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Department of Mechanical Engineering
Chung-Ang University
Metal Deformation Process
(Metal Forming)
Seok-min Kim
smkim@cau.ac.kr
- 1 -
Department of Mechanical Engineering
Chung-Ang University
Yielding
Transition from elastic to elastic-plastic deformation.
 For most aspects of design, yielding signifies the end of the deformation,
i.e., failure, while for processing, yielding signifies the beginning of the
process
 For both, we need to know stress when yielding is imminent (목전의)
- 2 -
Department of Mechanical Engineering
Chung-Ang University
Metal Forming
 Large group of manufacturing processes in which plastic
deformation is used to change the shape of metal
workpieces
• The tool, usually called a die, applies stresses that
exceed yield strength of metal
• The metal takes a shape determined by the
geometry of the die
- 3 -
Department of Mechanical Engineering
Chung-Ang University
Classification of
metal forming operations
- 4 -
Department of Mechanical Engineering
Chung-Ang University
Bulk Deformation Processes (1)
 Forging – work is squeezed and shaped between
opposing dies
 Rolling – slab or plate is squeezed between opposing
rolls
- 5 -
Department of Mechanical Engineering
Chung-Ang University
 Extrusion – work is squeezed through a die opening,
thereby taking the shape of the opening
 Wire and bar drawing – diameter of wire or bar is
reduced by pulling it through a die opening
Bulk Deformation Processes (2)
- 6 -
Department of Mechanical Engineering
Chung-Ang University
Sheet Deformation Processes
Bending Deep drawing
Shearing
- 7 -
Department of Mechanical Engineering
Chung-Ang University
Stresses in Metal Forming
• Stresses to plastically deform the metal are usually
compressive
Examples: rolling, forging, extrusion
• However, some forming processes
Stretch the metal (tensile stresses)
Others bend the metal (tensile and compressive)
Still others apply shear stresses
- 8 -
Department of Mechanical Engineering
Chung-Ang University
Material Properties in Metal Forming
 Desirable material properties:
Low yield strength and high ductility
 These properties are affected by temperature:
Ductility increases and yield strength decreases
when work temperature is raised
 Other factors:
Strain rate and friction
- 9 -
Department of Mechanical Engineering
Chung-Ang University
Material Behavior in Metal Forming
 Plastic region of stress-strain curve is primary
interest because material is plastically deformed
 In plastic region, metal's behavior is expressed by
the flow curve:
n
K
 
where K = strength coefficient; and n = strain
hardening exponent
 Flow curve based on true stress and true strain
- 10 -
Department of Mechanical Engineering
Chung-Ang University
Flow Stress
 For most metals at room temperature, strength
increases when deformed due to strain hardening
 Flow stress = instantaneous value of stress required
to continue deforming the material
where Yf = flow stress, that is, the yield
strength as a function of strain
n
f K
Y 

- 11 -
Department of Mechanical Engineering
Chung-Ang University
Average Flow Stress
 Determined by integrating
the flow curve equation
between zero and the final
strain value defining the
range of interest
where Yf = average flow
stress; and  = maximum
strain during deformation
process
n
K
Y
n
f


1

_
- 12 -
Department of Mechanical Engineering
Chung-Ang University
Temperature in Metal Forming
 Any deformation operation can be accomplished
with lower forces and power at elevated temperature
 Three temperature ranges in metal forming:
• Cold working
• Warm working
• Hot working
- 13 -
Department of Mechanical Engineering
Chung-Ang University
Cold Working
 Performed at room temperature or slightly above
 Many cold forming processes are important mass
production operations
 Minimum or no machining usually required
 These operations are near net shape or net shape
processes
- 14 -
Department of Mechanical Engineering
Chung-Ang University
Advantages of Cold Forming
vs. Hot Working
 Better accuracy, closer tolerances
 Better surface finish
 Strain hardening increases strength and hardness
 Grain flow during deformation can cause desirable
directional properties in product
 No heating of work required
- 15 -
Department of Mechanical Engineering
Chung-Ang University
Disadvantages of Cold Forming
- 16 -
 Higher forces and power required in the
deformation operation
 Surfaces of starting workpiece must be free of
scale and dirt
 Ductility and strain hardening limit the amount of
forming that can be done
 In some cases, metal must be annealed to allow
further deformation
 In other cases, metal is simply not ductile
enough to be cold worked
Department of Mechanical Engineering
Chung-Ang University
Warm Working
- 17 -
 Performed at temperatures above room temperature
but below recrystallization temperature
 Dividing line between cold working and warm
working often expressed in terms of melting point:
 0.3Tm, where Tm = melting point (absolute
temperature) for metal
 Lower forces and power than in cold working
 More intricate work geometries possible
 Need for annealing may be reduced or
eliminated
Advantages of warm working
Department of Mechanical Engineering
Chung-Ang University
Hot Working
- 18 -
 Deformation at temperatures above the
recrystallization temperature
 Recrystallization temperature = about one-half of
melting point on absolute scale
 In practice, hot working usually performed
somewhat above 0.5Tm
 Metal continues to soften as temperature increases
above 0.5Tm, enhancing advantage of hot working
above this level
Department of Mechanical Engineering
Chung-Ang University
Why Hot Working?
 Capability for substantial plastic deformation of the metal
- far more than possible with cold working or warm working
Why?
 Strength coefficient is substantially less than at room
temperature
 Strain hardening exponent is zero (theoretically)
 Ductility is significantly increased
- 19 -
Department of Mechanical Engineering
Chung-Ang University
Advantages of Hot Working
vs. Cold Working
- 20 -
 Workpart shape can be significantly altered
 Lower forces and power required
 Metals that usually fracture in cold working can be hot
formed
 Strength properties of product are generally isotropic
 No strengthening of part occurs from work hardening
 Advantageous in cases when part is to be
subsequently processed by cold forming
Department of Mechanical Engineering
Chung-Ang University
Disadvantages of Hot Working
 Lower dimensional accuracy
 Higher total energy required
(due to the thermal energy to heat the workpiece)
 Work surface oxidation (scale), poorer surface finish
 Shorter tool life
- 21 -
Department of Mechanical Engineering
Chung-Ang University
Friction in Metal Forming
- 22 -
 In most metal forming processes, friction is
undesirable:
 Metal flow is retarded
 Forces and power are increased
 Tooling wears faster
 Friction and tool wear are more severe in hot working
Department of Mechanical Engineering
Chung-Ang University
Lubrication in Metal Forming
 Metalworking lubricants are applied to tool-work
interface in many forming operations to reduce
harmful effects of friction
 Benefits:
• Reduced sticking, forces, power, tool wear
• Better surface finish
• Removes heat from the tooling
- 23 -
Department of Mechanical Engineering
Chung-Ang University
Considerations in Choosing a Lubricant
- 24 -
 Type of forming process
(rolling, forging, sheet metal drawing, etc.)
 Hot working or cold working
 Work material
 Chemical reactivity with tool and work metals
 Ease of application
 Cost
Department of Mechanical Engineering
Chung-Ang University
Bulk Deformation
- 25 -
 Metal forming operations which cause significant
shape change by deforming metal parts whose initial
form is bulk rather than sheet
 Starting forms:
 Cylindrical bars and billets,
 Rectangular billets and slabs, and similar shapes
 These processes stress metal sufficiently to cause
plastic flow into desired shape
 Performed as cold, warm, and hot working operations
Department of Mechanical Engineering
Chung-Ang University
Importance of Bulk Deformation
- 26 -
 In hot working, significant shape change can be
accomplished
 In cold working, strength is increased during
shape change
 Little or no waste - some operations are near net
shape or net shape processes
 The parts require little or no subsequent
machining
Department of Mechanical Engineering
Chung-Ang University
 Deformation process in which work thickness is
reduced by compressive forces exerted by two
opposing rolls
Figure 19.1 The rolling process (specifically, flat rolling).
Rolling
- 27 -
Department of Mechanical Engineering
Chung-Ang University
The Rolls & Types Of Rolling
 Rotating rolls perform two main functions:
 Pull the work into the gap between them by friction
between workpart and rolls
 Simultaneously squeeze the work to reduce its cross section
 Based on workpiece geometry :
 Flat rolling - used to reduce thickness of a rectangular
cross section
 Shape rolling - square cross section is formed into a shape
such as an I-beam
 Based on work temperature :
 Hot Rolling – most common due to the large amount of
deformation required
 Cold rolling – produces finished sheet and plate stock
- 28 -
Department of Mechanical Engineering
Chung-Ang University
Rolled Products Made of Steel
- 29 -
Department of Mechanical Engineering
Chung-Ang University
Flat Rolling – Terminology
Draft = amount of thickness reduction
where d = draft; to = starting
thickness; and tf = final thickness
f
o t
t
d 

