![Page 1: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/1.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging Analysis - 1
ver. 1
![Page 2: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/2.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Overview
• Slab analysis– frictionless– with friction– Rectangular– Cylindrical
• Strain hardening and rate effects• Flash• Redundant work
![Page 3: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/3.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Slab analysis assumptions• Entire forging is plastic
– no elasticity• Material is perfectly plastic
– strain hardening and strain rate effects later
• Friction coefficient (µ) is constant– all sliding, to start
• Plane strain– no z-direction deformation
• In any thin slab, stresses are uniform
![Page 4: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/4.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Open die forging analysis –rectangular part
F
F
h
w
dx
yx
unit depthinto figure
![Page 5: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/5.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Expanding the dx slice on LHS
• p = die pressure• σx, dσx from material on
side• τfriction = friction force = µp
p
p
σx σx + dσx
τf
τf
![Page 6: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/6.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Force balance in x-direction
p σx
k
dxh
d
dxhd
frictionx
frictionx
τσ
τσ
202
−=
=+
Mohr’s circle
(distortion energy (von Mises) criterion, plane strain)
flowflowx kp σσσ ⋅===+ 15.1322
N.B. all done on a perunit depth basis
![Page 7: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/7.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Force balanceDifferentiating, and substituting into Mohr’s
circle equation
noting: τfriction = µp
pdxh
dp µ2= dx
hpdp µ2
=
( ) ( )
dxh
dpdxh
d
ddppdkd
frictionfrictionx
xx
=∴−=
−=∴+=
ττσ
σσ22
2
![Page 8: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/8.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Sliding region
• Noting: @ x = 0, σx = 2k = 1.15 σflow
dxhp
dp xp
k
x
∫∫ =02
2µ
![Page 9: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/9.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging pressure – sliding region
( )
⋅⋅=
=
=−
hxp
hx
kp
hxkp
flowx
x
x
µσ
µ
µ
2exp15.1
2exp2
22lnln
Sliding region result (0 < x < xk)
N.B done on a per unit depth basis
![Page 10: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/10.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging pressure –approximation
• Taking the first two terms of a Taylor’s series expansion for the exponential about 0, for
+=
hx
kpx µ212
1≤x
yields
( ) ∑=
=+++++=n
k
kn
kx
nxxxxx
0
32
!!!3!21exp L
00
+⋅⋅=
hxp flowx
µσ 2115.1
![Page 11: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/11.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Average forging pressure –all sliding approximation
• using the Taylor’s series approximation
2
22
2
21
2
22
2
0
22
0
2
0
whxx
w
dxhx
w
dxkp
kp
www
x
ave
+
=
+
==∫∫
µµ
N.B done on a per unit depth basis
+=
hw
kpave
21
2µ
+⋅⋅=
hwp flowave 2
115.1 µσ
![Page 12: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/12.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging force –all sliding approximation
depthwhwF flowforging ⋅⋅
+⋅⋅=
2115.1 µσ
depthwidthpF aveforging ⋅⋅=
![Page 13: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/13.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Slab - die interface• Sliding if τf < τflow• Sticking if τf ≥ τflow
– can’t have a force on a material greater than its flow (yield) stress
– deformation occurs in a sub-layer just within the material with stress τflow
slidingregion
stickingregion
![Page 14: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/14.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Sliding / sticking transition• Transition will occur at xk
• using k = µp, in:
• hence:
µµ 21ln
21
=hxk
=hx
kpx µ2exp2
=hx
kk kµµ
2exp2
![Page 15: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/15.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Sticking region
• Using p = k/ µ
pdxh
dp µ2=
( )kxx xxhkpp
k−=−
2dxhkdp
x
x
p
p k
x
kx
∫∫ =2
dxkh
dpµ
µ2=
![Page 16: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/16.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Sticking region
We know that • at x = xk, pxk
= k/µ
• and
µµ 21ln
21
=hxk
![Page 17: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/17.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging pressure - sticking region
hx
kpx +
−=
µµ 21ln1
21
2
Combining (for xk < x < w/2)
+
−⋅⋅=
hxp flowx µµ
σ21ln1
2115.1
![Page 18: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/18.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging pressure –all sticking approximation
• If xk << w, we can assume all sticking, and approximate the total forging force per unit depth (into the figure) by:
x=0 x=w/20
pedge
∆p
![Page 19: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/19.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging pressure –all sticking approximation
kpedge 2=
+⋅⋅=
+=∴
hxp
hx
kp
flowx
x
115.1
12
σ
( )xhkkpx22 =−dx
hkdp
xp
k
x
∫∫ =02
2
![Page 20: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/20.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Average forging pressure –all sticking approximation
22
2
1
22
2
2
0
22
0
2
0
whxx
w
dxhx
w
dxkp
kp
www
x
ave
+
=
+
==∫∫
+=
hw
kpave
41
2
+⋅⋅=
hwp flowave 4
115.1 σ
![Page 21: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/21.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging force –all sticking approximation
depthwhwF flowforging ⋅⋅
+⋅⋅=
4115.1 σ
depthwidthpF aveforging ⋅⋅=
![Page 22: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/22.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Sticking and sliding
• If you have both sticking and sliding, and you can’t approximate by one or the other,
• Then you need to include both in your pressure and average pressure calculations.
