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

Abstract

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.

New analytical leakage models for tribological interfaces in axial piston pumps

“…The experimental results in Table 2 show that the pump's total leakage increases with the rotational speed. One may consider that the large measured leakage at high rotational speed results from the centrifugal flow that increases with the rotational speed, as shown in equations (20) and (28). However, at the same time, these two equations indicate that the centrifugal flow actually contributes little to the leakage flow.…”

“…The pump leakage approximately equals the sum of leakages of the three main tribological interfaces. Calculating leakage flow rate of each tribological interface requires known fluid film thickness, as shown in equations ( 20), (28), and (32). The fluid film thickness is set to 20 mm for the piston/cylinder block interface based on the assembly clearance of the test pump, while it is assumed to be 1-30 mm for the cylinder block/valve plate interface and slipper/swash plate interface based on the measurement results.…”

“…However, they have different velocity boundary conditions: the cylinder block purely rotates relative to the valve plate but the slippers slide against the swash plate in an elliptical trajectory. 28 Figure 3 shows the slipper kinematics with two coordinate systems. The global coordinate system X s Y s is defined relative to the stationary swash plate.…”

“…However, they have different velocity boundary conditions: the cylinder block purely rotates relative to the valve plate but the slippers slide against the swash plate in an elliptical trajectory. 28…”

Thermo-Hydrodynamic Lubrication Analysis of Slipper Pair Considering Wear Profile

“…where h g is the film thickness of the ideal rigid slipper bottom surface, ∆h m is the corrected film thickness caused by the wear, ∆h p is the change in film thickness caused by the elastic deformation, and ∆h T is the change in film thickness caused by the thermal deformation, which was presented in detail in [23]. As shown in Figure 2, if the film thickness h 1 , h 2 , and h 3 located at three reference points A 1 , A 2 , and A 3 were known, the film thickness h g at the random point could be determined as [15,24]…”