Stability analysis of rotating shaft under electromagnetic and bearing oil-film forces

2021 ◽  
pp. 146441932110154
Author(s):  
Mojtaba Eftekhari ◽  
Malihe Eftekhari ◽  
Asghar Dashti Rahmatabadi
Keyword(s):  
Pressure Distribution ◽  
Reynolds Equation ◽  
Nonlinear Behavior ◽  
Journal Bearings ◽  
Rotating Shaft ◽  
Chaotic Motions ◽  
Mass Eccentricity ◽  
Steady State Responses ◽  
The Stability ◽  
State Responses

The stability of the fixed pints of a flexible rotor supported by journal bearings is investigated through the Bifurcation diagrams. In this paper the effect of nonlinear electromagnetic harmonic force is added to the simultaneous consideration of the effects of the nonlinearity in curvature and inertia, mass eccentricity and hydrodynamic forces of the journal bearings. Solution of the Reynolds equation renders the pressure distribution in the bearings. The bearing forces are found from integrating the pressure distribution on the surface of bearings. Derivation of the equations is performed using the Hamilton's principle and the nonlinearity terms are related to the eccentricity and the curvature of shaft. Primary and combination resonances are imposed to the rotor-bearing system and steady state responses show the effects of magnetic and bearing forces on the stability of amplitudes. In combination resonance, frequency of the electromagnetic load is tuned as the average of the forward and backward natural frequencies of the rotor. Existence of unstable Hopf points demonstrates that periodic, quasi-periodic and chaotic motions may be arisen in the nonlinear behavior of rotor.

Dynamic stability of micropolar lubricated hydrodynamic offset-halves journal bearings

2020 ◽  
pp. 135065012093685
Author(s):  
Sanyam Sharma ◽  
Chimata M Krishna
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Critical Mass ◽  
Journal Bearings ◽  
Aspect Ratios ◽  
Input Parameters ◽  
Output Characteristics ◽  
The Stability ◽  
Offset Factor

The plain circular journal bearings are not found to be stable by researchers when used in high speed rotating machineries. Hence, extensive research in the study of stability characteristics of non-circular bearings or lobed bearings assumed importance, of late. Present article deals with the stability analysis of non-circular offset bearing by taking selected set of input and output parameters. Modified Reynolds equation for micropolar lubricated rigid journal bearing system is solved using finite element method. Two kinds of input parameters namely, offset factors (0.2, 0.4) and aspect ratios (1.6, 2.0) have been selected for the study. The important output characteristics such as load, critical mass, whirl frequency ratio, and threshold speed are computed and plotted for various set of values of input parameters. The results obtained indicate that micropolar lubricated circular offset bearing is highly stable for higher offset factor and higher aspect ratio.

Modelling and Analysis of the Dynamic Behavior of an Active Journal Bearing

1994 ◽  
Author(s):  
Linxiang Sun ◽  
Janusz M. Krodkiewski ◽  
Nong Zhang
Keyword(s):  
Pressure Distribution ◽  
Reynolds Equation ◽  
Hydrodynamic Pressure ◽  
Chamber Pressure ◽  
Oil Film ◽  
Simulation Based ◽  
Rotor Bearing ◽  
New Type ◽  
The Stability ◽  
Bearing System

Modelling and analysis of a rotor-bearing system with a new type of active oil bearing are presented. The active bearing basically consists of a flexible sleeve and a pressure chamber. The deformation of the sleeve can be controlled by the chamber pressure during the operation, and so can the pressure distribution of the oil film. Finite Element Methods (FEMs) and the Guyan condensation technique were utilised to create mathematical models for both the rotor and the flexible sleeve. The hydrodynamic pressure distribution of the oil film, for the instantaneous positions and velocities of the flexible sleeve and rotor, was approximated by Reynolds equation. The influence of the chamber pressure on the stability of the rotor system was investigated by numerical simulation based on the nonlinear model. The results showed that the stability of the rotor-bearing system can be improved effectively by implementation of the active bearing.

On the linear stability analysis of finite-hydrodynamic porous journal bearings under coupled stress lubrication

2007 ◽  
Vol 221 (7) ◽  
pp. 831-840 ◽  
Author(s):  
S. K. Guha ◽  
A. K. Chattopadhyay
Keyword(s):  
Reynolds Equation ◽  
Dynamic Performance ◽  
Slip Flow ◽  
Tangential Velocity ◽  
Continuum Theory ◽  
Transient State ◽  
Velocity Slip ◽  
Journal Bearings ◽  
The Stability ◽  
Coupled Stress

The objective of the present investigation is to study theoretically, using the finite-difference techniques, the dynamic performance characteristics of finite-hydrodynamic porous journal bearings lubricated with coupled stress fluids. In the analysis based on the Stokes micro-continuum theory of the rheological effects of coupled stress fluids, a modified form of Reynolds equation governing the transient-state hydrodynamic film pressures in porous journal bearings with the effect of slip flow of coupled stress fluid as lubricant is obtained. Moreover, the tangential velocity slip at the surface of porous bush has been considered by using Beavers-Joseph criterion. Using the first-order perturbation of the modified Reynolds equation, the stability characteristics in terms of threshold stability parameter and whirl ratios are obtained for various parameters viz. permeability factor, slip coefficient, bearing feeding parameter, and eccentricity ratio. The results show that the coupled stress fluid exhibits better stability in comparison with Newtonian fluid.

