the nondimensional frequency, Ω, and the modified bearing number, Λb, on the dynamic coefficients are discussed in this paper. As expected, the values of dynamic coefficients for various roughness orientations approach the smooth value as the ratio, Hs0, becomes greater and greater, and thus the roughness effect is getting smaller and smaller. The air film of two-sided longitudinal oriented roughness is stiffer than the other two-sided oriented cases. The effect on translational damping coefficients for various two-sided oriented roughnesses is reversed as D0 greater than some value, and this value is affected significantly by Λb. Transversely rough stationary case has the lowest critical value of Λb, at which the negative translational damping appears. The results show that the roughness effect and rarefaction effect on dynamic coefficients are significant, and they cannot be ignored for stability analysis.

Study of dynamic coefficients of water film in marine stern tube bearing considering roughness and deformation

2021 ◽  
Vol 235 (11) ◽  
pp. 2257-2271
Author(s):  
Zijun Leng ◽  
Fangrui Lv ◽  
Jianbo Zhang ◽  
Chunxiao Jiao ◽  
Gengyuan Gao ◽  
...  
Keyword(s):  
Dynamic Analysis ◽  
Water Film ◽  
Misalignment Angle ◽  
The Finite Element Method ◽  
Analysis Model ◽  
Roughness Effects ◽  
Roughness Effect ◽  
Dynamic Coefficients ◽  
Minimum Film Thickness ◽  
First Time

Dynamic analysis of water-lubricated marine stern tube bearing is incompatible with that of ordinary oil-lubricated bearing due to the deformation of compliant bushes and non-negligible roughness effects. A modified bearing dynamic analysis model embracing roughness and dynamic characteristics of a non-metal bush is proposed. Based on the model, Reynolds equations of perturbed pressures of water film considering roughness, deformation, and misalignment simultaneously are derived for the first time and solved by coupling the finite difference method and the finite-element method. The results show that dynamic coefficients are enhanced due to roughness when the minimum film thickness ratio exceeds a threshold around 2. The roughness effect is debilitated but the valid range of roughness is extended when bush deformation is considered. Additionally, dynamic coefficients of rougher bearing become obviously smaller than those of smoother bearing as the misalignment angle grows.

scholarly journals Alternation of the dynamic coefficients of short journal bearings due to wear

2015 ◽  
Vol 6 (5) ◽  
pp. 649-664
Author(s):  
Michael G. Papanikolaou ◽  
Michael G. Farmakopoulos ◽  
Chris A. Papadopoulos
Keyword(s):  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Fe Analysis ◽  
Operating Conditions ◽  
Wear Depth ◽  
Content Type ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Low Viscosity ◽  
Stiffness And Damping

Purpose – Wear in journal bearings occurs when the operating conditions (high load, high temperature, low angular velocity or low viscosity), downgrade the ability of the bearing to carry load. The wear depth increases because the rotor comes in contact with the bearing surface. Wear in journal bearings affects their characteristics because of its influence on the thickness of the fluid film. This influence can be detected in the dynamic behavior of the rotor and especially in the dynamic stiffness and damping coefficients. The paper aims to discuss these issues. Design/methodology/approach – In this paper, the effect of wear on the rotor dynamic stiffness and damping coefficients (K and C) of a short journal bearing is investigated. K and C in this work are estimated by using two methods a semi-analytical method and finite element (FE) analysis implemented in the ANSYS software. Findings – The main goal of this research is to make the identification of wear in journal bearings feasible by observing the alternation of their dynamic coefficients. Both of the methods implemented are proven to be useful, while FE analysis can provide more accurate results. Originality/value – This paper is original and has not been published elsewhere.

scholarly journals A Nonlinear Model for Prediction of Dynamic Coefficients in a Hydrodynamic Journal Bearing

2004 ◽  
Vol 10 (6) ◽  
pp. 507-513 ◽  
Author(s):  
Jerzy T. Sawicki ◽  
T. V. V. L. N. Rao
Keyword(s):  
Equilibrium Position ◽  
Nonlinear Dynamic ◽  
Static Pressure ◽  
Journal Bearing ◽  
Dynamic Pressure ◽  
Higher Order ◽  
Pressure Gradients ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Stiffness And Damping

This paper investigates the variation of nonlinear stiffness and damping coefficients in a journal orbit with respect to equilibrium position. The journal orbit is obtained by the combined solution of equations of motion and Reynolds equation. In the linearized dynamic analysis, dynamic pressure is written as a perturbation of static pressure and pressure gradients at equilibrium position. However, in order to obtain nonlinear dynamic coefficients about equilibrium position, the dynamic pressure gradients in the orbit are also written as the first order perturbation of static pressure gradients and higher order pressure gradients for displacement and velocity perturbations. The dynamic coefficients are functions of bearing displacement and velocity perturbations. The higher order pressure gradients at equilibrium position are evaluated at various eccentricity ratios and L/D ratios of 0.5 and 1.0. The variation of nonlinear dynamic coefficients is analyzed for three Sommerfeld numbers of a two-axial groove journal bearing under the action of an external synchronous load along and perpendicular to the radial journal load. Results indicate that the oil film nonlinearities affect the journal motion at lower eccentricity ratios (higher Sommerfeld numbers) with wide variation in stiffness and damping coefficients.

