Thermohydrodynamic Analysis for Laminar Flow Journal Bearing

1978 ◽  
Vol 100 (4) ◽  
pp. 510-512 ◽  
Author(s):  
Z. S. Safar
Keyword(s):  
Heat Flow ◽  
Radial Direction ◽  
Energy Equation ◽  
Journal Bearing ◽  
Separation Of Variables ◽  
Isoperimetric Problem ◽  
Momentum Equation ◽  
Journal Bearings ◽  
The Third ◽  
Semianalytical Method

This paper describes a semianalytical method for solving the thermohydrodynamic problem in journal bearings. It is assumed that the shaft is isothermal and the bearing heat flow is in the radial direction. The momentum equation is reduced to ordinary differential equations by separation of variables. Two of the resulting equations are integrated directly, while the third equation is interpreted and solved as an isoperimetric problem. The energy equation with its boundary conditions is solved by the Galerkin Kantarovich method.

Functionally Graded Hollow Sphere With Piezoelectric Internal and External Layers Under Asymmetric Transient Thermomechanical Loads

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
M. Jabbari ◽  
S. M. Mousavi ◽  
M. A. Kiani
Keyword(s):  
Hollow Sphere ◽  
Legendre Polynomials ◽  
Radial Direction ◽  
Energy Equation ◽  
Separation Of Variables ◽  
Functionally Graded ◽  
Power Functions ◽  
Legendre Series ◽  
Piezoelectric Layers ◽  
Transient Thermal

In this paper, an analytical method is developed to obtain the solution for the two-dimensional (2D) (r,θ) transient thermal and mechanical stresses in a hollow sphere made of functionally graded (FG) material and piezoelectric layers. The FGM properties vary continuously across the thickness, according to the power functions of radial direction. The temperature distribution as a function of radial and circumferential directions and time is obtained solving the energy equation, using the method of separation of variables and Legendre series. The Navier equations are solved analytically using the Legendre polynomials and the system of Euler differential equations.

Behavior of Finite Journal Bearings Under Dynamic Loading Conditions

1980 ◽  
Vol 102 (3) ◽  
pp. 333-338 ◽  
Author(s):  
G. S. A. Shawki ◽  
M. O. A. Mokhtar ◽  
Z. S. Safar
Keyword(s):  
Boundary Conditions ◽  
Computer Program ◽  
Variational Methods ◽  
Axial Length ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
The Third ◽  
Dynamic Loading Conditions ◽  
Generalized Reynolds Equation

Performance characteristics for a complete journal bearing of finite axial length are obtained analytically using a new set of boundary conditions. The generalized Reynolds equation is transformed, in the present analysis, into three ordinary differential equations, two of which being readily integrable while the third is solved by variational methods. By the aid of a specially devised computer program, the validity of the analysis has been assured when applied to prescribed journal loci including stationary, circular, elliptical, and linear harmonic journal oscillation.

scholarly journals Bifurcation Analysis of Rotor/Bearing System using Third Order Journal Bearings Stiffness and Damping Coefficients

2021 ◽  
Author(s):  
Tamer Elsayed ◽  
Hussein Sayed
Keyword(s):  
Journal Bearing ◽  
Journal Bearings ◽  
Third Order ◽  
The Third ◽  
Bifurcation Stability ◽  
Jeffcott Rotor ◽  
Load Carrying ◽  
Proper Design ◽  
Rotor Stiffness ◽  
Stiffness And Damping

Abstract Journal bearings have many applications in industry due to its high load carrying capacity. In addition proper design of journal bearings enables safe operation at very high speeds. However, they are susceptible to oil whirl instability which may cause bearing failure. The fluid film pressure distribution inside the journal bearing is described by Reynolds equation. Many studies had been done to approximate the bearing performance using first order bearing coefficients. Although this analysis is stable for evaluating the threshold speed but it is insensitive to limit cycles above the threshold speed. Mush literature show that above the threshold speed, subcritical or supercritical bifurcations may be observed. Therefore, the aim of the present paper is to evaluate the third order bearing coefficients for a finite length journal bearing using finite perturbation method. The values of these coefficients are evaluated using infinitesimal perturbation analysis. These values are used to investigate the bifurcation stability of flexible Jeffcott rotor supported by two symmetric journal bearings. The effect of rotor stiffness ratio on the bifurcation stability of the system is investigated. The results of this work show that the third order parameters can be used to evaluate the type of bifurcation above the threshold speed.

