HYDRODYNAMIC EFFECTS OF TEXTURE GEOMETRIES ON JOURNAL BEARING SURFACES

Paper presented at

Bucharest, Romania

HYDRODYNAMIC EFFECTS OF TEXTURE GEOMETRIES ON JOURNAL BEARING SURFACES

Nacer TALA-IGHIL

, Patrick MASPEYROT

, Michel FILLON

, Abdelhamid BOUNIF

1)

Université de Poitiers, Laboratoire de Mécanique des Solides (LMS), UMR CNRS 6610, FRANCE

2)

Université d’Oran, Faculté de Génie Mécanique, Laboratoire de Carburants Gazeux et Environnement, ALGERIE

nacer.tala-ighil@ext.univ-poitiers.fr

ABSTRACT

Lately, the expanding range of tribological applications to the microscopic levels has revived interest in this field. Actually, little is understood about the subtle effects of variations of a journal bearing’s profile upon its performance. The surface texturing is expected to make an important contribution to future technologies of bearing.

Numerical study based on finite difference methods is used to find the tendency of important tribological properties of a journal bearing such as minimum film thickness, maximum pressure, axial oil flow and friction torque.

The present work is a comparative study of the hydrodynamic effects of a few deterministic texture shapes in a journal bearing application. The geometry and the size of textures affect load capacity and friction torque. The parallelepipedic textures show advantages compared to the other geometries for the improvement of the performances of the bearing. In general, the impact of shapes is more visible for higher asperity area in accordance with the geometrical differences.

Keywords: texture, lubrication, hydrodynamic, journal bearing

1. INTRODUCTION

The field of tribology covers the study of lubrication, friction, wear, and contact mechanics in order to understand the surface interactions and to suggest solutions to underlying problems. The expanding range of tribological applications, traditionally from industrial machinery to micro/nano applications lately, has not only demonstrated its importance, but also revived interest in this field.

The introduction of a range of micro-fabrication techniques coupled with developments in microscopy has had a profound effect on the resurgence of tribological applications at the microscopic levels.

Etsion [1] reviews the current effort being made world wide on surface texturing in general and on laser surface texturing (LST) in particular and

describes some fundamental on going research around the world with LST.

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, improve- ment in reliability, increase in severity conditions and load capacity and lowering energy consumption.

The technology of surface texturing is expected to be an important component in future bearing structure design as demonstrated by Priest [2].

Wakuda [3] verifies the effect of micro-dimples on the 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 different size, density, and geometry.

It was found that the tribological characteristics depended greatly on the size and density of the micro- dimples, whilst the dimple shape did not significantly affect the friction coefficient regardless of rounded or angular profiles.

Kovalchenko [4] showed that laser texturing expanded the contact parameters in terms of load and speed for hydrodynamic lubrication. The beneficial effects of laser surface texturing are more pronounced at higher speeds and loads and with higher viscosity oil.

Pascovici [5] presents a theoretical investigation of a partially textured slider using both analytical and numerical approaches. The performance of the bearing was evaluated varying different parameters:

number of dimples, texture density, dimple depth and textured fraction of the slider.

Mehenny [6] has used a theoretical analysis to investigate the influence of circumferential waviness of the journal on the lubrication of the inter-main bearing of an automotive engine. The bearing and shaft surfaces were assumed to be rigid and the lubricant isoviscous.

The results show a significant influence of shaft lobbing on predicted maximum film pressure and minimum film thickness, particularly as the number and size of lobes increase.

Burstein [7] has developed a mathematical model for predicting the performance of laser- textured seals with pores. A solution of two- dimensional steady-state Reynolds equation was given for rectangular and exponential pores, as well as expression for the hydrodynamic pressure distribution over the control cell and for the cell load support. It was shown that the pore ensemble is an essential aspect in exact determination of the load support and better insight into the tribologic behaviour of pore-covered surfaces.

