The proportional directional valve is a fundamental component in electro-hydraulic control technology.Its function is to provide continuous control to the speed,direction,position,and output force of hydraulic actuators.During the operation of the proportional directional valve,it is observed that when the voltage command remains constant,an interesting phenomenon occurs:as the differential pressure at the valve port increases,the flow rate does not increase but rather decreases.In order to explain this phenomenon,two static simulation models for the proportional directional valve was developed.The first static simulation model was based on an empirical equation of the flow force and the flow rate at the valve port.The second static simulation model was based on the interpolated equations for the flow force and the orifice flow obtained through numerical calculations of the ANSYS Fluent flow field.The static simulation results show that the orifice flow rate decreases rather than increases because when the differential pressure increases,the increase in flow force leads to a decrease in spool displacement,which in turn leads to a decrease in flow rate.Experimental findings demonstrate that utilizing the derived interpolation formulas based on flow field simulation data for steady-state flow force and orifice flow yields static simulation results is closer to experimental data when compared to traditional empirical formulas.