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Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Bulk Deformation - 1
ME 206Manufacturing Processes 1
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
2
Outline
• What is bulk deformation?
• Cold vs hot working
• Forging introduction
• Forging analysis
• Forging defects
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
3
What is bulk deformation?• Bulk deformation (or forming): processes
characterized by large amount of plastic deformation (large strains) carried out at elevated or room temperature
• Bulk plastic flow of material under uniaxial or multi-axial stresses dominated by compression
• Mass conserving processes à volume is constant
ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
S.N. Melkote
4
Bulk Deformation Processes
• Examples include: forging, rolling, extrusion, rod
drawing etc.
Forging (heading)
Extrusion Rod Drawing
Rolling
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
5
Cold vs Hot Working
• Many bulk deformation processes carried out at elevated temperatures
• Cold working: T < 0.3Tm– Usually a finishing step
• Warm working: T = 0.3~0.5Tm– Intermediate or final step
• Hot working: T > 0.5Tm– Initial step
ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
S.N. Melkote
6
Cold Working
Advantages
– Better dimensional control
– Superior surface finish
– Strain hardening of surface layer can be
beneficial
Limitations
– Greater material strength à higher forces
– Stronger tooling required
– Lower ductility à small deformations
– Lower malleability à harder to shape material
– Anisotropic surface properties
ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
S.N. Melkote
7
Hot Working
Advantages
– Lower yield strength à lower forces
– High ductility à larger strains possible
– Higher malleability à easy to shape metal
Limitations
– Easily forms oxide layers (scales) on surface àpoor surface finish
– Harder to control dimensions
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
8
• Shape change via compressive forces• Types of forging processes
– Open die forging (upsetting)
– Closed or impression die forging
Forging
hi hf
flash
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
9
• Carried out between flat dies• Parts weighing few lbs ~ 150 tons e.g. solid
shafts, spindles/rotors, rings, etc.• Often carried out in steps• Wide range of ferrous and non-ferrous metals
Open Die Forging
Stepped shaft Spindles
Source: http://www.forging.org
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
10
• Carried out between shaped dies• Parts weighing few ounces ~ 25 tons e.g.
crankshafts,connecting rods, aircraft parts etc.• Most engineering metals: carbon steels,
stainless steels, aluminum, bronze, etc.
Closed Die Forging
Aircraft bulkhead Connecting rods
Source: http://www.forging.org
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forgings
• Coins• Landing gear• Crank shafts• Turbine shafts
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging presses
• Large machines– hold dies– form parts
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Press types• Servo-hydraulic presses• Servo-electrical presses• Mechanical presses• Screw presses• Hammers
– gravity drop– power drop– counter blow (two rams)– high pressure gas
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
50,000 ton press
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forges
Schematic illustration of the principles of various forging machines. (a) Hydraulic press. (b) Mechanical press with an eccentric drive; the eccentric shaft can be replaced by a crankshaft to give the up-and-down motion to the ram. (continued)
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forges
Schematic illustration of the principles of various forging machines. (c) Knuckle-joint press. (d) Screw press. (e) Gravity drop hammer.
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging steps
• Prepare slug– saw– flame cut– shear
• Clean slug surfaces – shot blast– flame
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging steps• For hot forging
– heat up and descale forging– make sure press is hot
• Lubricate– oil– soap– MoS2
– glass– graphite
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Lubrication purposes
• Reduce friction• Reduce die wear• Thermally insulate part
– to keep it warm
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging steps• Forge• Remove flash
– trim– machine
• Check dimensions• Post processing, if necessary
– heat treat– machine
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Effect on grain structure
• Large grains are broken up.• Grains can be made to flow.
