Viscous and magnetic force acting in a high speed solenoid valve

Viscous and the magnetic force acting on the armature of a high speed solenoid valve (SV) during its closure movement were identified numerically using a novel computational method. The numerical solutions were compared to the analytical ones. The derivation steps of the analytical formulas were presented. The convergence of the numerical solution was shown in figures. The deviation between the numerically and analytically obtained forces was listed in tables. The distribution of the calculation error was presented in figures by means of the magnitude of the magnetic flux density and the viscous stress.