One of the metal forming operation. Rolling- process, variables, geometry and load calculations, hot and cold rolling, rolling defects and remedies.

1. Rolling (Metal Working)
Introduction-
The process of deforming a metal plastically (as is done in any metal forming process) by
passing it between rolls (roll arrangement) is called rolling in simple terms. The friction and
the squeezing action between the rolls decreases the thickness or changes the cross section
and also help in imparting special properties to the material undergoing the explained
process. In current scenario applications, rolling is one of the most important metal working
operation. All metal products require rolling to be performed at some point of their
manufacturing process. Most of the materials are subjected to rolling before they can be
converted into proper raw materials.
Fig 1: A schematic of a basic flat rolling process. [9]
The ingot from the casting is not suitable raw material for any application since the columnar
structure of the grains impart brittle nature to the metal hence is subjected to rolling which
alloys the grains to change into a wrought grain structure which is more uniform and
equiaxed and can suitably be used as a raw material.

2. Fig 2: Grain structure of a hot rolled metal compared to a cast metal. [9]
Whatever the type of rolling process be hot or cold, the main objective is to decrease the size
or more precisely the thickness of the metal. The resultant products have certain
terminologies associated with them for their better classification which has to be understood
before the process and principle could be interpreted. The ingot is transformed into various
kind of structures after rolling-
Semi-Finished Products-
 Bloom is a premier product after processing an ingot and has a cross sectional area
greater than 200 cm2
.
 Billet is obtained after a further reduction by hot rolling and has a cross sectional area
greater than 1600 mm2
.
 Slab is a simple hot rolled ingot and has a cross sectional area greater than 100 cm2
with a width twice the thickness or more than that.
Fig: Rolling product terminologies. [4]
Further rolling steps lead to Mill products-
 Plate a final rolled product with a thickness >6 mm.
 Sheet a final rolled product with a thickness <6 mm and width >600 mm.
 Strip a final rolled product with a thickness <6 mm and width <600 mm.
Another aspect is the draft which can be defined as the difference between the thickness of
the rolled and unrolled metal or the reduction in thickness of the billet/bloom. Besides
reducing the thickness, friction is an intricate part of rolling process and no rolling process

3. can be supported without it. It act as a feeding force for the ingots to pass between the rolls
but too much friction is detrimental and may lead to various defects in the final product
which are discussed later. Therefore it is essential to control the level of friction between the
rolls and the work piece and this can be achieved by using process particular lubricants.
Fig 3: A schematic showing various factors and variables associated to a rolling process. [9]
A simple conservation of volume for the material undergoing rolling can give us the
information about the dimensions of the rolled product if the initial dimensions of the work
piece is known. The marked red region in the centre is the roll zone or the plastic zone which
is under the impact of the rolls for a particular interval of the process. The initial velocity ( Vi
) or the velocity of the material entering the plastic zone is less than the final velocity ( Vf ) or
the velocity of the material exiting the plastic zone this is also because of the friction and the
conservation of volume. The rolls themselves rotate at a constant speed so there has to be a
point in between the plastic zone where the velocity of the metal becomes equal to the
velocity of the rolls and this point is called the no slip point. And the significance of this
point is that before this point the rolls are moving faster than the material and after this point
the material is moving faster than the rolls. Beside these variables there can be an extra
variable which comes into picture by the introduction of front and back rolls and generally
considered in the operation which have more than one roll in series. The front tension and
back tension marked by the two blue arrows provide the additional force required to roll hard
to roll materials. Also sometimes due to the compressive force the metal tend to spread i.e.
the final width is more than the initial. Generally metal spreading is not an issue but in case
of bars or rods where low width to thickness ratio is involved side rolls are attached so as to
prevent spreading of the metal.

4. Since all the basic terminologies and variable associated to rolling have been introduced it is
suitable to proceed towards the selection and use of different kinds of rolling equipment for a
particular rolling process.
Rolling Equipment
Rolls for metal rolling-
Since the rolled metal has several sizes and specifications so the rolls used for producing such
sheets, strips or plates also have different sizes and are made of different materials according
to the process. In industrial manufacture process of flat rolling, rolls are generally 24 to 54
inches in diameter and in production of very thin metal sheets rolls can be as small as ¼
inches.
Rolls are subjected to extreme working condition during the process such as tormenting
compressive forces, shear, wear, thermal stresses and bending moments which lead to various
defects in rolls themselves. They tend to deflect form their original position and sometime
undergo roll flattening which is a kind of defect and is discussed later. Hence the selection of
roll materials typically depend on these factors or the capability of resisting these kind of
extreme conditions. Although roll materials vary from process to process but common roll
materials are cast steel, forged steel and cast iron. Forged rolls are generally preferred over
cast rolls because they are more rigid and have higher strength than cast rolls but at the same
time they are difficult to manufacture. In industries the rolls are generally made up of
nickel/molybdenum steel alloys. With the present advancements in the ceramic composites
various high hardness and toughness composites like tungsten carbide are used for making
rolls. The reason for using ceramic for rolling is obvious because they tend to perform well in
compressive condition than tensile ones and hence are the best choice for roll materials.
Certain rolls are also made up of Zirconium composites.
Roll mill-
In metal forming operation, rolls as such require a proper arrangement or other mechanical
instruments aligned in a fashion to hold the rolls so that rolling can be performed on the work
piece. Such an arrangement is called a rolling mill or a reduction mill. The construction of a
rolling mill depends on the type of the rolling operation to be performed. The basic parts of a
rolling mill are as follows:
1) Work rolls- These are the main roll arrangement that is to be used for performing the
operation and the one for which the mill has to be set.
2) Back-up rolls- Sometimes the main rolls tend to bend or undergo flattening because
they may not be able to handle the compression at some point in the operation. This
situation is highly undesirable and is controlled by using a set of back-up rolls, which
roll in a synchronised fashion with the front rolls and provide the support to the rolls
and hence make the whole system capable of providing extra compression force for
the rolling.

