A Dynamic Solenoid Model for Fuel Injectors

The fuel injection system strongly affects the engine combustion phenomena which determines pollutant emissions, combustion noise and fuel efficiency. Many studies have shown the advantages of using small quantity and closely-spaced multiple injections per combustion cycle for emission reduction and fuel efficiency improvement. However, closely-spaced multiple injections using electromagnetic fuel injectors, which predominate in almost all gasoline engines, are challenging, as there is residual energy (flux) in the injector coil when the injector is re-energized. The residual flux causes over-fueling in the subsequent injection event resulting in unacceptable injection instability. In this paper, we develop a simple and highly accurate dynamic model of a solenoid in electromagnetic fuel injectors to predict the residual energy/flux. Eddy current effect and magnetic saturation are considered to model the transient behavior of flux. The model parameters are derived from physical variables, which render the model easy to tune/calibrate. The predicted flux from the model showed very good agreement with experimental results over typical fuel injection profiles. The model is an enabler for model based fuel injector control to achieve accurate fuel metering in closely space multiple injection applications. The method is also applicable to solenoid in other applications, e.g., solenoid actuators in robotics, variable force solenoid in clutch systems, and so on.