The effect of turbulence on the performance of a two-lobe journal bearing lubricated with a couple stress fluid

2016 ◽  
Vol 68 (3) ◽  
pp. 336-340 ◽  
Author(s):  
Boualem Chetti
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Couple Stress ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Couple Stress Fluid ◽  
Turbulent Regime ◽  
Content Type ◽  
Couple Stress Fluids

Purpose This paper presents an analysis of the static characteristics of two-lobe journal bearings lubricated with couple stress fluids operating in a turbulent regime. The modified Reynolds equation for a couple stress fluids taking into consideration the effect of turbulence is solved using finite difference method. The load-carrying capacity, attitude angle, friction coefficient and side leakage are determined for various values of the couple stress parameter and Reynolds number. It is found that the couple stress fluids affect significantly on the performance of a two-lobe journal bearing in laminar and turbulent regime. Design/methodology/approach The modified Reynolds equation for a couple stress fluids taking into consideration the effect of turbulence is solved using finite difference method. Findings It is found that the couple stress fluids affect significantly on the performance of a two-lobe journal bearing in laminar and turbulent regime. Originality/value A couple stress fluid is used for lubrication of a two-lobe journal bearing in turbulent regime and laminar.

Investigation the combined effects of wear and turbulent on the performance of hydrodynamic journal bearing operating with couple stress fluids

2019 ◽  
Vol 10 (6) ◽  
pp. 825-837
Author(s):  
Mushrek A. Mahdi ◽  
Ahmed Waleed Hussein
Keyword(s):  
Couple Stress ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Performance Characteristics ◽  
Turbulent Regime ◽  
Hydrodynamic Bearings ◽  
Content Type ◽  
Hydrodynamic Journal Bearing ◽  
Local Reynolds Number ◽  
Couple Stress Fluids

Purpose The purpose of this paper is to investigate the combined effect of wear and turbulence on the performance of a hydrodynamic journal bearing operating under Newtonian and couple stress fluids (CSF). Design/methodology/approach The analysis consists of a modified Reynolds equation of incompressible thin viscous films, and the film thickness model taking into account the wear effect. The governing equation was solved numerically using the finite difference approach. Findings The effect of both the wear parameter and the local Reynolds number on the performance characteristics of bearing has been presented and discussed. The obtained results observed that the characteristics of the intact and worn bearing in turbulent and laminar have been enhanced due to the non-Newtonian fluid (CSF) effect. Also, the results display that bearing worn and the turbulent regime cannot be neglected in calculating the performance characteristics of the bearing lubricated with Newtonian and non-Newtonian fluids. The results achieved from this study, specify that the bearing characteristics are significantly affected by these effects. Originality/value The paper investigates the behavior of hydrodynamic bearings considering different aspects simultaneously is interesting, and the application meets the current needs of improvement in modeling hydrodynamic bearings under different conditions.

Analysis of Hybrid (Hydrodynamic/Hydrostatic) Journal Bearing

2013 ◽  
Vol 650 ◽  
pp. 385-390 ◽  
Author(s):  
Vijay Kumar Dwivedi ◽  
Satish Chand ◽  
K.N. Pandey
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Gas Turbines ◽  
High Speed ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Natural Boundary Condition ◽  
Dimensional Solution

The Hybrid (hydrodynamic/ hydrostatic) journal bearing system has found wide spread application in high speed rotating machines such as compressors, gas turbines, steam turbines, etc. The present studies include solution of Reynolds equation for hydrodynamic journal bearing with infinitely long approximation (ILA), infinitely short bearing approximation (ISA) and finite journal bearing approximation. Further Finite Journal bearing approximation considers two dimensional solution of Reynolds equation with natural boundary condition, which cannot be solved by analytical method. So, here the solutions for finite journal bearing have been done with finite difference method (a MATLAB® code is prepared for finite difference method) to get bearing performance parameters such as load capacity, Sommerfeld no., etc.

