Effects of Power—Law, Non-Newtonian Lubricants on Load Capacity and Friction for Plane Slider Bearings

1986 ◽  
Vol 108 (1) ◽  
pp. 86-91 ◽  
Author(s):  
R. H. Buckholz
Keyword(s):  
Power Law ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Lagrange Equation ◽  
Load Capacity ◽  
Approximate Solutions ◽  
Finite Width ◽  
Aspect Ratios ◽  
Modified Reynolds Equation ◽  
Power Law Index

The lubrication of a conventional, finite width plane bearing, using a power-law, non-Newtonian lubricant, is studied. The basic assumptions in this analysis are: thin fluid-film, no thermal effects, and a modified Reynolds’ equation for small bearing aspect ratios. Results from this study include bearing pressure, load, and friction formulas. Similar results for the not-so-small bearing aspect ratios are found via an Euler-Lagrange equation. This Euler-Lagrange equation is derived from the optimization integral for the modified Reynolds’ equation. Approximate solutions to the modified Reynolds’ equation and to the Euler-Lagrange equation are contrasted with numerical solutions for the modified Reynolds equation. Bearing aspect ratios in the range 0.1 to 0.6, clearance ratios in the range 1.2 to 4.0, and non-Newtonian power-law index in the range 0.4 to 1.0 are considered.

The Effect of Journal Bearing Misalignment on Load and Cavitation for Non-Newtonian Lubricants

1986 ◽  
Vol 108 (4) ◽  
pp. 645-654 ◽  
Author(s):  
R. H. Buckholz ◽  
J. F. Lin
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
Surface Boundary ◽  
Film Rupture ◽  
Aspect Ratios ◽  
Free Surface Boundary Condition ◽  
Load Carrying ◽  
Boundary Location ◽  
Surface Boundary Condition

An analysis for hydrodynamic, non-Newtonian lubrication of misaligned journal bearings is given. The hydrodynamic load-carrying capacity for partial arc journal bearings lubricated by power-law, non-Newtonian fluids is calculated for small valves of the bearing aspect ratios. These results are compared with: numerical solutions to the non-Newtonian modified Reynolds equation, with Ocvirk’s experimental results for misaligned bearings, and with other numerical simulations. The cavitation (i.e., film rupture) boundary location is calculated using the Reynolds’ free-surface, boundary condition.

Effect of non-Newtonian magneto-elastohydrodynamic on performance characteristics of slider-bearings

2019 ◽  
Vol 71 (10) ◽  
pp. 1158-1165
Author(s):  
Mouhcine Mouda ◽  
Mohamed Nabhani ◽  
Mohamed El Khlifi
Keyword(s):  
Friction Coefficient ◽  
Design Methodology ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Transverse Magnetic ◽  
Finite Width ◽  
Two Dimensional ◽  
Content Type ◽  
Slider Bearings ◽  
First Time

Purpose This study aims to examine the magneto-elastohydrodynamic effect on finite-width slider-bearings lubrication using a non-Newtonian lubricant. Design/methodology/approach Based on the magneto-hydrodynamic (MHD) theory and Stokes micro-continuum mechanics, the modified two-dimensional Reynolds equation including bearing deformation was derived. Findings It is found that the bearing deformation diminishes the load-capacity and increases the friction coefficient in comparison with the rigid case. However, the non-Newtonian effect increases load-capacity but decreases the friction coefficient. Moreover, the use of a transverse magnetic field increases both the friction coefficient and load capacity. Originality/value This study combines for the first time MHD and elastic deformation effects on finite-width slider-bearings using a non-Newtonian lubricant.

Modified Reynolds Equation for Non-Newtonian Fluid With Rheological Model in Frequency Domain

2005 ◽  
Vol 127 (4) ◽  
pp. 893-898 ◽  
Author(s):  
Chen Haosheng ◽  
Chen Darong
Keyword(s):  
Frequency Domain ◽  
Newtonian Fluid ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Pressure Profile ◽  
Thickness Variation ◽  
Lubrication Equation ◽  
Shear Dependent Viscosity ◽  
Modified Reynolds Equation ◽  
Dependent Viscosity

The purpose of this paper is to provide a lubrication equation for non-Newtonian fluid. Three nonlinear functions instead of common power law model are used to describe non-Newtonian properties more completely. They are shear dependent viscosity, first normal stress difference and stress relaxation. After the coordinate conversion which is needed for the lubricant film thickness variation, the functions are involved in the modified Reynolds equation and show their effects on the lubrication results. As the principle factor in lubrication, viscosity is expressed by a first order transfer function in frequency domain. Its variation process is described by the function’s amplitude frequency response curve, which is validated by rheological experiment. Numerical results of the modified Reynolds equation show that non-Newtonian lubricant’s load capacity is not always higher or lower than Newtonian lubricant’s, and non-Newtonian lubricant has flatter pressure profile at high working speed.

