Build orientation determination of multi-feature mechanical parts in selective laser melting via multi-objective decision making

doi:10.1007/s11465-022-0737-8

Frontiers of Mechanical Engineering

2023, Vol. 18

Issue (2): 21 https://doi.org/10.1007/s11465-022-0737-8

本期目录

Build orientation determination of multi-feature mechanical parts in selective laser melting via multi-objective decision making

Hongsheng SHENG³, Jinghua XU^1,^2,³, Shuyou ZHANG^1,^2,³(

), Jianrong TAN^1,^2,³, Kang WANG³

¹. State Key Laboratory of Fluid Power and Mechatronic Systems, Hangzhou 310027, China
². Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, Hangzhou 310027, China
³. Engineering Research Center for Design Engineering and Digital Twin of Zhejiang Province, Zhejiang University, Hangzhou 310027, China

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Abstract：

Selective laser melting (SLM) is a unique additive manufacturing (AM) category that can be used to manufacture mechanical parts. It has been widely used in aerospace and automotive using metal or alloy powder. The build orientation is crucial in AM because it affects the as-built part, including its part accuracy, surface roughness, support structure, and build time and cost. A mechanical part is usually composed of multiple surface features. The surface features carry the production and design knowledge, which can be utilized in SLM fabrication. This study proposes a method to determine the build orientation of multi-feature mechanical parts (MFMPs) in SLM. First, the surface features of an MFMP are recognized and grouped for formulating the particular optimization objectives. Second, the estimation models of involved optimization objectives are established, and a set of alternative build orientations (ABOs) is further obtained by many-objective optimization. Lastly, a multi-objective decision making method integrated by the technique for order of preference by similarity to the ideal solution and cosine similarity measure is presented to select an optimal build orientation from those ABOs. The weights of the feature groups and considered objectives are achieved by a fuzzy analytical hierarchy process. Two case studies are reported to validate the proposed method with numerical results, and the effectiveness comparison is presented. Physical manufacturing is conducted to prove the performance of the proposed method. The measured average sampling surface roughness of the most crucial feature of the bracket in the original orientation and the orientations obtained by the weighted sum model and the proposed method are 15.82, 10.84, and 10.62 μm, respectively. The numerical and physical validation results demonstrate that the proposed method is desirable to determine the build orientations of MFMPs with competitive results in SLM.

Key words： selective laser melting (SLM) build orientation determination multi-feature mechanical part (MFMP) fuzzy analytical hierarchy process multi-objective decision making (MODM)

收稿日期: 2022-04-17 出版日期: 2023-05-12

Corresponding Author(s): Shuyou ZHANG

引用本文:

. [J]. Frontiers of Mechanical Engineering, 2023, 18(2): 21.
Hongsheng SHENG, Jinghua XU, Shuyou ZHANG, Jianrong TAN, Kang WANG. Build orientation determination of multi-feature mechanical parts in selective laser melting via multi-objective decision making. Front. Mech. Eng., 2023, 18(2): 21.

链接本文:

https://academic.hep.com.cn/fme/CN/10.1007/s11465-022-0737-8
https://academic.hep.com.cn/fme/CN/Y2023/V18/I2/21

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Linguistic variables	TFN	Scale of TFN
Equal importance	1	(1, 1, 1)
Little importance	$1 ~$	(1, 1, 3)
Intermediate value between $1 ~$ and $3 ~$	$2 ~$	(1, 2, 4)
Moderate importance	$3 ~$	(1, 3, 5)
Intermediate value between $3 ~$ and $5 ~$	$4 ~$	(2, 4, 6)
Essential importance	$5 ~$	(3, 5, 7)
Intermediate value between $5 ~$ and $7 ~$	$6 ~$	(4, 6, 8)
Extreme importance	$7 ~$	(5, 7, 9)
Intermediate value between $7 ~$ and $9 ~$	$8 ~$	(6, 8, 10)
Absolute importance	$9 ~$	(7, 9, 11)

