/Tribology Engineers, Part J: Journal of Engineering
Proceedings of the Institution of Mechanical
/content/221/6/623The online version of this article can be found at:
DOI: 10.1243/13506501JET287
2007 221: 623
Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology N Tala-Ighil, P Maspeyrot, M Fillon and A Bounif
Effects of surface texture on journal-bearing characteristics under steady-state operating conditions
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623 Effects of surface texture on journal-bearing characteristics under steady-state operating conditions N Tala-Ighil1∗,P Maspeyrot1,M Fillon1,and A Bounif2
1Laboratoire de Mécanique des Solides(LMS),Universitéde Poitiers,UMR CNRS6610,Futuroscope C
hasneuil Cedex,France
2Laboratoire de Carburants Gazeux et Environnement,Facultéde Génie Mécanique,Universitéd’Oran,Oran,Algeria The manuscript was received on14March2007and was accepted after revision for publication on22May2007.
DOI:10.1243/13506501JET287
Abstract:Developments in microscopy have a profound effect on the resurgence of tribological
applications at the microscopic level.Using surfaces with controlled microgeometry may prove
an effective approach to improving bearing performance.It is conquently of interest to study
the lubrication of journal bearing systems taking into consideration the effect of surface geometry
design.
A numerical approach is ud in the analysis of texture effects on bearing characteristics.The
results from investigating the performance of bearing surfaces with spherical dimple textures
suggest that contact characteristics such as minimumfilm thickness,maximum pressure,axial oil
filmflow,and friction torque may be improved through an appropriate surface texture geometry
and appropriate textures distribution on the contact surface.
The main purpo of our work is to model and understand the evolution of journal-bearing
characteristics with textures.A rigorous methodology is recommended.The work is divided into
two steps.Thefirst one rves to quantify the evolution of the characteristics with the texture
parameters and to deduce their optimized values.The cond step enhance the performance
of the journal bearing by progressively taking into account the optimized values of texture
parameters,especially the textures disposition.
Keywords:textured surface,dimples,hydrodynamic lubrication,journal bearing,finite-
difference method
1INTRODUCTION
Tribology is the study of lubrication,friction,wear, and contact mechanics in order to understand surface interactions and to suggest solutions to fundamen-tal problems.The expanding range of tribological applications,from the traditional industrial machin-ery to the recent applications in micro fabrication has demonstrated its importance and also revived interest in thisfield.
∗Corresponding author:Laboratoire de Mécanique des Solides (LMS),Facultédes Sciences–SP2MI,Universitéde Poitiers,Bd Marie and Pierre Curie–BP30179,Futuroscope Chasneuil Cedex ail:nacer.tala-ighil@ext.univ-poitiers.fr
The introduction of a range of microfabrication techniques coupled with developments in microscopy has had a profound effect on the reappearance of tribological applications at the microscopic level.With the help of this new technology,it is now possible to produce microstructures on journal-bearing surfaces to improve the overall tribological performance including reduction in friction,improvement in relia-bility,increa in verity conditions and load capacity, and lowering energy consumption.
Using surfaces with controlled microgeometry may be an effective approach to improving bearing pe
r-formance.At the same time,the development of controlled texture in bearing design requires analy-s of the microfeature effect on lubrication.Surface texturing is claiming progressively more attention and is expected to be an important component in future
JET287©IMechE2007Proc.IMechE Vol.221Part J:J.Engineering Tribology
624N Tala-Ighil,P Maspeyrot,M Fillon,and A Bounif
bearing structure design as demonstrated by Priest and Taylor[1].
Wakuda et al.[2]verifies the effect of microdimples on frictional properties.Pin-on-disk tests modelling the contact between cylindrical and planar faces were carried out for a variety of surface morphologies in which dimples were pattern-machined with differ-ent size,density,and geometry.It was found that the tribological characteristics depended greatly on the size and density of the microdimples,whereas the dimple shape did not significantly affect the friction coefficient regardless of rounded or angular profiles. Kovalchenko et al.[3]showed that lar texturing expanded the contact parameters in terms of load and speed for hydrodynamic lubrication.The beneficial effects of lar surface texturing are more pronounced at higher speeds and loads and with higher viscosity oil.The surface texture has a positive effect on load capacity and on the coefficient of friction for cert
ain applications and loads.The mechanisms identified as being responsible for generating additional load capacity are microcavitation convective inertia and piezo-viscosity.
In recent publications[4–6]Navier–Stokes equa-tions have been solved for theflow between two parallel surfaces:one smooth,one having a single surface pocket.They showed that the pressure gen-erating effect of surface texture in fullfilm operation might result from convective inertia.Piezo-viscosity may play a role in heavily loaded lubricated contacts where in local converging regions;the pressure ri may be larger than the pressure drop in diverging regions.
