Formula Sheet: Metal Forming | Manufacturing Engineering - Mechanical Engineering PDF Download

 Page 1


F ormula Sheet: Metal F orming
Introduction to Metal F orming
• Definition : Metal forming involves plastic deformation of metals to shape
them into desired geometries using processes lik e forging, rolling, extru-
sion, and dr awing.
• K ey Concepts : Plastic deformation, yield criteria, flow stress, friction, and
temper ature effects .
Yield Criteria and Flow Stress
• von Mises Yield Criterion :
v
(s
1
-s
2
)
2
+(s
2
-s
3
)
2
+(s
3
-s
1
)
2
2
=s
y
wheres
1
,s
2
,s
3
= principal stresses,s
y
= yield stress.
• Tresca Yie ld Criterion :
s
1
-s
3
=s
y
• Flow Stre ss (Power Law Hardening) :
s =K?
n
where s = flow stress, K = strength coefficient, ? = true str ain, n = str ain
hardening exponen t.
• True Str ain :
? = ln
(
l
f
l
0
)
or ? = ln
(
A
0
A
f
)
wherel
0
,l
f
= initial and final lengths, A
0
,A
f
= initial and final cross-sectional
areas.
F orging
• F orging F orce (Plane Str ain, No Friction) :
F =s
y
A
whereA = contact area.
• F orging F orce with Friction :
F =s
y
A
(
1+
µb
h
)
whereµ = friction coefficient, b = width of workpiece,h = height.
1
Page 2


F ormula Sheet: Metal F orming
Introduction to Metal F orming
• Definition : Metal forming involves plastic deformation of metals to shape
them into desired geometries using processes lik e forging, rolling, extru-
sion, and dr awing.
• K ey Concepts : Plastic deformation, yield criteria, flow stress, friction, and
temper ature effects .
Yield Criteria and Flow Stress
• von Mises Yield Criterion :
v
(s
1
-s
2
)
2
+(s
2
-s
3
)
2
+(s
3
-s
1
)
2
2
=s
y
wheres
1
,s
2
,s
3
= principal stresses,s
y
= yield stress.
• Tresca Yie ld Criterion :
s
1
-s
3
=s
y
• Flow Stre ss (Power Law Hardening) :
s =K?
n
where s = flow stress, K = strength coefficient, ? = true str ain, n = str ain
hardening exponen t.
• True Str ain :
? = ln
(
l
f
l
0
)
or ? = ln
(
A
0
A
f
)
wherel
0
,l
f
= initial and final lengths, A
0
,A
f
= initial and final cross-sectional
areas.
F orging
• F orging F orce (Plane Str ain, No Friction) :
F =s
y
A
whereA = contact area.
• F orging F orce with Friction :
F =s
y
A
(
1+
µb
h
)
whereµ = friction coefficient, b = width of workpiece,h = height.
1
• Str ain in Op en Die F orging :
? = ln
(
h
0
h
f
)
whereh
0
,h
f
= initial and fin al heights.
Rolling
• Roll F orce :
F =s
y
Lb
(
1+
µL
2h
m
)
whereL = contact length,b = width,h
m
= mean thickness,µ = friction coef-
ficient.
• Contact L ength :
L =
v
R(h
0
-h
f
)
whereR = roll r adius,h
0
,h
f
= initial and final thicknesses.
• T orque per Roll :
T =
FL
2
• Power :
P = 2T?
where? = angular velocity of rolls.
Extrusion
• Extrusion Ra tio :
R =
A
0
A
f
whereA
0
,A
f
= initial and final cross-sectional areas.
• Extrusion P ressure (Ideal, No Friction) :
p =s
y
lnR
• Extrusion P ressure with Friction :
p =s
y
(
lnR+
2µL
D
)
whereL = length of bi llet,D = die diameter .
2
Page 3


