The Effects of Fluid Inertia Forces on the Dynamic Behavior of Short Journal Bearings in Superlaminar Flow Regime

1988 ◽  
Vol 110 (3) ◽  
pp. 539-545 ◽  
Author(s):  
H. Hashimoto ◽  
S. Wada ◽  
M. Sumitomo
Keyword(s):  
Dynamic Behavior ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Fluid Inertia ◽  
Oil Film ◽  
Euler’S Method ◽  
Onset Velocity ◽  
Nonlinear Equations Of Motion

The effects of fluid inertia on the dynamic behavior of oil film journal bearings are theoretically investigated. The dynamic oil film forces considering the combined effects of turbulence and fluid inertia are analytically obtained under the short bearing assumption. Based on the linearized analysis, the whirl onset velocity for a balanced rigid rotor supported horizontally in the oil film journal bearings are determined initially in the case of the length-to-diameter ratio of λ = 0.5 for Reynolds numbers of Re = 2750, 4580, and 5500. Moreover, the nonlinear equations of motion for the rotor are solved by the improved Euler’s method, and the relations between the transient journal motion and the pressure distribution corresponding to the above Reynolds numbers are examined. It is found that the fluid inertia significantly affects the dynamic behavior of turbulent journal bearings under certain operating conditions.

Dynamic Behavior of Unbalanced Rigid Shaft Supported on Turbulent Journal Bearings—Theory and Experiment

1990 ◽  
Vol 112 (2) ◽  
pp. 404-408 ◽  
Author(s):  
H. Hashimoto ◽  
S. Wada
Keyword(s):  
Dynamic Behavior ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Experimental Results ◽  
Fluid Film ◽  
Force Components ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Analytical Expressions

In this paper, the combined effects of turbulence and fluid film inertia on the dynamic behavior of an unbalanced rigid shaft supported horizontally on two identical aligned short journal bearings are investigated theoretically and experimentally. Utilizing analytical expressions for the dynamic fluid film force components considering the effects of turbulence and fluid film inertia, the nonlinear equations of motion for the rotor-bearing systems are solved by the improved Euler’s forward integration method. The journal center trajectories with unbalance eccentricity ratio of εμ = 0, 0.1 and 0.2 are examined theoretically for Reynolds number of Re = 2750, 4580, and 5500, and the theoretical results are compared with experimental results. From the theoretical and experimental results, it was found that the fluid film inertia improves the stability of unbalanced rigid shaft under certain operating conditions.

An Application of Short Bearing Theory to Dynamic Characteristic Problems of Turbulent Journal Bearings

1987 ◽  
Vol 109 (2) ◽  
pp. 307-314 ◽  
Author(s):  
Hiromu Hashimoto ◽  
Sanae Wada ◽  
Jin-ichi Ito
Keyword(s):  
Dynamic Characteristic ◽  
Equations Of Motion ◽  
Computation Time ◽  
Journal Bearings ◽  
Oil Film ◽  
Euler’S Method ◽  
Linearized Stability ◽  
Rotor Bearing ◽  
Time Required ◽  
Nonlinear Equations Of Motion

The dynamic characteristic problems of turbulent journal bearings are theoretically analyzed. The oil film forces considering the turbulent effects are analytically obtained under the short bearing assumption. The linearized stability analysis is developed for a perfectly rigid rotor supported horizontally in the two identical aligned oil film journal bearings and the whirl onset velocities for rotor-bearing systems are determined for various Reynolds numbers. In addition, the nonlinear equations of motion for rotor-bearing systems are solved by the improved Euler’s method and the journal center trajectories are examined for both cases with and without out-of-balance forces. The results obtained from the short bearing theory are compared with those from the finite bearing theory for the length-to-diameter ratio λ = 0.25 and 0.5. It is found that the turbulence has significant effects on the dynamic behavior of rotor-bearing systems and the short bearing theory has an advantage of reducing a computation time required for the calculation of journal center trajectories with an acceptable accuracy.

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.

Bifurcation Theory Applied to Oil Whirl in Plain Cylindrical Journal Bearings

1984 ◽  
Vol 51 (2) ◽  
pp. 244-250 ◽  
Author(s):  
C. J. Myers
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Equilibrium Position ◽  
Small Amplitude ◽  
Bifurcation Theory ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
The Self ◽  
Oil Whirl ◽  
Nonlinear Equations Of Motion

An analysis of the self-excited oscillations of a rotor supported in fluid film journal bearings is presented. It is shown that Hopf bifurcation theory may be used to investigate small-amplitude periodic solutions of the nonlinear equations of motion for rotor speeds close to the speed at which the steady-state equilibrium position becomes unstable. A numerical investigation supports the findings of the analytic work.