Dynamic Coefficients of Axial Spline Couplings in High-Speed Rotating Machinery

1994 ◽  
Vol 116 (3) ◽  
pp. 250-256 ◽  
Author(s):  
C. P. Roger Ku ◽  
J. F. Walton ◽  
J. W. Lund
Keyword(s):  
High Speed ◽  
Experimental Measurements ◽  
Viscous Damping ◽  
Bending Moments ◽  
Equivalent Viscous Damping ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Test Conditions ◽  
Spline Coupling ◽  
Stiffness And Damping

This paper provided the first opportunity to quantify the angular stiffness and equivalent viscous damping coefficients of an axial spline coupling used in highspeed turbomachinery. The bending moments and angular deflections transmitted across an axial spline coupling were measured while a nonrotating shaft was excited by an external shaker. A rotordynamics computer program was used to simulate the test conditions and to correlate the angular stiffness and damping coefficients. The effects of external force and frequency were also investigated. The angular stiffness and damping coefficients were used to perform a linear steady-state rotordynamics stability analysis, and the unstable natural frequency was calculated and compared to the experimental measurements.

scholarly journals Fluid Film Dynamic Coefficients in Mechanical Face Seals

1983 ◽  
Vol 105 (2) ◽  
pp. 297-302 ◽  
Author(s):  
I. Green ◽  
I. Etsion
Keyword(s):  
Small Perturbation ◽  
Equilibrium Position ◽  
Degrees Of Freedom ◽  
Fluid Film ◽  
Seal Ring ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Face Seals ◽  
Stiffness And Damping ◽  
Analytical Expressions

The stiffness and damping coefficients of the fluid film in mechanical face seals are calculated for the three major degrees of freedom of the primary seal ring. The calculation is based on small perturbation of the ring from its equilibrium position. Analytical expressions are presented for the various coefficients and a comparison is made with results of accurate but more complex analyses to establish the range of applicability.

Application of Average Flow Model to Thin Film Gas Lubrication

1993 ◽  
Vol 115 (1) ◽  
pp. 185-190 ◽  
Author(s):  
T. Makino ◽  
S. Morohoshi ◽  
S. Taniguchi
Keyword(s):  
Thin Film ◽  
Film Thickness ◽  
Mean Free Path ◽  
Perturbation Approach ◽  
Roughness Effects ◽  
Load Carrying ◽  
Gas Lubrication ◽  
Induced Flow ◽  
Average Film Thickness ◽  
Average Flow Model

The flow factors for the average Reynolds equation introduced by Patir and Cheng (1978, 1979) are extended to be valid for thin film gas lubrication. The effects of molecular mean free-path on the roughness-induced flow factors are included on the assumption that the local compressibility is small. The derivation of flow factors is carried out by means of the perturbation approach developed by Tripp (1983). The results are expressed in terms of Knudsen number, Peklenik parameter and nondimensional film thickness defined as the ratio of average film thickness and standard deviation of composite roughness. Two-dimensional roughness effects on the load-carrying capacity of a gas lubricated finite slider are also investigated.

scholarly journals The Experimental Identification of the Dynamic Coefficients of two Hydrodynamic Journal Bearings Operating at Constant Rotational Speed and Under Nonlinear Conditions

2017 ◽  
Vol 24 (4) ◽  
pp. 108-115 ◽  
Author(s):  
Łukasz Breńkacz
Keyword(s):  
Least Squares Method ◽  
Propulsion Systems ◽  
Hydrodynamic Bearings ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Experimental Identification ◽  
Research Procedure ◽  
Stiffness And Damping ◽  
Rotor Mass

