Group-based multiple pipe routing method for aero-engine focusing on parallel layout

doi:10.1007/s11465-021-0645-3

Front. Mech. Eng.

2021, Vol. 16

Issue (4) : 798-813 https://doi.org/10.1007/s11465-021-0645-3

RESEARCH ARTICLE

Group-based multiple pipe routing method for aero-engine focusing on parallel layout

Hexiang YUAN¹, Jiapeng YU^1,²(

), Duo JIA³, Qiang LIU⁴, Hui MA^1,²

¹. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China
². Key Laboratory of Vibration and Control of Aero-Propulsion System (Ministry of Education), Northeastern University, Shenyang 110819, China
³. Shenyang Engine Research Institute of AECC, Shenyang 110015, China
⁴. School of Information and Control Engineering, Liaoning Petrochemical University, Fushun 113001, China

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Abstract

External pipe routing for aero-engine in limited three-dimensional space is a typical nondeterministic polynomial hard problem, where the parallel layout of pipes plays an important role in improving the utilization of layout space, facilitating pipe assembly, and maintenance. This paper presents an automatic multiple pipe routing method for aero-engine that focuses on parallel layout. The compressed visibility graph construction algorithm is proposed first to determine rapidly the rough path and interference relationship of the pipes to be routed. Based on these rough paths, the information of pipe grouping and sequencing are obtained according to the difference degree and interference degree, respectively. Subsequently, a coevolutionary improved differential evolution algorithm, which adopts the coevolutionary strategy, is used to solve multiple pipe layout optimization problem. By using this algorithm, pipes in the same group share the layout space information with one another, and the optimal layout solution of pipes in this group can be obtained in the same evolutionary progress. Furthermore, to eliminate the minor angle deviation of parallel pipes that would cause assembly stress in actual assembly, an accurate parallelization processing method based on the simulated annealing algorithm is proposed. Finally, the simulation results on an aero-engine demonstrate the feasibility and effectiveness of the proposed method.

Keywords multiple pipe routing optimization algorithm aero-engine pipe grouping parallel layout

Corresponding Author(s): Jiapeng YU

Just Accepted Date: 06 August 2021 Online First Date: 07 September 2021 Issue Date: 28 January 2022

Cite this article:

Hexiang YUAN,Jiapeng YU,Duo JIA, et al. Group-based multiple pipe routing method for aero-engine focusing on parallel layout[J]. Front. Mech. Eng., 2021, 16(4): 798-813.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-021-0645-3
https://academic.hep.com.cn/fme/EN/Y2021/V16/I4/798

Fig.1 Convex hull of obstacle projection in 2D space.

Fig.2 Flowchart of CVG algorithm.

Fig.3 Visibility graph construction by CVG.

Fig.4 Evaluation of pipe difference degree.

Fig.5 Interference degree-based pipe group sequencing: (a) interference degree of the two groups, (b) preferred routing of the group with higher interference degree, and (c) preferred routing of the group with lower interference degree.

Fig.6 Cylindrical coordinate-based encoding mode for single pipe.

Fig.7 Regional grid construction example for accessory: (a) original accessory, and (b) construction result.

Fig.8 Flowchart of CIDE algorithm.

Fig.9 Comparison between parallel and nonparallel routing: (a) nonparallel routing, and (b) parallel routing.

Fig.10 Energy area around pipe.

Fig.11 Angular deviation between pipe segments.

Fig.12 Multiple pipe route encoding mode for parallelization processing.

Fig.13 Position relation of external pipes.

Fig.14 Flowchart of pipe parallelization processing.

Tab.1 Performance comparison of VG and CVG

Fig.15 Comparison of visibility graph construction results: (a) result obtained by the VG algorithm, and (b) result obtained by the CVG algorithm.

Tab.2 Parameter setting for aero-engine pipe routing

Tab.3 Difference degree of different clusters

Fig.16 Rough path searching result in 2D space.

Fig.17 Clustering result based on pipe difference degree.

Fig.18 Pipe routing results: (a) routing result obtained by the proposed method, and (b) routing result obtained by SVGAS.