Reduction = draft expressed as a
fraction of starting stock thickness:
where r = reduction
o
t
d
r 
f
f
f L
w
t
L
w
t 
0
0
0
Spreading = increasing of
work width
f
f
f v
w
t
v
w
t 
0
0
0
- 30 -
Department of Mechanical Engineering
Chung-Ang University
Friction in the Rolling
 Forward slip (S) =
r
r
f
v
v
v 
 Maximum draft
R
d 2
max 

- 31 -
 No-slip point (neutral point)
f
r V
V
V0 

Roll force
wL
Y
pdL
w
F f
L

 
0
Department of Mechanical Engineering
Chung-Ang University
)
/
ln(
)
( 0 f
t
t


Average flow stress
True strain
Roll force
wL
Y
pdL
w
F f
L

 
0
Required power
)
(
2
0
2
0
2
f
f
t
t
R
t
t
R
R
L 








 



)
(
2
)
(
2
2
2
5
.
0
2
5
.
0
0
mill
roll
roll
each
f
f
f t
t
wR
Y
N
L
wL
Y
N
NFL
T
P
FL
N
T
P
FL
T















Required power in Rolling
- 32 -
1
1
1
1
1
0
'
'






 n
k
n
k
d
k
Y
n
n
n 






Department of Mechanical Engineering
Chung-Ang University
Rolling Mill for Hot Flat Rolling
Rolling mill for hot flat rolling;
the steel plate is seen as the
glowing strip extending
diagonally from the lower left
corner
- 33 -
Department of Mechanical Engineering
Chung-Ang University
Changes in the grain sturucture
- 34 -
Department of Mechanical Engineering
Chung-Ang University
Rolling Mills
 Equipment is massive and expensive
 Rolling mill configurations:
 Two-high – two opposing rolls
 Three-high – work passes through rolls in both directions
 Four-high – backing rolls support smaller work rolls
 Cluster mill – multiple backing rolls on smaller rolls
 Tandem rolling mill – sequence of two-high mills
2-high rolling mill 3-high rolling mill
- 35 -
Department of Mechanical Engineering
Chung-Ang University
four-high rolling mill
cluster mill
- Multiple backing rolls allow even smaller roll diameters
tandem rolling mill
- A series of rolling stands in sequence
- 36 -
Department of Mechanical Engineering
Chung-Ang University
Shape Rolling
 Work is deformed into a contoured cross section
rather than flat (rectangular)
 Accomplished by passing work through rolls that have
the reverse of desired shape
 Products include:
 Construction shapes such as I-beams, L-beams,
and U-channels
 Rails for railroad tracks
 Round and square bars and rods
- 37 -
Department of Mechanical Engineering
Chung-Ang University
Thread Rolling
 Bulk deformation process used to form threads on
cylindrical parts by rolling them between two dies
 Important commercial process for mass producing
bolts and screws
 Performed by cold working in thread rolling machines
 Advantages over thread cutting (machining):
 Higher production rates
 Better material utilization
 Stronger threads and better fatigue resistance due
to work hardening
- 38 -
Department of Mechanical Engineering
Chung-Ang University
Thread Rolling with Flat Dies
(1) start of cycle (2) end of cycle
- 39 -
Department of Mechanical Engineering
Chung-Ang University
Ring Rolling
 Deformation process in which a thick-walled ring of smaller diameter
is rolled into a thin-walled ring of larger diameter
 As thick-walled ring is compressed, deformed metal elongates,
causing diameter of ring to be enlarged
 Hot working process for large rings and cold working process for
smaller rings
 Applications: ball and roller bearing races, steel tires for railroad
wheels, and rings for pipes, pressure vessels, and rotating
machinery
 Advantages: material savings, ideal grain orientation, strengthening
through cold working
- 40 -
Department of Mechanical Engineering
Chung-Ang University
Forging
 Deformation process in which work is compressed
between two dies
 Oldest of the metal forming operations, dating from about
5000 B C
 Components: engine crankshafts, connecting rods, gears,
aircraft structural components, jet engine turbine parts
• In addition, basic metals industries use forging to establish
basic form of large components that are subsequently
machined to final shape and size
- 41 -
Department of Mechanical Engineering
Chung-Ang University
1) Perfectly plastic with yield stress Y
1
0
1
1
1
1
)
(
)
(
1




