Novel Methods for Modeling and Online Measurement of Effective Bulk Modulus of Flowing Oil

Oil is a key medium for transmitting power and coupling information in the hydraulic transmission system. Accurate calculation and measurement of the dynamic compressibility of the oil have profound significance to the system performance analysis. The present study primarily focuses on the effect of steady pressure on the bulk modulus of static oil. However, changing pressure and flowing oil are the general working conditions in most of hydraulic apparatus. There are few researchers paying attention to the influence of pressure on the compressibility of flowing oil. Considering the log-normal distribution of bubble size in oil, an improved static oil model (Model B) is developed to calculate the bulk modulus of the motionless oil under the dynamic pressure. Then, by deriving Model B, this paper proposes an original flowing oil model (Model C) to determine the effective bulk modulus of flowing oil. Finally, based on the inherent pressure pulsation of the axial piston pump, an innovative online method for measurement of the bulk modulus of flowing oil is presented as it has the advantage of avoiding interference with flow stability. It has been proved that the changes in the flow velocity corresponds to the crucial effect on the effective bulk modulus of flowing oil, especially under the low-flow and low-pressure operation conditions. Those results and analysis provide promoting support for identifying and determining the effective bulk modulus of oil, analyzing the system stiffness, improving the control accuracy, as well as optimizing the mathematical models.