Turborotor Instability: Effect of Initial Transients on Plane Motion

1969 ◽  
Vol 91 (4) ◽  
pp. 625-630 ◽  
Author(s):  
R. H. Badgley ◽  
J. F. Booker
Keyword(s):  
Reynolds Equation ◽  
Approximate Solutions ◽  
Initial Position ◽  
Plane Motion ◽  
Journal Bearings ◽  
Rigid Body Dynamics ◽  
Fluid Film ◽  
Body Dynamics ◽  
Instability Effect ◽  
Static Eccentricity

The rigid-body dynamics of rotors supported in plain, cylindrical, cavitated, fluid-film journal bearings are investigated numerically by Runge-Kutta extrapolation techniques. Expressions for journal force due to the fluid-film are developed for the short-bearing (Ocvirk), long-bearing (Sommerfeld), and finite-length-bearing (Warner) approximate solutions to the Reynolds equation. Stability of plane motion is investigated for each solution under the assumption of light initial impact. The long-bearing solution appears to be most conservative (that is, it predicts the onset of instability at lower angular velocity ratios than the other solutions) for static eccentricity ratios between 0 and 0.5, while the finite-bearing solution, with bearing length-to-diameter ratio L/D equal to 1, appears most conservative at higher static eccentricity ratios. Variations in L/D between 0.5 and 2.0 appear not to affect journal path shapes appreciably. Variations in initial journal center velocity are found to be important, at least with the short-bearing solution: large initial velocities are observed to produce instability for certain parameter combinations which are stable under small initial position or velocity disturbances. In all cases investigated, instability is not observed above static eccentricity ratios of 0.83.

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.

On the Translatory Whirl Motion of a Vertical Rotor in Plain Cylindrical Gas-Dynamic Journal Bearings

1962 ◽  
Vol 84 (1) ◽  
pp. 152-158 ◽  
Author(s):  
C. H. T. Pan ◽  
B. Sternlicht
Keyword(s):  
Time Dependence ◽  
Reynolds Equation ◽  
Angular Speed ◽  
Journal Bearings ◽  
Fluid Film ◽  
Clearance Ratio ◽  
Gas Dynamic ◽  
Vertical Rotor ◽  
Attitude Angle ◽  
Small Clearance

For the theoretical prediction of the dynamical characteristics of a rotor system, it is necessary to have an accurate knowledge of the bearing fluid film forces under dynamical conditions. With a small clearance ratio and at a moderate speed, the motion of the lubricant is governed by the generalized Reynolds equation. If the lubricant is a gaseous medium, the Reynolds equation is complicated by the compressibility effects, which include nonlinearity and time-dependence under dynamic conditions [1]. In the case of a vertical rotor operating in plain cylindrical journal bearings, the steady whirl approximation is appropriate and time-dependence in the Reynolds equation can be removed by a co-ordinate transformation. The form of the transformed equation is identical to the static Reynolds equation except that the compressibility number is modified by a factor which depends on the angular speed of the whirl motion [2, 3]. The altitude angle, in the presence of the whirling motion, is quite different from the static attitude angle. On the other hand, the magnitudes of the forces are not very different. The steady whirl analysis may be used to determine the synchronous whirl motion of an unbalanced rotor. The phase angle between the fluid film force and the maximum film thickness plane is the complement of the attitude angle according to the quasi-static analysis. Experimental data are in excellent agreement with the results of the steady whirl analysis. Also, the modified compressibility number is reduced to zero at half-frequency whirl, and the Reynolds equation, for an isothermal gaseous film with the small eccentricity ratio approximation, becomes identical to that of the liquid film. Since it has been established that the threshold of half-frequency whirl for vertical rotors operating in plain cylindrical journal bearings is at zero speed in [4], the same conclusion applies to the corresponding gas-dynamic bearing.

