Three-dimensional numerical simulations were carried out to investigate the flow dynamic behavior and pressure characteristics of a variable force solenoid (VFS) valve used in automatic transmissions. To visualize the dynamic movement of the spool, a moving mesh with dynamic layering meshes for varying boundary conditions was employed. Relevant experiment was performed to validate the simulations. The VFS valve was characterized by determining the variation in the equivalent orifice area with the spool displacement. The pressure sensitivity was found to be precisely controlled by the relation between the depth and the area of the notch in the range of the characteristic length of the valve. The results of model C, which takes into account both seal leakage and notches, indicate that there are linear pressure sensitivities in the range of the valve overlap and that there are smooth pressure control characteristics in the range of the two notches. The VFS valve with a spool was shown to have an unavoidable and unique hysteresis, which is caused by the nonlinear electromagnetic forces at the end of strokes of the spool and by the friction forces in the valve overlap. The effects of varying the oil temperature on the pressure sensitivity curves and the seal leakage flow rates were also examined.

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