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Research Papers: Internal Combustion Engines

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

[+] Author and Article Information
A. Ferrari

Department of Energy,
Politecnico di Torino,
Corso Duca degli Abruzzi 24,
Torino 10129, Italy
e-mail: alessandro.ferrari@polito.it

F. Paolicelli

Department of Energy,
Politecnico di Torino,
Corso Duca degli Abruzzi 24,
Torino 10129, Italy

1Corresponding author.

Contributed by the IC Engine Division of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received November 26, 2016; final manuscript received January 18, 2018; published online July 30, 2018. Assoc. Editor: David L. S. Hung.

J. Eng. Gas Turbines Power 140(11), 112808 (Jul 30, 2018) (11 pages) Paper No: GTP-16-1549; doi: 10.1115/1.4039348 History: Received November 26, 2016; Revised January 18, 2018

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.

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Figures

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Fig. 1

Schematic of the CR hydraulic model (a) and fuel injector cross section (b)

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Fig. 2

Schematic of the analogous RLC system

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Fig. 3

Experimental pressure time history at the inlet of the injector: pnom = 600 bar, ET = 300 μs and n = 1000 rpm

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Fig. 4

Single-side power spectrum of pinj,in(t): pnom = 600 bar, ET = 300 μs, n = 1000 rpm

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Fig. 5

Single-side power spectrum of pinj,in(t): pnom = 400 bar, ET = 400 μs, n = 1000 rpm

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Fig. 6

Single-side power spectrum of pinj,in(t): pnom = 1400 bar, ET = 500 μs, n = 1000 rpm

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Fig. 7

Single-side power spectrum of pinj,in(t): pnom = 1600 bar, ET = 400 μs, n = 1000 rpm

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Fig. 8

Single-side power spectrum of pinj,in(t): pnom = 1800 bar, ET = 300 μs, n = 1000 rpm

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Fig. 9

Power spectrum of pinj,in(t) for different rotational speeds of the pump

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Fig. 10

Pressure eigenvector: pnom = 1600 bar and ET = 400 μs. First mode at 714 Hz.

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Fig. 11

Flow-rate eigenvector: pnom = 1600 bar and ET = 400 μs. First mode at 714 Hz.

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Fig. 12

Flow-rate into the system (first mode)

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Fig. 13

Pump delivered flow-rate: experimental time history (a) and Fourier power spectrum (b)

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Fig. 14

Flow-rate eigenvector: pnom = 1600 bar and ET = 400 μs. Second mode at 895 Hz.

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Fig. 15

Flow-rate into the system (second mode)

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Fig. 16

Injected fuel flow-rate: experimental time history (a) and Fourier power spectrum (b)

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Fig. 17

Flow-rate eigenvector: pnom = 1600 bar and ET = 400 μs. Third mode at 2436 Hz.

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Fig. 18

Flow-rate into the system (third mode)

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Fig. 19

Dynamic leakage of the injector: numerical time history (a) and Fourier power spectrum (b)

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Fig. 20

System transfer function according to three distinct approaches: SISO model, MISO model and Shin–Hammond's estimator (Hw): case pnom = 1000 bar, ET = 500 μs (a) and case pnom = 1400 bar, ET = 500 μs (b)

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Fig. 21

Coherence function between the Ginj and prail signals: case pnom = 1000 bar, ET = 500 μs (a) and case pnom = 1400 bar, ET = 500 μs (b)

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