On the pressure projection in elasto-hydrostatic lubrication problems—Part 1: Mechanical study of the Reynolds equation

The problems of elastic-hydrostatic lubrication (EHL) are discussed here from the mathematical and mechanical point of view. We begin with the formulation of the Reynolds equation and derive analytical solutions of the tilting plate and the disc models. We show that the so-called “Pressure spike” cannot be observed analytically and numerically by the newly developed computer codes, which is a reasonable simulation of one-dimensional flow from a mechanical point of view. Then, we discuss the possible factors that may be responsible for generating the conventional pressure spike including some unreasonable assumptions incorporated in formulating the numerical equation and in coding the computer program. A small pressure projection, however, has been experimentally observed. Therefore, some possible mechanical and mathematical explanations for it will be presented in a series of our subsequent papers.