Finite Journal Bearing With Nonlinear Stiffness and Damping. Part 2: Stability Analysis

1982 ◽  
Vol 104 (2) ◽  
pp. 406-411 ◽  
Author(s):  
E. Hashish ◽  
T. S. Sankar ◽  
M. O. M. Osman
Keyword(s):  
Stability Analysis ◽  
Journal Bearing ◽  
Linear Equations ◽  
Orbital Stability ◽  
Nonlinear Stiffness ◽  
Stability Behavior ◽  
Supply Pressure ◽  
The Stability ◽  
Stiffness And Damping ◽  
High Possibility

Stability analysis is performed on the linearized as well as the actual nonlinear finite bearing equations using the improved mathematical models for the hydrodynamic forces that are presented in Part I of this investigation. The results of the analysis using the linear equations show a significant trend, different from previous investigation, with respect to different L/d ratios and therefore can be considered as modified stability curves for the finite bearing. The nonlinear analysis, based on numerical integration of the equation of motion, is carried out for the commonly used L/d = 1. Details on the stability behavior of the finite bearing are established, including the orbital stability regions. It is also found that under certain light loading conditions, the supply pressure can introduce a high possibility of orbital stability to the system.

Lyapunov’s Stability of Nonlinear Misaligned Journal Bearings

1995 ◽  
Vol 117 (3) ◽  
pp. 576-581 ◽  
Author(s):  
P. G. Nikolakopoulos ◽  
C. A. Papadopoulos
Keyword(s):  
Journal Bearing ◽  
Direct Method ◽  
Equations Of Motion ◽  
Orbital Stability ◽  
Element Formulation ◽  
Nonlinear Stiffness ◽  
Lyapunov Direct Method ◽  
Rotor Bearing ◽  
The Stability ◽  
General Method

In this paper the stability of nonlinear misaligned rotor-bearing systems is investigated, using the Lyapunov direct method. A finite element formulation is used to determine the journal bearing pressure distribution. Then the linear and nonlinear stiffness, damping, and hybrid (depending on both displacement and velocity) coefficients are calculated. A general method of analysis based on Lyapunov’s stability criteria is used to investigate the stability of nonlinear misaligned rotor bearing systems. The equations of motion of the rigid rotor on the nonlinear bearings are used to find a Lyapunov function using some of these coefficients, which depend on L/D ratio and the misalignment angles ψx, ψy. The analytical conditions for the stability or instability of some examined cases are given and some examples for the orbital stability are also demonstrated.

Non-linear stability analysis of micropolar fluid lubricated journal bearings with turbulent effect

2019 ◽  
Vol 71 (1) ◽  
pp. 31-39
Author(s):  
Subrata Das ◽  
Sisir Kumar Guha
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Micropolar Fluid ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Turbulent Regime ◽  
Content Type ◽  
Non Linear ◽  
The Stability ◽  
Bearing System

Purpose The purpose of this paper is to investigate the effect of turbulence on the stability characteristics of finite hydrodynamic journal bearing lubricated with micropolar fluid. Design/methodology/approach The non-dimensional transient Reynolds equation has been solved to obtain the non-dimensional pressure field which in turn used to obtain the load carrying capacity of the bearing. The second-order equations of motion applicable for journal bearing system have been solved using fourth-order Runge–Kutta method to obtain the stability characteristics. Findings It has been observed that turbulence has adverse effect on stability and the whirl ratio at laminar flow condition has the lowest value. Practical implications The paper provides the stability characteristics of the finite journal bearing lubricated with micropolar fluid operating in turbulent regime which is very common in practical applications. Originality/value Non-linear stability analysis of micropolar fluid lubricated journal bearing operating in turbulent regime has not been reported in literatures so far. This paper is an effort to address the problem of non-linear stability of journal bearings under micropolar lubrication with turbulent effect. The results obtained provide useful information for designing the journal bearing system for high speed applications.

A Variable Viscosity Approach for the Analysis of Steady State and Dynamic Characteristics of Two-Lobe Journal Bearing With TiO2 Based Nanolubricant

2017 ◽  
Author(s):  
Ashutosh Kumar ◽  
Sashindra Kumar Kakoty
Keyword(s):  
Steady State ◽  
Dynamic Characteristics ◽  
Journal Bearing ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Flow Coefficient ◽  
Viscosity Model ◽  
Nano Lubricant ◽  
The Stability ◽  
Stiffness And Damping

Steady-state and dynamic characteristics of two-lobe journal bearing, operating on TiO2 based Nano-lubricant has been obtained. The effective viscosity is obtained by using Krieger-Dougherty viscosity model for a given volume fraction of nanoparticle in the base fluid. Various bearing performance characteristics are then obtained by solving modified Reynolds equation for variable viscosity model and couple stress model. The stiffness and damping coefficients are also determined for various values of the volume fraction of the nanoparticle in the nanofluid. Results reveal that load carrying capacity and flow coefficient increase whereas friction variable decreases without affecting the stability condition of two-lobe journal bearing operating on TiO2 based nanolubricant. On the other hand attitude angle and dynamic coefficients remains constant for all the values of volume fraction of nanoparticle.

