Hydrodynamic Lubrication of a Liquid Conducting Film Controlled by Magnetic Pressure at Rail–Armature Interface

When an armature slides along a pair of rails under the action of Lorentz forces, the serious material melted at the interface will appear due to frictional and Joule heating. A liquid conducting film composed of molten metal forms over the rail-armature contact surfaces. Magnetic field was concentrated in the trailing surface of the armature and liquid film due to the velocity skin effect resulting in a large magnetic pressure acting on them in these regions. Magnetic lateral force in the film squeezes the armature legs against the rails in the lateral direction forming a diverging gap. Magnetic pressure in the longitudinal direction propels the armature and liquid film moving at different speeds and could cause a self-acceleration in the film. The traditional lubrication theory suggests that the liquid film flowing along a diverging gap cannot form positive pressure to achieve hydrodynamic lubrication. This paper attempts to investigate whether a diverging film controlled by magnetic pressure can achieve hydrodynamic lubrication and uncover its control mechanism. The film is assumed to be linearly diverging with a specified magnetic pressure controlled at the trailing edge. Analytical solution of pressure distribution is obtained by integrating the generalized 1-D Reynolds equation, taking into account the acceleration of the liquid film. Mechanism controlled by magnetic pressure is analyzed. Furthermore, conditions for generating positive pressure distribution are also obtained. In the end, hydrodynamic lubrication of a diverging film under the influence of magnetic pressure is discussed.