Research on Energy Equation of Lubrication Model on Large-Scale Journal Bearing System

2010 ◽  
Vol 145 ◽  
pp. 139-144
Author(s):  
Jian Mei Wang ◽  
Qing Xue Huang ◽  
Jian Feng Kang ◽  
Yang Fan
Keyword(s):  
Service Life ◽  
Large Scale ◽  
Energy Equation ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Journal Bearings ◽  
Calculation Results ◽  
Major Factors ◽  
Energy Equations ◽  
Bearing System

To prolong the service life of large-scale journal bearings, the major factors that have influences on bearing performances should be taken into account. By consideration of the variations of viscosity and density with pressure and temperature, a more thorough thermo-hydrodynamic lubrication model was established. With designation of variables with nondimensional parameters, a series of equations were nondimensionied, and the corresponding energy equations at different oil-film layers and boundaries were obtained respectively according to proper difference formats, and then solved by the integration of Finite Difference Method (FDM) with Boundary Element Method (BEM). Calculation results have proved that such complete mathematical model could provide great theoretical guide meaning to improve the lubrication performances and to prolong the service life of contact components of heavy journal bearings.

A Comparative Thermal Analysis of Slot-Entry and Hole-Entry Hybrid Journal Bearings Lubricated With Non-Newtonian Lubricant

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
H. C. Garg ◽  
Vijay Kumar ◽  
H. B. Sharda
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Journal Bearing ◽  
Flow Equation ◽  
Journal Bearings ◽  
Constant Flow ◽  
Viscosity Variation ◽  
Bearing System ◽  
Flow Valve ◽  
Newtonian Behavior

The effect of viscosity variation due to temperature rise and non-Newtonian behavior of the lubricant on the performance of hole-entry and slot-entry hybrid journal bearings system is the focus of this investigation. The performance characteristics of nonrecessed hybrid journal bearings operating with different flow controlling devices, i.e., constant flow valve, capillary, orifice, and slot restrictors, have been compared. Finite element method has been used to solve the Reynolds equation governing the flow of lubricant in the bearing clearance space along with the restrictor flow equation, energy equation and conduction equation using suitable iterative technique. The non-Newtonian lubricant has been assumed to follow the cubic shear stress law. The results indicate that variation in viscosity due to rise in temperature and non-Newtonian behavior of the lubricant affects the performance of nonrecessed hybrid journal bearing system quite significantly. The results further indicate that bearing performance can be improved by selecting a particular bearing configuration in conjunction with a suitable compensating device.

Approximate analytical model for fluid film force of finite length plain journal bearing

2011 ◽  
Vol 226 (5) ◽  
pp. 1345-1355 ◽  
Author(s):  
Y L Wang ◽  
Z S Liu ◽  
W J Kang ◽  
J J Yan
Keyword(s):  
Analytical Model ◽  
Finite Length ◽  
Journal Bearing ◽  
Separation Of Variables ◽  
Current Model ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Force Model ◽  
Oil Film ◽  
Proposed Model

Non-linear dynamic performance of rotor–bearing systems supported by plain journal bearings strongly depends on the mathematical oil film force model. In this article, the analytical solution of oil film pressure for finite length plain journal bearing is obtained by employing the separation of variables method to analytically solve the Reynolds equation based on dynamic Gümbel boundary conditions. The analytical expression of oil film force is then derived by applying the integral method. The expression of the pressure is analysed to investigate the pressure distribution. The oil film force of the analytical model is compared with the results from other methods, namely, long bearing approximation, short bearing approximation, as well as the finite difference method. The results clearly validate the current model. The proposed model also proved to be efficient for analysing the dynamic characteristics of a rigid rotor supported by plain journal bearings.

