EHD Lubrication under forced oscillations: a combined theoretical and experimental approach

Malik Yahiaoui^1,2, Denis Mazuyer ², Juliette Cayer-Barrioz²

¹Laboratoire Génie de Production, Ecole Nationale d’Ingénieurs de Tarbes, France, ²Laboratoire de Tribologie et Dynamique des Systèmes, Ecole Centrale de Lyon, CNRS UMR5513, France

INTRODUCTION:  The combination of the piezoviscosity property of the fluid and the change in surface geometry by elastic deformation under pressure governs the physics of elastohydrodynamic lubrication¹. The pioneering work of Ertel² proposing a simplified framework of assumptions highlighted the fundamentals of elastohydrodynamics.

Transient conditions are often disregarded although the fluid film thickness is subject to additional phenomena, such as squeeze, starvation and cavitation.³

This paper proposes an analytical model, based upon Ertel’s hypothesis, to predict the evolution of the film thickness in transient conditions (cycles of acceleration and deceleration). This theoretical model was perfectly backed-up by experimental results in terms of film thickness. The link between friction and film thickness by means of the rheology under pressure of the sheared fluid was also explored.

METHODS:  The Reynolds equation models the coupling between the film thickness, h(x,t) and the pressure p(x) within a lubricated contact.

where u(t) is the velocity profile and h the viscosity. Considering the Ertel’s hypothesis, the Reynolds equation can be solved in the convergent zone, then by continuity in the high-pressure zone and the divergent. The velocity profile was chosen as triangular as a first approximation of the sinusoidal real velocity profile.

To experimentally validate the analytical model, experiments were performed using the CHRONOS tribometer⁴. This device allows synchronous measurements of the contact forces and the distribution of film thickness in a steel ball/glass disc contact under controlled forced oscillation kinematics. PolyAlphaOlefin (PAO) base oil with a viscosity of 820 mPa×s was used. The contact pressure ranged from 220 MPa to 800 MPa, the stroke length was 1 mm (i.e. larger than the contact area) and the oscillation frequency was 10 Hz. The film thickness distribution was obtained by means of optical interferometry.

RESULTS and DISCUSSION:  The data in Figure 1 shows the first significant result: the calculated film thickness converges towards its stable form after the second sliding cycle. A good agreement was observed between the theoretical evolution and the experimental one. Dynamic effects, such as the film thickness decrease when the velocity vanishes and the squeeze effect (shown in Figure 2), are perfectly predicted. The hysteresis between deceleration and acceleration is discussed.

The simultaneous contact force measurement permits to identify a strong coupling between friction and film thickness by means of the rheology of the under-pressure fluid sheared during one oscillation cycle.

Figure 1 – Central film thickness evolution (theoretical in continuous line and experimental with dots) as a function of time for two consecutive cycles. The deceleration is shown in blue and the acceleration is red.

Figure 2 – Examples of contact interferograms for a half period of oscillation. The change in direction happened in (b) and the maximum of velocity occurred in (a) and (d). the image (c) illustrates the heterogeneity of the film distribution during acceleration. The contact diameter is 200 mm.

CONCLUSION:  This work presents a simple analytical model to accurately describe the film thickness in an EHL contact under transient conditions, leading to a better understanding of the lubrication mechanisms.