Stability Analysis of Plate-Cone Reticulated Shell

2011 ◽  
Vol 71-78 ◽  
pp. 3760-3763
Author(s):  
Xing Wang
Keyword(s):  
Stability Analysis ◽  
Bearing Capacity ◽  
Double Layer ◽  
Geometrical Nonlinearity ◽  
Ultimate Bearing Capacity ◽  
Arc Length ◽  
Stability Behavior ◽  
Destruction Mechanism ◽  
The Stability ◽  
Complete Process

This paper carries out stability analysis on plate-cone reticulated shell considering geometrical nonlinearity of cooperating work between plates and members. In this paper, stability behavior of different kinds of plate-cone reticulated shell considering geometrical nonlinearity is analyzed by using the software ANSYS, tracking complete process balance path for load-displacement by using arc-length method, the several problems of plate-cone reticulated shell are studied, such as destruction mechanism, structural ductility, ultimate bearing capacity and strength reserve, some important conclusions are obtained. After analyzing the stability behavior of double-layer reticulated shell by ANSYS and comparing with plate-cone reticulated shell, it is proved that plate-cone reticulated shell is more advantageous than double-layer reticulated shell in the aspect of stability behavior.

Linear stability analysis of finite hydrodynamic journal bearing under turbulent lubrication with coupled-stress fluid

2016 ◽  
Vol 68 (3) ◽  
pp. 386-391 ◽  
Author(s):  
Abhishek Ghosh ◽  
Sisir Kumar Guha
Keyword(s):  
Stability Analysis ◽  
Newtonian Fluid ◽  
High Speed ◽  
Journal Bearing ◽  
Slenderness Ratio ◽  
Linear Perturbation ◽  
Content Type ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Coupled Stress

Purpose Several researchers have observed that to satisfy modern day’s need, it is essential to enhance the characteristics of journal bearing, which is used in numerous applications. Moreover, the use of Newtonian fluid as a lubricant is diminishing day by day, and the use of Non-Newtonian fluids is coming more into picture. Furthermore, if turbo-machinery applications are taken into account, then it can be seen that journal bearings are used for high speed applications as well. Thus, neglecting turbulent conditions may lead to erroneous results. Hence, this paper aims to present focuses on studying the stability characteristics of finite hydrodynamic journal bearing under turbulent coupled-stress lubrication. Design/methodology/approach First, the governing equation relevant to the problem is generated. Then, the dynamic analysis is carried out by linear perturbation technique, leading to three perturbed equations, which are again discretized by finite difference method. Finally, these discretized equations are solved with the help of Gauss-Seidel Iteration technique with successive over relaxation scheme. Consequently, the film response coefficients and the stability parameters are evaluated at different parametric conditions. Findings It has been concluded from the study that with increase in value of the coupled-stress parameter, the stability of the journal may increase. Whereas, with increase in Reynolds number, the stability of the journal decreases. On the other hand, stability increases with increasing values of slenderness ratio. Originality/value Researches have been performed to study the dynamic characteristics of journal bearing with non-Newtonian fluid as the lubricant. But in the class of non-Newtonian lubricants, the use of coupled-stress fluid has not yet been properly investigated. So, an attempt has been made to perform the stability analysis of bearings with coupled-stress fluid as the advanced lubricant.

Nonlinear Simulation Analysis and Experiment of Fluid Plain Journal Bearing With Incompressible Fluid

2003 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Atsuhiko Shintani ◽  
Koji Yoshioka ◽  
Kouhei Okuno ◽  
Hiroaki Tanaka ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Incompressible Fluid ◽  
Journal Bearing ◽  
Simulation Analysis ◽  
Journal Bearings ◽  
Stable Region ◽  
Flexible Rotor ◽  
Nonlinear Simulation ◽  
Fluid Forces ◽  
The Stability

Recently, in many areas such as computers and information equipments etc., the fluid journal bearings are required to rotate at higher speed. To satisfy this requirement, the strictly stability analysis of the journal is indispensable. In this paper, we investigate the stability analysis of the dynamic behavior of the fluid plain journal bearing with an incompressible fluid considering the nonlinear terms of fluid forces. The stability analysis is examined by the numerical simulations on each model of a rigid rotor and a flexible rotor. The stable regions by nonlinear analysis are compared with the regions by classical linear analysis. Performing the nonlinear simulation analysis, it becomes clear that there is rather a stable region which amplitude does not grow up abruptly, and this phenomenon can not only be pointed out, but also is judged to be unstable by linear stable analysis. Finally, the experiment using actual bearings is performed and compared with the numerical results.