Nonlinear Dynamic Analysis of a Flexible Rotor Supported by Externally Pressurized Porous Gas Journal Bearings

2002 ◽  
Vol 124 (3) ◽  
pp. 553-561 ◽  
Author(s):  
Cheng-Chi Wang ◽  
Cheng-Ying Lo ◽  
Cha’o-Kuang Chen
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Power Spectra ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Flexible Rotor ◽  
Bearing Number ◽  
Rotor Mass

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

scholarly journals Dynamic behavior of the nonlinear planetary gear model in nonstationary conditions

2020 ◽  
pp. 095440622094104
Author(s):  
Ahmed Hammami ◽  
Ayoub Mbarek ◽  
Alfonso Fernández ◽  
Fakher Chaari ◽  
Fernando Viadero ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Nonlinear Effects ◽  
Hertzian Contact ◽  
Mesh Stiffness ◽  
Planetary Gearbox ◽  
Time Frequency ◽  
Run Up ◽  
Nonlinear Equations Of Motion

The nonlinear effects in gearboxes are a key concern to describe accurately their dynamic behavior. This task is difficult for complex gear systems such as planetary gearboxes. The main aim of this work is to provide responses to overcome this difficulty especially in nonstationary operating regimes by investigating a back-to-back planetary gearbox in steady conditions and in the run-up regime. The nonlinear Hertzian contact of teeth pair is modeled in stationary and nonstationary run-up regime. Then it is incorporated in to a torsional model of the planetary gearbox through different mesh stiffness functions. In addition, motor torque and external load variation are taken into account. The nonlinear equations of motion of the back-to-back planetary gearbox are computed through the Newmark- β algorithm combined with the method of Newton–Raphson. An experimental validation of the proposed numerical model is done through a test bench for both stationary and run-up regimes. The vibration characteristics are extracted and correlated to speed and torque. Time–frequency analysis is implemented to characterize the transient regime during the run-up.

Hopf Bifurcation in Gas Journal Bearings

1993 ◽  
Vol 46 (7) ◽  
pp. 392-398 ◽  
Author(s):  
K. Czołczyn´ski
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Bifurcation Theory ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Fredholm Alternative ◽  
Stiffness Coefficients ◽  
Nonlinear Equations Of Motion ◽  
Gas Journal Bearing

This paper reviews a numerical investigation of the problem of small self-excited vibrations in gas journal bearings. The method of analysis is based on the Hopf bifurcation theory, in which the approximate periodic solutions of nonlinear equations of motion are computed using the Fredholm alternative. This theory enables us to construct the bifurcating periodic solutions and to determine their stability. The equations of motion of the investigated gas journal bearing have been formulated after estimating the damping and stiffness coefficients of a gas film. For this purpose, a new method of identification has been proposed.

Finite Element Modelling of Rotating Tires in the Time Domain

2002 ◽  
Vol 30 (1) ◽  
pp. 19-33 ◽  
Author(s):  
O. A. Olatunbosun ◽  
A. M. Burke
Keyword(s):  
Finite Element ◽  
Dynamic Behavior ◽  
Time Domain ◽  
Equations Of Motion ◽  
Operating Conditions ◽  
Element Analysis ◽  
Successful Model ◽  
Linear Effects ◽  
Tire Rotation ◽  
The Time Domain

Abstract Finite element analysis presents an opportunity for a detailed study of the dynamic behavior of a rotating tire under real operating conditions providing a better understanding of the influence of tire construction and material detail on tire dynamic behavior in such areas as ride, handling and noise and vibration transmission. Modelling issues that need to be considered include non-linear effects due to tire inflation and hub loading, tire/road contact and time domain solution of the equations of motion. In this paper techniques and strategies for tire rotation modelling are presented and discussed as a guide to the creation of a successful model.

Rotational Response and Slip Prediction of Serpentine Belt Drive Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 71-78 ◽  
Author(s):  
S.-J. Hwang ◽  
N. C. Perkins ◽  
A. G. Ulsoy ◽  
R. J. Meckstroth
Keyword(s):  
Numerical Solutions ◽  
Equations Of Motion ◽  
Operating Conditions ◽  
Equilibrium Analysis ◽  
Belt Drive ◽  
Theoretical Predictions ◽  
Serpentine Belt ◽  
Drive Systems ◽  
Nonlinear Equations Of Motion ◽  
Rotational Response

A nonlinear model is developed which describes the rotational response of automotive serpentine belt drive systems. Serpentine drives utilize a single (long) belt to drive all engine accessories from the crankshaft. An equilibrium analysis leads to a closed-form procedure for determining steady-state tensions in each belt span. The equations of motion are linearized about the equilibrium state and rotational mode vibration characteristics are determined from the eigenvalue problem governing free response. Numerical solutions of the nonlinear equations of motion indicate that, under certain engine operating conditions, the dynamic tension fluctuations may be sufficient to cause the belt to slip on particular accessory pulleys. Experimental measurements of dynamic response are in good agreement with theoretical results and confirm theoretical predictions of system vibration, tension fluctuations, and slip.

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