Y
volume
d
volume
Work
h
h
A
A
YA
F
o
o





2) strain Hardening
1
1
0
0
1
)
(
1
)
(
)
(
)
(
material
the
of
stress
flow
:
,
1
1











Y
volume
n
k
volume
d
k
volume
d
volume
work
k
Y
YA
F
k
n
n
n
f
n











Forging Force
1
1
1
1 1
1
1
1
0
1
1






 n
k
n
k
d
k
Y
n
n
n 






- 42 -
Department of Mechanical Engineering
Chung-Ang University
Classification of Forging Operations
- 43 -
 Cold vs. hot forging:
 Hot or warm forging – most common, due to the
significant deformation and the need to reduce
strength and increase ductility of work metal
 Cold forging – advantage: increased strength that
results from strain hardening
 Impact vs. press forging:
 Forge hammer - applies an impact load
 Forge press - applies gradual pressure
Department of Mechanical Engineering
Chung-Ang University
Types of Forging Dies
- 44 -
 Open-die forging - work is compressed between two
flat dies, allowing metal to flow laterally with
minimum constraint
 Impression-die forging - die contains cavity or
impression that is imparted to workpart
 Metal flow is constrained so that flash is created
 Flashless forging - workpart is completely
constrained in die
 No excess flash is created
Department of Mechanical Engineering
Chung-Ang University
Three types of forging
open-die forging impression-die forging
flashless forging
- 45 -
Department of Mechanical Engineering
Chung-Ang University
Open-Die Forging
 Compression of workpart between two flat dies
 Similar to compression test when workpart has
cylindrical cross section and is compressed along
its axis
 Deformation operation reduces height and
increases diameter of work
 Common names include upsetting or upset
forging
- 46 -
Department of Mechanical Engineering
Chung-Ang University
Open-Die Forging with No Friction
 If no friction occurs between work and die surfaces, then
homogeneous deformation occurs, so that radial flow is uniform
throughout workpart height and true strain is given by:
where ho= starting height; and h = height at some point during
compression
 At h = final value hf, true strain is maximum value
h
ho
ln