AbstractHydrodynamic bearings are commonly used in ship propulsion systems. Typically, they are calculated using numerical or experimental methods. This paper presents an experimental study through which it has been possible to estimate 24 dynamic coefficients of two hydrodynamic slide bearings operating under nonlinear conditions. During the investigation, bearing mass coefficients are identified by means of a newly developed algorithm. An impact hammer was used to excite vibration of the shaft. The approximation by means of the least squares method was applied to determine bearing dynamic coefficients. Based on the performed research, the four (i.e. two main and two crosscoupled) coefficients of stiffness, damping and mass for each bearing were obtained. The mass coefficients add up to the complex shaft weight. These values are not required for modeling dynamics of the machine because the rotor mass is usually known, however, they may serve as a good indicator to validate the correctness of the stiffness and damping coefficients determined. Additionally, the experimental research procedure was described. The signals of displacements in the bearings and the excitation forces used for determination of the bearing dynamic coefficients were shown. The study discussed in this article is about a rotor supported by two hydrodynamic bearings operating in a nonlinear manner. On the basis of computations, the results of bearing dynamic coefficients were presented for a selected speed.

The Effect of Thermal Distortion on the Characteristics of Large Hydrodynamic Bearings

1988 ◽  
Vol 202 (3) ◽  
pp. 219-225 ◽  
Author(s):  
P G Morton ◽  
J H Johnson ◽  
G D Wale
Keyword(s):  
Experimental Investigation ◽  
Steady State ◽  
Journal Bearing ◽  
Thermal Distortion ◽  
Hydrodynamic Bearings ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Oil Whirl ◽  
Stabilizing Effect ◽  
Stiffness And Damping

An experimental investigation has been carried out on a 350 mm partial arc journal bearing to determine the steady state characteristics and the stiffness and damping coefficients. The bearing was found to distort due to thermal influences and the pressure distribution and dynamic coefficients consequently differed markedly from those obtained using standard theoretical techniques. Calculations of the speed at which resonant oil whirl develops in a rotor supported by bearings of this type show that the threshold speed is far higher using experimental coefficients than theoretical coefficients. It is concluded that thermal distortion has a significant stabilizing effect on large hydrodynamic bearings.

Numerical Analysis on Dynamic Coefficients of Self-Acting Gas-Lubricated Tilting-Pad Journal Bearings

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Yang Lihua ◽  
Qi Shemiao ◽  
Yu Lie
Keyword(s):  
Dynamic Stiffness ◽  
Cross Coupling ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Coupling Stiffness ◽  
Perturbation Frequency ◽  
Stiffness And Damping ◽  
Gas Bearing

Although gas-lubricated tilting-pad bearings are widely used in high-speed turbomachinery, the theoretical prediction of the dynamic characteristics of tilting-pad gas bearings is also a very difficult problem because of its structural complexity. Several approaches have been proposed to solve this problem such as the pad assembly method and the small perturbation method. A numerical method by combining the partial derivative method with the equivalent coefficient method is presented in this paper to evaluate the dynamic stiffness and damping coefficients of self-acting tilting-pad gas bearing. The dynamic coefficients with the pads fixed and with the pads perturbation are, respectively, obtained for a typical self-acting tilting-pad gas bearing by using the proposed method to mainly explain the dependency of the bearing dynamic coefficients on the perturbation frequency. For bearings with the pads perturbation, the cross-coupling stiffness and damping coefficients are almost negligible compared with the direct ones. At lower perturbation frequency, the stiffness coefficients increase, while the damping coefficients decrease with an increasing frequency. The higher perturbation frequencies have very little effects on the bearing dynamic coefficients. Dynamic stiffness coefficients approach to the constant and damping coefficients to zero. However, with the pads fixed, in a low range of frequency, the absolute values of cross-coupling stiffness coefficients decrease with frequency. Furthermore, the cross-coupling coefficients are not negligible compared with the direct ones. In addition, the effects of pad inertia on dynamic coefficients are studied and compared with the results of pad inertia neglected.

Calculation of Stiffness and Damping Coefficients for Elastically Supported Gas Foil Bearings

1993 ◽  
Vol 115 (1) ◽  
pp. 20-27 ◽  
Author(s):  
J.-P. Peng ◽  
M. Carpino
Keyword(s):  
Reynolds Equation ◽  
Structural Model ◽  
Structural Equations ◽  
Perfect Gas ◽  
Foil Bearings ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Foil Bearing ◽  
Stiffness And Damping ◽  
Elastically Supported

The stiffness and damping coefficients of an elastically supported gas foil bearing are calculated. A perfect gas is used as the lubricant, and its behavior is described by the Reynolds equation. The structural model consists only of an elastic foundation. The fluid equations and the structural equations are coupled. A perturbation method is used to obtain the linearized dynamic coefficient equations. A finite difference formulation has been developed to solve for the four stiffness and the four damping coefficients. The effect of the bearing compliance on the dynamic coefficients is discussed in this paper.

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