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Dies• Final part shape determined by die
accuracy• Multiple parts can be made in one die• Progressive shaping can be done in one
die set• Need to be stronger than highest
forging stress
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
23
• Simple stress analysis possible for open die forging process
• Analysis method called “slab” analysis• Applicable to plane strain compression with
low sliding friction
Forging Analysis
Source: http://www.forging.org
hi hf
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• Three conditions exist: All sliding; Sliding-
sticking transition and Fully sticking
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Open die forging analysis –rectangular part
F
F
h
w
dx
yx
unit depthinto figure
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Expanding the dx slice on LHS
• p = die pressure• sx, dsx from material on
side• tfriction = friction force = µp
p
p
sx sx + dsx
tf
tf
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Force balance in x-direction
p sx
k
dxh
d
dxhd
frictionx
frictionx
ts
ts
202
-=
=+
Mohr’s circle
(distortion energy (von Mises) criterion, plane strain)
flowflowx kp sss ×===+ 15.1322
N.B. all done on a perunit depth basis
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Force balanceDifferentiating, and substituting into Mohr’s
circle equation
noting: tfriction = µp
pdxh
dpµ2
= dxhp
dp µ2=
( ) ( )
dxh
dpdxh
d
ddppdkd
frictionfrictionx
xx
÷÷ø
öççè
æ=\-=
-=\+=
tts
ss22
2
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Sliding region
• Noting: @ x = 0, sx = 2k = 1.15 sflow
dxhp
dp xp
k
x
òò =02
2µ
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging pressure – sliding region
( )
÷øö
çèæ××=
÷øö
çèæ=
=-
hx
p
hx
kp
hxkp
flowx
x
x
µs
µ
µ
2exp15.1
2exp2
22lnln
Sliding region result (0 < x < xk)
N.B done on a per unit depth basis
Increasing µ
X
÷÷ø
öççè
æ
f
y
Y15.1s
0
1
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
÷øö
çèæ +=
hx
kpx µ212
1£x
yields
( ) å=
=+++++=n
k
kn
kx
nxxx
xx0
32
!!!3!21exp !
00
÷øö
çèæ +××=
hxp flowxµs 2115.1
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÷÷ø
öççè
æ+
=÷øö
çèæ +
==òò
µµ
N.B done on a per unit depth basis
÷øö
çèæ +=
hw
kpave
21
2µ
÷øö
çèæ +××=
hwp flowave 2
115.1 µs
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging force –all sliding approximation
depthwhwF flowforging ××÷øö
çèæ +××=
2115.1 µs
depthwidthpF aveforging ××=
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
34
Example Problem
A rectangular workpiece has the following original dimensions: w = 100 mm, h = 25 mm, and depth d= 20 mm and is being open die forged in plane strain. The true stress-true strain curve of the metal is given by MPa and the coefficient of friction is µ = 0.3. Calculate the forging force required to reduce the height by 20%. Use both the “exact” and the average pressure methods.
5.0400 tt es =
w
h
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Slab - die interface• Sliding if tf < tflow
• Sticking if tf ³ tflow– 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 tflow
slidingregion
stickingregion
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
÷øö
çèæ=hx
kpx µ2exp2 ÷
øö
çèæ=hx
kk kµµ
2exp2
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Sticking region
• Using p = k/ µ
pdxh
dpµ2
=
( )kxx xxhkpp
k-=-
2dx
hk
dpx
x
p
p k
x
kx
òò =2
dxkh
dpµ
µ2=
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
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging pressure - sticking region
hx
kpx +÷÷
ø
öççè
æ÷÷ø
öççè
æ-=
µµ 21ln1
21
2
Combining (for xk < x < w/2)
úúû
ù
êêë
é+÷÷ø
öççè
æ÷÷ø
öççè
æ-××=
hxp flowx µµ
s21ln1
2115.1
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/2
0
pedge
Dp
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging pressure –all sticking approximation
kpedge 2=
÷øö
çèæ +××=
÷øö
çèæ +=\
hx
p
hx
kp
flowx
x
115.1
12
s
( )xhk
kpx22 =-dx
hk
dpxp
k
x
òò =02
2
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
w
hxx
w
dxhx
w
dxkp
kp
www
x
ave÷÷ø
öççè
æ+
=÷øö
çèæ +
==òò
÷øö
çèæ +=
hw
kpave
41
2
÷øö
çèæ +××=
hwp flowave 4
115.1 s
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging force –all sticking approximation
depthwhwF flowforging ××÷øö
çèæ +××=
4115.1 s
depthwidthpF aveforging ××=
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 +=
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Material Models
nflow KY es ==
Strain hardening (cold – below recrystallization point)
Strain rate effect (hot – above recrystallization point)
( )mflow CY es !==
heightousinstantanevelocityplaten
hv
dtdh
h1ε ===!