5. 3) Roll balance system- To ensure that the above mentioned arrangement of rolls stay in
the required or desired position all the time during operation a balance system is
required so that the lower rolls are maintained in a proper position relative to the
upper and the back-up rolls.
4) Roll changing device- Sometimes the roll arrangement has to be changed to meet the
rolling requirements for a particular operation and instead of taking the work force to
a new set of rolls or to a new mill, a roll changing system is introduced which can be
used to replace the rolls and insert and arrange the new set of rolls accordingly. An
overhead crane and a special unit attached to the neck of the rolls is used for replacing
or arranging the rolls.
5) Mill protection device- This unit is required to monitor the amount of force that has to
be deployed or applied to the back rolls such that the magnitude of force applied is in
the limits of operation i.e. the rolls do not undergo fracture or bending and damage the
mill house.
6) Roll cooling and lubricant system- The instalment of this unit is inevitable and
necessary as well because of the heat generated due to friction during operation.
Certain lubricants are used which act both as coolant and help in reducing the friction.
A detailed study on lubrication and friction in rolling operation is done later.
7) Pinions- They act as gears to switch power between the spindles such that they spin in
opposite direction but with same speed.
8) Gearing- The desired speed of rolling is achieved by setting the gear properly.
9) Drive motors- Finally to provide power for the whole system to work and allow rolls
to work at thousands of horse power so as to squeeze the rolling material accordingly.
The forces involved in rolling sometimes reach to an order of million pounds and
hence that much high power has to be supplied so as to compensate for the large
forces.
10) Electrical controls- For controlling the voltages needed to apply to the motors
periodically.
11) Product containers- The final finished product has to be collected in a container type.
For example: coilers and un-coilers are required to contain the final finished rolled
coils.
The rolling mills can be easily classified according to the number of rolls present and the kind
of arrangement in which they are performing the rolling operation. The basic arrangements
are as follows-
 Two High Rolling Mill- This is the simplest and most common arrangement of all. In
this the rolls are of same size and are made to rotate in same direction. The metal is
passed through the rolls and then is collected at the end to either send it back to the
rolls for further reduction in thickness or a belt arrangement can be provided for the
back to back feed for this arrangement. The belt arrangement earlier was controlled by

6. manual handling of the rolled slabs.
Fig 4: A schematic of a ‘two high rolling mill’ arrangement. [9]
 Two High Reversing Mill- This type of arrangement originated from the sole need of
increasing the rolling speed or to decrease the rolling time. The direction of the
rotation of the rolls could be reversed so that the required thickness could be achieved
by the same set of roles in minimal time without the need of a second pass. The major
drawback associated with this arrangement is the high power required to constantly
and continuously change the direction of the roles.
Fig 5: Two high reversing mill- work is fed through rolls in one direction. [9]

7. Fig 6: Two high reversing mill- direction of roll’s spin is reversed and the work is fed from
the opposite direction. [9]
 Three High Rolling Mill- It consists of three rolls the upper, lower and the middle
one which operates due to friction. These rolls rotate in same direction and an elevator
system is provided to pass the work back and forth through these rolls.
Fig 7: Three high rolling mill- all rolls continue to spin as work is lowered by elevator. [9]
 Four High Rolling Mill- It utilizes the principle that a lesser force is required if
smaller rolls are used. Hence a major drawback is the risk associated with the
deflection of smaller rolls from original position (figure at bottom).
Fig 8: Four high rolling mill- two main smaller rolls supported by two back up rolls. [9]

