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ME 324 Manufacturing Engineering
Prof. Sonal Padalkar
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Rolling Process
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Rolling Process
o Describe rolling process
o Slab method to analyze normal & frictional forces
o Neutral point
o Front & Back Tension
o Roll forces, Torque, Power
o Defects in Rolling
o Different rolling arrangements for complex geometries
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Flat-And-Shape-Rolling Processes
Schematic outline of various flat-and-shape-rolling processes.
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Changes In Grain Structure
o Changes in the grain structure of a cast or large-grain wrought metals during
hot rolling.
o Hot rolling is an effective way to reduce grain size in metals for improving
strength and lowering ductility.
o Cast structures of ingots or continuous castings are converted to a wrought
structure by hot working.
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Flat-Rolling Process
Schematic of flat-rolling
process. A greater surface area
of metal is formed by rolling
than by any other metalworking
process.
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Flat-Rolling Process
Bite angle o Relative velocity distribution
between roll and strip surfaces.
o Note the difference in the direction
of frictional forces.
o The arrows represent the frictional
forces acting on the strip.
Forward slip is a measure of relative
velocities at the exit of the work roll
Forward slip =
V f − Vr
Vr
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Flat-Rolling Process
Bite angle
V0 and Vf are velocities of the
work piece at the entrance
and exit of the rollers.
Vf >V0. Vr = constant
Since Vr remains constant and the
workpiece velocity increases, sliding
occurs to compensate for the increase in
velocity
A point in the rolling region where workpiece velocity = Vr.
This is Neutral Point
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Stresses In Rolling
Equilibrium of horizontal forces on the element:
(σ x + dσ x )(h + dh ) − 2 pRdφ sin φ − σ x h ± 2µpR dφ cos φ = 0
This expression can be simplified to
d (σ x h )
= 2 pR(sin φ  µ cos φ )
dφ
Using small angle approximations,
this further simplifies to
sinϕ = ϕ; cosϕ = 1
d (σ x h )
= 2 pR(φ  µ )
dφ
Stresses on an element in rolling:
(a) entry zone and (b) exit zone. 9
Roll Pressure Distribution
Bite angle
Since bite angle (α) is small, p assumed
as principal stress, the other principle
stress is 𝜎𝜎𝑥𝑥 and their relationship with
𝜎𝜎𝑓𝑓′ is
2
𝜎𝜎𝑓𝑓 = 𝜎𝜎𝑓𝑓′
𝑝𝑝 − 𝜎𝜎𝑥𝑥 =
3
Equilibrium of horizontal forces
𝑑𝑑 𝑝𝑝 − 𝜎𝜎𝑓𝑓′ ℎ
= 2𝑝𝑝𝑝𝑝 𝜙𝜙 ± 𝜇𝜇
𝑑𝑑𝑑𝑑

p
d
′
Differentiating

Y𝜎𝜎𝑓𝑓f′ h
′′
dφ  Y
yields
𝜎𝜎𝑓𝑓f
d (σ x h )
= 2 pR(φ  µ )
dφ
  p
 d
+

𝜎𝜎𝑓𝑓f′′ h = 2 pR (φ  µ )
−
1
Y
  Y𝜎𝜎f′′
 dφ
  𝑓𝑓

( )
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Roll Pressure Distribution
Simplifying leads to the expression
Letting hf be the
final thickness, we
have
d
dφ
 p 


