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Optimal design of high-pressure fuel pipe based on vibration response and strength using multi-objective genetic algorithm

  • Industrial Application Paper
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Abstract

Unexpected high-pressure fuel injection pipe failure under operational conditions is a crucial topic in the automotive industry. In this study, experimental modal test results as well as finite element analysis (FEA) of the fuel pipe due to the vibrational motion of an engine were reported. The standard tensile tests of actual samples were carried out to determine the mechanical properties of the material used in FE model. The experimental natural frequencies of fuel pipes were found in a good agreement with the numerical results obtained from the FE simulations in ABAQUS/Standard. The effect of the fuel and added mass (due to other equipment on the pipe response) on the frequency response was also discussed. Furthermore, an optimization procedure in conjunction with MATLAB, CATIA, and ABAQUS was developed using modeFRONTIER software to improve the performance of the fuel pipes via a Non-dominated Sorting Genetic Algorithm (NSGA-II). The first natural frequencies and maximum Von Mises stress were chosen to be the objective functions, and the spatial configuration of the pipe profile was considered as decision variables. The numerical results obtained from a series of case studies confirm the efficiency and accuracy of the proposed method in dealing with structural design optimization problems.

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Abbreviations

K :

Stiffness

m :

Mass of pipe

m a :

Mass of shaft

ω :

Natural frequency

R i (i = 1,2,3):

Curvature radius of ith bend on pipe’s sketch

X pi (i = 1,2,3,4,5):

X-coordinate of ith point on pipe’s sketch

Y pi (i = 1,2,3,4,5):

Y-coordinate of ith point on pipe’s sketch

Z pi (i = 1,2,3,4,5):

Z-coordinate of ith point on pipe’s sketch

NF[1](X):

Resultant Von Mises of pipes

NF[1]max :

Upper bound of pipe’s first natural frequency

(Von Mises)(X):

Resultant Von Mises of pipes

(Von Mises)max :

Upper bound of pipe’s Von Mises

D o :

Outside diameter of pipe

L Tot :

Total length of pipe

X initial :

X-coordinate of initial 4th point on pipe’s sketch

Y initial :

Y-coordinate of initial 4th point on pipe’s sketch

Z initial :

Z-coordinate of initial 4th point on pipe’s sketch

L i (i = 1,2,3,4):

ith line on pipe’s sketch

L f(i) (i = 1,2,3):

Length of ith fillet on pipe’s sketch

L t(i) (i = 1,2,3):

Trimmed length of ith line on pipe’s sketch (after bending)

P i (i = 1,2,3,4,5):

ith point on pipe’s sketch on pipe’s sketch

ϕ i (i = 1,2,3):

ith angle between intersecting lines on pipe’s sketch

a i (i = 1,2,3,4):

Normal vector of ith line on pipe’s sketch

X :

Design variables vector

X min :

Minimum values of feasible Range for design variables

X max :

Maximum values of feasible Range for design variables

F i (i = 1,2):

Objective functions

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Acknowledgements

The authors are grateful to Laboratory Department, Iran-Khodro Powertrain Company (IPCO) for their financial support and technical assistance, Dr. A. Ohadi and I. Chitsaz for assistance with experimentation. The authors also gratefully acknowledge the valuable comments given by M. Abolghasemzadeh (a PhD student at AUT, Tehran) concerning the multi-objective optimization.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran, 15875-4413, Iran

    Mehdi AbiarKashani, Younes Alizadeh Vaghasloo & Mostafa AghaMirsalim

  2. CAE Department, Irankhodro Research Center Co. (IKCO), Tehran, 13895-111, Iran

    Mehdi AbiarKashani

  3. Engine Research Centre of Irankhodro Powertrain Co. (IPCO), Tehran, 1398813711, Iran

    Mostafa AghaMirsalim

Authors
  1. Mehdi AbiarKashani
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  2. Younes Alizadeh Vaghasloo
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  3. Mostafa AghaMirsalim
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Correspondence to Younes Alizadeh Vaghasloo.

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The authors declare no conflict of interest.

Replication of results

The optimization process in this article is based on the coupling of MATLAB, CATIA, and ABAQUS through modeFRONTIER software. To facilitate the replication of the results, the matlab code and other necessary files are added to the attachment. It should be mentioned that the 15th-line in the Python code and the 7th-line catvbs script, which are inputted into modeFRONTIER Project File by script nodes, should be define by each user accordingly.

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AbiarKashani, M., Alizadeh Vaghasloo, Y. & AghaMirsalim, M. Optimal design of high-pressure fuel pipe based on vibration response and strength using multi-objective genetic algorithm. Struct Multidisc Optim 64, 935–956 (2021). https://doi.org/10.1007/s00158-021-02908-0

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  • DOI: https://doi.org/10.1007/s00158-021-02908-0

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