Mathematical Model for a Lubricant in a Sliding Bearing with a Fusible Coating Considering Viscosity Depending on the Pressure

Based on the flow equation of a truly viscous fluid for a thin layer, the continuity equation, and the equation that describes the profile of the molten contour of a guide coated with a fusible metal alloy, taking into account the formula for the rate of mechanical energy dissipation, an astatic and accurate self-similar solution is presented for the zero approximation (excluding the melt) and the first approximation (taking into account the melt) of a wedge-shaped sliding support adapted to the friction conditions owing to the supporting profile of the slide and to the fusible metal coating of the guide surface, taking into account the lubricant and rheological properties of the melt depending on pressure, provided a true-viscous behavior of the lubricant and melt in the laminar flow mode under an incomplete filling of the working gap. Analytical dependences are obtained for the molten surface profile of the fusible metal coating of the guide, as well as for the zero- and first-approximation field of velocities and pressures. The main operating characteristics of the friction pair under consideration, such as the bearing capacity and the friction force, are determined. The effect of the parameters caused by the coating melt, by the supporting profile adapted to the friction conditions, and by the parameter characterizing the lubricant viscosity depending on pressure, as well as by the loaded zone length exerted on the bearing capacity and friction force, is assessed.