Adiabatic Solutions for Finite Journal Bearings

1979 ◽  
Vol 101 (4) ◽  
pp. 492-496 ◽  
Author(s):  
Oscar Pinkus ◽  
Sargit S. Bupara
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Journal Bearing ◽  
Initial Conditions ◽  
Variable Viscosity ◽  
Full Range ◽  
Journal Bearings ◽  
Maximum Temperature ◽  
Performance Results ◽  
Bearing Analysis

The paper offers a method of including variable viscosity in bearing analysis by the use of a simple energy equation uncoupled from the Reynolds equation. The relevant adiabatic solutions are made independent of the specifics of the kind of lubricant used and of its initial conditions. Performance results such as load, friction, maximum temperature, flow, etc. are given for the two axial-groove journal bearing covering three L/D ratios, three values of the adiabatic parameter E, and the full range of eccentricities. The effect of variable viscosity on the performance of misaligned bearings is also examined.

Thermohydrodynamic Lubrication in Laminar and Turbulent Regimes

1974 ◽  
Vol 96 (1) ◽  
pp. 48-56 ◽  
Author(s):  
Z. Safar ◽  
A. Z. Szeri
Keyword(s):  
Boundary Condition ◽  
Effective Viscosity ◽  
Radial Direction ◽  
Energy Equation ◽  
Homogeneous Boundary Condition ◽  
Journal Bearings ◽  
Kantorovich Method ◽  
Local Shear ◽  
Energy Equations ◽  
Laminar And Turbulent Regimes

The distribution of “effective viscosity”—assumed dependent on local shear and temperature—is obtained via iteration between the “long bearing” momentum and energy equations. In this treatment the shaft is isothermal and the bearing conducts heat only in the radial direction. This last assumption leads to essential simplifications: the bearing is replaced by an equivalent homogeneous boundary condition of the energy equation, which thus becomes amenable to solution by the Galerkin-Kantorovich method. The resulting effective viscosity is used to calculate the performance of finite journal bearings.

A Variational Solution of the 120-Degree Partial Journal Bearing

1972 ◽  
Vol 14 (3) ◽  
pp. 221-228 ◽  
Author(s):  
Miss Zeinab S. Safar ◽  
A. Z. Szeri
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Separation Of Variables ◽  
Isoperimetric Problem ◽  
Variational Solution

Reynolds equation reduced to ordinary differential equations by separation of variables. Two resulting equations integrated directly. Third equation and boundary conditions interpreted and solved as an isoperimetric problem.

scholarly journals Surface roughness effect on thermohydrodynamic analysis of journal bearings lubricated with couple stress fluids

2019 ◽  
Vol 8 (1) ◽  
pp. 397-406 ◽  
Author(s):  
Vishwanath B. Awati ◽  
Ashwini Kengangutti
Keyword(s):  
Surface Roughness ◽  
Couple Stress ◽  
Reynolds Equation ◽  
Multigrid Method ◽  
Energy Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Journal Bearings ◽  
Roughness Effect ◽  
Hydrodynamic Analysis

Abstract The paper presents, surface roughness effect for thermo-hydrodynamic analysis of journal bearings extended to couple stress lubricants with high polymer additives. A modified energy equation is simultaneously solved with heat transfer equation as well as modified Reynolds equation by using Multigrid method. The effects of couple stress and surface roughness on the performances of a finite journal bearing are presented in detail. Further, it is shown that lubricants with couple stress and surface roughness, not only increases the load capacity and decreases the friction coefficient, but also generates a lower bearing temperature field. Thus, the lubricant with couple stress improves the performance of journal bearings. The characteristics of bearing are compared with numerical results.

Sign in / Sign up

Export Citation Format

Share Document