designed for analysis and optimisation of the liner surface topography for combustion engines
Centre of Mathematical Morphology, Paris School of Mines
Nowadays, the improvement of the efficiency of the combustion engines in the automotive field is the main key towards greenhouse gas (GHG) emission reduction. The performance of a combustion engine is tightly related to the friction force between the cylinder liner and the piston rings. It is believed that this friction can be significantly reduced by optimising the surface topography of the cylinder.
Traditionally, deterministic models or expensive experimental tests are used to solve these issues. We study here a numerical optimisation approach of this surface, the main purpose being the friction loss reduction, and without prejudice to the oil consumption. This approach consists in four numerical tools, described as follows.
A previous work in this field by Decencière and Jeulin using mathematical morphology techniques provided us with surface analysis, decomposition and simulation tools. We use these tools here for the analysis, filtering, decomposition or correction of the liner surface images.
A tool for texture simulation under constraints has been developed in order to generate new liner surface textures, characterised by better friction and oil consumption performances than those presented by a reference surface (M50). These new textures constitute the search space for latter optimisation tasks.
The 3D incompressible viscous flow of a fluid dragged by a smooth plate over a rough surface is studied within the framework of a friction prediction tool for the hydrodynamic contact between the liner and the segments. Navier-Stokes and Reynolds equations are used for the numerical resolution of the flow. The algorithms are tested by analysing and comparing their results with analytically known flows and the physical model will be validated by the experimental results provided by our partners. This 3D tool will enable us to compute local or global physical measures like friction power loss, drag, load or fluid flow and to come to significant results concerning the influence of the surface topography on the contact tribological performance.
Finally, the parametric optimisation of the liner surface texture is performed, over textures generated by the simulation tool and using as objective function the friction prediction tool, in order to find out useful information about the optimal values taken by the parameters of the new simulated textures. In parallel, stochastic optimisation tools have been developed in order to operate an exhaustive shape optimisation task of the elementary motifs encountered in the periodic texture definition. In the end, new liner surface textures are proposed for experimental tests.
KEY-WORDS: image processing, mathematical morphology, hydrodynamic friction, Navier-Stokes, fluid dynamics, CFD, incompressible flow, stochastic optimisation.
Energy loss and friction phenomena have always been domains of major
interest for the scientists. In this context, the present work tries
to build a numerical procedure in order to characterise the
tribological properties of rough surfaces in a particular
configuration: the incompressible viscous flow in the hydrodynamic
contact between a smooth plate and a rough surface. The geometry of
the contact is strongly related to the physical parameters of the
flow. Generally, in such conditions, the fluid film is relatively
thin but always thicker than the surface roughness characteristic
size, so that no solid contact occurs.
Michail and Barber [5,6]
developed a theoretical model of the segment-cylinder liner
hydrodynamic contact, based on the average Reynolds equation
developed by Patir and Cheng , to study the
effects of the roughness of the skirt, the angle of striation and
the surface grinding on the thickness of the oil film in the
Ronen and al. , following the work of Etsion et
al. on mechanical seals, examined the piston-cylinder liner contact
equipped with laser textured piston rings. They developed two
computation models for hydrodynamic contacts based on the Reynolds
equation, a rigourous one, which takes into account the effects of
inertia and the effect of film shock absorber, and one more
approximate, which neglects these two effects.
From a theoretical point of view, there are many models designed for
hydrodynamic contacts simulation, and more specifically for the
piston ring-cylinder liner study. They are generally based on the
Reynolds equation, which simulates exclusively laminar flows in thin
A novel 3D numerical model of hydrodynamic lubrication and friction
between rough liner surfaces and flat piston rings, based on the
incompressible Navier-Stokes equations, was introduced by Caciu and
Initially designed to study the piston ring-cylinder liner contact
friction, this model was developed as a numerical
tribometer bench, well suited to a general characterisation of
hydrodynamic contacts, in presence of various rough surfaces.
The 3D simulation tool permits to analyse in detail the tribological
performance of rough surfaces. Real or simulated rough surfaces are
sampled and introduced into the model as topographic images. Thus,
the model is able to simulate non-laminar viscous flows over any
surface topography. Starting from local rugosity information, the
model makes a prediction on the global performance of the tested
surface or classifies different surfaces.
