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.

References

References
1.
Graf
,
B.
, and
Chen
,
L.
,
2010
, “
Correlation of Acoustic Fluid-Structural Interaction Method for Modal Analysis With Experimental Results of a Hydraulic Prototype Turbine Runner in Water
,”
International Conference on Noise and Vibration
(
ISMA
2010), Leuven, Belgium, Sept. 20–22, p.
2489
.http://past.isma-isaac.be/downloads/isma2010/papers/isma2010_0112.pdf
2.
Sigrist
,
J. F.
, and
Broc
,
D.
,
2008
, “
Homogenisation Method for the Modal Analysis of Tube Bundle With Fluid-Structure Interaction Modelling
,”
Finite Elem. Anal. Des.
,
44
(
6–7
), pp.
323
333
.
3.
Bratland
,
M.
,
Haugen
,
B.
, and
Rølvåg
,
T.
,
2014
, “
Modal Analysis of Active Flexible Multibody Systems Containing Controllers With Non-Collocated Sensors and Actuators
,”
Finite Elem. Anal. Des.
,
91
, pp.
16
29
.
4.
Ebrahimi
,
R.
,
Esfahanian
,
M.
, and
Ziaei-Rad
,
S.
,
2013
, “
Vibration Modelling and Modification of Cutting Platform in a Harvest Combine by Means of Operational Modal Analysis (OMA)
,”
Measurement
,
46
(
10
), pp.
3959
3967
.
5.
Cunha
,
A.
, and
Caetano
,
E.
,
2005
, “
From Input-Output to Output-Only Modal Identification of Civil Engineering Structures
,”
First International Operational Modal Analysis Conference
(
IOMAC
), Copenhagen, Denmark, Apr. 26–27.https://www.researchgate.net/publication/228654000_From_input-output_to_output-only_modal_identification_of_civil_engineering_structures
6.
Brincker
,
R.
,
Zhang
,
L.
, and
Andersen
,
P.
,
2001
, “
Modal Identification of Output-Only Systems Using Frequency Domain Decomposition
,”
Smart Mater. Struct.
,
10
(
3
), pp.
441
445
.
7.
Rodrigues
,
J.
,
Brincker
,
R.
, and
Andersen
,
P.
,
2004
, “
Improvement of Frequency Domain Output-Only Modal Identification From the Application of the Random Decrement Technique
,”
23rd International Modal Analysis Conference
, Deaborn, MI, Jan. 26–29.http://www.svibs.com/Documents/2004_4.pdf
8.
Juang
,
J. N.
, and
Pappa
,
R. S.
,
1985
, “
An Eigensystem Realization Algorithm for Modal Parameter Identification and Model Reduction
,”
AIAA J. Guid. Control Dyn.
,
8
(
5
), pp.
620
627
.
9.
Van Overschee
,
P.
, and
de Moor
,
B.
,
1993
, “
Subspace Algorithms for the Stochastic Identification Problem
,”
Automatica
,
29
(
3
), pp.
649
660
.
10.
Peeters
,
B.
, and
de Roeck
,
G.
,
1999
, “
Reference-Based Stochastic Subspace Identification for Output-Only Modal Analysis
,”
Mech. Syst. Signal Process.
,
13
(
6
), pp.
855
878
.
11.
Rainieri
,
C.
,
Fabbrocino
,
G.
,
Cosenza
,
E.
, and
Manfredi
,
G.
,
2007
, “
Implementation of OMA Procedures Using LabView: Theory and Application
,”
Second International Operational Modal Analysis Conference
(
IOMAC
), Copenhagen, Denmark, Apr. 30–May 2.http://www.iomac.dk/sync/uploads/485ec6a3991a8ccc473d3d4ce37aff74.pdf
12.
Bendat
,
J. S.
, and
Piersol
,
A. G.
,
1993
,
Engineering Applications of Correlation and Spectral Analysis
,
Wiley
, New York.
13.
Brincker
,
R.
,
Zhang
,
L.
, and
Andersen
,
P.
,
2000
, “
Modal Identification From Ambient Responses Using Frequency Domain Decomposition
,”
18th International Modal Analysis Conference
(
IMAC
), San Antonio, TX, Feb. 7–10, pp.
625
630
.http://vbn.aau.dk/files/12765845/Modal_Identification_from_Ambient_Responses_using_Frequency_Domain_Decomposition
14.
Liu
,
K.
,
1999
, “
Extension of Modal Analysis to Linear Time-Varying Systems
,”
J. Sound Vib.
,
226
(
1
), pp.
149
167
.
15.
Catania
,
A. E.
,
Ferrari
,
A.
,
Manno
,
M.
, and
Spessa
,
E.
