Modal Analysis of Fuel Injection Systems and the Determination of a Transfer Function Between Rail Pressure and Injection Rate

A detailed analysis of a common rail (CR) fuel injection system, equipped with solenoid injectors for Euro 6 diesel engine applications, has been performed in the frequency domain. A lumped parameter numerical model of the high-pressure hydraulic circuit, from the pump delivery to the injector nozzle, has been realized. The model outcomes have been validated through a comparison with frequency values that were obtained by applying the peak-picking technique to the experimental pressure time histories acquired from the pipe that connects the injector to the rail. The eigenvectors associated with the different eigenfrequencies have been calculated and physically interpreted, thus providing a methodology for the modal analysis of hydraulic systems. Three main modal motions have been identified in the considered fuel injection apparatus, and the possible resonances with the external forcing terms, i.e., pump delivered flow rate, injected flow rate, and injector dynamic fuel leakage through the pilot valve, have been discussed. The investigation has shown that the rail is mainly involved in the first two vibration modes. In the first mode, the rail performs a decoupling action between the high-pressure pump and the downstream hydraulic circuit. Consequently, the oscillations generated by the pump flow rates mainly remain confined to the pipe between the pump and the rail. The second mode is centered on the rail and involves a large part of the hydraulic circuit, both upstream and downstream of the rail. Finally, the third mode principally affects the injector and its internal hydraulic circuit. It has also been observed that some geometric features of the injection apparatus can have a significant effect on the system dynamics and can induce hydraulic resonance phenomena. Furthermore, the lumped parameter model has been used to determine a simplified transfer function between rail pressure and injected flow rate. The knowledge obtained from this study can help to guide designers draw up an improved design of this kind of apparatus, because the pressure waves, which are triggered by impulsive events and are typical of injector working, can affect the performance of modern injection systems, especially when digital rate shaping strategies or closely coupled multiple injections are implemented.