First, a brief description of the physical model is given. Next, the
numerical tribometer tool is described. Finally, the local and
global information given by this novel tool are presented and
The physical model
We consider a viscous incompressible fluid, at time t, inside a
volume limited on the upper side by a smooth plate P
(the piston ring) and on the lower side by a rough surface
R (textured surface). We obtain a bounded domain of
R3, that we denote Ω, illustrated in
Figure 1: The 3D hydrodynamic contact model
In the direct orthogonal reference
, Ω is defined as follows:
f being the function describing the rough surface R.
Ω dimensions are l1, l2 and l3 and we denote
∂Ω the boundary of Ω. We assume that
f(x1,x2) < l3 for all (x1,x2) such that 0 < x1 < l1 and 0 < x2 < l2.
The rough surface R is motionless and the smooth plate
P moves with the velocity
∀x ∈ R3, x=(x1,x2,x3) ∈ Ω⇔ |||
movement of the fluid generated by the displacement of the smooth
plate P is defined by its velocity
and by its pressure p=p(x,t).
The downstream and upstream pressures are settled to
p(l1,x2,x3) = p1 and p(0,x2,x3) = p2.
The viscous fluid is considered as Newtonian and incompressible; the
physical parameters of the fluid (density ρ, viscosity η)
are considered constant, the fluid adheres totaly to solids and the
remote forces (gravity) are neglected. The study is stationary in
time. No-slip wall boundary conditions are required on plate
P and on the rough surface R. On the x2
axis, periodic, restrictive or unsettled boundary conditions are
used. In addition, these conditions are completed by the imposed
upwind and downwind pressures. Swift-Steiber cavitation
conditions are equally included [1,7].
The general equations governing the previous physical model are
those of Navier-Stokes, stationary and
incompressible . Under particular simulation
conditions and for specific rough surfaces, generating thin and
laminar fluid films, Reynolds equation may be employed. This
simplified flow model is usually employed for the tribological
characterisation of hydrodynamic
contacts [3,8]. The physical model is
described with more details
The numerical tool
Numerical relaxation or prediction-correction computation
methods  working in finite differences were
used to solve the flow previously described. The implementation of
the computation methods was performed within the framework of a
hydrodynamic friction prediction tool, that we also called a
numerical tribometer. Both Navier-Stokes and Reynolds
models were considered, which yielded in 3 different computation
techniques (2 for Navier-Stokes and 1 for Reynolds). Thus, the
model is able to simulate non-laminar contact flows, and may also
use simplified and less expensive computational methods for laminar
Initially designed to study the piston ring-cylinder liner contact
friction, this model was developed as part of a numerical tribometer
bench, well suited to a general characterisation of hydrodynamic
contacts, in presence of various rough surfaces. An overview of this
numerical tool is given in Figure 2.
Figure 2: Overview of the numerical tribometer
The inputs are the topographic image of a real or simulated (rough)
surface, the physical and geometrical parameters of the contact
(density ρ, viscosity μ, pressures p1, p2,
velocity vp, l1, l2, contact thickness l3, grid
spacing dx1, dx2, input image level scale
dx3). The output will consist in the velocity and
pressure fields inside the contact which enable us to compute
numerous local and global physical measures. The model was validated
by comparison of the predicted friction behaviour to experimental
Local physical measures
The detailed pressure and velocity fields give access to various
local and global physical measures, which permit to analyse and
compare the performance of rough surfaces under hydrodynamic contact
conditions. Starting from the pressure field, the velocity field and
the fluid properties, one can compute global measures like the
viscous power loss, the friction force or the load exerted by the
fluid on P, or the characteristic friction coefficient
of the texture.
Velocity and pressure
Figure 4 illustrates a 3D
representation of the fluid streams in the vicinity of the textured
Figure 4: Velocity: streamlines over the rough surface
The representation employs streamlines, coloured according to the
velocity modulus. The lubricant velocity varies between 0 m/s,
near the rough surface, and 13 m/s for the mobile plate
P. The flow is carried out mainly along the axis of
motion of the plate P, x1.
