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.

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.

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.

Coupled Lateral and Torsional Nonlinear Transient Rotor–Bearing System Analysis With Applications

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Jianming Cao ◽  
Paul Allaire ◽  
Timothy Dimond
Keyword(s):  
Rotational Speed ◽  
System Analysis ◽  
Equations Of Motion ◽  
Squeeze Film ◽  
Rotor Bearing ◽  
Nonlinear Transient ◽  
Gyroscopic Effects ◽  
Nonlinear Equations Of Motion ◽  
Torsional Analysis ◽  
Bearing System

This paper provides a time transient method for solving coupled lateral and torsional analysis of a flexible rotor–bearing system including gyroscopic effects, nonlinear short journal bearings, nonlinear short squeeze film dampers (SFDs), and external nonlinear forces/torques. The rotor is modeled as linear, and the supporting components, including bearings and dampers, are modeled as nonlinear. An implicit Runge–Kutta method is developed to solve the nonlinear equations of motion with nonconstant operating speed since the unbalance force and the gyroscopic effect are related to both the rotational speed and the acceleration. The developed method is compared with a previous torsional analysis first to verify the nonlinear transient solver. Then the coupled lateral and torsional analysis of an example flexible three-disk rotor, perhaps representing a compressor, with nonlinear bearings and nonlinear dampers driven by a synchronous motor is approached. The acceleration effects on lateral and torsional amplitudes of vibration are presented in the analysis. The developed method can be used to study the rotor motion with nonconstant rotational speed such as during startup, shutdown, going through critical speeds, blade loss force, or other sudden loading.

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.

scholarly journals Bifurcation analysis of rotor/bearing system using third-order journal bearing stiffness and damping coefficients

2021 ◽  
Author(s):  
T. A. El-Sayed ◽  
Hussein Sayed
Keyword(s):  
Equations Of Motion ◽  
Journal Bearings ◽  
Third Order ◽  
Damping Coefficients ◽  
The Third ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Rotor Stiffness ◽  
Stiffness And Damping ◽  
Bearing System

AbstractHydrodynamic journal bearings are used in many applications which involve high speeds and loads. However, they are susceptible to oil whirl instability, which may cause bearing failure. In this work, a flexible Jeffcott rotor supported by two identical journal bearings is used to investigate the stability and bifurcations of rotor bearing system. Since a closed form for the finite bearing forces is not exist, nonlinear bearing stiffness and damping coefficients are used to represent the bearing forces. The bearing forces are approximated to the third order using Taylor expansion, and infinitesimal perturbation method is used to evaluate the nonlinear bearing coefficients. The mesh sensitivity on the bearing coefficients is investigated. Then, the equations of motion based on bearing coefficients are used to investigate the dynamics and stability of the rotor-bearing system. The effect of rotor stiffness ratio and applied load on the Hopf bifurcation stability and limit cycle continuation of the system are investigated. The results of this work show that evaluating the bearing forces using Taylor’s expansion up to the third-order bearing coefficients can be used to profoundly investigate the rich dynamics of rotor-bearing systems.

Explicit forms of the rotational equations of motion for digital simulation

SIMULATION ◽  
1969 ◽  
Vol 12 (2) ◽  
pp. 97-102 ◽  
Author(s):  
Richard Economy ◽  
George Burgin
Keyword(s):  
Explicit Form ◽  
Digital Simulation ◽  
Equations Of Motion ◽  
Computation Time ◽  
Iterative Solution ◽  
Simultaneous Equations ◽  
Rotational Acceleration ◽  
Substitution Method ◽  
Time Required ◽  
Special Case

The rotational acceleration for a rigid body has traditionally been represented by three simultaneous equations. Be cause of the computation time required for the iterative solution of simultaneous equations using a digital com puter, it is desirable to transform these equations to an explicit form for digital solution. The rotational equations are linear in the acceleration components. Thus, an explicit form can be obtained by either a determinate or a substi tution method. For problems where solution requires two or more of the cross-products-of-inertia terms, the determ inate method yields the most efficient equation form for digital solution. For the special case of body-plane sym metry (i.e., two cross-products-of-inertia terms are neg lected), the substitution method yields the most efficient form.

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.