 Y f′′ 
 𝜎𝜎𝑓𝑓  = 2 R (φ  µ )
p
h
Y
𝜎𝜎f′′
𝑓𝑓
d
dφ
 p

 Y f′′
 𝜎𝜎𝑓𝑓
p
Y ′f′



 = 2 R (φ  µ )
h
𝜎𝜎𝑓𝑓
Substituting the value of h into Eq.(6.26a) produces
h

µ
H
p = CY ′ e
R
𝜎𝜎𝑓𝑓f′
where


H = 2 R tan −1  R φ 
 hf 
hf


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Roll Pressure Distribution
Looking first at just the entry zone
R
µH i
C=
e
hf
and
p
At the exit zone
R
µH i
C= e
hf
and
p
= Y𝜎𝜎𝑓𝑓f′′
′
= Y𝜎𝜎𝑓𝑓f′
h e µ (H 0 − H )
h0
h e µ (H 0 − H )
h0
@ H f = H (φ = 0 ) = 0
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Pressure Distribution in Rolling
o Pressure distribution in the roll gap as a
function of the coefficient of friction.
o Note that as friction increases, the neutral
𝑝𝑝
𝑆𝑆𝑦𝑦′
point shifts toward the entry.
o Without friction, the rolls slip, and the
neutral point shifts completely to the exit.
Plane strain condition
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Pressure Distribution in Rolling
o Pressure distribution in the roll gap as
a function of reduction in thickness.
𝑝𝑝
𝑆𝑆𝑦𝑦′
o Note the increase in the area under
the curves with increasing reduction in
thickness.
o Thus, increasing the roll-separating
force.
Plane strain condition
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Determination of the Neutral Point
The neutral point is determined by equating the following:
p (@ neutral pt.) entry = p (@ neutral pt.) exit
µ (H − H f )
′
′
h
h
(
µ
H0 −H )
Y
Y𝑓𝑓f′
= 𝜎𝜎
@H = H n
e
𝜎𝜎𝑓𝑓f′ h e
h
0
where
µH 0
h0
e
µ (H 0 − 2 H n )
=
=e
2 µH n
hf
e
f
 R 
R
−1 
H =2
φ
tan
 hf 
hf


OR
1
1 ℎ0
𝐻𝐻𝑛𝑛 =
𝐻𝐻0 − 𝑙𝑙𝑙𝑙
2
𝜇𝜇 ℎ𝑓𝑓
Substituting red equation into the blue,
φn =
 hf H 
tan
⋅ n
 R
R
2 


hf
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Effects of Front And Back Tension
Entry Zone:
pb
pf
Exit Zone:
𝑝𝑝 =
𝑝𝑝 =
𝜎𝜎𝑓𝑓′
𝜎𝜎𝑓𝑓′
− 𝑝𝑝𝑏𝑏
− 𝑝𝑝𝑓𝑓
P increases with:
Pressure distribution as function of front
& back tension.
ℎ 𝜇𝜇
𝑒𝑒
ℎ0
𝐻𝐻0 −𝐻𝐻
ℎ 𝜇𝜇𝜇𝜇
𝑒𝑒
ℎ𝑓𝑓
• Increasing strength of materials;
• Increasing coefficient of friction;
• Increasing R/hf ratio (larger
To reduce the pressure, longitudinal tension
is applied at the entry or exit or both
reduction)
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Roll Forces
Roll force on the strip is product of area under pressure vs. contact –length curve
(L) and strip width (w)
The roll force, F, given by
F=
φn
∫
α
∫φ
wpR dφ + wpR dφ
0
w = Strip width
n
Another method to calculate the roll force is to use
𝐹𝐹 = (𝐿𝐿𝐿𝐿)𝑝𝑝𝑎𝑎𝑎𝑎
Contact area
Average contact pressure
L is contact-length curve and can be approximated as
L = R∆h
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Roll Forces
For low friction conditions an approximation for the roll force can
be made as
𝐹𝐹 = 𝐿𝐿𝐿𝐿
𝜎𝜎𝑓𝑓′
𝜎𝜎𝑓𝑓′ is average flow stress in plane strain of
material in the roll gap
For higher friction conditions, the following expression approximates the
roll force
𝐹𝐹 = 𝐿𝐿𝐿𝐿
𝜎𝜎𝑓𝑓′
𝜇𝜇𝜇𝜇
1+
2ℎ𝑎𝑎𝑎𝑎𝑎𝑎
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Roll Torque
The roll torque, T, for each roll can be calculated analytically from the
expression
Frictional forces
T=
α
∫φ
wµpR dφ −
2
n
(entry zone)
φn
∫0
wµpR dφ
2
(exit zone)
The torque per roll can be estimated—assuming the roll force acts in
the middle of the contact –length & is perpendicular to the plane of the
strip—as
FL
T=
2
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Roll Power
The power required per roll is
Power = Tω
ω = 2πN
where N = Revolution per minute
The power per roll is
Power =
πFLN
60
kW
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Strain Rate and Friction in Flat Rolling
The average strain rate in flat rolling can be approximated as
𝑉𝑉𝑟𝑟
ℎ0
ln
𝜖𝜖̇ ̅ =
𝐿𝐿
ℎ𝑓𝑓
The maximum possible draft, that is (h0-hf) or ∆hmax , in flat rolling can be
related to friction and roller radius
Friction affects the maximum possible draft (∆hmax), such that
∆hmax = µ R
2
The maximum angle of acceptance is
α max = tan −1 µ
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Defects In Rolling
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Roll Bending and Workpiece Spreading
Bending forces
(a) Bending of straight cylindrical
rolls (exaggerated) because of
the roll force.
(b) Bending of rolls, ground with
camber, that produce a sheet
of uniform thickness during
rolling.
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Roll Bending and Workpiece Spreading
o High strip width to thickness ratio is
condition for plan strain
o If strip width is increased, spreading occurs
in flat rolling.
o Spreading can be similarly observed when
dough is rolled with a rolling pin.
Distorted Roll Radius