- 47 -
Department of Mechanical Engineering
Chung-Ang University
Open-Die Forging with Friction
 Friction between work and die surfaces constrains lateral
flow of work, resulting in barreling effect
 In hot open-die forging, effect is even more pronounced due
to heat transfer at and near die surfaces, which cools the
metal and increases its resistance to deformation
barrel
- 48 -
Department of Mechanical Engineering
Chung-Ang University
Impression-Die Forging
 Compression of workpart by dies with inverse of part shape
 Flash is formed by metal that flows beyond die cavity into small gap
between die plates
 Flash must be later trimmed, but it serves an important function during
compression:
 As flash forms, friction resists continued metal flow into gap,
constraining material to fill die cavity
 In hot forging, metal flow is further restricted by cooling against die
plates
- 49 -
Department of Mechanical Engineering
Chung-Ang University
Impression-Die Forging Practice
 Several forming steps often required, with separate die
cavities for each step
 Beginning steps redistribute metal for more uniform
deformation and desired metallurgical structure in
subsequent steps
 Final steps bring the part to final geometry
 Impression-die forging is often performed manually by
skilled operator
- 50 -
Department of Mechanical Engineering
Chung-Ang University
Examples of Forging
- 51 -
Department of Mechanical Engineering
Chung-Ang University
Impression-Die Forging
Advantages and Limitations
 Advantages of impression-die forging compared to
machining from solid stock:
 Higher production rates
 Less waste of metal
 Greater strength
 Favorable grain orientation in the metal
 Limitations:
 Not capable of close tolerances
 Machining often required to achieve accuracies
and features needed
- 52 -
Department of Mechanical Engineering
Chung-Ang University
Flashless Forging
 Compression of work in punch and die tooling whose cavity does
not allow for flash
 Starting workpart volume must equal die cavity volume within
very close tolerance
 Process control more demanding than impression-die forging
 Best suited to part geometries that are simple and symmetrical
 Often classified as a precision forging process
- 53 -
Department of Mechanical Engineering
Chung-Ang University
Forging Hammers (Drop Hammers)
Apply impact load against workpart
 Two types:
 Gravity drop hammers - impact energy from falling
weight of a heavy ram
 Power drop hammers - accelerate the ram by
pressurized air or steam
 Disadvantage: impact energy transmitted through anvil
into floor of building
 Commonly used for impression-die forging
- 54 -
Department of Mechanical Engineering
Chung-Ang University
Drop forging hammer
Drop forging hammer, fed by
conveyor and heating units
at the right of the scene
(photo courtesy of Chambersburg
Engineering Company)
Diagram showing details of a drop
hammer for impression-die forging
- 55 -
Department of Mechanical Engineering
Chung-Ang University
Forging Presses
 Apply gradual pressure to accomplish compression
operation
 Types:
 Mechanical press - converts rotation of drive
motor into linear motion of ram
 Hydraulic press - hydraulic piston actuates ram
 Screw press - screw mechanism drives ram
- 56 -
Department of Mechanical Engineering
Chung-Ang University
Heading and Upsetting
 Forging process used to form heads on nails, bolts,
and similar hardware products
 More parts produced by upsetting than any other
forging operation
 Performed cold, warm, or hot on machines called
headers or formers
 Wire or bar stock is fed into machine, end is headed,
then piece is cut to length
 For bolts and screws, thread rolling is then used to
form threads
- 57 -
Department of Mechanical Engineering
Chung-Ang University
Upset Forging (heading) Operation
 An upset forging operation to form a head on a bolt
or similar hardware item The cycle consists of:
(1) wire stock is fed to the stop
(2) gripping dies close on the stock and the stop is retracted
(3) punch moves forward
(4) bottoms to form the head
- 58 -
Department of Mechanical Engineering
Chung-Ang University
Heading (Upset Forging) Operations
Examples of heading (upset forging) operations:
(a) heading a nail using open dies
(b) round head formed by punch
(c) and (d) two common head styles for screws formed by die
(e) carriage bolt head formed by punch and die
- 59 -
Department of Mechanical Engineering
Chung-Ang University
Trimming
 Cutting operation to remove flash from workpart in
impression-die forging
 Usually done while work is still hot, so a separate trimming
press is included at the forging station
 Trimming can also be done by alternative methods, such
as grinding or sawing
- 60 -
Department of Mechanical Engineering
Chung-Ang University
Extrusion
- 61 -
 Compression forming process in which work metal is
forced to flow through a die opening to produce a
desired cross-sectional shape
 Process is similar to squeezing toothpaste out of a
toothpaste tube
 In general, extrusion is used to produce long parts of
uniform cross sections
 Two basic types:
 Direct extrusion
 Indirect extrusion
Department of Mechanical Engineering
Chung-Ang University
Direct Extrusion
- 62 -
 Also called forward extrusion
 As ram approaches die opening, a small portion of billet
remains that cannot be forced through die opening
 This extra portion, called the butt, must be separated from
extrudate by cutting it just beyond the die exit
 Starting billet cross section usually round
 Final shape of extrudate is determined by die opening
Department of Mechanical Engineering
Chung-Ang University
Hollow and Semi-Hollow Shapes
(a) Direct extrusion to produce a hollow or semi-hollow cross-section;
(b) hollow and (c) semi-hollow cross- sections
- 63 -
Department of Mechanical Engineering
Chung-Ang University
Indirect Extrusion to Produce
- 64 -
 Also called backward extrusion and reverse extrusion
 No friction force between billet and container
 Limitations of indirect extrusion are imposed by
 Lower rigidity of hollow ram
 Difficulty in supporting extruded product as it exits die
(a) a solid cross-section (b) a hollow cross-section
Department of Mechanical Engineering
Chung-Ang University
Advantages of Extrusion
- 65 -
 Variety of shapes possible, especially in hot extrusion
 Limitation: part cross section must be uniform
throughout length
 Grain structure and strength enhanced in cold and
warm extrusion
 Close tolerances possible, especially in cold extrusion
 In some operations, little or no waste of material
Department of Mechanical Engineering
Chung-Ang University
Hot vs. Cold Extrusion
- 66 -
 Hot extrusion - prior heating of billet to above its
recrystallization temperature
 Reduces strength and increases ductility of the
metal, permitting more size reductions and more
complex shapes
 Cold extrusion - generally used to produce discrete
parts
 The term impact extrusion is used to indicate
high speed cold extrusion
Department of Mechanical Engineering
Chung-Ang University
Example of Extrusion
A complex extruded cross-section for a heat sink
(photo courtesy of Aluminum Company of America)
- 67 -
Department of Mechanical Engineering
Chung-Ang University
Wire and Bar Drawing
- 68 -
 Cross-section of a bar, rod, or wire is reduced by pulling it
through a die opening
 Similar to extrusion except work is pulled through die in
drawing (it is pushed through in extrusion)
 Although drawing applies tensile stress, compression also
plays a significant role since metal is squeezed as it
passes through die opening
Department of Mechanical Engineering
Chung-Ang University
Drawing of bar, rod, or wire
Wire and Bar Drawing
- 69 -
Department of Mechanical Engineering
Chung-Ang University
Wire Drawing vs. Bar Drawing
- 70 -
 Difference between bar drawing and wire drawing is
stock size
 Bar drawing - large diameter bar and rod stock
 Wire drawing - small diameter stock - wire sizes
down to 0.03 mm (0.001 in.) are possible
 Although the mechanics are the same, the methods,
equipment, and even terminology are different
Department of Mechanical Engineering
Chung-Ang University
Drawing Practice and Products
- 71 -
 Drawing practice:
 Usually performed as cold working
 Most frequently used for round cross sections
 Products:
 Wire: electrical wire; wire stock for fences,
coat hangers, and shopping carts
 Rod stock for nails, screws, rivets, and springs
 Bar stock: metal bars for machining, forging, and
other processes
Department of Mechanical Engineering
Chung-Ang University
Bar Drawing
Hydraulically operated draw bench
for drawing metal bars
- 72 -
Department of Mechanical Engineering
Chung-Ang University
Wire Drawing
Continuous drawing of wire
- 73 -
Department of Mechanical Engineering
Chung-Ang University
Sheet Metal Working
 Forming and related operations performed on
metal sheets, strips, and coils
 High surface area-to-volume ratio of starting metal, which
distinguishes these from bulk deformation
 Often called pressworking because presses perform these
operations
• Parts are called stampings
• Usual tooling: punch and die
- 74 -
Department of Mechanical Engineering
Chung-Ang University
- 75 -
Basic Types of Sheet Metal Processes
1. Cutting
 Shearing to separate large sheets
 Blanking to cut part perimeters out of sheet metal
 Punching to make holes in sheet metal
2. Bending
 Straining sheet around a straight axis
3. Drawing
 Forming of sheet into convex or concave shapes
Department of Mechanical Engineering
Chung-Ang University
- 76 -
Sheet Metal Cutting
Department of Mechanical Engineering
Chung-Ang University
- 77 -
Shearing
 Sheet metal cutting operation along a straight line
between two cutting edges
 Typically used to cut large sheets
(a) side view of the shearing operation;
(b) front view of power shears equipped with inclined upper cutting
blade.
Department of Mechanical Engineering
Chung-Ang University
- 78 -
Blanking and Punching
 Blanking - sheet metal cutting to separate piece
(called a blank) from surrounding stock
 Punching - similar to blanking except cut piece is scrap,
called a slug
(a) Blanking and (b) punching.
Department of Mechanical Engineering
Chung-Ang University
- 79 -
Clearance in Sheet Metal Cutting
 Distance between punch cutting edge and die cutting edge
 Typical values range between 4% and 8% of stock thickness
Department of Mechanical Engineering
Chung-Ang University
- 80 -
 For a round blank of diameter Db:
 Blanking punch diameter = Db - 2c
 Blanking die diameter = Db
where c = clearance
 For a round hole of diameter Dh:
 Hole punch diameter = Dh
 Hole die diameter = Dh + 2c
where c = clearance
Punch and Die Sizes
Department of Mechanical Engineering
Chung-Ang University
Basic sheet metalworking operations
- Bending
 Straining sheetmetal around a straight axis to take
a permanent bend
- 81 -
Department of Mechanical Engineering
Chung-Ang University
Springback in Bending
- 82 -
 Increase in included angle of bent part relative to included
angle of forming tool after tool is removed
 Reason for springback:
 When bending pressure is removed, elastic energy
remains in bent part, causing it to recover partially
toward its original shape
Department of Mechanical Engineering
Chung-Ang University
Basic sheet metalworking operations
– Deep Drawing
- 83 -
Department of Mechanical Engineering
Chung-Ang University
- 84 -
Punch and Die Components
Components of a punch and die for a blanking operation
Department of Mechanical Engineering
Chung-Ang University
- 85 -
Progressive Die
Department of Mechanical Engineering
Chung-Ang University
- 86 -
Department of Mechanical Engineering
Chung-Ang University
- 87 -