( ) ( )stickingaveslidingaveforging ApApF ⋅+⋅=
stickingslidingforging FFF +=
![Page 23: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/23.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Material Models
nflow KY εσ ==
Strain hardening (cold – below recrystallization point)
Strain rate effect (hot – above recrystallization point)
( )mflow CY εσ &==
heightousinstantanevelocityplaten
hv
dtdh
h1ε ===&
![Page 24: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/24.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-1• Lead 1” x 1” x 36”• σy = 1,000 psi• hf = 0.25”, µ = 0.25• Show effect of friction on total forging force.• Use the slab method.• Assume it doesn’t get wider in 36” direction.• Assume cold forging.
1”
1”
36”
![Page 25: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/25.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-2• At the end of forging:hf = 0.25”, wf = 4” (conservation of mass)
• Sliding / sticking transition
"347.025.02
1ln25.0225.021ln
21
=××
=
=
k
k
x
hx
µµ
![Page 26: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/26.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-3
• Sliding region:
( )xhxpf
flowx
2exp1150
2exp15.1
⋅=
⋅⋅=
µσ
![Page 27: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/27.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-4
• Sticking region
( )xhxpf
flowx
46.01150
21ln1
2115.1
+⋅=
+
−⋅⋅=
µµσ
![Page 28: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/28.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-5
0
200040006000
800010000
12000
0 0.5 1 1.5 2 2.5 3 3.5 4
Distance from forging edge (in)
Forg
ing
pres
sure
(psi
)
P(sticking)P(sliding)
stickingsliding slidingfriction hill
xkxk
![Page 29: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/29.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-6
• Friction hill– forging pressure must be large (8.7x) near the
center of the forging to “push” the outer material away against friction
![Page 30: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/30.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-7
• Determine the forging force from:
• since we have plane strain
dApForce ∫∫ ⋅=
dxpdepthunitF x
x∫=0
![Page 31: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/31.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-8
• We must solve separately for the sliding and sticking regions
sticking
w
xx
sliding
x
xforging depthdxpdepthdxpFk
k
+
= ∫∫ .2.2
2/
0
![Page 32: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/32.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-9
Sliding first
k
k
x
k
x
flow
ave
hxh
x
dxhx
depthunit
p
0
0 2exp20
2exp15.1
=
−
=∫ µ
µ
µσ
( )0
12exp2
−
−
=k
k
xhxh µ
µ
![Page 33: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/33.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-12Substituting values
( ) 44.10347.0
125.0
347.025.02exp25.0225.0
15.1=
−
−
××
×=
depthunit
pflow
ave
σ
3.5
347.024
347.044
25.021347.0
24
25.021ln1
25.021
15.12
2
=
−
−
×+
−
×−
×=
depthunit
pflow
ave
σ
sliding
sticking
![Page 34: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/34.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-10
Sticking next
k
w
xflow
ave
xw
dxhx
depthunit
p
k
−
+
−
=∫
2
21ln1
21
15.1
2
µµσ
22
2
221ln1
21
w
x
k
k
xwhxx
−
+⋅
−
=µµ
![Page 35: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/35.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-11
( )k
kkflow
ave
xw
xwh
xw
depthunit
p
−
−+−
−
=2
421
221ln1
21
15.12
2
µµσ
![Page 36: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/36.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-13
Now calculate the area/unit depth
31.3347.024
69.02347.0
=×−=
=×=
sticking
sliding
A
A
![Page 37: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/37.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-14Now calculate the forces
( ) ( )( )stickingaveslidingaveflow ApApdepthunitF
⋅+⋅= σ15.1
( ) ( )( )
inchlbdepthunitF
/110,21
31.33.569.044.11150
=
×+××=
![Page 38: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/38.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-15
• Now, assume all sticking, so:
depthinchlb
hw
wlengthunitF
f
ffflow
/000,2325.044141150
4115.1
=
⋅+⋅⋅=
+⋅⋅= σ
![Page 39: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/39.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-16or since the part is 36” deep:F(both) = 759,960 lbs = 380 tons
F(all sticking) = 828,000 lbs = 414 tons
F(all sliding) = 496,800 lbs = 225 tons
All sticking over-estimates actual value.
depthwhwF flowforging ⋅⋅
+⋅⋅=
4115.1 σ
depthwhwF flowforging ⋅⋅
+⋅⋅=
2115.1 µσ
![Page 40: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/40.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging – Effect of friction• Effect of friction coefficient (µ) – all sticking
• Friction is very important
Friction coefficient Fmax (lbf/in depth) xk Stick/slide0 4600 2 slide
0.1 11365 2 slide0.2 19735 0.573 both
0.25 21331 0.347 both0.3 22182 0.213 both0.4 22868 0.070 both0.5 23000 0 stick
![Page 41: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/41.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-17Forging force vs. stroke – all sticking
0
5000
10000
15000
20000
25000
0 0.2 0.4 0.6 0.8
Stroke (in)
Forg
ing
forc
e (lb
f/in
dept
h)
mu=0mu=0.1mu=0.2mu=0.25mu=0.3mu=0.4mu=0.5
![Page 42: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/42.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-19Maximum forging force vs. friction coefficient (µ)
all sticking
0
5000
10000
15000
20000
25000
0 0.1 0.2 0.3 0.4 0.5 0.6
Friction coefficient
Max
forg
ing
forc
e (lb
f/in
dept
h)
![Page 43: Forging Analysis - 1 - Indian Institute of Technology Bombayramesh/courses/ME649/Forming_2.pdf · Slab analysis assumptions • Entire forging is plastic – no elasticity • Material](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa330237f8b9ada698defb9/html5/thumbnails/43.jpg)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Summary• Slab analysis
– frictionless– with friction– Rectangular– Cylindrical
• Strain hardening and rate effects• Flash• Redundant work