Optimum Dimensional Analysis With Applications to Elastohydrodynamic Lubrication

A robust, straightforward technical procedure referred to as “optimum dimensional analysis” that is a hybrid of conventional dimensional analysis and optimum similarity analysis is proposed here to find a smallest set of system dimensionless power products of dimensions for nondimensionalizing a set of system equations. With these dimensionless parameters, the system behavior can be fully described by a most concise set of dimensionless governing equations and boundary/initial conditions. Functional relationships between the system dependent dimensionless parameters and a smallest set of system independent dimensionless parameters are thereby established. All alternative sets of optimum dimensionless parameters can be identified without any computational complications. A simple illustration is given first to analyze a time-dependent initial value problem. Applications to EHL of rectangular and elliptical contacts then follow. Because the inference process of the optimum dimensional analysis always arrives at clearest and simplest formulas for system dependency equations, especially for initial value problems, this process may be simply referred to as “optimum analysis.”