Effects of Foil Bending Rigidity on Spacing Height Characteristics of Hydrostatic Porous Foil Bearings for Web Handling Processes

1997 ◽  
Vol 119 (3) ◽  
pp. 422-427 ◽  
Author(s):  
H. Hashimoto
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Computation Time ◽  
Finite Width ◽  
Bending Rigidity ◽  
Weighted Residual Method ◽  
Web Handling ◽  
Foil Bearings ◽  
Wide Range ◽  
Foil Bending

In this paper, the effects of foil bending rigidity on the spacing height characteristics of hydrostatic foil bearings with a hollow porous shaft for web handling processes are analyzed by the finite width bearing theory. In the analysis, in order to save computation time and to improve the convergence of solutions, the two-dimensional modified Reynolds equation considering the added flow through porous shaft is reduced to an ordinary differential equation based on the weighted residual method. The reduced Reynolds equation and elastic equation for the foil are discretized by the finite difference method and solved numerically by the iterative technique. The numerical solutions for the pressure and film thickness distributions between foil and shaft are obtained for a wide range of bearing width-to-diameter ratio under various combinations of foil bending rigidity and foil wrap angle, and the spacing height characteristics of the foil bearings are examined theoretically.

Inflow Conditions and Suddenly Expanding Annular Shear-Thinning Flows

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Power Law ◽  
Numerical Solutions ◽  
Shear Thinning ◽  
Diameter Ratio ◽  
Inflow Velocity ◽  
Flow Recirculation ◽  
Shear Thinning Fluids ◽  
Power Law Index ◽  
The Impact ◽  
Inflow Conditions

The impact of inflow conditions on the flow structure and evolution characteristics of annular flows of Newtonian and shear-thinning fluids through a sudden pipe expansion are studied. Numerical solutions to the elliptic form of the governing equations along with the power-law constitutive equation were obtained using a finite-difference scheme. A parametric study is performed to reveal the influence of inflow velocity profiles, annular diameter ratio, k, and power-law index, n, over the following range of parameters: inflow velocity profile = {fully-developed, uniform}, k = {0, 0.5, 0.7} and n = {1, 0.8, 0.6}. Flow separation and entrainment, downstream of the expansion plane, creates central and a much larger outer recirculation regions. The results demonstrate the influence of inflow conditions, annular diameter ratio, and rheology on the extent and intensity of both flow recirculation regions, the wall shear stress distribution, and the evolution and redevelopment characteristics of the flow downstream the expansion plane. Fully-developed inflows result in larger reattachment and redevelopment lengths as well as more intense recirculation, within the central and corner regions, in comparison with uniform inflow conditions.

The Load Capacity of Short Journal Bearings With Oscillating Effective Speed

1964 ◽  
Vol 86 (2) ◽  
pp. 348-353 ◽  
Author(s):  
B. K. Gupta ◽  
R. M. Phelan
Keyword(s):  
Significant Contribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Numerical Solutions ◽  
Load Capacity ◽  
Journal Bearings ◽  
Squeeze Film ◽  
Major Conclusion ◽  
Angular Velocities ◽  
Effective Speed

The development of the Reynolds equation for the general case of dynamically loaded journal bearings is extended to include the concept of an effective speed that combines in one term the angular velocities of the journal, bearing, and load. Numerical solutions for the short-bearing approximation are presented for the case of an oscillating effective speed and a load that is constant or varying sinusoidally. Results are compared with available experimental data. The major conclusion is that for those cases involving an oscillating effective speed and a reversing load, the only significant contribution to load capacity comes from the squeeze film and the wedge film can safely be ignored when designing such bearings.

A study of a journal bearing lubricated by couple stress fluids considering thermal and cavitation effects

2002 ◽  
Vol 216 (5) ◽  
pp. 293-305 ◽  
Author(s):  
X-L Wang ◽  
K-Q Zhu ◽  
C-L Gui
Keyword(s):  
Couple Stress ◽  
Heat Conduction Equation ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Theoretical Study ◽  
Journal Bearing ◽  
Fluid Model ◽  
Load Capacity ◽  
Modified Reynolds Equation ◽  
Couple Stress Fluids

A theoretical study of a finite grooved journal bearing lubricated with couple stress fluids is made considering both thermal and cavitation effects. On the basis of the Stokes couple stress fluid model, the modified Reynolds equation and the energy equation are derived and then numerically solved together with the heat conduction equation. The solution to the modified Reynolds equation is determined using the Elrod cavitation algorithm. The effects of couple stress on the performance of a journal bearing are investigated. It is observed that the lubricants with couple stress, compared with Newtonian lubricants, not only yield an obvious increase in load capacity and decrease in coefficient of friction but also produce a slight increase in the temperature of lubricants and bush and a slight decrease in the side leakage flow.

