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

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.

Graphical abstract

Keywords

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

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Nomenclature

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
\tilde{A}	Triangular fuzzy number
A^{+}	Positive ideal solution
A^{-}	Negative ideal solution
A_{\mathrm{g}}	Area of the grid generated in the projection of the bounding box on the platform
A_i^{\mathrm{f}}	Area of the ith facet
Aplatform	Area of the fabrication platform
Blength	Length of the part’s bounding box along the x-axis
Bwidth	Width of the part’s bounding box along the y-axis
Cbuild	Build cost of an SLM part
Cenergy	Energy cost for building an SLM part
Ci	Relative closeness to the ideal solution of the ith alternative
C_i^{\prime }	Normalized relative closeness to the ideal solution of the ith alternative
C_{\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}}	Indirect build cost of an SLM part
C_{\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}	Material cost used for the part, support structure, and wasted material
d	Ordinate of the highest intersection point D between {\mu }_{S_1} and {\mu }_{S_2}
d(S_i)	Normalized weight of the ith object
d^{\prime }(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_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{u}\mathrm{m}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}	Energy consumption rate
f_i\left({\theta }_x,{\theta }_y\right)	Estimation model function of the ith objective
F_i	ith facet
F_{\mathrm{w}\mathrm{s}\mathrm{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_{\mathrm{d}}^{\mathrm{p}}	Hatch distance for filling the part
H_{\mathrm{d}}^{\mathrm{s}}	Hatch distance of the lattice support structure
H_{\mathrm{p}}	Part’s height
H_{\mathrm{p}\mathrm{p}}	Height between the part and the platform
IV	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_{\mathrm{e}}	Edge length of the grid
l_{g_i}^j	Lower bound of the TFN M_{g_i}^j
l_{\mathrm{t}}	Layer thickness
l_{S_i}	Lower bound of the TFN Si
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 Si
M_{\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{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^{\prime }	Normalized CSM value between the ith alternative and the positive ideal solution
M_{\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}}	Porosity of the material
{\mathit{M}}_{n\times q}	Fuzzy judgment matrix used in the FAHP
n	Number of the objects
nf	Number of facets of the manifold mesh model
nfg	Number of the feature groups
n_{\mathrm{f}}^{\mathrm{n}}	Number of the facets without supports
n_{\mathrm{f}}^{\mathrm{s}}	Number of the facets with supports
ng	Number of the grids
n_{\mathrm{g}}^x	Number of the grids along the x-axis
n_{\mathrm{g}}^y	Number of the grids along the y-axis
no	Number of the considered objectives
nr	Number of the rays intersected with the overhang facets
{\mathit{n}}_i^{\mathrm{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_{\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}	Energy price
P_{\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}	Material price
q	Number of the factors of one object
{\mathit{Q}}_i^{\mathrm{f}\mathrm{g}}	Pairwise fuzzy comparison matrix of the feature groups of the ith part
{\mathit{Q}}_{\mathrm{o}}	Pairwise fuzzy comparison matrix of the optimization objectives
r_{i,j}	Normalized value of the jth objective for the ith alternative
R_{\mathrm{b}}^{\mathrm{p}}	Build rate of the part
R_{\mathrm{b}}^{\mathrm{s}}	Build rate of the support
R_{\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}}	Indirect cost rate
R_{\mathrm{w}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{e}}	Material waste rate
R{a}_{\mathrm{a}\mathrm{s}\mathrm{r}}	Average surface roughness of an SLM part
R{a}_{\mathrm{a}\mathrm{s}\mathrm{r},i}	Average surface roughness of the ith feature group
R{a}_i^{\mathrm{f}}	Surface roughness of the ith facet
R{a}_i^{\mathrm{f}\mathrm{s}}	Surface roughness of the ith supported facet
R{a}_{\mathrm{w}\mathrm{a}\mathrm{s}\mathrm{r}}	Weighted average surface roughness of an SLM part
S_{\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}}	Volume fraction of the lattice support structure
S_i	Fuzzy synthetic extent concerning the ith object
T_{\mathrm{b}}	Build time of an SLM part
T_{\mathrm{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 Si
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_{\mathrm{s}}	Laser scanning speed
V_i^{\mathrm{g}}	Support volume of the ith grid
V_{\mathrm{p}}	Part volume
V_{\mathrm{s}}	Support volume of an SLM part
Vwve	Weighted volumetric error of an SLM part
VE	Volumetric error of an AM part
V{E}_i^{\mathrm{f}\mathrm{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^{\mathrm{f}\mathrm{g}}	Weight of the ith feature group
w_i^{\mathrm{o}}	Weight of the ith objective
W	Normalized non-fuzzy weight vector
{\mathit{W}}_i^{\mathrm{f}\mathrm{g}}	Weight vector of the feature groups of the ith part
{\mathit{W}}_{\mathrm{o}}	Weight vector of the considered objectives
x	Real value
x_{i,j}	Value of the jth objective for the ith ABO
{\alpha }_i	Angle between the build direction and normal vector of the ith facet
{\theta }_x	Rotation angle of the part around x-axis
{\theta }_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
{\mu }_{\tilde{A}}\left(x\right)	Membership function of the TFN \tilde{A}
{\mu }_{S_i}(x)	Membership function of the TFN S_i

Acknowledgements

This work was funded by the National Key R&D Program of China (Grant No. 2018YFB1700700), and the National Natural Science Foundation of China (Grant Nos. 51935009 and 51821093).

RIGHTS & PERMISSIONS

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