OPTIMUM SIMILARITY ANALYSIS WITH APPLICATIONS TO ELASTOHYDRODYNAMIC LUBRICATION

A new method for deriving similarity solutions is introduced. The application proves to be very simple and straightforward. For any set of analytical relations, whether dimensionally homogeneous or not, the greatest possible reduction in the number of quantities may easily be accomplished. The method is introduced by means of simple applications and the results are compared with the results of conventional dimensional analysis. In elastohydrodynamic lubrication in particular, this method may readily be accepted as a very helpful tool when dealing with the extensive sets of analytical relations involved. Yet it is certainly not restricted to lubrication problems only. Furthermore, the results show that physical properties seem to have no place in similarity analysis. Similarity analysis is pure string manipulation. Consequently, the method has proved to be perfectly suitable for personal computer applications.