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Cold Forging Process for Manufacturing a High-Strength One-Body Input Shaft

  • 1. Department of Mechanical Engineering Chung-Ang University Metal Deformation Process (Metal Forming) Seok-min Kim smkim@cau.ac.kr - 1 -
  • 2. Department of Mechanical Engineering Chung-Ang University Yielding Transition from elastic to elastic-plastic deformation.  For most aspects of design, yielding signifies the end of the deformation, i.e., failure, while for processing, yielding signifies the beginning of the process  For both, we need to know stress when yielding is imminent (목전의) - 2 -
  • 3. Department of Mechanical Engineering Chung-Ang University Metal Forming  Large group of manufacturing processes in which plastic deformation is used to change the shape of metal workpieces • The tool, usually called a die, applies stresses that exceed yield strength of metal • The metal takes a shape determined by the geometry of the die - 3 -
  • 4. Department of Mechanical Engineering Chung-Ang University Classification of metal forming operations - 4 -
  • 5. Department of Mechanical Engineering Chung-Ang University Bulk Deformation Processes (1)  Forging – work is squeezed and shaped between opposing dies  Rolling – slab or plate is squeezed between opposing rolls - 5 -
  • 6. Department of Mechanical Engineering Chung-Ang University  Extrusion – work is squeezed through a die opening, thereby taking the shape of the opening  Wire and bar drawing – diameter of wire or bar is reduced by pulling it through a die opening Bulk Deformation Processes (2) - 6 -
  • 7. Department of Mechanical Engineering Chung-Ang University Sheet Deformation Processes Bending Deep drawing Shearing - 7 -
  • 8. Department of Mechanical Engineering Chung-Ang University Stresses in Metal Forming • Stresses to plastically deform the metal are usually compressive Examples: rolling, forging, extrusion • However, some forming processes Stretch the metal (tensile stresses) Others bend the metal (tensile and compressive) Still others apply shear stresses - 8 -
  • 9. Department of Mechanical Engineering Chung-Ang University Material Properties in Metal Forming  Desirable material properties: Low yield strength and high ductility  These properties are affected by temperature: Ductility increases and yield strength decreases when work temperature is raised  Other factors: Strain rate and friction - 9 -
  • 10. Department of Mechanical Engineering Chung-Ang University Material Behavior in Metal Forming  Plastic region of stress-strain curve is primary interest because material is plastically deformed  In plastic region, metal's behavior is expressed by the flow curve: n K   where K = strength coefficient; and n = strain hardening exponent  Flow curve based on true stress and true strain - 10 -
  • 11. Department of Mechanical Engineering Chung-Ang University Flow Stress  For most metals at room temperature, strength increases when deformed due to strain hardening  Flow stress = instantaneous value of stress required to continue deforming the material where Yf = flow stress, that is, the yield strength as a function of strain n f K Y   - 11 -
  • 12. Department of Mechanical Engineering Chung-Ang University Average Flow Stress  Determined by integrating the flow curve equation between zero and the final strain value defining the range of interest where Yf = average flow stress; and  = maximum strain during deformation process n K Y n f   1  _ - 12 -
  • 13. Department of Mechanical Engineering Chung-Ang University Temperature in Metal Forming  Any deformation operation can be accomplished with lower forces and power at elevated temperature  Three temperature ranges in metal forming: • Cold working • Warm working • Hot working - 13 -
  • 14. Department of Mechanical Engineering Chung-Ang University Cold Working  Performed at room temperature or slightly above  Many cold forming processes are important mass production operations  Minimum or no machining usually required  These operations are near net shape or net shape processes - 14 -
  • 15. Department of Mechanical Engineering Chung-Ang University Advantages of Cold Forming vs. Hot Working  Better accuracy, closer tolerances  Better surface finish  Strain hardening increases strength and hardness  Grain flow during deformation can cause desirable directional properties in product  No heating of work required - 15 -
  • 16. Department of Mechanical Engineering Chung-Ang University Disadvantages of Cold Forming - 16 -  Higher forces and power required in the deformation operation  Surfaces of starting workpiece must be free of scale and dirt  Ductility and strain hardening limit the amount of forming that can be done  In some cases, metal must be annealed to allow further deformation  In other cases, metal is simply not ductile enough to be cold worked
  • 17. Department of Mechanical Engineering Chung-Ang University Warm Working - 17 -  Performed at temperatures above room temperature but below recrystallization temperature  Dividing line between cold working and warm working often expressed in terms of melting point:  0.3Tm, where Tm = melting point (absolute temperature) for metal  Lower forces and power than in cold working  More intricate work geometries possible  Need for annealing may be reduced or eliminated Advantages of warm working
  • 18. Department of Mechanical Engineering Chung-Ang University Hot Working - 18 -  Deformation at temperatures above the recrystallization temperature  Recrystallization temperature = about one-half of melting point on absolute scale  In practice, hot working usually performed somewhat above 0.5Tm  Metal continues to soften as temperature increases above 0.5Tm, enhancing advantage of hot working above this level
  • 19. Department of Mechanical Engineering Chung-Ang University Why Hot Working?  Capability for substantial plastic deformation of the metal - far more than possible with cold working or warm working Why?  Strength coefficient is substantially less than at room temperature  Strain hardening exponent is zero (theoretically)  Ductility is significantly increased - 19 -
  • 20. Department of Mechanical Engineering Chung-Ang University Advantages of Hot Working vs. Cold Working - 20 -  Workpart shape can be significantly altered  Lower forces and power required  Metals that usually fracture in cold working can be hot formed  Strength properties of product are generally isotropic  No strengthening of part occurs from work hardening  Advantageous in cases when part is to be subsequently processed by cold forming
  • 21. Department of Mechanical Engineering Chung-Ang University Disadvantages of Hot Working  Lower dimensional accuracy  Higher total energy required (due to the thermal energy to heat the workpiece)  Work surface oxidation (scale), poorer surface finish  Shorter tool life - 21 -
