Identification de piézoviscosité en lubrification

Abstract

In order to design better mechanisms, the piezoviscosity, i.e., the sensitivity of lubricant viscosity to pressure changes, needs to be accounted for. A strategy for identifying piezoviscosity based on image analysis and numerical identification is devised in two steps. Firstly, the identifiability of three piezoviscosity models (Barus, Roelands and WLF) is analyzed by minimizing a least squares distance between pressure–viscosity responses. Numerical difficulties stem from magnitude differences between parameters and from the wide range of viscosity/pressure values. A strategy based on an improved Levenberg–Marquardt algorithm is proposed. Improvements concern respect of parameter bounds and scaling. The non-identifiability of the WLF piezoviscosity model at constant temperature is proved. Secondly, the piezoviscosity identification strategy is applied to data for noisy lubricant thickness and pressure fields. In this case, piezoviscosity can be recovered by minimizing the Reynolds equations residual globally in the field. A method for smoothing and numerical differentiation of the measurements is described. It is based on building a local polynomial approximation to the field. Using noisy field measurements, piezoviscosity parameters are finally estimated within 5% accuracy.