A considerable amount of publications have been devoted to EHL problems[7–12],where the surface geometric profiles,such as digitized rough surfaces and even measured real engineering surfaces,are involved in lubrication calculations.Only a limited amount of information is available on lubrication solutions for journal-bearing contact systems with real engineering surfaces[13–15].This is due to the diffi-culty insofar as journal-bearing lubrication involves a much larger area of surface interaction when com-pared to that in point contact problems.Similar dif-ficulties exist in the analysis of the heavily loaded journal bearings operating under a mixed lubrication regime[16].
Siripuram and Stephens[17]prent a numerical study of the effects of different shapes of microaspe
ri-ties in sliding surface lubrication when hydrodynamic films are found.Positive and negative asperities of constant height(depth)are considered with circular, square,diamond,hexagonal,and triangular cross-ctions.The results indicate that triangular asperities give the smallest leakage rate and square asperities the largest.The minimum coefficient of friction for all shapes is found to occur at an asperity area fraction of0.2for positive asperities and0.7for negative asperities.
This prent work focus on hydrodynamic lubri-cation of journal-bearing surfaces with deterministic textures that ensure lubrication in a hydrodynamic region and thereby reduce friction and increa load capacity.
Analys of engineering surfaces in lubrication require detailed surface measurement;refined surface mesh and calculation,as well as substantial computa-tional power.The numerical method described below is applied to investigate the lubrication performance of a textured surface with spherical dimples.
2PROBLEM FORMULATION
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Using the classical lubrication hypothesis,it is assumed thatflow is laminar;inertia is neglected.The fluid is Newtonian and incompressible.Density and viscosity are assumed to be constant.For Cartesi
an coordinates,when the thickness of the lubricantfilm h is in the direction of the y-axis(Fig.1(a)),the pres-sure in the lubricatingfilm is governed by the following Reynolds’equation
∂
∂x
h3
12μ
∂P
∂x
+
∂
∂z
h3
12μ
∂P
∂z
纹头发=
(u2−u1)
2
∂h
∂x
父亲歌词+
∂h
∂t
(1)
where P is the lubricant pressure,h thefilm height,μthe dynamic viscosity,and u1,u2are the velocities of the journal and the bearing,respectively.
The bearing geometry is shown in Fig.1.When using the following variables:Z=z/L,θ=x/R,(ω2−ω1)= (u2−u1)/R,and for a journal operating at steady state, Reynolds’equation(1)becomes
∂
∂θ
h3
∂P
∂θ
+
R
L
2
∂
∂Z
h3
∂P
∂Z
=6μR2
(ω2−ω1)
∂h
∂θ
(2)
Equation(3)describes thefilm thickness h.The thick-ness of thefluidfilm can be written as follows
h(θ,Z)=C(1+εcosθ)+ h(θ,Z)(3)
where C is the radial clearance bearing,ε=e/C the eccentricity ratio,and h(θ,Z)thefilm thickness variation due to the textured surface.
The Reynolds classical boundary conditions have been ud with the Reynolds’equation.The con-ditions ensure that∂P/∂θ=∂P/∂Z=0and P=P c at the rupture limits of thefilm lubricant.P c is the critical pressure,generally assimilated to atmospheric
Proc.IMechE Vol.221Part J:J.Engineering Tribology JET287©IMechE2007
Effects of surface texture on journal-bearing characteristics
625
Fig.1Journal bearing in the hydrodynamic lubrication:(a)geometry of the bearing;(b)right ction of the bearing;(c)texture geometry
pressure(the reference pressure).The hydrodynamic
美丽的作文pressure is t to zero at the inlet zone of thefluidfilm
(θ=0).
F is the static external force applied to the bearing
journal.In the ca of the prent study,the bearing is
operating under steady-state conditions;the applied
load F is constant and its direction is vertical(ψ=0).
The hydrodynamics load components W X and W Y,in
the global coordinate system(O2,X,Y),are calculated
by integrating the pressurefield along the surface con-
tact of the journal bearing.Then the total load W,
supported by the contact and the attitude angleφ,is
finally obtained,as shown in Fig.1(b).
The friction torques,ζ1on the journal andζ2on
the bearing,are,respectively,obtained by integrat-
ing the shearing stress along the journal surface
(y=h)and along the bearing surface(y=0).The
expression for shearing stress in the lubricantfilm
isτxy=[±h/2·(∂p/∂x)+μ·(u1−u2)/h].The dissipa-
tion power generated by thefluid friction between the
surfaces of contact can be determined by the equation
℘=(ζ1·ω1+ζ2·ω2).The axialfluidflow is obtained
by the integration of thefluid speed in the axial
direction z,and through thefilm ction d s=d x d y.
All the characteristics described above for the hydro-
dynamic lubricated contact of the journal bearing are
calculated numerically.The details of the calculations
are reported in Frêne et al.[18].