The streamlines present slight deviations over the grooves, which
implies the appearance of consequent velocity components on the
x2 and x3 axes. This shows the draining role played by the
grooves. It is also necessary to note higher velocity values over
the grooves, indicated by slightly different colours on the
In Figure 5 we present the pressure
distribution inside the hydrodynamic contact. To each pressure value
is associated a height and a colour.
Figure 5: Pressure: represented values are those of a plane parallel
to the plate P and close to the rough surface
The pressure values vary between the atmospheric pressure p0
(which is also the value used in the cavitation conditions) and
6.44 bar. One distinguishes overpressures at the exit (in the
direction of the flow) of the grooves, responsible for the load on
the plan which simulates the piston ring.
Local viscous power loss
Having local access to the velocity we can also build the 3D field
of the power dissipated by friction in the contact (in mW/mm3).
Its expression is:
A 3D representation of the power dissipated by friction at the local
level, in the hydrodynamic contact, is given in
Figure 8: Local viscous power loss: represented values are those of a
plane parallel to the plate P and close to the rough
The values of the power dissipated by friction vary between 0 and
3.0 ×105 mW/mm3. One can notice the influence of the
texture of the surface on this measure. It appears that the plateaux
are the most friction generating structures. We observe that the
zones generating most of the friction appear at the entry and
especially at the exit of the grooves.
Global physical measures
The local physical measures previously presented enable us to
compute the associated global measures. These measures will be used
to classify surfaces according to one or more specified criteria.
The average fluid flow in the
directions can be easily computed, in each co-ordinate x1 or
x2, by integrating the speed on the right area, as illustrated
in Figure 10.
Figure 11: Average flow computation
The expressions of the average flows are:
This measure allows the classification of textures from the point of
view of the lubricant quantities transported in the two mentioned
directions. This classification criterion may be correlated to the
oil consumption for the tested surfaces.
v1(x1,x2,x3)dx3 dx2, ||(3)|
v2(x1,x2,x3) dx3dx1 .||(4)|
Average physical measures
The average values of the preceding local physical measures are
gathered in Table 2. The computation of the
average dissipated power by friction deserves a detailed attention.
From the 2D map of dissipated power, and knowing the topography of
the surface and the reference level of the plateaux, it is possible
to compute this measure separately, on the one hand for the zones
corresponding to the plateaux and on the other hand for the grooves
zones. The values given in Table 2 show the
beneficial role of the grooves in friction reduction.
Table 2: Measures: average values
As expected, we observe that the values of flow on the x1 axis
are much higher than those on the x2 axis, which shows a
prevalent flow along the x1 axis.
From the values given in Table 2 it seems that
the inertial forces could be neglected compared to the viscous
forces, under this running conditions. We saw in
Figure 6 that this is not the
case, since the forces ratio can strongly vary locally; indeed, the
significant values of these two forces types are not localised in
the same areas of the contact. Moreover, for different simulation
parameters, the ratio between the two forces may change: higher
velocity values, lower viscosity or higher density values for the
lubricant would create higher inertial forces.
|Measure ||Value ||Unity|
|Dissipated power - global ||335.70 ||mW/mm2|
|Dissipated power - plateaux ||355.12 ||mW/mm2|
|Dissipated power - grooves ||314.22 ||mW/mm2|
|Friction force / surface unit ||535.78 ||millibar|
|Load ||1.84 ||bar|
|Flow x1 ||15.62 ||mm3/s|
|Flow x2 ||−5.5 ×10−4 ||mm3/s|
|Velocity x1 ||5.86 ||m/s|
|Velocity x2 ||−0.21 ×10−4 ||m/s|
|Inertial forces ||0.17 ||N/mm3|
|Viscous forces ||11.65 ||N/mm3|
The research reported here is the result of a cooperation between
CMM-ENSMP (Centre de Morphologie Mathématique, École des Mines de
Paris/ARMINES), LMS-ENSMM (Laboratoire de Microanalyse des Surfaces,
École Nationale Supérieure de Mécanique et des Microtechniques de
Besançon), Total, Mecachrome (JPX), PSA (Peugeot-Citroën), Renault
and ADEME (Agence de l'Environnement et de la Maîtrise de
l'Energie). The partners' support is gratefully acknowledged by the
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