Combined effects of turbulence and elastic deformation on the performance of a journal bearing lubricated with a couple stress fluid

2018 ◽  
Vol 232 (12) ◽  
pp. 1597-1603 ◽  
Author(s):  
Boualem Chetti
Keyword(s):  
Elastic Deformation ◽  
Couple Stress ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Numerical Study ◽  
Performance Characteristics ◽  
Couple Stress Fluid ◽  
Turbulent Regime ◽  
Load Carrying ◽  
Modified Reynolds Equation

This paper presents a numerical study of the effect of turbulence and elastic deformation on the performance of a journal bearing operating with couple stress fluids, following Constantinescu’s turbulent lubrication theory. The modified Reynolds equation is derived taking into consideration the effect of turbulence and couple stresses. The modified Reynolds equation is solved using finite difference method. The results in terms of the load-carrying capacity, the attitude angle, friction coefficient and the side leakage are reported for various values of the couple stress parameter, the elastic coefficient, and Reynolds number. According to the obtained results, the couple stress fluid improves the performance characteristics of the rigid and deformed journal bearing in laminar and turbulent regimes. The results also show that bearing deformation and the turbulent regime cannot be neglected in calculating the performance characteristics of journal bearings lubricated with a Newtonian and a couple stress fluid.

Analysis of Infinitely Short and Infinitely Long Hydrodynamic Journal Bearings Under Micro-Polar Fluid by Direct Integration Method

2017 ◽  
Author(s):  
Bikash Routh
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Integration Method ◽  
Pressure Profile ◽  
Journal Bearings ◽  
Direct Integration ◽  
Polar Fluid ◽  
Direct Integration Method

In the present paper Reynolds equation of lubrication under micro-polar fluid for journal bearing is solved by direct-integration method under infinitely long and infinitely short journal bearing assumptions [1]. Infinitely long-bearing and infinitely short bearing solutions are the two available approximate closed form solutions for journal bearings. In the present investigation, solution of Reynolds equation i.e. pressure profile is compared with pressure profile obtained by previously used approximate method like finite difference method (FDM). Mentionable here that any approximation method needs lots of calculation and computer programing to get the result. In the present work it has been found that direct-integration method leads the almost same result as the conventionally used complex finite difference method. CFD analysis is also presented in the present work to justify the profile obtained by direct numerical method. It has seen here that theoretical and simulation results are in good agreement to each other’s.

Combined Influence of Misalignment and Orifice Diameter on the Static Performances of Hydrostatic, Water-Lubricated Journal Bearings

2014 ◽  
Vol 607 ◽  
pp. 608-611
Author(s):  
Hui Hui Feng ◽  
Chun Dong Xu ◽  
Feng Feng Wang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Film Thickness ◽  
Power Loss ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Orifice Diameter ◽  
Rigid Rotor ◽  
Static Performance

The water-lubricated bearings have gained an increasing focus to overcome the disadvantages of the oil film bearings and gas bearings. In this paper, the influences of orifice diameter in aligned and misaligned conditions on the static performance of two hydrostatic, four-recess, water-lubricated journal bearings used to support a rigid rotor, are investigated. The steady Reynolds equation for the journal bearing for the turbulent bulk flow and the film thickness expression considering tilting angles are used and numerically solved by finite difference method. Results demonstrate that the static performances, such as the quality, power loss and temperature rise are affected by the tilting angles, orifice diameter to some degree.

Averaging effect on pitch errors in hydrostatic lead screws considering helical recess layout and nut misalignment

2017 ◽  
Vol 232 (9) ◽  
pp. 1181-1192
Author(s):  
Yongtao Zhang ◽  
Changhou Lu ◽  
Yunpeng Liu
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Radial Displacement ◽  
Continuity Equation ◽  
Reynolds Equation ◽  
Spatial Frequencies ◽  
The Finite Difference Method ◽  
Low Speeds ◽  
Flank Surface