′
R ′ = R1 + CF
 h0 − h f
 F’ = Roll force per unit width
 C = 2.3 x 10-2 mm2/kN for steel rolls &


4.5 x 10-2 mm2/kN for cast-iron
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Defects In Flat Rolling
Schematic illustration of typical defects
in flat rolling: (a)wavy edges; (b) zipper
cracks in the center of strip; (c) edge
cracks; (d) alligatoring.
o Wavy edges: due to bending of
the rolls that causes thinner
edges of strip than center
o Zipper & Edge cracks: due to
low material ductility and
barreling of the edges
o Alligatoring: due to
inhomogeneous deformation of
the material during rolling
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Effects of Roll Radius
Leads to
surface
deformation
Leads to
deformation in
the bulk of the
workpiece
The effect of roll radius on the type of residual stresses developed in flat
rolling: (a) small rolls, or small reduction in thickness; and (b) large rolls, or
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large reduction in thickness.
Methods of Roller Leveling
Schematic illustration of methods of roller leveling. These processes
are used to flatten rolled sheets.
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Various Roll Arrangements
Schematic illustration of various roll arrangements: (a) two high; (b)
three high; (c) four high; (d) cluster; (e) tandem rolling with three
stands; (f) planetary.
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Cluster Mill
Schematic illustration of a cluster (Sendzimir) mill. These mills are very rigid
and are used in rolling thin sheets of high-strength materials, with good control
of dimensions.
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Shape Rolling
o Stages in shape rolling of an Hsection part.
o Various other structural
sections, such as channels and
I-beams, are also rolled by this
process.
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Ring-Rolling
(a) Schematic of a ring-rolling operation. Reducing the thickness results
in an increase in the part’s diameter.
(b) Examples of cross-sections that can be formed by ring rolling.
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Thread-Rolling Processes
Thread-rolling processes: (a) flat dies and (b) two-roller dies. These
processes are used extensively in making threaded fasteners at high
rates of production.
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Machined And Rolled Threads
(a) Schematic of machined or rolled threads. (b) Grain-flow lines in
machined and rolled threads. Unlike machined threads, which are cut
through the grains of the metal, rolled threads follow the grains and are
stronger, because of the cold working involved.
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Mannesmann Process
Cavity formation by secondary tensile stresses in a solid round bar and its use
in the rotary-tube-piercing process. This procedure uses the principle of the
Mannesmann mill for seamless tube making. The mandrel is held in place by
the long rod, although techniques have been developed in which the mandrel
remains in place without the rod.
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https://www.youtube.com/watch?v=ztcEyel47Kg
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