8.  Cluster Mill or Sendzimir Mill- In this kind of arrangement each roll is supported by
two back up rolls. It can easily reduce the thickness of a high strength material during
cold rolling operation. Very thin sheets can be rolled in a system with smaller
diameter rolls.
Fig 9: Cluster mill- each roll is supported by a group of rolls for providing excess
compression. [9]
 Four Stand Continuous Mill or Tandem Mill- To decrease the number of passes
and to increase the production rate continuous mills came into picture. There is a
continuous arrangement of rolls and each set is called ‘stand’. Since the reduction at
each stand is different from the other (i.e. the reduction increases) the velocity of the
rolls at each stand is different. Since the speed of the material so passing is
continuously increasing with each stand problems occur when the synchronisation is
lost. This kind of system provides front tension and back tension to the work which
helps in achieving higher reduction without prior failure of the work. A special type
of reversible mill called the ‘Steckel Mill’ fetch power from the power reels and the
rolls does not move at all. The reduction achieved is less but higher tolerances can be
expected if this is used.

9. Fig 10: A schematic of a Tandem Mill- Continuous reduction in the work. [9]
 Planetary Mill- To reduce the number of passes planetary roll mills are most
effective. The metal can be reduced to a thin sheet with a single pass alone. There are
heavy backing rolls surrounded by other rolls in a planetary fashion such that when
one of the roll is in contact with the work the other is free. The overall reduction is the
summation of reduction provided by each set of rolls. The operation requires two
other separate set of rolls for feeding the work to the mill and receiving the reduced
sheet.
Fig 11: A schematic of the planetary mill- the round arrangement allows the reduction to be
maximum in a single pass. [4]
Rolling Processes
There are various rolling processes but all of them can be stacked into two conventional
rolling processes i.e. Hot Rolling and Cold Rolling.
All the rolling process which involve simple flat rolling of the work can be classified under
plain strain conditions (material gets longer and thinner but not wider) since the length of
contact, L, between the work piece and the rolls is generally much smaller than the sheet

10. width, W (refer fig: 12). The sheet or the plastic region of the sheet is free to expand in the
rolling direction, x, because of the compressive stress, σz, acting on the sheet. The lateral
expansion (in the y- direction) has to be neglected or is assumed to be zero as it is limited by
the un-deformed material on both sides of the roll gap. So except at the edges we get a net
effect similar to the plane strain condition, εy = 0 and εz = −εx.
Fig 12: Schematic of the plain strain condition and the plastic zone. [7]
Hot Rolling-
Hot rolling like any other hot forming operation is carried out at a temperature greater than
the recrystallization temperature (0.3~0.5 melting temperature) of the metal being deformed.
The recrystallization temperature can be defined as the minimum temperature at which
formation of new grains occur. Recrystallization is followed by grain growth and preceded by
recovery. The driving force for both recrystallization and recovery processes comes from the
difference between the energies of the strained and the unstrained material. There are two
ways in which recrystallization can take place i.e. static or dynamic recrystallization. The
static one occurs after the process if the metal is kept high temperature. The dynamic ones
occur during the operation itself which can lead to a more isotropic microstructure.
During recovery the kinetic energy of the dislocations present within the crystals increase and
they annihilate or come down to lower energy configurations leading the way for nucleation
of new grains at the dislocation clusters or the grain boundaries. There are several recovery
mechanism involved during the static and the dynamic recovery as in case of
recrystallization. These are-
 Dislocation pile-ups- at the site of a dislocation pile up the increase in the strain at the
pile up origin can lead to cross slipping of the dislocation from one plane to another
releasing strain energy.

11.  Climb- the edge dislocations climb because of the high vacancy diffusion at this
elevated temperature leading to a reduction in strain at the pile up.
 Polygonization- besides annihilation an important phenomena that leads to recovery is
polygonization. There are regions of dense and sparse dislocations, the dense ones
arrange themselves in a particular fashion leading to formation of dislocation cluster
or cells within the crystal and hence these clusters act as the nucleation sited for the
new grains.
Grain growth is the final stage where the newly formed grains grow. Larger grains grow at
the expense of smaller ones and this involves all kinds of boundary energy calculations. The
driving force for grain growth mechanism comes from the reduction in grain boundary
energy of the grains because as the grain size increase with time the grain boundary area
decreases which results in total decrease in the energy of the metal. This final stage has to be
controlled if a finer microstructure is desired, hence the temperature is brought down during
the final stages to ensure that the newly formed grains do not undergo coarsening.
Fig 13: Effect of temperature on the metal during hot rolling. [4]
There are various mills in which the metal can be subjected and are discussed already like the
continuous mill, universal mill, steckel mill, cluster mill etc. If the billet or the bloom is
product of continuous casting then it can directly be subjected to rolling mill (blooming mill)
but for smaller operation the material starts at room temperature and must be heated to
proceed. This is performed gas or oil fired soaking pits for smaller work pieces and for larger
work pieces this is done using induction furnaces. The major challenge is to keep the
temperature above the recrystallization temperature during the whole process hence a safety
factor of 500
C -1000
C is provided. The behaviour of the metal is affected by this increase in

