The bulk modulus of hydraulic fluid is dependent on the quantity of entrained gas in the fluid. In this paper, an effective fluid bulk modulus model that captures dynamic gas absorption during pressure transients is derived from the overall mass transfer theory. Optical measurement of a microgas bubble volume is used to determine the interfacial mass transport. Compared to traditional models, the proposed model is able to capture the 10% gap in the pressure profile between the first and second cycles, when simulating multiple compression cycles of an oil sample with 0.65% entrained gas by volume at 8 MPa.
Direct acting solenoid on–off valves are key fluid power components whose efficiency is dependent upon the state of the spool’s axial motion. By sensing the trajectory of the valve spool, more efficient control schemes can be implemented. Therefore, the goal of this study is to derive an analytical model for spool displacement sensing based on coil inductance. First, a mathematical model of the coil inductance as a function of air gap width and lumped magnetic reluctance is derived. Second, to solve the inductance from coil current, an optimization to obtain an initial value based on physical constraints is proposed. Furthermore, an experiment using a laser triangulation sensor is designed to correlate the magnetic reluctance to the air gap. Lastly, using the obtained empirical reluctance model to eliminate unknowns from the proposed air gap-inductance model, the model in atmosphere or hydraulic oil environments was tested. Initial results showed that the proposed model is capable of calculating the spool displacement based on the coil current, and the estimation errors compared to the laser measurement are within ±7% in air environment.
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