MHD Stability for a Class of Tokamak Equilibria with Fixed Boundaries

1978 ◽  
Vol 33 (7) ◽  
pp. 792-798
Author(s):  
W. Kerner
Keyword(s):  
Stability Analysis ◽  
Normal Mode ◽  
Cross Sections ◽  
Stability Limit ◽  
Stability Behavior ◽  
Mhd Stability ◽  
The Stability ◽  
High Beta ◽  
Fixed Boundaries ◽  
Flat Current

The stability behavior with respect to internal modes is discussed for a class of tokamak equilibria with non-circular cross-sections and essentially flat current profiles. The stability analysis is done by computer both symbolically and numerically with the help of a normal mode code, which extremizes the Lagrangian of the system . It is found that the stability limit agrees well with that of the Mercier criterion. There are stable high-beta equilibria in this model.

Dynamic and Stability Analysis of the Rotating Nanobeam in a Nonuniform Magnetic Field Considering the Surface Energy

2016 ◽  
Vol 08 (04) ◽  
pp. 1650048 ◽  
Author(s):  
M. Baghani ◽  
M. Mohammadi ◽  
A. Farajpour
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Angular Velocity ◽  
Surface Energy ◽  
Axial Load ◽  
Nonuniform Magnetic Field ◽  
Small Scale ◽  
Stability Behavior ◽  
Compressive Axial Load ◽  
The Stability

It is well-known that rotating nanobeams can have different dynamic and stability responses to various types of loadings. In this research, attention is focused on studying the effects of magnetic field, surface energy and compressive axial load on the dynamic and the stability behavior of the nanobeam. For this purpose, it is assumed that the rotating nanobeam is located in the nonuniform magnetic field and subjected to compressive axial load. The nonlocal elasticity theory and the Gurtin–Murdoch model are applied to consider the effects of inter atomic forces and surface energy effect on the vibration behavior of rotating nanobeam. The vibration frequencies and critical buckling loads of the nanobeam are computed by the differential quadrature method (DQM). Then, the numerical results are testified with those results are presented in the published works and a good correlation is obtained. Finally, the effects of angular velocity, magnetic field, boundary conditions, compressive axial load, small scale parameter and surface elastic constants on the dynamic and the stability behavior of the nanobeam are studied. The results show that the magnetic field, surface energy and the angular velocity have important roles in the dynamic and stability analysis of the nanobeams.

Stability Analysis of an Industrial Gas Compressor Supported by Tilting-Pad Bearings Under Different Lubrication Regimes

2011 ◽  
Author(s):  
Alejandro Cerda Varela ◽  
Ilmar Ferreira Santos
Keyword(s):  
Stability Analysis ◽  
Dynamic Behavior ◽  
Journal Bearing ◽  
Lubrication Regimes ◽  
Lubrication Regime ◽  
Stable Operating ◽  
Tilting Pad ◽  
The Stability ◽  
Tilting Pad Journal Bearing ◽  
Bearing System

This work is aimed at theoretically study the dynamic behavior of a rotor-tilting pad journal bearing system under different lubrication regimes, namely thermohydrodynamic (THD), elastohydrodynamic (EHD) and hybrid lubrication regime. The rotor modeled corresponds to an industrial compressor. Special emphasis is put on analyzing the stability map of the rotor when the different lubrication regimes are included into the TPJB modeling. Results show that, for the studied rotor, the inclusion of a THD model is more relevant when compared to an EHD model, as it implies a reduction on the instability onset speed for the rotor. Also, results show the feasibility of extending the stable operating range of the rotor by implementing a hybrid lubrication regime.

Moment Stability of Stochastic Regenerative Cutting Process

2010 ◽  
Vol 97-101 ◽  
pp. 3038-3041
Author(s):  
Xiao Qin Zhou ◽  
Wen Cai Wang ◽  
Hong Wei Zhao
Keyword(s):  
Stability Analysis ◽  
Stability Boundary ◽  
Cutting Process ◽  
Damping Coefficients ◽  
Cutting Stability ◽  
Stationary Stochastic Processes ◽  
The Stability ◽  
Stiffness And Damping ◽  
Moment Stability ◽  
Stochastic Uncertainties

The stochastic uncertainties of regenerative cutting process (RCP) are taken into consideration, and both cutting stiffness and damping coefficients are modeled as two stationary stochastic processes. The eigenvalue equations are established for the stability analysis of stochastic RCP, corresponding to the differential equations of the first and second order moments. Thus the stability analysis of stochastic RCP is transformed into that of the first two order moments. The influence of stochastic uncertainties on the cutting stability of RCP is discussed. The numerical experiments have verified that with the increase of stochastic uncertainties, the cutting stability boundary was shifted downwards significantly, and the number of lobes was also multiplied.

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