12. temperature. There are various advantages and drawbacks related to hot rolling operation
which are as follows:
Advantages-
1) Low flow stress- at the recrystallization temperature the metal yields prior to the
actual yield point or the yield point of the metal is reduced. This will decrease the
amount of flow stress required to produce the same amount of deformation with
previous yield point. This is a consequence of the extra energy available due to
increased temperature so as to overcome the activation energy for the dislocations to
move.
2) No strain hardening- strain hardening is a result of increase in the yield point of the
material due to excess deformation. The dislocations get entangled into each other and
further movement requires higher flow stress which ultimately leads to material
failure. Since the yield point decreases in hot rolling, the problem of strain hardening
is solved.
3) Higher strain rates- with the easy flow of material and little or no strain hardening it is
possible to work at very high strain rates and hence speed up the process.
4) Ductility and toughness- the ability of the metal to undergo massive shape changes
prior to early failure is enhanced by increased ductility and toughness since the
microstructure becomes fine and hardness decreases but ductility increases.
5) Isotropic nature- most of the hot rolled products are isotropic in nature i.e. there
properties are same throughout the metal. This is because of the homogeneity in the
microstructure so formed after the recrystallization process. The old weak cast grain
structure is consumed and a new fine wrought structure is evolved which has uniform
equiaxed grains.
Drawbacks-
1) Poor surface finish- due to increased temperature and presence of oils or lubricants or
exposure to air surface reactions take place and give rise to oxide formation which
causes embrittlement. In case of steels surface decarburisation occurs. So the layer has
to be machined off or is chemically removed via pickling which adds the additional
costs to the process. Otherwise the problem of rolled in oxides come into picture
which can break and enter the metal during rolling.
2) Lower dimensional accuracy- the increased temperature softens the material and
cause a major increase in the width with a decrease in thickness which is undesirable
in some cases like rod or bar formation in which higher tolerances are required.
3) Surface inhomogeneity- due to Newton’s Law of Cooling the surface cools first and
the core cools at last which gives large grains at the centre and small grains at the
surface as more recrystallization may occur at the surface.
4) Higher power input- to increase the temperature and to maintain it consumes a large
amount of power, example in case of steel the recrystallization temperature is around
9500
C and to maintain the work at this temperature is a separate challenge.

13. 5) Deterioration of tools and machinery- the elevated temperatures reduce the life of
tools and machinery. They undergo constant increase and decrease in temperature
which result in fatigue conditions and after certain cycles they fail.
Fig 14: A multiple stand continuous hot rolling process (blooming mill). [11]
Cold Rolling-
Cold rolling or room temperature rolling is performed at temperatures less than 0.3 times the
melting temperatures and is used to get better dimensional accuracy surface finish. Hot
rolling is often accompanied by cold rolling in last stages so as to increase the strength of the
metal. For some non-ferrous metals like Pb and Sn, room temperature rolling can be hot
rolling and for W even temperature of 10000
C is not enough to provide hot rolling
environment, so the temperature has to be maintained during cold rolling as well. The cold
rolling operation often results in reduced ductility of the metal. Cold rolling certainly does
not allow the metal to recover or recrystallize dynamically because of the high activation
energy requirement which cannot be crossed at the cold rolling temperatures. Hence the metal
has to be subjected to certain heat treatment operations like annealing or normalising.
Annealing- The temperature of the metal is increased after the rolling process and it is
allowed to cool in the furnace itself this give metal the time to statically recover and
recrystallize and give rise to fine grains and hence increase ductility.
Normalising- It is similar to annealing but gives a finer microstructure than annealing
because the metal is allowed to cool down in air. This results and fast cooling and less
coarsening and is often used to get a balance between the toughness and hardness. There are
two other types of heat treatment techniques namely quenching and tempering which are used
extensively for ferrous metals as they are required to provide a specific microstructure or get
a specific phase formation in the metal matrix.
Cold rolling has its own advantages and drawbacks which are as follows:

14. Advantages-
1) Anisotropy- The grains elongate themselves in the direction of the rolling and hence
gives the directionality required in certain tensile applications.
2) Better surface finish- The cold rolling operation generally does not use lubricants and
also the temperature is not high enough to cause any surface damage or surface
reaction which would give rise surface inhomogeneity (no oxide formation takes
place).
3) Increased hardness- The increased work hardening results in increase strength of the
metal as the yield point increase with each pass.
4) Better tolerances- The problem of material softening is eliminated in cold rolling and
hence better dimensional accuracy can be achieved and hence cold rolling can be used
for bars and rods formation.
5) Less energy requirements- The cold rolling operation does not require elevated
temperature which reduce the excess cost and also the material waste involved in cold
rolling is much less than the hot rolling operation.
Drawbacks-
1) High flow stress- As the yield point increases with each pass so the amount of flow
stress required to produce same deformation also increases and hence higher flow
stress is required.
2) Excess hardening- As the metal is not able to recover during cold rolling so the
dislocations entangle and never annihilate which leads to increased hardening and can
lead to prior failure and makes the metal unsuitable for ductile operations.
3) Increased residual stress- The increase in the residual stress due to buckling can lead
to prior failure of the metal under the conditions superimposing on residual stresses.
Fig 15: A single pass two high cold roll mill with an attached coiler. [12]

