Mathematical model for bulk modulus of hydraulic oil containing air bubbles

Abstract

Hydraulic systems have high-power density because its oil transmitting power has high rigidity. However, when air bubbles are mixed into oil, they reduce oil stiffness and decrease system efficiency. This study mitigates this problem by removing air bubbles from the oil using an active bubble elimination device that uses a swirl flow to eliminate air bubbles from a hydraulic fluid. We focus on the relationship between the change in the bulk modulus and elimination of air bubbles from the hydraulic fluid and experimentally measure the bulk modulus of the hydraulic oil with and without air bubbles. Moreover, to clarify the relationship between the amount of air bubbles and the effective bulk modulus of oil, we propose a mathematical model of the bulk modulus of oil containing air bubbles. The experimental results indicate that the effective bulk modulus of oil increases by eliminating the air bubbles in oil, and the curve of the bulk modulus with the bubble eliminator turned off has a small hysteresis depending on whether it is pressurized or depressurized. We investigate the calculation method of the effective bulk modulus by considering the amount of air bubbles and the amount of air being dissolved and released. Finally, we confirm that the effective bulk modulus calculated using the mathematical model agrees well with the experimental results. We conclude that the volume of air contained in the oil and the differences due to the process of dissolving and releasing air significantly influence the bulk modulus of the hydraulic fluid.

Keywords

• air entrainment
• bubble
• bubble eliminator
• effective bulk modulus
• tangent bulk modulus