Temporal and Convective Inertia Effects in Plain Journal Bearings With Eccentricity, Velocity and Acceleration

2011 ◽  
Author(s):  
Saeid Dousti ◽  
Jianming Cao ◽  
Amir Younan ◽  
Paul Allaire ◽  
Tim Dimond
Keyword(s):  
Reynolds Number ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Navier Stokes ◽  
Inertia Effect ◽  
Inertia Effects ◽  
Low Viscosity ◽  
Fluid Film Bearings

Fluid film bearings are commonly analyzed with the conventional Reynolds equation, without any temporal inertia effects, developed for oil or other high viscosity lubricants. In applications with rapidly time varying external loads, e.g. ships on wavy oceans, temporal inertia effect should be taken into account. As rotating speeds increase in industrial machines and the reduced Reynolds number increases above the turbulent threshold, a form of linearized turbulence model is often used to increase the effective viscosity to take the turbulence into account. Other than the turbulence effect, with high reduced Reynolds number, convective inertia effect gains importance. Water or other low viscosity fluid film bearings used in subsea machines and compressors are potential applications with a highly reduced Reynolds number.” This paper extends the theory originally developed by Tichy [1] for impulsive loads to high reduced Reynolds number lubrication in different bearing configurations. Both fluid shear and pressure gradient terms are included in the velocity profiles across the lubricant film. The incompressible continuity equation and Navier Stokes equations, including the temporal inertia term, are simplified using an averaged velocity approach to obtain an extended form of Reynolds equation which applies to both laminar and turbulent flow. All terms in the Navier Stokes equation, including both the convective and temporal inertia terms are included in the analysis. The inclusion of the temporal inertia term creates a fluid acceleration term in the extended Reynolds equation. A primary advantage of this formulation is that fluid film bearings lubricated with low viscosity lubricants which are subject to high force slew rates can be analyzed with this extended Reynolds equation. A short bearing form of the extended Reynolds equation is developed with appropriate boundary conditions. A full kinematic analysis of the short journal bearing is developed including time derivatives up to and including shaft accelerations. Linearized stiffness, damping and mass coefficients are developed for a plain short journal bearing. A time transient solution is developed for the pressure and bearing loads in plain journal bearings supporting a symmetric rigid rotor when the rotor is subjected to rapidly applied large forces. The change in the rotor displacements when subjected to unbalance forces is explored. Several comparisons between conventional Reynolds equation solutions and the extended Reynolds number form with temporal inertia effects will be presented and discussed.

scholarly journals Vibration Characteristics of Hydrodynamic Fluid Film Pocket Journal Bearings

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
N. S. Feng ◽  
E. J. Hahn
Keyword(s):  
Reynolds Equation ◽  
Natural Frequencies ◽  
Journal Bearings ◽  
Vibration Characteristics ◽  
Fluid Film ◽  
Critical Speeds ◽  
Fluid Film Bearings ◽  
Theoretical Analyses

Theoretical analyses of hydrodynamic fluid film bearings with different bearing profiles rely on solutions of the Reynolds equation. This paper presents an approach used for analysing the so-called pocket bearings formed from a combination of offset circular bearing profiles. The results show that the variation of the dynamic bearing characteristics with different load inclinations for the pocket bearings is less than that for the elliptic bearing counterpart. It is shown that the natural frequencies as well as the critical speeds, and hence the vibrational behaviour, can also be significantly different for an industrial rotor supported by the different bearings.

Theoretical Pressure Distribution in Journal Bearings

1961 ◽  
Vol 28 (4) ◽  
pp. 497-506 ◽  
Author(s):  
Kichiye Habata
Keyword(s):  
Reynolds Equation ◽  
Variable Viscosity ◽  
Slenderness Ratio ◽  
Approximate Solutions ◽  
Journal Bearings ◽  
Oil Viscosity ◽  
Pressure Distributions ◽  
Hill’S Method ◽  
Ritz’S Method ◽  
Theoretical Pressure