The hydrostatic nut usually has different helical recess layouts and the nut misalignment (including radial displacement and tilt) may occur during movement, which will influence the averaging effect on pitch errors, i.e. the motion accuracy of the hydrostatic nut. This paper researches the averaging effect on pitch errors in capillary compensated hydrostatic lead screws, under low speeds and considering the helical recess layout and the nut misalignment. Based on the equivalent plane of the flank surface of threads, whose normal clearance is calculated by vector operations, the Reynolds equation and the flow continuity equation are solved using the finite difference method. The results show that (a) the averaging coefficient presents bulges at corresponding spatial frequencies for the hydrostatic nut with discontinuous helical recesses, (b) the positions of the first and second periodical fluctuations of the averaging coefficient are the same for the hydrostatic nut with symmetric continuous helical recesses, symmetric discontinuous helical recesses, or asymmetric continuous helical recesses, and (c) The nut misalignment has little influence on the averaging coefficient.

Accuracy analysis of narrow groove theory for spiral grooved gas seals: A comparative study with numerical solution of Reynolds equation

2018 ◽  
Vol 233 (6) ◽  
pp. 899-910
Author(s):  
Wanjun Xu ◽  
Jiangang Yang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Reynolds Equation ◽  
Compressible Fluids ◽  
Accuracy Analysis ◽  
Performance Parameters ◽  
Typical Performance ◽  
Gas Seals ◽  
Film Stiffness

This study examined the accuracy of narrow groove theory for spiral grooved gas seals. Designed for compressible fluids, a finite difference method was proposed to solve the two-dimensional compressible Reynolds equation. The predictions of narrow groove theory were compared with those of the Reynolds equation. The typical performance parameters including gas film force, leakage, gas film stiffness, and torque were analyzed. The results show that the predictions of narrow groove theory generally agree with those of finite difference method when the number of grooves is more than eight. The gas film force, leakage, and gas film stiffness were slightly overestimated by narrow groove theory, with better accuracy for gas film force, leakage, and torque than for gas film stiffness. Although some cases showed deviation for gas film stiffness of as much as 52%, most deviations can be effectively ignored. Therefore, it is feasible to use narrow groove theory for qualitative analysis such as groove shape optimization. The present analysis provides the optimum groove parameters for the investigated seal.

An implementation of adjoint-based topology optimization in magnetostatics

2019 ◽  
Vol 38 (3) ◽  
pp. 1023-1035 ◽  
Author(s):  
Rtimi Youness ◽  
Frederic Messine
Keyword(s):  
Topology Optimization ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Design Problem ◽  
Large Scale ◽  
Adjoint Method ◽  
Processing Unit ◽  
Original Design ◽  
Content Type

Purpose In magnetostatics, topology optimization (TO) addresses the problem of finding the distributions of both current densities and ferromagnetic materials to comply with fixed magnetic specifications. The purpose of this paper is to develop TO in order to design Hall-effect Thrusters (HETs). Design/methodology/approach In fact, TO problems are known to be large-scale optimization problems. The authors therefore adopt the adjoint method to reduce the computation time required to obtain the gradient information. In this paper, they illustrate the continuous variant of the adjoint method in the context of magnetostatics TO. Herein, the authors propose an implementation of the adjoint method then use it within a gradient-based optimization solver fmincon-MATLAB to solve a HET TO design problem. Findings By comparison with finite difference method, the authors validate the accuracy of the suggested implementation of the adjoint method. Then, they solve a large-scale HET TO design problem. The resultant design of TO is distinctly original and not intuitive. Research limitations/implications In this paper, the authors introduce TO as a tool that has allowed them to explore new and innovative design of a HET. However, although the design presented is original, its manufacture is not feasible. Thus, a discussion section has been included at the end of paper to suggest a possible way to concretize topological solutions. Practical implications TO helps to explore more original design possibilities. In this paper, the authors present an implementation of the adjoint method that makes it possible to solve efficiently and in less central processing unit time large-scale TO design problem. Originality/value An easy implementation of the adjoint method is presented in magnetostatics TO. This implementation was first validated by comparison with the finite difference method and then used to solve a large-scale design problem. The result of the TO design problem is distinctly original and non-intuitive.

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.

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