mf f313 2014 l5 (1)
TRANSCRIPT
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BITS Pilani, Pilani Campus
Forging analysis
Outline
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Types of forgings
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Strip Forging
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Assumption forging forcefattains its maximum value at the end of the
operation
variation of stress field along y-axis is negligible
plane strain case
entire w/p is plastic in state during the process
constantis
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Let at any instant the thickness of the element is h and
width is 2l
Consider an element of width dx at a distance x from
origin.
Consider the equilibrium of the element in xdirection.
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02
)1(
)2....(..........
]2
,
2/)(
[
)1......(..........02
12
dxhdp
drdph
inputing
ddp
kp
criteriaMISESVONapply
p
areaplaneofcaseabeingit
stressesprincipalarepandxletnow
dxdh
x
x
x
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zonestickingahavewelxtoxx
zonestickingnonslidingahavewexxtox
s
s
,
/,0
Now as we move along the x- axis from origin,
the friction stress are increasing and when
(say) it reaches a value equal to shear yield
stress and it remains constant then after. Inother words from
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lxkep
ekpor
hxkpkc
kpxatequfrom
cfindto
chxpdp
dxhpdp
becomesequ
p
xxtoxZONESLIDINGFOR
hx
hx
s
0)4(..........2
2/
/2)2/ln(2ln
2),0(0)2(
/2/
)/2(
)3(
)0(
/21
/2
1
1
1
)6(]........./)([2
]/[2
2),4(sin
)/2(
)/2(
,
tan
)5.....(..........)/2(
],[
/2
)3(sin
/2
/22
/2
2
2
2
.2
haveweg,integratinandequ.aboveinkputing
hxxekp
hxekc
kepequgunow
xhkpc
cxhkp
ppxx
tcconsfindto
cxhkp
kpxhavexwe
hdxdp
equguagainZONESTICKINGFOR
s
hx
shxs
hxs
ss
ss
ss
ss
s
s
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hxhk
hxhekp
getweequinxputing
hx
hxor
e
kekp
wegetequinthisputing
kpskpxdxFINDTO
s
hh
s
s
s
hx
hx
s
s
s
s
s
)7....(}]......../)2/1ln(1{2/1[2
)}]2/1ln(2/{/12/1[2
)}]2/1ln(2/{/1[2
),6(
)2/1ln(2/
)2/1ln(/2
2/1
2/
),4(
/,
2
)2/1ln()2/)(/2(
/2
]/2[
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]21[2
/
0
l
xs
xs
dxpdxpf
lengthunitforceforgingtotal
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DISC FORGING
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Let in a typical open die forging of a disc as shown infigure, thickness and force at the end of the operation
are h and F respectively:
Consider an elemental disc subtending an angle d at the
centre, between radii r and r + dr.Considering the radial equilibrium of strip,
For the cylindrical symmetry (Assumption)
Now neglecting the higher order term
0.22/sin.2..))(( drrddhdrhrdhddrrd rrr
r
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)1________(______________________________02.
02...
drhd
drrdhrdhrddhrd
r
rrr
)2(________________________________________3
6)()()(
,
Pr,,
2213
232
221
kp
getWe
k
eqinvaluesthesePuttingTherefore
StressesincipalarepandLet
r
n
r
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)3(________________________________________02
)1(
drhdp
eqinPut
dpd
or
n
r
zonestickingrr
zoneslidingRrr
ei
s
s
_______0
_______
..
placetakesslidingwhichbeyondradiustheisrLet s
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rhRh
sl
Rh
Rh
Rh
n
r
eekpor
ekrhpHence
ekCor
ekCor
CRhk
kp
eqfromTherefore
RrCf indTo
)/2()/2(
)/2(
)/2(
1
)/2(
1
1
1
.3
3ln)/2(ln,
3
)3/(
)/2()3ln(
3
)2(
,0,
Rrrekp srRh
sl
)4_______(____________________3 ))(/2(
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)5____(____________________)/2(,
)/2(
02
)3(,
,,
:
2CrhkpgIntegratin
drhkdpor
kdrhdp
eqinkPutting
palsokrrAt
ZoneStickingFor
n
ss
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)6___(____________________3))(/2(
3)/2()/2(
),5()/2(3
),4(
)/2(
)/2(
),5(
,
:
))(/2(
))(/2(
2
))(/2(
2
2
2
2
s
s
s
rRhs
rRhs
ns
rRh
ns
n
ss
ss
n
ss
ekrrhkp
ekrhkrhkp
getweeqinCPuttingrhkekC
eqaboveinvaluetheputandrrputtingbyeqFrom
rhkpCor
Crhkp
eqinPutting
pprrAt
CFindTo
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)6(,
)3/1ln()2/(
)3/1ln()2/(
)3/1ln())(/2(
3/1
3/
)4(
/
,
:
))(/2(
))(/2(
n
s
s
s
s
rRh
rRh
n
s
ss
s
eqinvaluerPutting
hRr
hrR
rRh
e
ekk
eqinthisPutting
kpor
pkrrAt
rFindTo
s
s
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drrpdrrp
drrpdrrpF
ForceForgingTotal
s
s
s
s
r R
r
r R
r
....2
.2..2.
:
0
12
0
12
R
r
rRhr
rRhr
R
r
rRhrr
s
s
s
s
ss
hrhkekrrRrhk
drrkerrkrRrhk
drrkedrrkdrrrRhk
)/2(1)4/.(32)3ln(1)2/(3/2/)/2(2
..32)2/)(3ln()2/(/(2)3/()2/()/2(2
..32.)3ln(1)/(2.))(/2(2
22))(/2(
0
22
))(/2(22
0
32
))(/2(
00
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Grain Flow Comparison
(a) casting, (b) machining, (c) forging
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Smith forging
Drop forging
Press forging
Upset forging
Swaging
Roll forging
Types of Forging
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Roll Forging
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Fillet radius
Draft
Flash gutter
Shrinkage allowance (hot forging)
Die Features
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Forging Defects
(a) Laps formed by web buckling during forging; web thickness should be increasedto avoid this problem.
(b) (b) Internal defects caused by oversized billet; die cavities are filled prematurely,
and the material at the center flows past the filled regions as the dies close.
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Thanks