aspects of flow and viscoelasticity in a model elastohydrodynamically lubricated contact
In order to extend the service life of rolling bearings and other heavily loaded lubricated contacts, the need of lubricant film thickness control significantly increases under more extreme conditions of mechanical and thermal loading and with reduced lubricant supply. To ensure maximum service life, all lubricated contacts should be designed such that under all circumstances a sufficiently large protective layer of lubricant is present to prevent direct contact between the moving parts. Pressures in the order of several gigapascals can be encountered in the contact zone between the moving parts. The field of Elasto- Hydrodynamic Lubrication (EHL) studies cases for which the elastic deformation of (one of) the solids is of the same order of magnitude, or larger, than the film thickness of the lubricant.
This thesis focuses on the research of highly-loaded circular-shaped EHL contacts, under pure rolling conditions in the low velocity regime. Experimental results for film thicknesses under these conditions show discrepancies with the results from the conventional EHL model. The conventional EHL model assumes that there is always a sufficient supply of lubricant to the contact zone. Extensions of this model for the situation of mixed lubrication (i.e. when one or more parts of the contact do not have a protective ubricant layer present) are not based on first principles and their results depend on the employed computational grid density. The purpose of the present study is to gain more knowledge about how the flow of lubricant around the contact influences the ability to form an enduring lubricant film in the contact zone. A second objective is the development of a model for mixed lubrication from first principles regarding the physics of contact and flow. The model should open a way to better predict EHL contacts in bearings operating in the extreme thin film regime. The approach taken in this research is threefold and involves experimental, analytical and numerical aspects.
1: Optical interferometry ball-on-disc experiments
To investigate the ability to form an enduring lubricant film in elasto-hydrodynamic contacts and how it depends on the flow of lubricant around the contact, optical interferometry experiments with a ball-on-disc apparatus have been performed and the aspects of the flow in the vicinity of a lubricated EHL contact have been studied. Two flow states can be recognized. The first state, flow pattern I, appears when the lubricant supply at the inlet side is sufficient. A flooded region envelopes the entire Hertzian contact region, and the outer meniscus of the flooded region is closed. Furthermore, a cavitation bubble is present at the outlet side of the contact. The bubble length depends on the rolling velocity and the lubricant viscosity. A dimensionless relation has been derived that relates the ratio of cavitation bubble length and Hertzian contact radius to a combination of the Reynolds, cavitation and Weber number. After a sudden stop this bubble breaks up into smaller bubbles that subsequently escape the flooded region.
The second state, flow pattern II, appears for decreased lubricant supply, e.g. when the rolling velocity is increased and no extra lubricant is added. Typical for this state is a concave-shaped inlet meniscus and an open downstream wake. In a starved situation, state II dominates and has a butterfly-shaped flooded region.
2: Cavitation modeling
A standard EHL-model has been coupled with an elementary 2-phase pressure-density model, which yields a strong density decrease for sub-atmospheric pressures. The extended EHL model is able to predict a cavitation bubble. However, its length is highly under predicted when compared with available experimental results. This suggests a lack of essential physics included in the model. So, more advanced fluid modeling, e.g. including more detailed physics of cavitation and aspects of three-dimensional two-phase flow is needed for accurate prediction.
3: A viscoelastic layer model
A new viscoelastic layer model has been developed. This model is based on first principles and a ‘bottom-up’ approach that allows for a natural transition to dry contact. When oil is trapped in a loaded rolling contact and subjected to high pressures, the lubricant behaves as a ‘solid’ layer that is transported from the inlet side towards the outlet side of the contact. This assumption agrees with the velocity distributions in the contact region obtained with a standard fluid-based EHL model. Inspired by this observation, an exploratory model is proposed which predicts the thickness- and pressure- distribution of a thin lubricant layer inside the contact zone of an elasto-hydrodynamically lubricated ball-on-plate contact.
The new model is based on a standard dry contact model with a solid layer added to the gap equation. The layer is modeled with multiple one-dimensional viscoelastic elements, only allowing displacements in the direction of the layer thickness. Each viscoelastic element consists of a pressure- and strain-dependent spring connected in parallel to a pressure-dependent viscous damper. Various simulations of fully flooded-, squeeze-, and mixed-lubrication conditions have been performed. In general, the proposed model applies to thin layers and it shows the characteristic behaviour of an EHL contact in these situations remarkably well. The results indicate a good prospect for developing alternative EHL models that can predict local/partial/mixed surface separation and do not have the disadvantages of Reynolds based fluid film models.
Furthermore, simulations with a region with zero layer thickness show that the proposed model can be used to simulate mixed contact situations. However, the model predictions for features fixed on the ball geometry show local differences with physical expectations. Since this model is meant as an exploratory model, the results are an invitation to search for viscoelastic element properties that drive the model towards more accurate physical behaviour. The developed model has the potential to predict mixed lubrication conditions for which the contact consists of multiple isolated contacts on a local scale. Therefore, further development including parametrical studies is recommended.
