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Mixed Lubrication in Hydrodynamic Bearings von Bonneau, Dominique (eBook)

  • Erscheinungsdatum: 08.08.2014
  • Verlag: Wiley-ISTE
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Mixed Lubrication in Hydrodynamic Bearings

This Series provides the necessary elements to the development and validation of numerical prediction models for hydrodynamic bearings. This book is dedicated to the mixed lubrication.


    Format: ePUB
    Kopierschutz: AdobeDRM
    Seitenzahl: 100
    Erscheinungsdatum: 08.08.2014
    Sprache: Englisch
    ISBN: 9781119008057
    Verlag: Wiley-ISTE
    Größe: 17016 kBytes
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Mixed Lubrication in Hydrodynamic Bearings



The numerical modeling of thin film flows and the deformation under pressure of the walls that bound the film requires a discretization of the domain occupied by the film using the methods described in Chapter 3 of [BON 14] for research into the field of pressure (Reynolds equation) and in Chapter 4 of [BON 14] for the deformations (elasticity equations). These numerical methods require even finer spatial discretizations when the shape of the walls that delimit the film domain is rough. Seen from a certain distance, the surfaces of a shaft and a sleeve appear smooth. When the finite element method is used to discretize equations, elements that are a few millimeters in length seem suitable. However, fine profilometric measurements reveal defects in the forms (flatness, cylindrical shape, etc.) whose amplitude is of the order of micrometers and wavelengths varying from a few tens of micrometers to several millimeters. When the average local thickness of the film becomes equivalent to the height of the surface defects, the local pressure varies considerably under the influence of the numerous convergents and divergents that cause these defects. The size of the subdomains required to describe these variations should be of the order of magnitude of the shortest wavelengths - in other words some tens of micrometers. The numerous elements involved in such an approach mean that the computation time becomes prohibitive.

This chapter describes the main parameters used in the modeling of rough surfaces.
1.1. Lubrication regimes - Stribeck curve

An average reference surface is defined for each facing surface (see section The roughness of each surface is characterized by its standard deviation (see section, which allows us to define an equivalent roughness σ for the pair of the two surfaces. Therefore, the dimensionless average distance between the two surfaces is defined by:


where h is the distance between the average surfaces of each surface. Three lubrication regimes are distinguished, depending on the value of ( Figure 1.1 1 ):
- 3: hydrodynamic regime; - 3 ≥ 0.5: mixed regime; - ≤ 0.5: boundary regime.
Passage from one regime to another can be characterized by a graph representing the friction as a function of Hersey's number written as He , a dimensionless characteristic involving the viscosity μ , of the lubricant in Pa.s, the relative velocity of the surfaces, the average pressure p in Pa. For a bearing, this is expressed as:

where ω is the frequency of rotation of the bearing in revolutions per second (rps).

Figure 1.1. Lubrication regimes as a function of the film thickness: a) hydrodynamic; b) mixed; c) boundary

The resulting graph, of which an example is shown in Figure 1.2 , is known as the Stribeck curve.

Figure 1.2. Stribeck curve and lubrication regimes

After intense friction at low values of He (low speed or major stress) due to frequent contact between the surface asperities typical in a boundary regime, the friction diminishes as the hydrodynamic aspect increases (the mixed regime). When the thickness has increased sufficiently, the effect of roughness is no longer detectable, and the friction coefficient increases linearly with the speed, as the shear stress in the case of a hydrodynamic regime. In the case of boundary lubrication regimes, the friction coefficient remains markedly less than that obtained for dry surfaces because of the molecular layers of additives that remain adsorbed on them.

The bearings of internal combustion engines function principally in hydrodynamic and mixed modes.
1.2. Topography of ro

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