15. There are several other subsidiary rolling processes, they are as follows:
1) Transverse Rolling or Cross Rolling- Circular wedge rolls are used and are made to
revolve in the same direction. It is a typical hot rolling process in which heated bar is
chopped to length and is fed transversely between rolls. It is used for making gear
teeth and other parts.
Fig 16: A schematic of the transverse rolling process. [10]
2) Shaped Rolling or Section Rolling- Various I- beam and H- beam slabs are prepared
using this cold rolling process. The flat slab can be bent easily into complex shapes
using driven rolls, there is no appreciable change in the thickness and can be used for
making difficult to mould parts.
Fig 17: A schematic of a sectioned rolling process for processing V- beams. [10]
3) Skew Rolling- Is a typical hot rolling operation in which round rods are fed to
specially designed rolls (threaded) to get metal balls. This is a combination of metal
rolling and metal forging operation.
Fig 18: A schematic of skew rolling process. [10]

16. 4) Ring Rolling- It is a hot rolling operation in which rings of smaller diameter are fed
to get rings of larger diameter and reduced cross section. Rings of different shape with
high precision can be obtained without mush waste of material.
Fig 19: A schematic of the ring rolling operation and examples of different cross sections that
can be formed. [10]
5) Thread Rolling- It is used to make rolled threads which are much stronger than the
machined ones. A die presses the cylindrical feed into a system of threaded rolls so
that the material flow radially outwards to get thread cuts.
Fig 20: Illustration of the thread rolling process and a collection of threaded parts prepared
using thread rolling process. [10]
6) Tube Rolling- It is a hot rolling operation in which tubes of different cross sections
can be formed by fixing a mandrel between the rod feed. The mandrel can be in fixed
position or moving position. The rolls have to be shaped accordingly so that a tube
cross section can be processed.

17. Fig 21: An illustration of tube rolling with a fixed mandrel and movable mandrel. [10]
7) Powder Rolling- With advancement in technology the contamination involved due to
hot rolling can be eliminated using powder rolling operation in which powdered feed
(metal powder) is compacted between rolls into a green strip which is then sintered to
achieve the required densification. A fine grain sized metal is obtained if the sintering
parameters are controlled properly.
Fig 22: A powdered rolling illustration for making Titanium slabs which are finally subjected
to hot or cold rolling to achieve desired characteristics. [4]
Geometrical Assessment and Load Calculations
Analysing the geometry involved and the nature and quantity of the loads required for a
material undergoing rolling helps in identifying the variables affecting the process and
produce ways to control those variables for increasing the overall efficiency of the process.
Assumptions-
Various assumptions have to be made for the sake of simplicity in calculation and better
understating of the system. These are as follows:
 The arc of contact or the region in touch with the metal and the rolls is considered to
be a part of a perfect circle.
 The coefficient of friction, μ, is assumed to be constant so that the differential
calculus related to it can be avoided.
 Plastic deformation is assumed.

18.  Conservation of volume- The volume of the material entering the rolls and the volume
of the material at the exit is assumed to be equal. In normal conditions the volume
tend to decrease as the pores close with application of the compressive force.
 Velocity of the rolls- The velocity of the rolls is assumed to be constant throughout
the process.
 Plain Strain Condition- As discussed earlier the condition of plain strain is assumed
i.e. there is change in size of the work piece in only two dimensions. In our case we
have assumed the width to remain constant.
 Cross Sectional Area- The sectional area normal to the rolling direction is assumed to
be constant.
System-
A metal sheet enters the rolling arrangement at the entrance plane, XX front, with an initial
thickness, h0, and leaves the arrangement at the exit plane, YY front with a reduced thickness
or the final thickness, hf. The corresponding entrance and the exit velocities are V0 and Vf
respectively. Obviously Vf is greater than V0.
Fig 23: A schematic showing various geometrical parameters and forces acting on the work
piece during rolling process. [1]
Since there is no change in metal volume as we have assumed so we have the following
relation:
bh0v0 = bhv = bhfvf ............ Eq: 1; [4]
So from equation 1 we have,