Ronen [8] presents a model to study the poten- tial use of micro-surface structure in the form of micro pores to improve tribological properties of reci- procating automotive components. It is shown that surface texturing can efficiently be used to maintain hydrodynamic effects even with nominally parallel surfaces, and that optimum surface texturing may substantially reduce the friction losses in reciproca- ting automotive components. Brizmer [9], shows the potential use of a new technology of laser surface texturing in parallel thrust bearings. The surface tex- ture has the form of micro-dimples with preselected diameter, depth, and area density. Optimum parame- ters of the dimples, and best LST mode, are found in order to obtain maximum load carrying capacity for a thrust bearing having parallel mating surfaces.

Siripuram [10] presents a numerical study of the effects of different shapes of micro-asperities 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-sections.

The results indicate that triangular asperities giving the smallest leakage rate and square asperities giving a largest leakage rate. The minimum coefficient of friction for all shapes is found to occur at an asperity area fraction of 0.2 for positive asperities and 0.7 for negative asperities.

Analyses of engineering surfaces in lubrication require detailed surface measurement; refined surface mesh and calculation, as well as substantial computational power.

In this present work, focus is made on hydro- dynamic lubrication of a journal bearing surfaces with deterministic textures which ensure the provision of lubrication in hydrodynamic region, and thus reduce the friction and increase the load capacity.

PROBLEM FORMULATION

Governing equations

Using the classical lubrication hypothesis, it is assumed that the flow is laminar and that the inertia is neglected. The fluid is Newtonian and income- pressible. The density and the viscosity are assumed to be constant. In a hydrodynamic lubrication pro- blem, the governing equations in a full hydrodynamic lubrication region can be described by the well- known Reynolds’ equation.

For Cartesian coordinates, when the thickness of the lubricant film h is in the direction of the y axis (fig. 1a), the pressure in the lubricating film for a journal operating at steady state, is governed by the following equation :

3 3

2 1

u u

h P h P h

x 12µ x z 12µ z 2 x

⎛ ⎞ ⎛ ⎞ −

∂ ∂ ∂ ∂ ∂

+ =

⎜ ⎟ ⎜ ⎟

⎜ ⎟ ⎜ ⎟

∂ ⎝ ∂ ⎠ ∂ ⎝ ∂ ⎠ ∂ (1)

In equation (1), P is the lubricant pressure, h is the film height, µ is the dynamic viscosity and u1, u2

are the velocities of the journal and the bearing, respectively.

Fig. 1. Hydrodynamic journal bearing (a) Bearing geometry; (b) Right section of the bearing; (c)

Texture geometry.

The bearing geometry is shown in figure 1.

When using the following variables: Z=z/L, θ=x/R

and (u2-u1)=R(ω₂-ω₁), Reynolds’ equation (1) becomes:

( )

2

3 3

2

2 1

P R P

h h

L Z Z

6 R h

θ θ

µ ω ω

θ

∂ ⎛⎜ ∂ ⎞ ⎛ ⎞⎟ ⎜ ⎟+ ∂ ⎛⎜ ∂ ⎞⎟

∂ ⎝ ∂ ⎠ ⎝ ⎠ ∂ ⎝ ∂ ⎠

∂

=

⎡ ⎤

= ⎢⎣ − ∂ ⎥⎦

(1)

where R is the radius of the shaft, L the length of the bearing and ω1, ω2 are the angular velocities of the journal and the bearing.

Equation (3) describes the film thickness h which can be written as follows.

( ) (

h=C 1+εcosθ +∆ θh ,Z

) )

(2) In the equation above, is the film thickness variation due to the textured surface, e the relative eccentricity of the journal and C the radial clearance bearing.

(

h ,Z

∆ θ

The boundary conditions, known as Reynolds boundary conditions, are used to determine the rupture zone of the film. They consist in ensuring that

P / θ P / Z 0

∂ ∂ = ∂ ∂ = and P=0 at the rupture limits of the film lubricant.

In the case of the present study, the bearing is operating under steady state conditions; the applied load F is constant and its direction is vertical (ψ =0).

T tal load W (supported by the contact) is calculated by integrating the pressure field along the surface contact of the journal bearing, than the attitude angle f is obtained (figure 1b).

he to

The friction torques, ζ₁ on the journal and ζ₂ on the bearing, are obtained by integrating the shea- ring stresses

( ) ( )

xy h / 2 p / x u1 u2 / h τ = ±⎡⎣ ∂ ∂ +µ − ⎤⎦

along the journal surface (y=h) and along the bearing surface (y=0), respectively. The axial fluid flow is obtained by the integration of the fluid speed component in the axial direction z, and through the film section ds=dxdy.

