Relationship between elliptical form error and rotation accuracy of hydrostatic journal bearing

2017 ◽  
Vol 69 (6) ◽  
pp. 905-911 ◽  
Author(s):  
Jun Zha ◽  
Yaolong Chen ◽  
Penghai Zhang
Keyword(s):  
Kinetic Equation ◽  
Continuity Equation ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Form Error ◽  
Machining Error ◽  
Content Type ◽  
Precision Design ◽  
Error Averaging

Purpose The form error of shaft and hole parts is inevitable because of the machining error caused by rotation error of tool axis in machine tools where the elliptical form error is the most common in shaft and bearing bush. The purpose of this paper is to present the relationship between the elliptical form error and rotation accuracy for hydrostatic journal bearing in precision spindle and rotation table. Design/methodology/approach An error averaging effect model of hydrostatic journal bearing is established by using Reynolds equation, pressure boundary conditions, flux continuity equation of the land and kinetic equation of shaft in hydrostatic journal bearing. The effects of shaft and bearing bush on rotation accuracy were analyzed quantitatively. Findings The results reveal that the effect of shaft elliptical form error on rotation accuracy was six times larger than bearing bush. Therefore, to improve the rotation accuracy of hydrostatic journal bearing in spindle or rotation table, the machining error of shaft should be controlled carefully. Originality/value An error averaging model is proposed to evaluate the effect of an elliptical form error on rotation accuracy of hydrostatic journal bearings, which solves the Reynolds equation, the flux continuity equation and the kinetic equation. The determination of form error parameters of shaft and bearing bush can be yielded from finding results of this study for precision design of hydrostatic journal bearings.

Dynamic Stiffness and Damping Coefficients of Aerostatic, Porous, Journal Bearings

1978 ◽  
Vol 20 (5) ◽  
pp. 291-296 ◽  
Author(s):  
N. S. Rao ◽  
B. C. Majumdar
Keyword(s):  
Continuity Equation ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Dynamic Pressure ◽  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Damping Coefficients ◽  
Design Charts ◽  
Stiffness And Damping

A periodic (displacement) disturbance is imposed on an aerostatic, porous, journal bearing of finite length under steady-state conditions. The dynamic pressure distribution is obtained by a pressure perturbation analysis of Reynolds equation and a modified flow continuity equation in a porous medium. Dynamic stiffness and damping coefficients for different operating conditions are calculated numerically, using a digital computer, and presented in the form of design charts.

Restrictor-based studies of hybrid hole-entry conical journal bearings

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Prashant G. Khakse ◽  
Vikas M. Phalle
Keyword(s):  
Numerical Simulation ◽  
Design Methodology ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Constant Flow ◽  
Hybrid Mode ◽  
Content Type ◽  
Conical Bearing ◽  
Flow Valve

Purpose This paper aims to describe how successfully a particular restrictor delivers its best in increasing the conical journal bearing performance. The restrictors are used in the hole-entry conical journal bearing subjected to hybrid mode. Thus, the restrictors, like constant flow valve (CFV), orifice and capillary, are studied comparatively. Design/methodology/approach Numerical simulation for the bearing results with the three restrictors are obtained by using finite element method (FEM) under the well-known modified Reynolds equation. Findings When the hole-entry conical journal bearings, with the restrictor design parameter range C¯s2 = 0.03 – 0.09, are operated, the results obtained are quite distinctive and significant. It indicates that the CFV restrictor-based conical bearing gives enhanced performance in comparison to orifice and capillary restrictors. Moreover, it suggests the performance-wise sequence of the restrictors in hybrid bearings as CFV > Orifice > Capillary. Originality/value The outcome of the research paper will give insight to help the bearing designer to choose the particular restrictor in hybrid conical bearing depending on the industrial need.