19. (h0L0)/t = (hfLf)/t given that width remain same, we get, h0v0 = hfvf
Or finally v0/vf = hf/ h0……….Eq: 2; [4]
Where,
b= width of the sheet
V=velocity at any thickness
h= average height between h and h0
L0 and Lf = initial and final length of the sheet respectively
At some point on the contact arc there are two kinds of forces acting between the roll and the
sheet, (a) A radial force, Pr, and (b) A tangential force, F. If the velocity of the sheet is equal
to the velocity of the rolls at any point then that point is called the no-slip point or the neutral
point, in our case point N is the neutral point as shown in figure.
Fig 24: geometric illustration showing the neutral point and the forces acting. [4]
In between the entrance plane XX and the neutral point the velocity of the sheet is slower
than the velocity of the roll surface. The tangential force shown acts in the forward direction
helping to draw the metal into the roll gap.
On the side of the exit YY and the neutral point the sheet moves faster than the surface of the
rolls due conservation of volume and then the frictional force acting is reversed and opposes
the motion of the sheet into the roll gap.
The radial load has a vertical component called rolling load, P, it is the force with which the
rolls press against the metal. This can help us in calculating the specific roll pressure, p. The
specific roll pressure is the rolling load divided by the contact area.
p = P/ (bLp)………Eq: 3; [4], where, Lp is the projected length of the arc of
contact.
Hence the projected length of the arc of contact, Lp, can be given as follows:

20. ……… Eq: 4; [7]
If (h0-hf) = Δh then we get, , where R= roll radius.
The distribution of roll pressure along the arc of contact is such that the pressure rises to a
maximum value at the neutral point and then falls off again. The pressure distribution shows
that neutral point as such is not a line on the contact surface but an area since the pressure at
the neutral point does not show a sharp peak.
Fig 25: The neutral point relation and the pressure distribution leading to friction hill. [4]
The area under the pressure distribution depict three things which are as follows-
 The area under the whole curve is directly proportional to the rolling load.
 The shaded area represents the force required to overcome the frictional forces
between the sheet and the roll surface.
 The force required to deform the material in plane homogenous compression is given
by the part which is under the dashed line, AB.
Fig 26: Roll pressure distribution along the arc of contact. [1]
Major Variables- There are four major variables associated with rolling. They are as
follows-

21.  The roll diameter.
 The deformation resistance offered by the metal.
 The friction between the roll surface and the metal surface.
 The front tension and the back tension in continuous rolling systems.
Maximum Reduction-
Fig 27: The condition of roll flattening. [7]
The condition of maximum reduction in the thickness of the sheet is a critical scenario. The
Roll Flattening condition can help us derive the ways in which we can achieve very thin
sheets.
Neglecting the curvature of the roll contact area we have following result with us from the
equation 4, Pav = h/µL ( exp[µL/h] – 1 ) σ0………..Eq: 5; [7], where, σ0
is the average plane-strain flow stress in the roll gap. If the concept of back tension and front
tension is considered then we reach to the following conclusion,
Pav = h/µL ( exp[µL/h] – 1 ) [ σ0 – (σft + σbt)/2 ]………. Eq: 6; [7],
where, σbt and σft are the back and front tensile stresses.
Two major type of elastic distortions come into picture when the high rolling forces are
transmitted to the rolls from the work piece:
1) The roll being restrained at the ends to tend bend along their length as the work piece
tends to separate them.
2) The radius of the curvature of the rolls increase at the point of contact, i.e. R -> R’
.
According to Hitchcock’s analysis the new radius of curvature can be given by,
R’
= R (1 + 16 Fs / (π E’
Δ h))…………. Eq: 7; [7], where, E’
= E/(1 − ν2) and ν
is Poisson’s ratio. With L = (√R’h) the roll separating force per unit length becomes,
Fs = Pav Sqrt[R’
Δh]...Eq: 8; [7], where,
Pav = h/(µ Sqrt[R’
Δh]) (exp (µ Sqrt[R’
Δh])/h – 1) (σ0 – σt)

22. and σt = (σft + σbt)/2. The roll separating force, Fs = PavL, may be written as,
Fs = h/µ [exp (µ Sqrt[R’
Δh]/h) -1] (σ0 – σt) , and,
Pav = h/(µ Sqrt[R’
Δh]) (exp (µ Sqrt[R’
Δh])/h – 1) (σ0 – σt)
………..Eq: 9; [7].
The effect of roll flattening is to increase the roll separating force because both the average
pressure L increase along the process. So with the excessive roll flattening or the maximum
roll flattening one can achieve the minimum thickness of the sheet that can be achieved and is
given as, hmin = (CµR/E’
) (σ0 – σt)……. Eq: 10; [7], where, C= constant between
6 and 7, E’
= modified modulus. There are various ways of circumventing the above equation
and hence by controlling the variables appearing in the above equation we can reduce the
thickness of the sheets to even lesser value. These are as follows:
1) Reducing friction- Reducing friction will decrease the coefficient of friction and
hence will decrease the h value. This can be achieved by using a suitable lubricant for
the process.
2) Front and Back Tension- Applying front tension and back tension will increase the σt
value which in turn will decrease the overall σ0. This can be achieved by using a
continuous rolling mill.
3) Lowering the yield stress- Lowering the yield stress or the σ0 value will help in
achieving sheets of much smaller thickness. This can be achieved by using a proper
heat treatment operation like annealing.
4) Using smaller rolls- Smaller rolls mean smaller radius which in turn increase the roll
pressure and hence help in achieving the lower h value. This increase the chances for
roll buckling but can be controlled by using back up rolls, which makes system more
complex.
5) Increasing the modulus value- Using higher strength rolls like carbide rolls instead
steel rolls will provide a much larger value of modulus as it will increase the extent of
roll flattening and hence will help in achieving sheets of lower thickness.
Simplified Rolling Load Analysis-
1) No friction situation- This condition can be achieved by using a thin film lubricant
which will give uniform spread of the compressive force over the surface of the metal.
The rolling load P in this situation can be given as:
P = pbLp = σ0 b Sqrt[RΔh]……..Eq: 11; [4]

