An Accurate Mathematical Model and Experimental Research of Pressure Distribution in the Spool Valve Clearance Film

As an actuator control element of the electrohydraulic system in aerospace, airplanes, and other equipment, the spool valve is prone to the “hydraulic lock†problem, which may cause major accidents of these electrohydraulic systems. The grooves engraved on the spool can effectively eliminate this problem by migrating the uneven pressure distribution in the clearance film between the sleeve and the spool. The effect of migrating uneven pressure distribution depends on the groove parameters. This paper proposed an accurate mathematical model with rectangular grooves to investigate the effect. Unlike previous mathematical models based on the Reynolds equation, the proposed model is based on the Navier–Stokes equation, which is more valid in the range where the clearance film thickness is much less than the groove depth. Meanwhile, the mathematical model takes the distributions, width, depth, and the number of grooves into consideration. Then, the proposed mathematical model was used to investigate the effects of mitigating the uneven pressure distribution under various parameters of grooves. To verify the accuracy of the mathematical model, the volume flow leakage in the clearance film obtained by the proposed model and the Reynolds equation, respectively, is compared with that obtained by the experimental test. The comparison results indicate that the results obtained by the Reynolds equation could reach a maximum of 14.75% different from the experimental results, while the results obtained by the NS equation are only 5.57% different under the same conditions, implying that the mathematical model derived from the NS equation is more accurate.