  • 22. Department of Mechanical Engineering Chung-Ang University Friction in Metal Forming - 22 -  In most metal forming processes, friction is undesirable:  Metal flow is retarded  Forces and power are increased  Tooling wears faster  Friction and tool wear are more severe in hot working
  • 23. Department of Mechanical Engineering Chung-Ang University Lubrication in Metal Forming  Metalworking lubricants are applied to tool-work interface in many forming operations to reduce harmful effects of friction  Benefits: • Reduced sticking, forces, power, tool wear • Better surface finish • Removes heat from the tooling - 23 -
  • 24. Department of Mechanical Engineering Chung-Ang University Considerations in Choosing a Lubricant - 24 -  Type of forming process (rolling, forging, sheet metal drawing, etc.)  Hot working or cold working  Work material  Chemical reactivity with tool and work metals  Ease of application  Cost
  • 25. Department of Mechanical Engineering Chung-Ang University Bulk Deformation - 25 -  Metal forming operations which cause significant shape change by deforming metal parts whose initial form is bulk rather than sheet  Starting forms:  Cylindrical bars and billets,  Rectangular billets and slabs, and similar shapes  These processes stress metal sufficiently to cause plastic flow into desired shape  Performed as cold, warm, and hot working operations
  • 26. Department of Mechanical Engineering Chung-Ang University Importance of Bulk Deformation - 26 -  In hot working, significant shape change can be accomplished  In cold working, strength is increased during shape change  Little or no waste - some operations are near net shape or net shape processes  The parts require little or no subsequent machining
  • 27. Department of Mechanical Engineering Chung-Ang University  Deformation process in which work thickness is reduced by compressive forces exerted by two opposing rolls Figure 19.1 The rolling process (specifically, flat rolling). Rolling - 27 -
  • 28. Department of Mechanical Engineering Chung-Ang University The Rolls & Types Of Rolling  Rotating rolls perform two main functions:  Pull the work into the gap between them by friction between workpart and rolls  Simultaneously squeeze the work to reduce its cross section  Based on workpiece geometry :  Flat rolling - used to reduce thickness of a rectangular cross section  Shape rolling - square cross section is formed into a shape such as an I-beam  Based on work temperature :  Hot Rolling – most common due to the large amount of deformation required  Cold rolling – produces finished sheet and plate stock - 28 -
  • 29. Department of Mechanical Engineering Chung-Ang University Rolled Products Made of Steel - 29 -
  • 30. Department of Mechanical Engineering Chung-Ang University Flat Rolling – Terminology Draft = amount of thickness reduction where d = draft; to = starting thickness; and tf = final thickness f o t t d   Reduction = draft expressed as a fraction of starting stock thickness: where r = reduction o t d r  f f f L w t L w t  0 0 0 Spreading = increasing of work width f f f v w t v w t  0 0 0 - 30 -
  • 31. Department of Mechanical Engineering Chung-Ang University Friction in the Rolling  Forward slip (S) = r r f v v v   Maximum draft R d 2 max   - 31 -  No-slip point (neutral point) f r V V V0   Roll force wL Y pdL w F f L    0
  • 32. Department of Mechanical Engineering Chung-Ang University ) / ln( ) ( 0 f t t   Average flow stress True strain Roll force wL Y pdL w F f L    0 Required power ) ( 2 0 2 0 2 f f t t R t t R R L               ) ( 2 ) ( 2 2 2 5 . 0 2 5 . 0 0 mill roll roll each f f f t t wR Y N L wL Y N NFL T P FL N T P FL T                Required power in Rolling - 32 - 1 1 1 1 1 0 ' '        n k n k d k Y n n n       
  • 33. Department of Mechanical Engineering Chung-Ang University Rolling Mill for Hot Flat Rolling Rolling mill for hot flat rolling; the steel plate is seen as the glowing strip extending diagonally from the lower left corner - 33 -
  • 34. Department of Mechanical Engineering Chung-Ang University Changes in the grain sturucture - 34 -
  • 35. Department of Mechanical Engineering Chung-Ang University Rolling Mills  Equipment is massive and expensive  Rolling mill configurations:  Two-high – two opposing rolls  Three-high – work passes through rolls in both directions  Four-high – backing rolls support smaller work rolls  Cluster mill – multiple backing rolls on smaller rolls  Tandem rolling mill – sequence of two-high mills 2-high rolling mill 3-high rolling mill - 35 -
  • 36. Department of Mechanical Engineering Chung-Ang University four-high rolling mill cluster mill - Multiple backing rolls allow even smaller roll diameters tandem rolling mill - A series of rolling stands in sequence - 36 -
  • 37. Department of Mechanical Engineering Chung-Ang University Shape Rolling  Work is deformed into a contoured cross section rather than flat (rectangular)  Accomplished by passing work through rolls that have the reverse of desired shape  Products include:  Construction shapes such as I-beams, L-beams, and U-channels  Rails for railroad tracks  Round and square bars and rods - 37 -
  • 38. Department of Mechanical Engineering Chung-Ang University Thread Rolling  Bulk deformation process used to form threads on cylindrical parts by rolling them between two dies  Important commercial process for mass producing bolts and screws  Performed by cold working in thread rolling machines  Advantages over thread cutting (machining):  Higher production rates  Better material utilization  Stronger threads and better fatigue resistance due to work hardening - 38 -
  • 39. Department of Mechanical Engineering Chung-Ang University Thread Rolling with Flat Dies (1) start of cycle (2) end of cycle - 39 -
  • 40. Department of Mechanical Engineering Chung-Ang University Ring Rolling  Deformation process in which a thick-walled ring of smaller diameter is rolled into a thin-walled ring of larger diameter  As thick-walled ring is compressed, deformed metal elongates, causing diameter of ring to be enlarged  Hot working process for large rings and cold working process for smaller rings  Applications: ball and roller bearing races, steel tires for railroad wheels, and rings for pipes, pressure vessels, and rotating machinery  Advantages: material savings, ideal grain orientation, strengthening through cold working - 40 -
  • 41. Department of Mechanical Engineering Chung-Ang University Forging  Deformation process in which work is compressed between two dies  Oldest of the metal forming operations, dating from about 5000 B C  Components: engine crankshafts, connecting rods, gears, aircraft structural components, jet engine turbine parts • In addition, basic metals industries use forging to establish basic form of large components that are subsequently machined to final shape and size - 41 -