23. 2) Normal friction situation- Under the given plane strain conditions, the rolling load P
under this situation is derived using the average pressure,
(2/Sqrt[3])σ0[1/Q(exp(Q) -1) b Sqrt[RΔh]]… Eq: 12; [4]
Where, Q = μLp/h
Using this equation certain conclusions can be drawn:
a) The rolling load increase with square root of the roll radius.
b) As the sheet entering the rolls become thinner the rolling load again increases.
c) If the deformation resistance of the sheet exceeds the roll pressure no further
reduction in sheet thickness is possible.
d) Frictional force is needed to pull the metal into the rolling arrangement and is a
major contributor towards the rolling load. High friction will result in high rolling
load and will increase the tendency for edge cracking.
3) Sticky friction situation- This situation occurs when the lubricant does not provide
enough reduction in friction and hence crazing occurs at the contact surface. The
rolling load for this situation is given:
P = pavbLp …………. Eq: 13; [4]
Where, p bar is the average pressure.
Rolling Defects/Problems and Remedies
There are various defects associated with rolling process as are associated with any metal
forming process. The defects can rise before rolling that is in the ingot stage of production or
after rolling. The defects from cast ingots generally are the defects other than cracks. They
could be due to the porosity, blow holes, cavities, etc. These are all related to the defects
related to solidification process of the cast ingot. Also longitudinal pieces of non-metallic
inclusions and pearlite banding in steels are related solidification defects. These pores and
cavities can be easily filled during rolling process. The major defects and the remedies are
discussed in the following section:
1) Flatness and Shape- There are two aspects of the problem with sheet shape these are
flatness and uniform thickness. The flatness is deviation of the sheet from the original
geometric dimensions. This is a consequence of difference in the relaxation times of
the various parts of the work piece before and after cold and hot rolling. This can also
be caused due to the non-uniform compression from the rolls.

24. Fig 28: Uniform thickness profile and flatness deflection defect. [4]
Remedies:
 These defects can be easily controlled by managing a uniform temperature
throughout the material after the rolling process, which can be done by using a
furnace treatment.
 Also using uniform radii rolls will prevent any deviation from the desired
geometry.
 The roll gap must be completely parallel to produce sheets of uniform on both
sides.
 Also the rolling speed is very critical in changing the dimensions, hence the
rolling speed should be kept same for each portion of the sheet.
 Un-cambered give variation in rolling thickness, so camber and crown can be
used to prevent deflection at a constant value of the force.
Fig 29: Difference between cambered (to compensate for change in rolling thickness)
and un-cambered rolls (cause variation in thickness). [7]
 Hydraulic jacks can be used to permit the roll deflection to prevent variation in
thickness.
 The best solution for maintaining the uniformity in shape is use a pair of side
rolls to set back the change in width.
2) Mill Spring- Mill spring is defect when the thickness of the rolling sheet is greater
than the required thickness. Elastic deformation of roll mill equipment or the rolls
lead to mill spring. Normally elastic constant for mills may range from 1 to 4 GNm-1.
Remedies:
 Use of a stiffer material for making rolls can solve this problem. Higher elastic
modulus rolls like tungsten carbide rolls can solve this problem.

25. 3) Profile variation- The profile consists of two important factors to consider, crown and
wedge. Crown is the thickness in the centre as compared to the average thickness at
the edges of the work piece. Wedge is the measure of thickness at one edge as
compared to another edge. Crown is sometimes desirable in the work piece for a
stable pass.
Fig 30: The crowing and wedging of the rolling sheet during the process. [4]
Remedies:
 Using a proper crown control system at the mill.
 The roll cross angles should be uniform and set at a predetermined value to get
required thickness.
4) Roll Deflection and Roll Flattening- Maintaining a uniform gap between the rolls
during the process is a challenge as the force involved are high in magnitude. The
high forces and the increased speed can lead to flattening of the roll or the deflection
of the rolls from the original axis of rotation. This can lead to variation in thickness
and all other defects.
Fig 31: Compensating methods for the roll deflection situation. [4]