,
2008
, “
Experimental Investigation of Dynamics Effects on Multiple-Injection Common Rail System Performance
,”
ASME J. Eng. Gas Turbines Power
,
130
(
3
), p.
032806
.
16.
Catania
,
A. E.
,
Ferrari
,
A.
, and
Manno
,
M.
,
2008
, “
Development and Application of a Complete Multijet Common-Rail Injection System Mathematical Model for Hydrodynamic Analysis and Diagnostics
,”
ASME J. Eng. Gas Turbines Power
,
130
(
6
), p.
062809
.
17.
Bosch
,
W.
,
1966
, “The Fuel Rate Indicator: A New Measuring Instrument for Display of the Characteristics of Individual Injection,”
SAE
Paper No. 660749.
18.
Catania
,
A. E.
, and
Ferrari
,
A.
,
2011
, “
Experimental Analysis, Modeling, and Control of Volumetric Radial-Piston Pumps
,”
ASME J. Fluids Eng.
,
133
(
8
), p. 081103.
19.
Ferrari
,
A.
,
Paolicelli
,
F.
, and
Pizzo
,
P.
,
2015
, “
The New-Generation of Solenoid Injectors Equipped With Pressure-Balanced Pilot Valves for Energy Saving and Dynamic Response Improvement
,”
Appl. Energy
,
151
, pp.
367
376
.
20.
Catania
,
A. E.
,
Ferrari
,
A.
, and
Spessa
,
E.
,
2009
, “
Numerical-Experimental Study and Solutions to Reduce Dwell Time Threshold for Fusion Free Consecutive Injections in a Multijet Solenoid-Type CR System
,”
ASME J. Eng. Gas Turbines Power
,
131
(
2
), p.
022804
.
21.
Huber
,
B.
, and
Ulbrich
,
H.
,
2014
, “Modeling and Experimental Validation of the Solenoid Valve of a Common Rail Diesel Injector,”
SAE
Paper No. 2014-01-0195.
22.
Jelali
,
M.
, and
Kroll
,
A.
,
2012
,
Hydraulic Servo-Systems: Modelling, Identification and Control
,
Springer Science & Business Media
, London.
23.
Baratta
,
M.
,
Catania
,
A. E.
, and
Ferrari
,
A.
,
2008
, “
Hydraulic Circuit Design Rules to Remove the Dependence of the Injected Fuel Amount on Dwell Time in Multijet CR Systems
,”
ASME J. Fluids Eng.
,
130
(12), p.
121104
.
24.
Wagner
,
N.
, and
Adhikari
,
S.
,
2003
, “
Symmetric State-Space Method for a Class of Nonviscously Damped Systems
,”
AIAA J.
,
41
(
5
), pp. 951–956.
25.
Fasana
,
A.
, and
Marchesiello
,
S.
,
2006
,
Meccanica Delle Vibrazioni
,
CLUT
,
Torino, Italy
.
26.
Jablokow
,
A. G.
,
Nagarajan
,
S.
, and
Turcic
,
D. A.
,
1993
, “
A Modal Analysis Solution Technique to the Equations of Motion for Elastic Mechanism System Including the Rigid-Body and Elastic Motion Coupling Terms
,”
ASME J. Mech. Des.
,
115
(
2
), pp.
314
323
.
27.
Baur
,
R.
,
Blath
,
J.
,
Bohn
,
C.
,
Kallage
,
F.
, and
Schultalbers, M.
,
2014
, “Modeling and Identification of a Gasoline Common Rail Injection System,”
SAE
Paper No. 2014-01-0196.
28.
Ferrari
,
A.
, and
Pizzo
,
P.
,
2015
, “
Optimization of an Algorithm for the Measurement of Unsteady Flow-Rates in High-Pressure Pipelines and Application of a Newly Designed Flowmeter to Volumetric Pump Analysis
,”
ASME J. Eng. Gas Turbines Power
,
138
(
3
), p.
031604
.
29.
Ferrari
,
A.
,
Paolicelli
,
F.
, and
Pizzo
,
P.
,
2014
, “Common Feeding Injection System Equipped With Reduced-Leakage Solenoid Injectors,”
SAE
Paper No. 2014-01-2735.
30.
Ferrari
,
A.
, and
Salvo
,
E.
,
2016
, “
Determination of the Transfer Function Between the Injected Flow-Rate and High-Pressure Time Histories for Improved Control of Common Rail Diesel Engines
,”
Int. J. Engine Res.
,
18
(3), pp. 212–225.
31.
Shin
,
K.
, and
Hammond
,
J.
,
2008
,
Fundamentals of Signal Processing for Sound and Vibration Engineers
,
Wiley
, Chichester, UK.
You do not currently have access to this content.