  • 42. Department of Mechanical Engineering Chung-Ang University 1) Perfectly plastic with yield stress Y 1 0 1 1 1 1 ) ( ) ( 1     Y volume d volume Work h h A A YA F o o      2) strain Hardening 1 1 0 0 1 ) ( 1 ) ( ) ( ) ( material the of stress flow : , 1 1            Y volume n k volume d k volume d volume work k Y YA F k n n n f n            Forging Force 1 1 1 1 1 1 1 1 0 1 1        n k n k d k Y n n n        - 42 -
  • 43. Department of Mechanical Engineering Chung-Ang University Classification of Forging Operations - 43 -  Cold vs. hot forging:  Hot or warm forging – most common, due to the significant deformation and the need to reduce strength and increase ductility of work metal  Cold forging – advantage: increased strength that results from strain hardening  Impact vs. press forging:  Forge hammer - applies an impact load  Forge press - applies gradual pressure
  • 44. Department of Mechanical Engineering Chung-Ang University Types of Forging Dies - 44 -  Open-die forging - work is compressed between two flat dies, allowing metal to flow laterally with minimum constraint  Impression-die forging - die contains cavity or impression that is imparted to workpart  Metal flow is constrained so that flash is created  Flashless forging - workpart is completely constrained in die  No excess flash is created
  • 45. Department of Mechanical Engineering Chung-Ang University Three types of forging open-die forging impression-die forging flashless forging - 45 -
  • 46. Department of Mechanical Engineering Chung-Ang University Open-Die Forging  Compression of workpart between two flat dies  Similar to compression test when workpart has cylindrical cross section and is compressed along its axis  Deformation operation reduces height and increases diameter of work  Common names include upsetting or upset forging - 46 -
  • 47. Department of Mechanical Engineering Chung-Ang University Open-Die Forging with No Friction  If no friction occurs between work and die surfaces, then homogeneous deformation occurs, so that radial flow is uniform throughout workpart height and true strain is given by: where ho= starting height; and h = height at some point during compression  At h = final value hf, true strain is maximum value h ho ln   - 47 -
  • 48. Department of Mechanical Engineering Chung-Ang University Open-Die Forging with Friction  Friction between work and die surfaces constrains lateral flow of work, resulting in barreling effect  In hot open-die forging, effect is even more pronounced due to heat transfer at and near die surfaces, which cools the metal and increases its resistance to deformation barrel - 48 -
  • 49. Department of Mechanical Engineering Chung-Ang University Impression-Die Forging  Compression of workpart by dies with inverse of part shape  Flash is formed by metal that flows beyond die cavity into small gap between die plates  Flash must be later trimmed, but it serves an important function during compression:  As flash forms, friction resists continued metal flow into gap, constraining material to fill die cavity  In hot forging, metal flow is further restricted by cooling against die plates - 49 -
  • 50. Department of Mechanical Engineering Chung-Ang University Impression-Die Forging Practice  Several forming steps often required, with separate die cavities for each step  Beginning steps redistribute metal for more uniform deformation and desired metallurgical structure in subsequent steps  Final steps bring the part to final geometry  Impression-die forging is often performed manually by skilled operator - 50 -
  • 51. Department of Mechanical Engineering Chung-Ang University Examples of Forging - 51 -
  • 52. Department of Mechanical Engineering Chung-Ang University Impression-Die Forging Advantages and Limitations  Advantages of impression-die forging compared to machining from solid stock:  Higher production rates  Less waste of metal  Greater strength  Favorable grain orientation in the metal  Limitations:  Not capable of close tolerances  Machining often required to achieve accuracies and features needed - 52 -
  • 53. Department of Mechanical Engineering Chung-Ang University Flashless Forging  Compression of work in punch and die tooling whose cavity does not allow for flash  Starting workpart volume must equal die cavity volume within very close tolerance  Process control more demanding than impression-die forging  Best suited to part geometries that are simple and symmetrical  Often classified as a precision forging process - 53 -
  • 54. Department of Mechanical Engineering Chung-Ang University Forging Hammers (Drop Hammers) Apply impact load against workpart  Two types:  Gravity drop hammers - impact energy from falling weight of a heavy ram  Power drop hammers - accelerate the ram by pressurized air or steam  Disadvantage: impact energy transmitted through anvil into floor of building  Commonly used for impression-die forging - 54 -
  • 55. Department of Mechanical Engineering Chung-Ang University Drop forging hammer Drop forging hammer, fed by conveyor and heating units at the right of the scene (photo courtesy of Chambersburg Engineering Company) Diagram showing details of a drop hammer for impression-die forging - 55 -
  • 56. Department of Mechanical Engineering Chung-Ang University Forging Presses  Apply gradual pressure to accomplish compression operation  Types:  Mechanical press - converts rotation of drive motor into linear motion of ram  Hydraulic press - hydraulic piston actuates ram  Screw press - screw mechanism drives ram - 56 -
  • 57. Department of Mechanical Engineering Chung-Ang University Heading and Upsetting  Forging process used to form heads on nails, bolts, and similar hardware products  More parts produced by upsetting than any other forging operation  Performed cold, warm, or hot on machines called headers or formers  Wire or bar stock is fed into machine, end is headed, then piece is cut to length  For bolts and screws, thread rolling is then used to form threads - 57 -
  • 58. Department of Mechanical Engineering Chung-Ang University Upset Forging (heading) Operation  An upset forging operation to form a head on a bolt or similar hardware item The cycle consists of: (1) wire stock is fed to the stop (2) gripping dies close on the stock and the stop is retracted (3) punch moves forward (4) bottoms to form the head - 58 -
  • 59. Department of Mechanical Engineering Chung-Ang University Heading (Upset Forging) Operations Examples of heading (upset forging) operations: (a) heading a nail using open dies (b) round head formed by punch (c) and (d) two common head styles for screws formed by die (e) carriage bolt head formed by punch and die - 59 -
  • 60. Department of Mechanical Engineering Chung-Ang University Trimming  Cutting operation to remove flash from workpart in impression-die forging  Usually done while work is still hot, so a separate trimming press is included at the forging station  Trimming can also be done by alternative methods, such as grinding or sawing - 60 -