Coupled Lateral and Torsional Nonlinear Transient Solver With Application to Flexible Rotor-Bearing System

2014 ◽  
Author(s):  
Jianming Cao ◽  
Tim Dimond ◽  
Paul Allaire
Keyword(s):  
Rotational Speed ◽  
Equations Of Motion ◽  
Squeeze Film ◽  
Flexible Rotor ◽  
Rotor Bearing ◽  
Nonlinear Transient ◽  
Gyroscopic Effects ◽  
Nonlinear Equations Of Motion ◽  
Torsional Analysis ◽  
Bearing System

This paper provides a time transient method for solving coupled lateral and torsional analysis of a flexible rotor-bearing system including gyroscopic effects, nonlinear short journal bearings, nonlinear short squeeze film dampers, and external nonlinear forces/torques. The rotor is modeled as linear, and the supporting components, including bearings and dampers, are modeled as nonlinear. An implicit Runge-Kutta method is developed to solve the nonlinear equations of motion with non-constant operating speed since the unbalance force and the gyroscopic effect are related to both the rotational speed and the acceleration. The developed method is compared with previous torsional analysis first to verify the nonlinear transient solver. Then the coupled lateral and torsional analysis of a flexible 3-disk rotor with nonlinear bearings and nonlinear dampers driven by a synchronous motor is approached. The acceleration effects on lateral and torsional amplitudes is presented in the analysis. The developed method can be used to study the rotor motion with non-constant rotational speed, such as during startup, shutdown, going through critical speeds, blade loss force, or other sudden loading.

Hydrodynamic Journal Bearings Optimization Considering Rotor Dynamics Restrictions

2018 ◽  
Author(s):  
Leonid Moroz ◽  
Leonid Romanenko ◽  
Roman Kochurov ◽  
Evgen Kashtanov
Keyword(s):  
Film Thickness ◽  
Induction Motor ◽  
Rotor Dynamics ◽  
Journal Bearings ◽  
Oil Film ◽  
Critical Speeds ◽  
Bearing Clearance ◽  
Rotor Bearing ◽  
Dynamics Analyses ◽  
Bearing System

In this study, optimal designs of hydrodynamic journal bearings for 13.5 MW induction motor prototype is developed based on the design of experiment approach and best sequences method which involves entire rotor-bearing system multidisciplinary simulations. These simulations consist of bearing hydrodynamic characteristics calculation and optimization and rotor dynamics analyses for a rotor-bearing system. The results of rotor dynamics analyses are taken into account as the constraints during optimization. Several journal bearings such as plain cylindrical with a different configuration of pockets, elliptical type, and 4-lobe fixed pad have been considered to select the most appropriate design for the application. The bearing clearance, length, diameter, pockets positions, lobe width, oil viscosity, are applied as design input variables. To find the bearing optimal design, following objective functions were considered: 1) Minimum oil film thickness. Optimal bearing clearance is designed to produce the maximum possible level of minimum oil film thickness in order to avoid or reduce possible metal-to-metal contact; 2) Maximization of the performance is done by minimization of friction power loss. 3) Rotor dynamics simulation for the rotor-bearing system is embedded in the optimization process in order to avoid resonances by providing sufficient critical speeds separation margins from operating speed. The methodology for the bearing simulation is based on the mass-conserving mathematical model, proposed by Elrod & Adams and numerical solution for the equations is generated using finite difference method. Rotor dynamics analyses are performed using finite element method. As the result of the study, optimized bearing designs for 13.5 MW induction motor were generated. Optimized bearings provide sufficient frequency margins for critical speeds for the rotor-bearing system and, at the same time, improved hydrodynamic bearing characteristics: maximized oil film thickness and increased efficiency compared to the starting design. Through the considered bearings examples, the study shows how different parameters, such as bearing clearance, length, diameter, and etc., influence key performance characteristics like bearing minimum oil film thickness, friction power losses, rotor-bearing system critical speeds.

Research on Dynamic Characteristic and Experiments of Double-Disc Rotor System with Oil Film Support

2012 ◽  
Vol 442 ◽  
pp. 235-239
Author(s):  
Chao Feng Li ◽  
Jie Liu ◽  
Qin Liang Li ◽  
Bang Chun Wen
Keyword(s):  
Dynamic Characteristic ◽  
Period Doubling ◽  
Continuous System ◽  
Rotor System ◽  
Small Eccentricity ◽  
Oil Film ◽  
Rotor Bearing ◽  
Calculation Results ◽  
Bifurcation Solution ◽  
Bearing System

Multi-DOF model of double-disc rotor-bearing system taking oil film support into account is established, and Newmark method is also applied to dynamic response of continuous system. To simplify the calculation in double-disc eccentric situation, the research aims at time domain, frequency response and bifurcation solution, simultaneously qualitative experiments are also carried out on the experiment bench. Experiments show that the numerical algorithm and calculation results are credible. The conclusions conclude: For the rotor system shown in the paper, with the other parameters constant, small eccentricity system is prone to appear quasi-periodic instability, but for big eccentricity system it is period-doubling instability, and the instability speed will increase with eccentricity enlargement; initial eccentric phase has severe effects on the dynamic characteristic of system, so it is worth studying it more in depth. This method and results in this paper provides a theoretical reference for stability analysis and vibration control in more complex relevant rotor-bearing system.

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