Comparison of steady and dynamic models for the bulk modulus of hydraulic oils

Fluid bulk modulus has important effect on the dynamic characteristics of the hydraulic system, but the existing models still cannot accurately capture the dynamic features when the fluid is compressed or expands rapidly. Four steady-state models (Wylie, Nykanen, Ruan and AMESim) of fluid bulk modulus based on lumped parameter approach are analyzed. Considering the dynamic transport processes of free air and vapor in the oil, a dynamic effective bulk modulus model which is time-dependent is derived. In addition, the difference among the four steady-state models both in the high and low pressure regions is studied. The proposed dynamic model is compared to AMESim model and validated using experimental data. Results show that Wylie model is close to Nykanen model in the whole pressure range since they both assume constant air contents. In the high pressure region, Ruan model predicts a slight larger fluid bulk modulus, while AMESim model performs most differently and is strongly affected by the air apart pressure. In the low pressure region, the values of Ruan Model and Wylie Model are very close, but the effective bulk modulus calculated by AMESim model is nearly zero when the pressure is lower than the vapor saturation pressure, the fluid bulk modulus-pressure curve- predicted by the proposed dynamic model seems more reasonable when Henry's law is used, although its advantage depends on the coupling with the dynamic transport equations. Finally, the comparison of the results obtained from a fluid compression and expansion test cycle indicates that the proposed model is more precise.