  • 61. Department of Mechanical Engineering Chung-Ang University Extrusion - 61 -  Compression forming process in which work metal is forced to flow through a die opening to produce a desired cross-sectional shape  Process is similar to squeezing toothpaste out of a toothpaste tube  In general, extrusion is used to produce long parts of uniform cross sections  Two basic types:  Direct extrusion  Indirect extrusion
  • 62. Department of Mechanical Engineering Chung-Ang University Direct Extrusion - 62 -  Also called forward extrusion  As ram approaches die opening, a small portion of billet remains that cannot be forced through die opening  This extra portion, called the butt, must be separated from extrudate by cutting it just beyond the die exit  Starting billet cross section usually round  Final shape of extrudate is determined by die opening
  • 63. Department of Mechanical Engineering Chung-Ang University Hollow and Semi-Hollow Shapes (a) Direct extrusion to produce a hollow or semi-hollow cross-section; (b) hollow and (c) semi-hollow cross- sections - 63 -
  • 64. Department of Mechanical Engineering Chung-Ang University Indirect Extrusion to Produce - 64 -  Also called backward extrusion and reverse extrusion  No friction force between billet and container  Limitations of indirect extrusion are imposed by  Lower rigidity of hollow ram  Difficulty in supporting extruded product as it exits die (a) a solid cross-section (b) a hollow cross-section
  • 65. Department of Mechanical Engineering Chung-Ang University Advantages of Extrusion - 65 -  Variety of shapes possible, especially in hot extrusion  Limitation: part cross section must be uniform throughout length  Grain structure and strength enhanced in cold and warm extrusion  Close tolerances possible, especially in cold extrusion  In some operations, little or no waste of material
  • 66. Department of Mechanical Engineering Chung-Ang University Hot vs. Cold Extrusion - 66 -  Hot extrusion - prior heating of billet to above its recrystallization temperature  Reduces strength and increases ductility of the metal, permitting more size reductions and more complex shapes  Cold extrusion - generally used to produce discrete parts  The term impact extrusion is used to indicate high speed cold extrusion
  • 67. Department of Mechanical Engineering Chung-Ang University Example of Extrusion A complex extruded cross-section for a heat sink (photo courtesy of Aluminum Company of America) - 67 -
  • 68. Department of Mechanical Engineering Chung-Ang University Wire and Bar Drawing - 68 -  Cross-section of a bar, rod, or wire is reduced by pulling it through a die opening  Similar to extrusion except work is pulled through die in drawing (it is pushed through in extrusion)  Although drawing applies tensile stress, compression also plays a significant role since metal is squeezed as it passes through die opening
  • 69. Department of Mechanical Engineering Chung-Ang University Drawing of bar, rod, or wire Wire and Bar Drawing - 69 -
  • 70. Department of Mechanical Engineering Chung-Ang University Wire Drawing vs. Bar Drawing - 70 -  Difference between bar drawing and wire drawing is stock size  Bar drawing - large diameter bar and rod stock  Wire drawing - small diameter stock - wire sizes down to 0.03 mm (0.001 in.) are possible  Although the mechanics are the same, the methods, equipment, and even terminology are different
  • 71. Department of Mechanical Engineering Chung-Ang University Drawing Practice and Products - 71 -  Drawing practice:  Usually performed as cold working  Most frequently used for round cross sections  Products:  Wire: electrical wire; wire stock for fences, coat hangers, and shopping carts  Rod stock for nails, screws, rivets, and springs  Bar stock: metal bars for machining, forging, and other processes
  • 72. Department of Mechanical Engineering Chung-Ang University Bar Drawing Hydraulically operated draw bench for drawing metal bars - 72 -
  • 73. Department of Mechanical Engineering Chung-Ang University Wire Drawing Continuous drawing of wire - 73 -
  • 74. Department of Mechanical Engineering Chung-Ang University Sheet Metal Working  Forming and related operations performed on metal sheets, strips, and coils  High surface area-to-volume ratio of starting metal, which distinguishes these from bulk deformation  Often called pressworking because presses perform these operations • Parts are called stampings • Usual tooling: punch and die - 74 -
  • 75. Department of Mechanical Engineering Chung-Ang University - 75 - Basic Types of Sheet Metal Processes 1. Cutting  Shearing to separate large sheets  Blanking to cut part perimeters out of sheet metal  Punching to make holes in sheet metal 2. Bending  Straining sheet around a straight axis 3. Drawing  Forming of sheet into convex or concave shapes
  • 76. Department of Mechanical Engineering Chung-Ang University - 76 - Sheet Metal Cutting
  • 77. Department of Mechanical Engineering Chung-Ang University - 77 - Shearing  Sheet metal cutting operation along a straight line between two cutting edges  Typically used to cut large sheets (a) side view of the shearing operation; (b) front view of power shears equipped with inclined upper cutting blade.
  • 78. Department of Mechanical Engineering Chung-Ang University - 78 - Blanking and Punching  Blanking - sheet metal cutting to separate piece (called a blank) from surrounding stock  Punching - similar to blanking except cut piece is scrap, called a slug (a) Blanking and (b) punching.
  • 79. Department of Mechanical Engineering Chung-Ang University - 79 - Clearance in Sheet Metal Cutting  Distance between punch cutting edge and die cutting edge  Typical values range between 4% and 8% of stock thickness
  • 80. Department of Mechanical Engineering Chung-Ang University - 80 -  For a round blank of diameter Db:  Blanking punch diameter = Db - 2c  Blanking die diameter = Db where c = clearance  For a round hole of diameter Dh:  Hole punch diameter = Dh  Hole die diameter = Dh + 2c where c = clearance Punch and Die Sizes
  • 81. Department of Mechanical Engineering Chung-Ang University Basic sheet metalworking operations - Bending  Straining sheetmetal around a straight axis to take a permanent bend - 81 -
  • 82. Department of Mechanical Engineering Chung-Ang University Springback in Bending - 82 -  Increase in included angle of bent part relative to included angle of forming tool after tool is removed  Reason for springback:  When bending pressure is removed, elastic energy remains in bent part, causing it to recover partially toward its original shape
  • 83. Department of Mechanical Engineering Chung-Ang University Basic sheet metalworking operations – Deep Drawing - 83 -
  • 84. Department of Mechanical Engineering Chung-Ang University - 84 - Punch and Die Components Components of a punch and die for a blanking operation
  • 85. Department of Mechanical Engineering Chung-Ang University - 85 - Progressive Die
  • 86. Department of Mechanical Engineering Chung-Ang University - 86 -
  • 87. Department of Mechanical Engineering Chung-Ang University - 87 -