All the characteristics cited above for the hydrodynamic lubricated contact of the journal bearing are calculated numerically. The details of the calculations are reported in [11].

Texture shapes

Figure 2 shows the three textures shapes used in this study. Where rx, ry and rz are the dimensions of the texture, respectively in the x, y and z directions as shown on figure below (xc,yc,zc) are the coordinates of the texture centre Oc. The centre of the texture is located on the surface of the bearing, making yc=0.

The depth at point M on the surface bearing situated on the texture geometry is defined by ∆h (fig. 1c).

• The spherical texture geometry is defined by,

(

) (

) (

)

2 2 2

y

x x h y z z

r r r 1

∆

− − − ²

+ + = (4)

In the case of spherical geometry rx=rz=r, where r is the radius of the circle on the bearing surface. Finally,

( ) (

)

y 2

c

h r r x x z z

∆ = r − − − − _c ² (5)

• The cylindrical texture geometry (rx=rz=r) is defined by,

(

) (

)

• The parallelepipedic texture geometry is defined by,

0≤ ≤x rx; 0≤ ≤z r_z and ∆h=r_y (7)

Fig. 2. Three cases of texture shapes.

Resolution method

The determination of the pressure field in the lubricant film consists of the numerical resolution of equation (2) by using the Finite Difference Method.

The most usual resolution method is that of Christopherson [12] and is used here. The resolution of linear systems obtained after discretisation is obtained by the iterative method of Gauss-Seidel. The use of an iterative method for the resolution is justified by the application of the Reynolds boundary conditions. The analysis only leaves pressure as the unknown to be solved, while the eccentricity is given (e.g. 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 (2) is used to form the final equation system for obtaining P, while a cavitation conditions should also be satisfied.

For a steady-state regime, the computational procedure consists of giving initial values to the eccentricity e. The pressure field, at each nodal point under a steady external loading F (shown in figure 1b) is obtained, verifying the pressure convergence condition ∆P / P_{i i} ≤ε_P at each node i of the bearing surface mesh.

The supported load W and bearing attitude angle Φ are calculated. The calculated load W and fixed load F are compared; the process stopping after the load convergence condition F−W / F ≤ε_W is satisfied. If this error control is not satisfied, the eccentricity value is updated and the process of calculation begins.

RESULTS AND DISCUSSION

Computational conditions

Bearing surfaces with cylindrical textures are analysed for the journal bearing structure presented in figure 1a.

The bearing surface has a texture and it is stationary (ω2=0), the journal surface is smooth and is moving (ω₁≠0). Only one half of the journal bearing system is studied because of the symmetry of the bearing and uniform meshes are used. Geometrical parameters, as well as operating conditions for the journal bearing studied by Vincent [13], are:

• magnitude of the external force F: 12600 N,

• angular speed of the shaft .1: 625.4 rad/s,

• shaft radius R: 0.0315 m,

• bearing length L: 0.063 m,

• radial clearance C: 0.00003 m,

• lubricant viscosity µ: 0.0035 Pa.s .

For the results presented below, the imposed precisions for the calculations of the pressure P and the load W are ε_P=10^-4 and ε_W=10^-5. The mesh size used is 891 nodes along circumferential direction and 142 nodes along axial direction.

Validation

In relation to the journal bearing with smooth surfaces, the most important contact characteristics are computed, the results obtained being listed in Table 1. The results derived using the computational code of the authors, are compared to those calculated by Vincent [13].

Table 1. Smooth journal-bearing characteristics.

Eccentricity Attitude angle (º)

0.601 50.4

0.600 50.2 Maximum pressure (MPa) 7.7 7.0 Minimum thickness 10^-6 (m) 11.96 12.00 Axial flow 10^-5 (m³/s) 1.74 1.73

Friction torque (N⋅m) 1.13 -

Dissipation power (Watt) 708.6 -

The table 1 shows the very good concordance between the results of the two studies.

