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

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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.

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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

à :

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 f i :

Area of the ith facet

A plat form :

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 indirect :

Indirect build cost of an SLM part

C material :

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′(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 consumption :

Energy consumption rate

f i(θ x :

θy) Estimation model function of the ith objective

F i :

ith facet

F wsm :

WSM evaluation value of one solution

g i :

ith object

H i,j :

Height of the jth segment of the ith supported ray

H pd :

Hatch distance for filling the part

H sd :

Hatch distance of the lattice support structure

H p :

Part’s height

H pp :

Height between the part and the platform

IV :

Integrated MODM evaluation value

IV 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 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 density :

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 porosity :

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 nf :

Number of the facets without supports

n sf :

Number of the facets with supports

n g :

Number of the grids

n x g :

Number of the grids along the x-axis

n y g :

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 fi :

Unit normal vector of the ith facet

OV i :

Value of the ith objective

OV max i :

Maximum value of the ith objective

OV min i :

Minimum value of the ith objective

P energy :

Energy price

P material :

Material price

q :

Number of the factors of one object

Q fg i :

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 pb :

Build rate of the part

R sb :

Build rate of the support

R indirect :

Indirect cost rate

R waste :

Material waste rate

Ra asr :

Average surface roughness of an SLM part

Ra asr,i :

Average surface roughness of the ith feature group

Ra f i :

Surface roughness of the ith facet

Ra fs i :

Surface roughness of the ith supported facet

Ra wasr :

Weighted average surface roughness of an SLM part

S density :

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 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 s :

Laser scanning speed

V g i :

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

VE fg i :

Volumetric error of the ith feature group

V(S 2 :

⩾ S1) Degree of possibility of a TFN S2 greater than a TFN S1

V(S :

⩾ S1, S2, …, Sk) Degree of possibility for a convex fuzzy number to be greater than k convex fuzzy numbers

w fg i :

Weight of the ith feature group

w o i :

Weight of the ith objective

W :

Normalized non-fuzzy weight vector

W fg i :

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 αà (x) Membership function of the TFN Ã

\({\mu _{{S_i}}}(x)\) :

Membership function of the TFN Si

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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).

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Authors and Affiliations

  1. State Key Laboratory of Fluid Power and Mechatronic Systems, Hangzhou, 310027, China

    Jinghua Xu, Shuyou Zhang & Jianrong Tan

  2. Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, Hangzhou, 310027, China

    Jinghua Xu, Shuyou Zhang & Jianrong Tan

  3. Engineering Research Center for Design Engineering and Digital Twin of Zhejiang Province, Zhejiang University, Hangzhou, 310027, China

    Hongsheng Sheng, Jinghua Xu, Shuyou Zhang, Jianrong Tan & Kang Wang

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  1. Hongsheng Sheng
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Correspondence to Shuyou Zhang.

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Sheng, H., Xu, J., Zhang, S. et al. Build orientation determination of multi-feature mechanical parts in selective laser melting via multi-objective decision making. Front. Mech. Eng. 18, 21 (2023). https://doi.org/10.1007/s11465-022-0737-8

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