On The Steady State and Dynamic Performance Characteristics of Floating Ring Bearings

1981 ◽  
Vol 103 (3) ◽  
pp. 389-397 ◽  
Author(s):  
Chin-Hsiu Li ◽  
S. M. Rohde
Keyword(s):  
Steady State ◽  
Linear Theory ◽  
High Speed ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Journal Bearings ◽  
Transient Problem ◽  
The Stability ◽  
Bearing System

An analysis of the steady state and dynamic characteristics of floating ring journal bearings has been performed. The stability characteristics of the bearing, based on linear theory, are given. The transient problem, in which the equations of motion for the bearing system are integrated in real time was studied. The effect of using finite bearing theory rather than the short bearing assumption was examined. Among the significant findings of this study is the existence of limit cycles in the regions of instability predicted by linear theory. Such results explain the superior stability characteristics of the floating ring bearing in high speed applications. An understanding of this nonlinear behavior, serves as the basis for new and rational criteria for the design of floating ring bearings.

Stability analysis of a rigid rotor supported by two-lobe hydrodynamic journal bearings operating with a non-Newtonian lubricant

2018 ◽  
Vol 233 (6) ◽  
pp. 884-898 ◽  
Author(s):  
Saurabh K Yadav ◽  
Arvind K Rajput ◽  
Nathi Ram ◽  
Satish C Sharma
Keyword(s):  
Reynolds Equation ◽  
Pressure Field ◽  
Equation Of Motion ◽  
Journal Bearings ◽  
Rigid Rotor ◽  
Linear Finite Element ◽  
Runge Kutta Method ◽  
The Stability ◽  
Ellipticity Ratio ◽  
Bearing System

In the present work, an investigation has been performed on a rigid rotor supported by two-lobe journal bearings operating with a non-Newtonian lubricant. The governing Reynolds equation for pressure field is solved by using non-linear finite element method. Further to study the dynamic stability of the bearing system, governing equation of motion for the rotor position is solved by fourth order Runge–Kutta method. Bifurcation and Poincaré maps of two-lobe bearings are presented for different values of the non-Newtonian parameter and bearing ellipticity ratio. The numerical results illustrate that the ellipticity of a bearing with a dilatant lubricant improve the stability of the rotordynamic system.

Misalignment Effect on the Static and Dynamic Characteristics of Hydrodynamic Journal Bearings

1995 ◽  
Vol 117 (4) ◽  
pp. 717-723 ◽  
Author(s):  
Z. L Qiu ◽  
A. K. Tieu
Keyword(s):  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Static Load ◽  
Load Capacity ◽  
Vertical Direction ◽  
Journal Bearings ◽  
Static And Dynamic Characteristics ◽  
Flow Friction ◽  
The Stability ◽  
Side Flow

This paper solves the Reynolds equation by the finite difference method in a fixed coordinate system with the static load acted in the vertical direction. All static and dynamic characteristics (including load capacity, attitude angle, side flow, friction force, misaligned moments, and eight linear force coefficients) of a horizontally grooved bearing under different eccentricity and misalignment conditions are presented and compared with available experimental data. The effects of misalignment on all these bearing characteristics and on the stability of the rotor-bearing system are analyzed.

Parametric Excitation of a Pendulum With Bilinear Hysteresis

1970 ◽  
Vol 37 (4) ◽  
pp. 1061-1068 ◽  
Author(s):  
W. K. Tso ◽  
K. G. Asmis
Keyword(s):  
Steady State ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Viscous Damping ◽  
Sinusoidal Oscillation ◽  
Effective Mechanism ◽  
Steady State Responses ◽  
The Stability ◽  
State Responses ◽  
Steady State Solutions

The steady-state responses of a simple pendulum with a hinge exhibiting bilinear hysteretic moment-rotation characteristics and parametrically excited by a sinusoidal oscillation at the base is given. The stability of the steady-state solutions is discussed. It is shown that in contrast with viscous damping, the bilinear hysteresis is an effective mechanism to limit the growth of the response during parametric resonance.

Nonlinear Dynamic Behaviors of an Imbalance Rotor Supported on Fixed-Tilting Pad Journal Bearings

2011 ◽  
Vol 291-294 ◽  
pp. 1941-1951
Author(s):  
Xiao Bing Qi ◽  
Lei Feng ◽  
Yong Fang Zhang ◽  
Yan Jun Lu
Keyword(s):  
Pressure Distribution ◽  
Reynolds Equation ◽  
Axial Direction ◽  
Journal Bearings ◽  
Nonlinear Phenomena ◽  
Dynamic Behaviors ◽  
Oil Film ◽  
Tilting Pad ◽  
Field Dynamic ◽  
Tilting Pad Journal Bearings

Based on the unsteady Reynolds equation with Reynolds boundary, two-dimensional (2D) Reynolds equation is transformed into one-dimensional (1D) by taking the assumption of parabolic pressure distribution in axial direction in oil film field. Finite difference method was employed to solve 1D Reynolds equation, and the approximate pressure distribution was obtained in oil film field. Dynamic behaviors of a flexible rotor system with fixed-tilting pad journal bearings support were analyzed while the inertia of the pads was taken into consideration in the model. Imbalance responses of a symmetrical rotor-combination journal bearings (fixed-tilting pad journal bearings) system were investigated using Poincaré map and self-adaptive Runge-Kutta method. Numerical results reveal rich and complex nonlinear phenomena, such as periodic, quasi-periodic motion, etc.

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