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

The Effect of Lubricant Inertia in Journal-Bearing Lubrication

1957 ◽  
Vol 24 (4) ◽  
pp. 494-496
Author(s):  
J. F. Osterle ◽  
Y. T. Chou ◽  
E. A. Saibel
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Hydrodynamic Theory ◽  
Simple Relationship ◽  
Inertia Effect ◽  
Laminar Regime ◽  
Steady State Operation

Abstract The Reynolds equation of hydrodynamic theory, modified to take lubricant inertia into approximate account, is applied to the steady-state operation of journal bearings to determine the effect of lubricant inertia on the pressure developed in the lubricant. A simple relationship results, relating this “inertial” pressure to the Reynolds number of the flow. It is found that the inertia effect can be significant in the laminar regime.

Numerical and Experimental Investigations on Preload Effects in Air Foil Journal Bearings

2017 ◽  
Author(s):  
Marcel Mahner ◽  
Pu Li ◽  
Andreas Lehn ◽  
Bernhard Schweizer
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Compressible Fluids ◽  
Experimental Investigations ◽  
Hysteresis Curves ◽  
Numerical Predictions ◽  
Bearing Stiffness ◽  
Gasdynamic Model ◽  
Good Agreement

A detailed elasto-gasdynamic model of a preloaded three-pad air foil journal bearing is presented. Bump and top foil deflections are herein calculated with a nonlinear beamshell theory according to Reissner. The 2D pressure distribution in each bearing pad is described by the Reynolds equation for compressible fluids. With this model, the influence of the assembly preload on the static bearing hysteresis as well as on the aerodynamic bearing performance is investigated. For the purpose of model validation, the predicted hysteresis curves are compared with measured curves. The numerically predicted and the measured hysteresis curves show a good agreement. The numerical predictions exhibit that the assembly preload increases the bearing stiffness (in particular for moderate shaft displacements) and the bearing damping.

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.

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.

Numerical study on steady state performance enhancement of partial textured hydrodynamic journal bearing

2019 ◽  
Vol 71 (9) ◽  
pp. 1055-1063 ◽  
Author(s):  
Sanjay Sharma ◽  
Gourav Jamwal ◽  
R.K. Awasthi
Keyword(s):  
Steady State ◽  
Journal Bearing ◽  
Performance Enhancement ◽  
Surface Texturing ◽  
Journal Bearings ◽  
Enhancement Ratio ◽  
Content Type ◽  
Maximum Value ◽  
Static Performance ◽  
Hydrodynamic Journal Bearing

Purpose The purpose of this paper is to provide the various steady state parameters of hydrodynamic journal bearings have been determined to get maximum performance enhancement ratio. For this, the bearings inner surface is textured with triangular shape with different texture depths and a number of textures in pressure increasing region. The textured region acts as a lubricant reservoir, which provides additional film-thickness and reduce friction. Therefore, enhance the overall performance of bearing. Design/methodology/approach In the present study, the effect of triangular shaped texture on the static performance characteristics of a hydrodynamic journal bearing has been studied. Different values of texture depths and a number of textures have been numerically simulated in pressure developing region. The static performance characteristics have been calculated by solving the fluid flow governing Reynolds equation using the finite element method, assuming iso-viscous Newtonian fluid. The performance enhancement ratio, which is the ratio of load carrying capacity (LCC) to the coefficient of friction (COF) has been calculated from results to finalized optimum design parameters. Findings The paper provides numerically obtained results indicate that surface texturing can improve bearing performance if the textured region is placed in the pressure increasing region. Moreover, surface texturing is the most effective at bearing performance enhancement when the bearing operates at lower eccentricity ratios and texture depth. The performance enhancement ratio, which is the ratio of LCC to the COF is found to be a maximum value of 2.198 at texture depth of 1.5, eccentricity ratio of 0.2 and the textured region located in the increasing pressure region. Research limitations/implications The present study is based on a numerical based research approach, which has its limitations. So, researchers are encouraged to investigate the same work experimentally. Practical implications The paper includes implications to be beneficial for designers for designing better hydrodynamic journal bearings. Originality/value For the triangular shaped texture, considered in the present study, the optimum values of texture depth and texture distribution region have also been determined. While designing, designers should focus on those values of texture depth, texture region and a number of textures, which give the maximum value of performance enhancement ratio, which represents maximum LCC at the lowest value of the COF.

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.

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.

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