Tab.1

Tab.2

Parameter	Value
$l t$	0.03 mm
$T r$	20 s
$v s$	1250 mm/s
$H d p$	0.07 mm
$H d s$	1 mm
$H p p$	3 mm
$M d e n s i t y$	4.43 g/cm³
$M p o r o s i t y$	99.5%
$R w a s t e$	0.1
$S d e n s i t y$	0.3
$P m a t e r i a l$	300 USD/kg
$P e n e r g y$	0.18 USD/(kW·h)
$E c o n s u m p t i o n$	162.13 kW·h/kg
$R i n d i r e c t$	53.35 USD/h
$A p l a t f o r m$	62500 mm²

Tab.3

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Orientation	$V wve / m m 3$	$R a wasr / μm$	$V s / m m 3$	$T b / s$	IV
Original	8.1129	10.8011	6041.0644	23547.7393	0.00970
OBO	7.8981	10.5099	2836.6676	35423.6799	0.01137

Tab.4

Orientation	$V wve / m m 3$	$R a wasr / μm$	$V s / m m 3$	$C build / U S D$	IV
Original	9.6181	10.9872	39258.6953	82.1573	0.00414
OBO	9.2628	10.5730	1292.4769	64.5985	0.01297

Tab.5

Fig.11

Tab.6

Tab.7

Method	$V wve / m m 3$	$R a wasr / μm$	$V s / m m 3$	$T b / s$	IV
WSM	8.2895	10.7758	4654.8951	24039.8217	0.01050
Proposed method	7.8981	10.5099	2836.6676	35423.6799	0.01137

Tab.8

Method	$V wve / m m 3$	$R a wasr / μm$	$V s / m m 3$	$C build / U S D$	IV
WSM	6.6203	10.584	28077.8537	74.5537	0.00743
Proposed method	9.2628	10.573	1292.4769	64.5985	0.01470

