Duality-Derived Models of High-Speed Electromagnetic Valves

The article analyzes a high-speed solenoid valve (HSV) whose core and moving armature are massive elements characterized by strong eddy currents, hysteresis, and saturation. The feedback control employed in obtaining a predetermined nonsinusoidal current in the core coil necessitates the use of a high-frequency pulsewidth modulation (PWM)-like voltage with parameters varying in a manner unknown in advance during the uninterrupted transient. In view of the known difficulties in using finite-element solvers, physical Cauer circuits are found to be a reliable engineering alternative. The use of the duality transformation is proposed to obtain a pure electric model of the core and armature. As a preliminary result, it is found that a threefold reduction in eddy-current loss is achieved by using the slotted core. The results obtained with the model are in a reasonable agreement with the experimental magnetizing current and the armature movement during successive valve operations.