The results obtained for a journal bearing with textured surfaces will be compared with those presented in table 1 for the bearing journal with smooth surfaces.

RESULTS

The influence of texture dimensions and texture shapes on the main bearing characteristics (maximum pressure, minimum film thickness, axial film flow and friction torque) will be presented and discussed.

Values of minimum film thickness, friction torque, axial film flow, maximum pressure and rupture film

angle for smooth and textured surfaces are compared for different texture area fraction δ². The obtained results are shown in figure 5.

Influence of texture dimensions

The cylindrical texture is used to investigate the effect of the texture size on the lubrication characteristics. The texture numbers along the circumferential and axial directions are defined respectively by the parameters Ntx=24 and Ntz=10.

Just an appropriate repartition of textures on the bearing surface can affects positively the most impor- tant characteristics of a lubricated contact and will improve the performances of the journal bearing sys- tem Tala-ighil [14]. As shown on figure 3, a part of the bearing surface is textured (r=1mm and rx=0.015mm).

Fig. 3. Film thickness and cylindrical textures.

The figure 4 shows variation of texture area fraction δ² defined as the fraction of the area of the texture (S=π⋅r²) in a unit cell area (S=LxxLz), with the sizes of the cylindrical textures (r,ry), r varies from 0.6 to 2.0 mm and ry=0.015 mm.

Fig. 4. Variation of texture area fraction with the size of the texture.

Values of minimum film thickness, friction torque, axial film flow, maximum pressure and rupture film angle for smooth and textured surfaces are compared for different texture area fraction δ². The obtained results are shown in figure 5.

a)

b)

c)

d)

e)

Fig. 5. Variation of the a) minimum film thickness, 1.76 b) friction torque, c) axial oil flow, d) maximum

pressure and e) rupture film angle with the texture area 1.75 fraction δ².

This figure indicates that minimum film thickness, friction torque, axial oil flow, maximum pressure and rupture film angle are obviously different from the corresponding values involving smooth surfaces. This difference becomes greater as the texture area fraction increases.

This discrepancy, also rises with a rise in δ², especially for the case of the biggest texture size (2 mm, 0.015 mm) corresponding to the values of δ²=0.7.

This means that for specific distributions of texture on the bearing surface, and at higher asperity area fractions δ² the texture has more influence on the contact characteristics.

Influence of texture shapes

In order to analyze the variation of the bearing characteristics with the depth of texture (along the y direction) for three texture geometries, we take the dimple size r=1 mm and increase the depth ry from 0.001 to 0.040 mm. The results are given in figure 6.

Figure 6 shows the comparative graph for all shapes. The values for minimum film thickness, friction torque, axial film flow, maximum pressure and rupture film angle are clearly different from those for smooth surfaces. This difference becomes larger as the depth ry of the texture increases, it sharply rises for values of depth ry>0.005 mm, especially for the case of the parallelepipedic shape.

The values of the fiction torque as shown on figure 6b decreases with the rise of the texture depth.

Considering the parallelepipedic shape and for the biggest value of the texture depth, the friction torque diminishes about 23%.

Fig. 6. Variation of the a) minimum film thickness, b) friction torque, c) axial oil flow, d) maximum pressure and e) rupture film angle with the depth of

texture.

The positive effect of texture on contact characteristics becomes obviously significant for the parallelepipedic shape rather than for the cylindrical or spherical shapes, suggesting the advantage of parallelepipedic shape over the other geometries.

CONCLUSION

Different configurations have been analyzed, assuming the shaft is smooth and rigid and the bearing surface is numerically textured. A finite difference numerical model is used to study the effect

of surface textures on the lubrication of a journal bearing under steady state conditions.

The numerical results indicate that textures affect the most important bearing characteristics.

These analyses of cylindrically textured surfaces indicate that an appropriate selection of size, depth and geometry of textures may affect the bearing characteristics.

An appropriate size and shape of textures on the bearing surface affects positively the most important characteristics of a lubricated contact and will improve the performances of the journal bearing.

In a future work, the effects of textures taking into account the Jakobsson, Floberg and Olsson (JFO) cavitation theory and the dynamically load conditions on hydrodynamic lubrication journal bearing performances will be investigated.

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