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-1• Lead 25 mm x 25 mm x 900 mm • sy = 6.89 MPa• hf = 6.25 mm, µ = 0.25• Show effect of friction on total forging force.• Use the slab method.• Assume it doesn’t get wider in 900 mm
direction.• Assume cold forging.
25
25
900
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-2• At the end of forging:hf = 6.25 mm, wf = 100 (conservation of mass)
• Sliding / sticking transition
"347.025.02
1ln25.0225.021ln
21
=´´
=
=
k
k
x
hx
µµ
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-3
• Sliding region:
( )xhx
pf
flowx
2exp1150
2exp15.1
×=
÷÷ø
öççè
æ××=
µs
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-5
020004000600080001000012000
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
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
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-7
• Determine the forging force from:
• since we have plane strain
dApForce òò ×=
dxpdepthunitF x
xò=0
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
÷÷
ø
ö
çç
è
æ
÷÷ø
öççè
æ+÷
÷ø
öççè
æ÷÷ø
öççè
æ= òò .2.2
2/
0
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-16or since the part is 36” deep:F(both) = 337 Tonnes
F(all sticking) = 363 tonnes
F(all sliding) = 496,800 lbs = 218 tonsCan we use exact solution for this???All sticking over-estimates actual value.
depthwhw
F flowforging ××÷øö
çèæ +××=
4115.1 s
depthwhw
F flowforging ××÷øö
çèæ +××=
2115.1 µs
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
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 0.8Stroke (in)
Forg
ing
forc
e (lb
f/in
dept
h)
mu=0mu=0.1mu=0.2mu=0.25mu=0.3mu=0.4mu=0.5
Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Forging - Ex. 1-19Maximum forging force vs. friction coefficient (µ)
all sticking
0
5000
1000015000
20000
25000
0 0.1 0.2 0.3 0.4 0.5 0.6Friction coefficient
Max
forg
ing
forc
e (lb
f/in
dept
h)
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
57
Deformation WorkIn general, work done in bulk deformation processes has three
components
Total work, W = Wideal + Wfriction + Wredundant
Work of ideal plastic deformation, Wideal
= (area under true stress-true strain curve)(volume)
= (volume)
For a true stress-true strain curve :
÷÷ø
öççè
æò ttdt
ese
0
ntt Kes =
( ) ( ) tf
nt
ideal YnKW ee
volume1
volume1
=÷÷ø
öççè
æ+
=+
stress flow Avg. =fY
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
58
Deformation Work
Friction between dies and workpiece causes inhomogeneous (non-uniform) deformation called barreling
Barreling Effect
Frictional Forces
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
59
Deformation Work
Internal shearing of material requires redundant work to be expended
Ideal Deformation Redundant Deformation
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
60
Redundant Zone
ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
S.N. Melkote
61
Closed/Impression Die Forging
• Analysis more complex due to large variation in
strains in different parts of workpiece
• Approximate approaches
– Divide forging into simple part shapes e.g. cylinders,
slabs etc. that can be analyzed separately
– Consider entire forging as a simplified shape
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
62
Closed/Impression Die Forging
Steps in latter analysis approach• Step 1: calculate average height from volume V
and total projected area At of part (including flash area)
• Step 2:
LwV
AVht
avg ==
÷÷ø
öççè
æ==
avg
iavg h
hlnstrain avg.e
avgavg h
v== ratestrain avg.e!
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
63
Closed/Impression Die Forging
• Step 3: calculate flow stress of material Yf for cold/hot working
• Step 4:
Kp = pressure multiplying factor= 3~5 for simple shapes without flash= 5~8 for simple shapes with flash= 8~12 for complex shapes with flash
tfpavg AYKF == load forging Avg.
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
64
Other Analysis Methods
• Complex closed die forging simulated using finite element software
Source: http://nsmwww.eng.ohio-state.edu/html/f-flashlessforg.html
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
65
Forging Defects
• Surface cracking due to tensile stresses
• Internal cracking in thick webs
Surface Crack
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
66
Forging Defects
• Laps due to buckling of thin webs
• Cold shuts due to small radii fillets in die
ME 4210: Manufacturing Processes & Engineering
Instructor: Ramesh Singh Notes by Prof. S.N. Melkote
67
Summary
• What is bulk deformation?• Cold vs hot working• Forging analysis
– Slab analysis• Forging defects