Experimental characterization and gray-box modeling of spool-type automotive variable-force-solenoid valves with circular flow ports and notches

In automatic transmission design, electronic control techniques have been adopted through proportional variable-force-solenoid valves, which typically consist of spool-type valves (Christenson, W. A., 2000, SAE Technical Paper Series, 2000-01-0116). This paper presents an expert. mental investigation and neural network modeling of the fluid force and flow rate for a spool-type hydraulic valve with symmetrically distributed circular ports. Through extensive data analysis, general trends of fluid force and flow rate are derived as functions of pressure drop and valve opening. To further reveal the insights of the spool valve fluid field, equivalent jet angle and discharge coefficient are calculated from the measurements, based on the lumped parameter models. By incorporating physical knowledge with nondimensional artificial neural networks (NDANN), gray-box NDANN-based hydraulic valve system models are also developed through the use of equivalent jet angle and discharge coefficient. The gray-box NDANN models calculate fluid force and flow rate as well as the intermediate variables with useful design implications. The network training and testing demonstrate that the gray-box NDANN fluid field estimators can accurately, capture the relationship between the key geometry parameters and discharge coefficient/jet angle. The gray-box NDANN maintains the nondimensional network configuration, and thus possesses good scalability with respect to the geometry parameters and key operating conditions. All of these features make the gray-box NDANN fluid field estimator a valuable tool for hydraulic system design.