F ormula Sheet: Metal F orming
Introduction to Metal F orming
• Definition : Metal forming involves plastic deformation of metals to shape
them into desired geometries using processes lik e forging, rolling, extru-
sion, and dr awing.
• K ey Concepts : Plastic deformation, yield criteria, flow stress, friction, and
temper ature effects .
Yield Criteria and Flow Stress
• von Mises Yield Criterion :
v
(s
1
-s
2
)
2
+(s
2
-s
3
)
2
+(s
3
-s
1
)
2
2
=s
y
wheres
1
,s
2
,s
3
= principal stresses,s
y
= yield stress.
• Tresca Yie ld Criterion :
s
1
-s
3
=s
y
• Flow Stre ss (Power Law Hardening) :
s =K?
n
where s = flow stress, K = strength coefficient, ? = true str ain, n = str ain
hardening exponen t.
• True Str ain :
? = ln
(
l
f
l
0
)
or ? = ln
(
A
0
A
f
)
wherel
0
,l
f
= initial and final lengths, A
0
,A
f
= initial and final cross-sectional
areas.
F orging
• F orging F orce (Plane Str ain, No Friction) :
F =s
y
A
whereA = contact area.
• F orging F orce with Friction :
F =s
y
A
(
1+
µb
h
)
whereµ = friction coefficient, b = width of workpiece,h = height.
1
• Str ain in Op en Die F orging :
? = ln
(
h
0
h
f
)
whereh
0
,h
f
= initial and fin al heights.
Rolling
• Roll F orce :
F =s
y
Lb
(
1+
µL
2h
m
)
whereL = contact length,b = width,h
m
= mean thickness,µ = friction coef-
ficient.
• Contact L ength :
L =
v
R(h
0
-h
f
)
whereR = roll r adius,h
0
,h
f
= initial and final thicknesses.
• T orque per Roll :
T =
FL
2
• Power :
P = 2T?
where? = angular velocity of rolls.
Extrusion
• Extrusion Ra tio :
R =
A
0
A
f
whereA
0
,A
f
= initial and final cross-sectional areas.
• Extrusion P ressure (Ideal, No Friction) :
p =s
y
lnR
• Extrusion P ressure with Friction :
p =s
y
(
lnR+
2µL
D
)
whereL = length of bi llet,D = die diameter .
2
Wire Dr awing
• Dr awing Str ess :
s
d
=s
y
(
1+
µ
tana
)
ln
(
A
0
A
f
)
wherea = die semi-angle,µ = friction coefficient.
• Dr awing F orce :
F
d
=s
d
A
f
Sheet Metal F orming
• Bending F orce :
F =
ks
y
Lt
2
W
wherek = constant (depends on die geometry),L = length of bend,t = sheet
thickness,W = die opening width.
• Springback :
R
i
R
f
= 1-
3s
y
R
i
Et
whereR
i
,R
f
= initia l and final r adii, E = Y oung’ s modul us.
• Deep Dr awing F orce :
F =pd
p
ts
y
(
D
0
d
p
-0.7
)
whered
p
= punch diameter ,D
0
= blank diameter .
Friction and Lubrication
• Coulomb Fr iction :
F
friction
=µN
whereN = normal force.
• Friction Hill (F orging/Rolling) : Pressure increases towards the center due
to friction, model ed as:
p =s
y
e
µx
h
wherex = distance from edge,h = thickness.
3
Page 4


F ormula Sheet: Metal F orming
Introduction to Metal F orming
• Definition : Metal forming involves plastic deformation of metals to shape
them into desired geometries using processes lik e forging, rolling, extru-
sion, and dr awing.
• K ey Concepts : Plastic deformation, yield criteria, flow stress, friction, and
temper ature effects .
Yield Criteria and Flow Stress
• von Mises Yield Criterion :
v
(s
1
-s
2
)
2
+(s
2
-s
3
)
2
+(s
3
-s
1
)
2
2
=s
y
wheres
1
,s
2
,s
3
= principal stresses,s
y
= yield stress.
• Tresca Yie ld Criterion :
s
1
-s
3
=s
y
• Flow Stre ss (Power Law Hardening) :
s =K?
n
where s = flow stress, K = strength coefficient, ? = true str ain, n = str ain
hardening exponen t.
• True Str ain :
? = ln
(
l
f
l
0
)
or ? = ln
(
A
0
A
f
)
wherel
0
,l
f
= initial and final lengths, A
0
,A
f
= initial and final cross-sectional
areas.
F orging
• F orging F orce (Plane Str ain, No Friction) :
F =s
y
A
whereA = contact area.
• F orging F orce with Friction :
F =s
y
A
(
1+
µb
h
)
whereµ = friction coefficient, b = width of workpiece,h = height.
1
• Str ain in Op en Die F orging :
? = ln
(
h
0
h
f
)
whereh
0
,h
f
= initial and fin al heights.
Rolling
• Roll F orce :
F =s
y
Lb
(
1+
µL
2h
m
)
whereL = contact length,b = width,h
m
= mean thickness,µ = friction coef-
ficient.
• Contact L ength :
L =
v
R(h
0
-h
f
)
whereR = roll r adius,h
0
,h
f
= initial and final thicknesses.
• T orque per Roll :
T =
FL
2
• Power :
P = 2T?
where? = angular velocity of rolls.
Extrusion
• Extrusion Ra tio :
R =
A
0
A
f
whereA
0
,A
f
= initial and final cross-sectional areas.
• Extrusion P ressure (Ideal, No Friction) :
p =s
y
lnR
• Extrusion P ressure with Friction :
p =s
y
(
lnR+
2µL
D
)
whereL = length of bi llet,D = die diameter .
2
Wire Dr awing
• Dr awing Str ess :
s
d
=s
y
(
1+
µ
tana
)
ln
(
A
0
A
f
)
wherea = die semi-angle,µ = friction coefficient.
• Dr awing F orce :
F
d
=s
d
A
f
Sheet Metal F orming
• Bending F orce :
F =
ks
y
Lt
2
W
wherek = constant (depends on die geometry),L = length of bend,t = sheet
thickness,W = die opening width.
• Springback :
R
i
R
f
= 1-
3s
y
R
i
Et
whereR
i
,R
f
= initia l and final r adii, E = Y oung’ s modul us.
• Deep Dr awing F orce :
F =pd
p
ts
y
(
D
0
d
p
-0.7
)
whered
p
= punch diameter ,D
0
= blank diameter .
Friction and Lubrication
• Coulomb Fr iction :
F
friction
=µN
whereN = normal force.
• Friction Hill (F orging/Rolling) : Pressure increases towards the center due
to friction, model ed as:
p =s
y
e
µx
h
wherex = distance from edge,h = thickness.
3
Applications
– Used in manufacturing components lik e gears, shafts, and sheet metal
parts.
– Essential for analyzing process par ameters, die design, and material
flow in GA TE problems.
4