Formula Sheet: Additive Manufacturing | Manufacturing Engineering - Mechanical Engineering PDF Download

 Page 1


F ormula Sheet: A dditive Manufacturing
Introduction to A dditive Manufacturing
• Definition : A dditive Manufacturing (AM), also known as 3D printing, builds
parts la yer b y la yer from digital models, enabling complex geometries with
minimal materia l waste.
• K ey Processes : Fused Deposition Modeling (FDM), Stereolithogr aph y (SLA),
Selective Laser Sintering (SLS), Direct Metal Laser Sintering (DMLS), Binder
Jetting.
• A dvantages : Rapid prototyping, customization, reduced material waste,
complex shap es.
• Limitations : Surface finish, build speed, material limitations, anisotrop y .
K ey Par ameters
• La yer Thickness (t ) : Thickness of each deposited la yer , typically 0.01 mm
to0.3 mm, affects resolution and build time.
• Build Time (T
b
) :
T
b
=
V
part
v
s
A
s
+T
setup
+T
aux
whereV
part
= part volume,v
s
= scanning speed,A
s
= cross-sectional area of
la yer ,T
setup
= setup time,T
aux
= auxiliary time (e.g., recoating).
• V olume of Ma terial Deposited :
V
part
=A
part
·H
whereA
part
= aver age cross-sectional area,H = total height of part.
• Number o f La yers :
N =
H
t
wheret = la yer thickness.
Material and Energy Consider ations
• Power Re quirement (Laser-Based AM) :
P =
E
?t
where P = laser power , E = energy required to melt/sinter material, ?t =
exposure time.
1
Page 2


F ormula Sheet: A dditive Manufacturing
Introduction to A dditive Manufacturing
• Definition : A dditive Manufacturing (AM), also known as 3D printing, builds
parts la yer b y la yer from digital models, enabling complex geometries with
minimal materia l waste.
• K ey Processes : Fused Deposition Modeling (FDM), Stereolithogr aph y (SLA),
Selective Laser Sintering (SLS), Direct Metal Laser Sintering (DMLS), Binder
Jetting.
• A dvantages : Rapid prototyping, customization, reduced material waste,
complex shap es.
• Limitations : Surface finish, build speed, material limitations, anisotrop y .
K ey Par ameters
• La yer Thickness (t ) : Thickness of each deposited la yer , typically 0.01 mm
to0.3 mm, affects resolution and build time.
• Build Time (T
b
) :
T
b
=
V
part
v
s
A
s
+T
setup
+T
aux
whereV
part
= part volume,v
s
= scanning speed,A
s
= cross-sectional area of
la yer ,T
setup
= setup time,T
aux
= auxiliary time (e.g., recoating).
• V olume of Ma terial Deposited :
V
part
=A
part
·H
whereA
part
= aver age cross-sectional area,H = total height of part.
• Number o f La yers :
N =
H
t
wheret = la yer thickness.
Material and Energy Consider ations
• Power Re quirement (Laser-Based AM) :
P =
E
?t
where P = laser power , E = energy required to melt/sinter material, ?t =
exposure time.
1
• Energy fo r Melting (SLS/DMLS) :
E =m(c?T +L
f
)
wherem = mass of material per la yer , c = specific heat, ?T = temper ature
rise,L
f
= latent heat of fusion (if applicable).
• Shrinkage ( Thermal Effects) :
?L=aL?T
where a = coefficient of thermal expansion, L = original dimension, ?T =
temper ature change.
Surface Finish and A ccur acy
• Surface Ro ughness (R
a
) :
R
a
?t· cos?
where? = angle of surface relative to build direction (s tair-step effect).
• Dimensional A ccur acy :
Error=±
t
2
(Depends on l a yer thickness and process resolution.)
Process-Specific Relationships
• Fused Depo sition Modeling (FDM) :
Q=v
e
·A
n
where Q = material flow r ate, v
e
= extrusion velocity , A
n
= nozzle cross-
sectional ar ea.
• Stereolithogr aph y (SLA) :
t
c
=
E
c
P
·A
s
where t
c
= curing time per la yer , E
c
= critical energy for resin curing, P =
laser po wer ,A
s
= la yer area.
• Selective L aser Sintering (SLS) :
v
s
=
P
h·E
d
wherev
s
= scanning speed,h = hatch spacing,E
d
= energy density .
2
Page 3


F ormula Sheet: A dditive Manufacturing
Introduction to A dditive Manufacturing
• Definition : A dditive Manufacturing (AM), also known as 3D printing, builds
parts la yer b y la yer from digital models, enabling complex geometries with
minimal materia l waste.
• K ey Processes : Fused Deposition Modeling (FDM), Stereolithogr aph y (SLA),
Selective Laser Sintering (SLS), Direct Metal Laser Sintering (DMLS), Binder
Jetting.
• A dvantages : Rapid prototyping, customization, reduced material waste,
complex shap es.
• Limitations : Surface finish, build speed, material limitations, anisotrop y .
K ey Par ameters
• La yer Thickness (t ) : Thickness of each deposited la yer , typically 0.01 mm
to0.3 mm, affects resolution and build time.
• Build Time (T
b
) :
T
b
=
V
part
v
s
A
s
+T
setup
+T
aux
whereV
part
= part volume,v
s
= scanning speed,A
s
= cross-sectional area of
la yer ,T
setup
= setup time,T
aux
= auxiliary time (e.g., recoating).
• V olume of Ma terial Deposited :
V
part
=A
part
·H
whereA
part
= aver age cross-sectional area,H = total height of part.
• Number o f La yers :
N =
H
t
wheret = la yer thickness.
Material and Energy Consider ations
• Power Re quirement (Laser-Based AM) :
P =
E
?t
where P = laser power , E = energy required to melt/sinter material, ?t =
exposure time.
1
• Energy fo r Melting (SLS/DMLS) :
E =m(c?T +L
f
)
wherem = mass of material per la yer , c = specific heat, ?T = temper ature
rise,L
f
= latent heat of fusion (if applicable).
• Shrinkage ( Thermal Effects) :
?L=aL?T
where a = coefficient of thermal expansion, L = original dimension, ?T =
temper ature change.
Surface Finish and A ccur acy
• Surface Ro ughness (R
a
) :
R
a
?t· cos?
where? = angle of surface relative to build direction (s tair-step effect).
• Dimensional A ccur acy :
Error=±
t
2
(Depends on l a yer thickness and process resolution.)
Process-Specific Relationships
• Fused Depo sition Modeling (FDM) :
Q=v
e
·A
n
where Q = material flow r ate, v
e
= extrusion velocity , A
n
= nozzle cross-
sectional ar ea.
• Stereolithogr aph y (SLA) :
t
c
=
E
c
P
·A
s
where t
c
= curing time per la yer , E
c
= critical energy for resin curing, P =
laser po wer ,A
s
= la yer area.
• Selective L aser Sintering (SLS) :
v
s
=
P
h·E
d
wherev
s
= scanning speed,h = hatch spacing,E
d
= energy density .
2
Mechanical Properties
• Anisotrop y : Strength varies with build direction due to la yer bonding.
s
z
<s
xy
wheres
z
= strength in build direction,s
xy
= strength in la yer plane.
• Porosity E ffect :
s =s
0
(1-P)
n
wheres
0
= strength of fully dense material,P = porosity fr action,n = mate-
rial constant.
Applications
• Used in r apid prototyping, aerospace, biomedical, and customized manu-
facturing.
• Essential for GA TE problems on AM process par ameters, build time, and
material proper ties.
3