Tab.9

Fig.12

Fig.13

Fig.14

Fig.15

Fig.16

Fig.17

Fig.18

Fig.19

Fig.20

Fig.21

Fig.22

Abbreviations
ABO	Alternative build orientation
AM	Additive manufacturing
CSM	Cosine similarity measure
FAHP	Fuzzy analytical hierarchy process
FDM	Fused deposition modeling
FG	Feature group
GA	Genetic algorithm
MADR	Machining accuracy design requirement
MFMP	Multi-feature mechanical part
MODM	Multi-objective decision making
MOO	Many-objective optimization
NSGA-II	Non-dominated sorting genetic algorithm II
OBO	Optimal build orientation
SLA	Stereolithography
SLM	Selective laser melting
SLS	Selective laser sintering
STL	Standard tessellation language
TFN	Triangular fuzzy number
TOPSIS	Technique for order of preference by similarity to ideal solution
WSM	Weighted sum model
Variables
$A ~$	Triangular fuzzy number
$A +$	Positive ideal solution
$A −$	Negative ideal solution
$A g$	Area of the grid generated in the projection of the bounding box on the platform
$A i f$	Area of the ith facet
A_platform	Area of the fabrication platform
B_length	Length of the part’s bounding box along the x-axis
B_width	Width of the part’s bounding box along the y-axis
C_build	Build cost of an SLM part
C_energy	Energy cost for building an SLM part
C_i	Relative closeness to the ideal solution of the ith alternative
$C i ′$	Normalized relative closeness to the ideal solution of the ith alternative
$C i n d i r e c t$	Indirect build cost of an SLM part
$C m a t e r i a l$	Material cost used for the part, support structure, and wasted material
d	Ordinate of the highest intersection point D between $μ S 1$ and $μ S 2$
$d (S i)$	Normalized weight of the ith object
$d ′ (S i)$	Weight of the ith object obtained by the FAHP
$D i +$	Distance of the ith alternative to the positive ideal solution
$D i −$	Distance of the ith alternative to the negative ideal solution
d	Build direction vector
DM	Decision matrix of an MODM problem
$E c o n s u m p t i o n$	Energy consumption rate
$f i (θ x, θ y)$	Estimation model function of the ith objective
$F i$	ith facet
$F w s m$	WSM evaluation value of one solution
$g i$	ith object
$H i, j$	Height of the jth segment of the ith supported ray
$H d p$	Hatch distance for filling the part
$H d s$	Hatch distance of the lattice support structure
$H p$	Part’s height
$H p p$	Height between the part and the platform
$I V$	Integrated MODM evaluation value
$I V i$	Integrated MODM evaluation value of the ith alternative
$k$	Number of convex fuzzy numbers
l	Lower bound of a TFN
$l e$	Edge length of the grid
$l g i j$	Lower bound of the TFN $M g i j$
$l t$	Layer thickness
$l S i$	Lower bound of the TFN S_i
m	Most promising value of a TFN
$m g i j$	Most promising value of the TFN $M g i j$
$m S i$	Most promising value of the TFN S_i
$M d e n s i t y$	Density of the material
$M g i j$	Extent analysis value of the jth factor to the ith object
$M i$	CSM value between the ith alternative and the positive ideal solution
$M i ′$	Normalized CSM value between the ith alternative and the positive ideal solution
$M p o r o s i t y$	Porosity of the material
$M n × q$	Fuzzy judgment matrix used in the FAHP
n	Number of the objects
n_f	Number of facets of the manifold mesh model
n_fg	Number of the feature groups
$n f n$	Number of the facets without supports
$n f s$	Number of the facets with supports
n_g	Number of the grids
$n g x$	Number of the grids along the x-axis
$n g y$	Number of the grids along the y-axis
n_o	Number of the considered objectives
n_r	Number of the rays intersected with the overhang facets
$n i f$	Unit normal vector of the ith facet
$O V i$	Value of the ith objective
$O V i max$	Maximum value of the ith objective
$O V i min$	Minimum value of the ith objective
$P e n e r g y$	Energy price
$P m a t e r i a l$	Material price
$q$	Number of the factors of one object
$Q i f g$	Pairwise fuzzy comparison matrix of the feature groups of the ith part
$Q o$	Pairwise fuzzy comparison matrix of the optimization objectives
$r i, j$	Normalized value of the jth objective for the ith alternative
$R b p$	Build rate of the part
$R b s$	Build rate of the support
$R i n d i r e c t$	Indirect cost rate
$R w a s t e$	Material waste rate
$R a a s r$	Average surface roughness of an SLM part
$R a a s r, i$	Average surface roughness of the ith feature group
$R a i f$	Surface roughness of the ith facet
$R a i f s$	Surface roughness of the ith supported facet
$R a w a s r$	Weighted average surface roughness of an SLM part
$S d e n s i t y$	Volume fraction of the lattice support structure
$S i$	Fuzzy synthetic extent concerning the ith object
$T b$	Build time of an SLM part
$T r$	Recoating time of each layer
u	Upper bound of a TFN
$u g i j$	Upper bound of the TFN $M g i j$
$u S i$	Upper bound of the TFN S_i
$v i, j$	Weighted normalized value of the jth objective for the ith alternative
$v j +$	Positive ideal weighted normalized value of the jth objective among all alternatives
$v j −$	Negative ideal weighted normalized value of the jth objective among all alternatives
$v s$	Laser scanning speed
$V i g$	Support volume of the ith grid
$V p$	Part volume
$V s$	Support volume of an SLM part
V_wve	Weighted volumetric error of an SLM part
VE	Volumetric error of an AM part
$V E i f g$	Volumetric error of the ith feature group
$V (S 2 ? S 1)$	Degree of possibility of a TFN $S 2$ greater than a TFN $S 1$
$V (S ? S 1, S 2, . . ., S k)$	Degree of possibility for a convex fuzzy number to be greater than k convex fuzzy numbers
$w i f g$	Weight of the ith feature group
$w i o$	Weight of the ith objective
W	Normalized non-fuzzy weight vector
$W i f g$	Weight vector of the feature groups of the ith part
$W o$	Weight vector of the considered objectives
x	Real value
$x i, j$	Value of the jth objective for the ith ABO
$α i$	Angle between the build direction and normal vector of the ith facet
$θ x$	Rotation angle of the part around x-axis
$θ y$	Rotation angle of the part around y-axis
ρ	Coefficient to adjust the relative importance of the TOPSIS and CSM
σ	Weight for the surface roughness calculation of a supported facet
$μ A ~ (x)$	Membership function of the TFN $A ~$
$μ S i (x)$	Membership function of the TFN $S i$

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