Numerical Tribometer

designed for analysis and optimisation of the liner surface topography for combustion engines

Costin CACIU, Etienne DECENCIÈRE and Dominique JEULIN

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 [2], 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 contact.
Ronen and al. [8], 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 contacts.
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 Decencière [10,12,13]. 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 discussed.

Numerical tribometer

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.
Figure 1: The 3D hydrodynamic contact model
In the direct orthogonal reference







, Ω is defined as follows:
∀x ∈ R3, x=(x1,x2,x3)   ∈  Ω⇔

0 < x1 < l1
0 < x2 < l2
f(x1,x2) < x3 < l3
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



. The 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 [4]. 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 in [10,12,13].

The numerical tool

Numerical relaxation or prediction-correction computation methods [9] 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 flows.
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 data [10,12,13].

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 surface.
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 illustration.
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:
Pvisc.  local




+ ∂vj



A 3D representation of the power dissipated by friction at the local level, in the hydrodynamic contact, is given in Figure 8.
Figure 8: Local viscous power loss: represented values are those of a plane parallel to the plate P and close to the rough surface
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:




v1(x1,x2,x3)dx3 dx2,




v2(x1,x2,x3) dx3dx1 .
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.

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.
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
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.


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 authors.


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