Steady-state performance of a circular journal bearing lubricated with a non-Newtonian fluid considering the elastic deformation of the liner

2019 ◽  
Vol 233 (9) ◽  
pp. 1389-1396
Author(s):  
Boualem Chetti ◽  
Hamid Zouggar
Keyword(s):  
Friction Coefficient ◽  
Elastic Deformation ◽  
Power Law ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Carrying Capacity ◽  
Static Characteristics ◽  
Load Carrying ◽  
Power Law Index

In this work, a numerical study of the effect of elastic deformation on the static characteristics of a circular journal bearing operating with non-Newtonian fluids obeying to the power law model is presented. The modified Reynolds equation has been derived taking into consideration the effect of non-Newtonian behavior of the fluids. To obtain the pressure distribution, the Reynolds equation has been solved using finite difference technique with appropriate iterative technique incorporating Reynolds boundary conditions. The static performance characteristics for finite-width journal bearing in terms of the load-carrying capacity, the attitude angle, friction coefficient, and the side leakage have been studied for various values of the non-Newtonian power law index n and the elastic coefficient. The results show that the increase of the power law index produces a higher load-carrying capacity, a higher side leakage, a lower attitude angle, and a lower friction coefficient. From this study, it can be concluded that the elastic deformation has an important influence on the static characteristics of the journal bearing lubricated with a non-Newtonian fluid, and this influence is more significant for the journal bearing operating at larger values of the eccentricity ratio.

Rarefaction Effect on the Characteristics of Micro Gas Journal Bearings

2009 ◽  
Author(s):  
Haijun Zhang ◽  
Qin Yang
Keyword(s):  
Knudsen Number ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Slip Boundary Condition ◽  
Journal Bearings ◽  
Radial Clearance ◽  
Clearance Ratio ◽  
Attitude Angle ◽  
Modified Reynolds Equation ◽  
Bearing Number

Journal bearings, which are used to support radial loads in a rotating machine, have somewhat unusual requirements in MEMS deriving from the extremely shallow structures. Thus, the micro gas journal bearings are characterized by a very small length-diameter ratio, defined as the ratio of the bearing length to its diameter and a paradoxically large bearing clearance ratio, defined as the ratio of the average radial clearance to the bearing radius. Given the definition of the reference Knudsen number for micro gas journal bearings, the range of the reference Knudsen number is illustrated according to the viscosity values of air under different temperatures. With the reference Knudsen number being included, the modified Reynolds equation for micro gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The finite difference method (FDM) is employed to solve the modified Reynolds equation to obtain the pressure distribution, load capacities and attitude angles for micro gas journal bearings under different reference Knudsen numbers, bearing numbers and eccentricity ratios. Numerical analysis shows that the pressure profiles and non-dimensional load capacities decrease obviously with gas rarefaction strengthened, and the attitude angle changes conversely. Moreover, when the bearing number is smaller, the effect of gas rarefaction on the non-dimensional load capacity and attitude angle is less.

On the Analytical Evaluation of the Lubricant Pressure in the Finite Journal Bearing

2012 ◽  
Author(s):  
Athanasios Chasalevris ◽  
Dimitris Sfyris
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Numerical Solutions ◽  
Load Capacity ◽  
Separation Of Variables ◽  
Closed Form Expression ◽  
Linear Ordinary Differential Equations ◽  
Definition Of

The Reynolds equation for the pressure distribution of the lubricant in a journal bearing with finite length is solved analytically. Using the method of the separation of variables in an additive and in a multiplicative form, a set of particular solutions of the Reynolds equation is added in the general solution of the homogenous Reynolds equation and a closed form expression for the definition of the lubricant pressure is presented. The Reynolds equation is split in four linear ordinary differential equations of second order with non constant coefficients and together with the boundary conditions they form four Sturm-Liouville problems with the three of them to have direct forms of solution and one of them to be confronted using the method of power series. The mathematical procedure is presented up to the point that the application of the boundaries for the pressure distribution yields the final definition of the solution with the calculation of the constants. The current work gives in detail the mathematical path with which the analytical solution is derived, and it ends with the pressure evaluation and a comparison with past numerical solutions and an approximate analytical solution for a finite bearing. Also the parameters of primary interest to the bearing designer, such as load capacity, attitude angle, and stiffness and damping coefficients are evaluated and compared with numerical results.

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