Tab.4 Comparison of routing results obtained by the two methods

Variables
B _i	Length of the ith bending pipe segment
CR	Crossover rate for DE
D	Inner diameter of pipe
D _i	Distance between endpoint and its effective projection point
d ₁, d ₂, d ₃, d ₄	Minimum projection distance from one pipe segment endpoint to other segments
d _int	Interval distance set for discrete pipe path
d _P	Distance between two pipes
d _s	Extension distance of starting port
d _t	Extension distance of ending port
e _j	Energy value of the jth grid cell
F	Scaling factor for DE
f _c( x)	Generatrix function of engine casing
f _d	Distance between pipes and engine casing
f _dif	Difference degree value of two pipe routes
f _i	Fitness value of the ith individual
f _L	Length of the whole pipe
f _P	Parallelism degree value
F _b	Expected value for parallelization processing
F _M	Fitness value of multiple pipe
F _{M i}	Fitness value of all pipes in the ith pipe group
f _PS	Pressure drop of fluid in straight segment
f _PE	Pressure drop of fluid in elbow pipe segment
F _S	Fitness value of single pipe
F _{S i}	Fitness value of the ith pipe
K	A constant with large value
$L c o i n 1$	Projection overlap length of $S 1$ to $S 2$
$L c o i n 2$	Projection overlap length of $S 2$ to $S 1$
$L c o i n j$	Projection overlap length of the jth segment to the segment with maximal parallelism degree
$L E$	Visible edge set
$L i$	Length of the ith straight pipe segment
$L P$	Projection overlap length of one pipe to the other
$L S$	Start point set of CVG
$L S 1$	Length of pipe centerline S ₁
$L S 2$	Length of pipe centerline S ₂
$L V$	Exploration vector set
M	Difference degree matrix
$M i, j$	Difference degree of two pipes with index of i and j
$N E$	Number of all effective projection points
$N G$	Number of grid cells that one pipe passes through
$N S$	Number of straight pipe segments in a pipe
NP	Population capacity of DE
P	Penalty term of single pipe evaluation function
P _r	Random number between 0 and 1

$P c$	Reference value for random number P _r
$P i$	The ith endpoint of the pipe segment
$P i ′$	The effective projection point corresponding to $P i$
$r 1$ , $r 2$	Radius of pipe1 and pipe2
$R$	Representative individual pool
$R B$	Bending radius of pipe
$S T$	Exploration vector constructed by points $S$ and $T$
$S V i$	Exploration vector constructed by points $S$ and $V i$
$S$	Starting point in visibility graph
$T$	Ending point in visibility graph
$u ¯$	Average velocity of fluid
$U G$	Trail population under the Gth iteration
$U i, G$	The ith individual of $U G$
$u i, G j$	The jth variable in $U i, G$
$V G$	Mutant population under the Gth iteration
$V i, G$	The ith individual of $V G$
$v i, G j$	The jth variable in $V i, G$
$x ′$ , $y ′$	Coordinate components of the projected vertex in 2D space
$X G$	Population under the Gth iteration
$X i, G$	The ith individual of $X G$
$x i, G j$	The jth variable in $X i, G$
$X G, max$	Upper limit of individuals
$X G, min$	Lower limit of individuals
$X r a n d 1, G$ ,	Three nonrepetitive individuals randomly selected from $X G$
$X r a n d 2, G$ ,
$X r a n d 2, G$
$z i$	Coordinate component of the ith discrete point
$α i$	The ith bending angle of one pipe
$γ$	Volumetric weight of fluid
$δ min$	Minimum clearance distance between two parallel pipes
$δ max$	Maximum clearance distance between two parallel pipes
$ρ i$	Distance between the ith discrete point and engine casing axis
$θ P$	Included angle of two pipes
$ρ$ , $θ$ , $z$	Cylindrical coordinate components of the spatial point
$λ$	Friction factor of fluid
$ω 1$	Weight coefficient of $f L$
$ω 2$	Weight coefficient of $f P S + f P E$
$ω 3$	Weight coefficient of $f S$
$ω d$	Weight coefficient of $d P$
$ω e$	Weight coefficient of e _j
$ω p$	Weight coefficient that reflect the contribution of the pipe clearance and the projection overlap length to difference degree
$ω L$	Weight coefficient of $L c o i n j$
$ω θ$	Weight coefficient of $θ P$

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