By assuming oil viscosity constant, Reynolds’ equation for journal bearings has been solved in a manner similar to Hill’s method. Two approximate solutions using E. O. Waters’ method and Ritz’s method have been added. Numerical computations have been carried out for a centrally supported 120-deg bearing with a unity slenderness ratio. Isobarriers have been determined from the pressure distributions. In order to show a justification for assuming the viscosity constant, the Reynolds equation was solved for the infinitely long bearing with variable viscosity, and the solution compared with that of Sommerfeld.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

Time-Accurate Simulation of Longitudinal Flight Mechanics with Control by CFD/RBD Coupling

2012 ◽  
Vol 226-228 ◽  
pp. 788-792 ◽  
Author(s):  
Dong Guo ◽  
Min Xu ◽  
Shi Lu Chen
Keyword(s):  
Computational Study ◽  
Rigid Motion ◽  
Rigid Body Dynamics ◽  
Flight Mechanics ◽  
Control Surface ◽  
Free Flight ◽  
Body Dynamics ◽  
Computational Fluid Dynamics Cfd ◽  
Coupled Solution ◽  
Surface Deflections

This paper describes a multidisciplinary computational study undertaken to compute the flight trajectories and simultaneously predict the unsteady free flight aerodynamics of aircraft in time domain using an advanced coupled computational fluid dynamics (CFD)/rigid body dynamics (RBD) technique. This incorporation of the flight mechanics equations and controller into the CFD solver loop and the treatment of the mesh, which must move with both the control surface deflections and the rigid motion of the aircraft, are illustrated. This work is a contribution to a wider effort towards the simulation of aeroelastic and flight stability in regions where nonlinear aerodynamics, and hence potentially CFD, can play a key role. Results demonstrating the coupled solution are presented.

Bifurcation Analysis of Self-Acting Gas Journal Bearings

2001 ◽  
Vol 123 (4) ◽  
pp. 755-767 ◽  
Author(s):  
Cheng-Chi Wang ◽  
Cha’o-Ku`ang Chen
Keyword(s):  
Dynamic Behavior ◽  
Reynolds Equation ◽  
Rotational Velocity ◽  
Power Spectra ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Finite Differences Method ◽  
Subharmonic Response ◽  
Rotor Center ◽  
Rotor Mass

This paper studies the bifurcation of a rigid rotor supported by a gas film bearing. A time-dependent mathematical model for gas journal bearings is presented. The finite differences method and the Successive Over Relation (S.O.R) method are employed to solve the Reynolds’ equation. The system state trajectory, Poincare´ maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor center in the horizontal and vertical directions under different operating conditions. The analysis shows how the existence of a complex dynamic behavior comprising periodic and subharmonic response of the rotor center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems.

New solutions of classical problems in rigid body dynamics

2015 ◽  
Vol 69 ◽  
pp. 40-44
Author(s):  
H.M. Yehia ◽  
E. Saleh ◽  
S.F. Megahid
Keyword(s):  
Rigid Body ◽  
Rigid Body Dynamics ◽  
Body Dynamics

The Effect of Journal Bearing Misalignment on Load and Cavitation for Non-Newtonian Lubricants

1986 ◽  
Vol 108 (4) ◽  
pp. 645-654 ◽  
Author(s):  
R. H. Buckholz ◽  
J. F. Lin
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
Surface Boundary ◽  
Film Rupture ◽  
Aspect Ratios ◽  
Free Surface Boundary Condition ◽  
Load Carrying ◽  
Boundary Location ◽  
Surface Boundary Condition

An analysis for hydrodynamic, non-Newtonian lubrication of misaligned journal bearings is given. The hydrodynamic load-carrying capacity for partial arc journal bearings lubricated by power-law, non-Newtonian fluids is calculated for small valves of the bearing aspect ratios. These results are compared with: numerical solutions to the non-Newtonian modified Reynolds equation, with Ocvirk’s experimental results for misaligned bearings, and with other numerical simulations. The cavitation (i.e., film rupture) boundary location is calculated using the Reynolds’ free-surface, boundary condition.

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