2.1Texture geometry
The elliptically dimple texture geometry is defined by
(x−x c)2
r2
x +
( h−y c)2
r2
y
+
(z−z c)2
r2
z
=1(4)
where r x,r y,and r z are the radius of the elliptical
dimples,respectively,in the x,y,and z directions.
In the ca of spherical geometry r x=r z=r,where
r is the radius of the circle on the bearing surface. h
is thefilm thickness variation in the textured surface
(Fig.1(c)).O c(x c,y c,z c)are the coordinates of the dim-
ple centre.The centre of the dimple is located on the
surface of the bearing,making y c=0.
Finally,the depth at point M on the surface bear-
ing situated on the spherically dimple geometry is
defined by
h=r y
雷锋简介r
r2c2c2(5)
2.2Solution of Reynolds’equation
The determination of the pressurefield in the lubricant
film consists of the numerical resolution of equation
(2)by using thefinite-difference method(FDM).After
application of the FDM to the Reynolds’equation(2),
a system of linear equations is obtained
P i,j=(1− )P i,j+ [AP i+1,j+BP i−1,j
+C(P i,j+1+P i,j−1)+D](6)
where P i,j is the pressure value at a node(i,j)of the
mesh,A,B,C,and D are coefficients.The resolution of
the system(6)of Nθ·N Z equations is obtained by the
iterative method of Gauss–Seidel with over-relaxation
parameter ,in lubrication the value of this parameter
is generally between1.5and1.85.
The u of an iterative method for the resolution is
justified by the application of the Reynolds’bound-
ary conditions.The analysis only leaves pressure as
JET287©IMechE2007Proc.IMechE Vol.221Part J:J.Engineering Tribology
626N Tala-Ighil,P Maspeyrot,M Fillon,and A
Bounif
Fig.2Flow chart for steady-state ca
the unknown to be solved,while the eccentricity is
according to the load difference between
the given value F and the computational one W,at the
previous iteration step).It implies that only equation
(1)is ud to form thefinal system equation for obtain-
ing P,while a cavitation condition should also be
satisfied.For a steady-state regime,the computational
procedure is shown in the followingflow chart(Fig.2).干部教育培训条例
Initial values are t for eccentricityε.The pressure
field at each nodal point under a steady external load-
ing F(shown in Fig.1(b))is obtained,verifying the
pressure convergence condition(equation(7))at each
node i of the bearing surface mesh
上课走神咋办P i P i
ε
P
(7)
The supported load W and bearing attitude angleφare calculated.The calculated load W andfixed load F are compared;the process is stopped after the load convergence condition is satisfied.
F−W
F
ε
W
(8)
whereεP andεW are the errors in the calculations of the pressure P and the load W,respectively.If the error control(equation(8))is not satisfied,the eccentricity value is updated and the process of calculation begins.
3RESULTS AND DISCUSSION
3.1Computational conditions and validation The bearing surface is stationary(ω2=0)and the jour-nal is moving(ω1=0).Only one-half of the journal-bearing system is studied becau of the symmetry of the bearing and becau refined uniform meshes are ud.Geometrical parameters,as well as operating conditions for the journal bearing studied by Vincent et al.[19],are:
(a)magnitude of the external force F=12600or
81591N;
(b)angular speed of the journalω1=625.4rad/s;
(c)journal radius R=0.0315m;
(d)bearing length L=0.063m;
(e)radial clearance C=0.00003m;
(f)lubricant viscosityμ=0.0035Pa s.
For smooth surfaces of the journal bearing,the contact parameters vary with the mesh refinement Nθ×N Z and with the convergence criteriaεP andεW in relation to pressure and load calculation,respectively.
For the results prented below,the impod preci-sions for the calculations of the pressure P and the load W areεP=10−4andεW=10−5.The mesh size ud is Nθ=391and N Z=142.
In relation to the journal bearing with smooth sur-faces,the most important contact characteristics are computed,the results obtained are listed in Table1. The results derived using the computational code of the authors are compared to tho calculated by Vincent et al.[19].Table1shows the very good con-cordance between the results of the two studies in two operating conditions(F=12600N and F=81591N).
Table1Smooth journal-bearing characteristics
L/D=1
Our results Vincent’s results[19]
Amplitude of the external force,F(N)12600815911260081591历史比较语言学
Sommerfeld number,S0.12100.01870.12100.0187
Eccentricity ratio,ε0.6010.9010.6000.900
Attitude angle,φ(deg)50.526.3550.226.03
Maximum pressure,P max(MPa)7.783.587.081.71
Minimumfilm thickness,h min×10−6(m)11.96 2.9712.00 3.00
Axialflow,Q×10−5(m3/s−1) 1.74 2.58 1.73 2.55
Proc.IMechE Vol.221Part J:J.Engineering Tribology JET287©IMechE2007
