## Abstract

The performance prediction of elastohydrodynamic lubricated contacts with rough surfaces is currently an important issue, because in many engineering applications, the ratio of film thickness to surface roughness is small and decreasing.

The classical way of introducing roughness in the lubrication equations is through the approach pioneered by Patir and Cheng. This approach treats the roughness in a statistical manner and it cannot be used to predict the behaviour of a particular surface texture. Furthermore, the main hypotheses stem from hydrodynamic lubrication and neglect the viscosity change with pressure and the elastic surface deformation.

The opposite approach uses the full transient EHL equations, introduces a real, measured roughness, and studies the lubrication of this surface. This approach has several drawbacks. First, it is difficult to analyse the precision of the results obtained. Furthermore, this direct approach of surface roughness is difficult to generalize as each roughness, or set of operating conditions is unique, and general trends are difficult to extract.

A third approach has emerged over the last decade, in which the amplitude reduction of a sinusoidal waviness is studied as a function of the amplitude, the wavelength, and the operating conditions. The simplification of the roughness to a sinusoidal waviness can be justified in several ways. The first and simplest justification points out that many engineering surface finishes have one dominant wavelength and amplitude. Even if the geometry is removed from the sinusoidal one, a first approximation of the roughness behaviour can be obtained through the study of the waviness with the same wavelength and amplitude.

A second argument is slightly more sophisticated; it argues that if the amplitude reduction is approximately linear, Fourier decomposition of the roughness into sinusoidal components is permitted. Next, the amplitude reduction of each Fourier component is computed, and finally, the deformed waviness signals are assembled to yield the deformed roughness signal.

The major results of this amplitude reduction work are reviewed in this article.

The classical way of introducing roughness in the lubrication equations is through the approach pioneered by Patir and Cheng. This approach treats the roughness in a statistical manner and it cannot be used to predict the behaviour of a particular surface texture. Furthermore, the main hypotheses stem from hydrodynamic lubrication and neglect the viscosity change with pressure and the elastic surface deformation.

The opposite approach uses the full transient EHL equations, introduces a real, measured roughness, and studies the lubrication of this surface. This approach has several drawbacks. First, it is difficult to analyse the precision of the results obtained. Furthermore, this direct approach of surface roughness is difficult to generalize as each roughness, or set of operating conditions is unique, and general trends are difficult to extract.

A third approach has emerged over the last decade, in which the amplitude reduction of a sinusoidal waviness is studied as a function of the amplitude, the wavelength, and the operating conditions. The simplification of the roughness to a sinusoidal waviness can be justified in several ways. The first and simplest justification points out that many engineering surface finishes have one dominant wavelength and amplitude. Even if the geometry is removed from the sinusoidal one, a first approximation of the roughness behaviour can be obtained through the study of the waviness with the same wavelength and amplitude.

A second argument is slightly more sophisticated; it argues that if the amplitude reduction is approximately linear, Fourier decomposition of the roughness into sinusoidal components is permitted. Next, the amplitude reduction of each Fourier component is computed, and finally, the deformed waviness signals are assembled to yield the deformed roughness signal.

The major results of this amplitude reduction work are reviewed in this article.

Original language | English |
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Pages (from-to) | 303-312 |

Number of pages | 10 |

Journal | Proceedings of the Institution of Mechanical Engineers. Part J: Journal of engineering tribology |

Volume | 219 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2005 |

## Keywords

- Elastohydrodynamic lubrication
- Surface roughness
- Roughness deformation
- Line contact
- Point contact
- Elliptical contact