بررسی معادله رینولدز برای مدل سازی یاتاقان مخروطی در پمپ های پیستونی محوری Discussion on the Reynolds equation for the slipper bearing modeling in axial piston pumps

1. Introduction Axial piston pumps are widely used in many applications because of their advantages such as high working pressure, great power density, convenient flow regulation, and long service life [1]. A typical axial piston pump is shown in Fig. 1. The cylinder block containing nine pistons rotates together with the shaft by a spline mechanism. The piston connects itself with the slipper through a ball-and-socket joint. All the pistons reciprocate within the cylinder bores and the slippers slide on the inclined swash plate during the cylinder block rotation. A reasonable contact between the slipper and swash plate is maintained using the retainer. The displacement chambers in the cylinder block are communicated with the suction or discharge port by the kidney-shaped ports in the valve plate. When the piston passes over the suction side, it is pulled out of the cylinder bore and the low-pressure fluid flows into the cylinder bore. When the piston passes over the discharge side, it is pushed into the cylinder bore and the high-pressure fluid flows out of the cylinder bore. The above reciprocating motion repeats itself for each revolution of the shaft, accomplishing the basic task of converting the low-pressure fluid into the high-pressure fluid. The pump performance strongly depends on the lubricating interfaces where the fluid film forms to separate heavily loaded relatively movable parts from each other. There are three main lubricating interfaces within an axial piston pump, the cylinder block/valve plate interface, the piston/cylinder block interface, and the slipper/swash plate interface. These lubricating interfaces serve as sealing and bearing functions, which are one of the critical design issues for axial piston pumps. As for the slipper/ swash plate interface, it prevents the pressurized fluid in the displacement chamber from leaking into the pump case through the slipper land. Additionally, the fluid film within it fulfills the function of carrying the pressure load exerted by the piston. Both the sealing and bearing functions of the slipper/swash plate interface are determined by the lubrication characteristics of the slipper bearing, which depend on the slipper’s motion on the swash plate. In addition to the macro motion governed by the pump kinematics, the slipper also undergoes some micro motions including tilting motion, squeezing motion, and spinning motion due to the additional degrees of freedom on the micro scale. The performance of the slipper bearing is often represented by its leakage flow, load-carrying capacity, and power losses etc. These critical performance parameters are related to the fluid film thickness and pressure across the slipper bearing which require to be calculated by the Reynolds equation for the slipper bearing.