Derivation of the Reynolds equation in cylindrical coordinates applicable to the slipper/swash plate interface in axial piston pumps

Although many tribology references have presented the Reynolds equation in cylindrical coordinates, they may not be applicable to the slipper/swash plate interface in axial piston pumps due to complex macro and micro motions of slippers. Therefore, this paper derives the generalized Reynolds equation in cylindrical coordinates for this interface from momentum and continuity equations. Also, the boundary velocity conditions for the Reynolds equation are evaluated based on the kinematics of slippers, which accounts for the spinning motion. Compared with the traditional Reynolds equation for the slipper/swash plate interface, the new Reynolds equation in this work considers the geometric squeeze and centrifugal terms and has a different form of Couette terms.

Automated summary

This paper derives a generalized Reynolds equation in cylindrical coordinates for the slipper/swash plate interface in axial piston pumps to account for the complex motion of slippers, evaluating boundary velocity conditions based on the kinematics of slippers. The new Reynolds equation considers geometric squeeze and centrifugal terms, along with a different form of Couette terms compared to traditional equations.