Impact of the pulse width modulation on the temperature distribution in the armature of a solenoid valve

In order to estimate the inductive power set in the armature of the high-speed solenoid valve (HSV) during the open loop control (OLC) using pulse width modulation (PWM) an analytical explicit formula has been derived. The simplifications taken both in the geometry and in the physical behavior of the HSV were described. The inductive power was calculated for different boundary conditions and shown as a function of the frequency of the coil current. The power set in the armature was used as an input to the thermal calculation. The thermal calculation had an objective to estimate the time dependent temperature distribution in the armature of the HSV. All the derivation steps were presented and the influence of different boundary conditions was shown and discussed. The increase of the temperature during the heating with inductive power has been evaluated both in the core and on the side surface of the HSV.