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 solenoidinjectors for Euro 6 diesel engine applications, has been performed in the frequencydomain. A lumped parameter numerical model of the high-pressure hydraulic circuit,from the pump delivery to the injector nozzle, has been realized. The model outcomeshave been validated through a comparison with frequency values that were obtained byapplying the peak-picking technique to the experimental pressure time histories acquiredfrom the pipe that connects the injector to the rail. The eigenvectors associated with thedifferent eigenfrequencies have been calculated and physically interpreted, thus provid-ing a methodology for the modal analysis of hydraulic systems. Three main modalmotions have been identified in the considered fuel injection apparatus, and the possibleresonances with the external forcing terms, i.e., pump delivered flow rate, injected flowrate, and injector dynamic fuel leakage through the pilot valve, have been discussed. Theinvestigation 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 pumpand the downstream hydraulic circuit. Consequently, the oscillations generated by thepump flow rates mainly remain confined to the pipe between the pump and the rail. Thesecond 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 theinjector and its internal hydraulic circuit. It has also been observed that some geometricfeatures of the injection apparatus can have a significant effect on the system dynamicsand can induce hydraulic resonance phenomena. Furthermore, the lumped parametermodel has been used to determine a simplified transfer function between rail pressureand injected flow rate. The knowledge obtained from this study can help to guide design-ers 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 affectthe performance of modern injection systems, especially when digital rate shaping strat-egies or closely coupled multiple injections are implemented.[