Theoretical background of the operating parameters of the satellite working mechanism of the hydraulic positive displacement machine

This article describes a method for determining the instantaneous geometric working volume of a satellite mechanism that is commonly used as a working mechanism in positive displacement machines (pump and motor). A new mathematical formula for calculating the instantaneous geometric working volume as a function of the angle of rotation of the shaft (rotor) has been proposed. For the satellite mechanism operating as a pump, the mathematical formula for the instantaneous flow rate in this mechanism as a function of the angle of rotation of the rotor (shaft) has been developed. The mathematical formula for the torque indicated in this mechanism (pumping operation) was also developed. Similarly, analyses were carried out for a satellite mechanism operating as a motor. Mathematical formulae were presented to calculate the instantaneous speed of the motor shaft and the instantaneous pressure in the motor's supply port. To confirm the results of the mathematical analyses, experimental tests were carried out with a prototype satellite machine at a low constant speed. The satellite machine was tested in both pump and motor mode. The results of the tests confirmed that the torque on the shaft is not constant in both pump and motor operation at a constant pressure drop in this machine. This torque depends strictly on the instantaneous working volume of the machine and is therefore a function of the angle of rotation of the shaft. Similarly, at a constant speed, the flow rate (motor absorption) in the machine is also not constant.