26. Remedies:
 Using crowned rolls is one of the solution to the problem, the parabolic curvature of
the roll will be sufficient to cover only one set of the problem specifically the
material, temperature and the amount of deformation.
 Other modern methods of solving this problem is using CVC (Continual Varying
Crown), pair cross rolling, and work roll bending. CVC provides a way of introducing
a parabolic roll gap and the controlling the parameter dynamically to ensure uniform
thickness.
 Pair cross rolling involves shifting of the roll ends at an angle so that the variation in
edge thickness can be dynamically controlled.
 The work roll bending involves use of hydraulic cylinders for rolling and hence
compensate for the deflection.
5) Insufficient Camber and Consequences- Lack in the curvature of the rolls to prevent
variation in thickness can lead to various defects which are as follows:
Fig 32: The condition of insufficient camber. [7]
a) Residual Stresses- The thicker centre leads to compressive residual stress at
edges and tensile one at the centre.
b) Centre Line Cracking- The tensile stresses at the centre will lead to the rise and
fall of the sheet with respect to the centre.
c) Warping- Warping is any kind of deflection from the original state. This mainly
occurs at the centre of the sheets as the tensile forces are greater there due to
insufficient camber.
d) Edge Wrinkling- Also known as creep paper effect or wavy edge. This is a
consequence of high tensile stresses at the edges than at the centre.

27. Fig 33: Residual stress (a), Centre cracking (b), Warping (c), Edge Wrinkling (d).
[7]
6) Over Cambering- Over cambering is the condition when the rolls are given a larger
convex curvature than the desired. This causes the sheet to thinner at the centre than at
the edges. This is the reverse of the under cambered situation and hence the tensile
forces are more at the edges and the compressive forces are at the centre. The possible
defects produced due to this situation are as follows:
Fig 34: The condition of over cambering. [7]
a) Centre wrinkling- This is due to the high compressive forces at the centre which
leads to the condition of wrinkling at the centre because of excess compression.
Fig 35: A centre wrinkled sheet. [7]
b) Edge cracking- This is due to the high tensile forces acting along the edge
portion. This causes the material at the edges to yield before the actual yield point
and hence cause cracking as a result of failure.
Fig 36: Edge cracked sheet. [7]

28. c) Centre Splitting- This is a severe case of the edge cracking since the centre is
under a much higher compressive force so the resulting friction at the centre can
lead to splitting of the metal sheet from the centre.
Fig 37: The condition of centre splitting. [7]
7) Over Hanging and Alligatoring- The overhanging material is the region which does
not undergo rolling in the subsequent passes and as a result the edges come under
tensile condition and tend to crack. Alligatoring is a consequence of the higher lateral
speed than at the centre, this puts the central region compression cause a condition
similar to centre splitting. The elongation at the top and bottom surface is greater than
the central region due to friction at the roll interfaces and hence cause the Alligatoring
defect.
Fig 38: The overhanging and the Alligatoring defects in an aluminium sheet. [13]
8) Laminations- Laminations is the formation of layers within the rolling material. This
occurs if the ingot had porosity, blow holes or cavities. Non-metallic inclusion can
also lead to lamination during rolling.
9) Surface defects- The presence of surface defects during rolling are more prevalent
than other metal forming processes because of the high surface to volume ratio. Some
of the major surface defects and there remedies are as follows:

29. a) Laps- These appear in the form of seams across the surface and are due to the
folding of a corner or a film during rolling because of improper welding.
b) Mill shearing- This appears as feather like laps. Flakes appear in coarse grained
ingots which leads to decrease in ductility.
c) Scales- The oxide scales so formed during hot rolling of a particular metal can
result into penetration of the scales inside the surface due to the surface
deformation. Seams may also form due to the presence of the scales on the
surface.
d) Scabs- These are rolled in long patches of the loose metal. This may lead to the
scenario of surface lamination.
e) Sliver, scratches and cooling cracks- Slivers are the major surface ruptures. The
scratches may come into picture due to improper machining operations. Cooling
cracks along the edges are a result of non-uniformity in the cooling temperature.
Fig 39: Scabs (a), Slivers (b), Scales (c), Laps (d). [4]
Remedies:
 Roll displacement is the major cause of the laps. This can controlled by using back-up
rolls.
 Improper welding or loose welding conditions can lead to the inclusion metal pieces
along with rest of the sheet.
 Pickling is performed to remove the oxide scales from the surface.
 High pressure water jet cleaning of the surface of the metal can also help in
preventing metal inclusions.
 Uniform cooling after the rolling process can reduce the chances of residual stress
being developed and hence reduce the chances of cracking.

30. REFERENCES-
1) Dieter, G.E., Mechanical metallurgy, 1988, SI metric edition, McGraw-Hill, ISBN 0-
07-100406-8.
2) Edwards, L. and Endean, M., Manufacturing with materials, 1990, Butterworth
Heinemann, ISBN 0-7506-2754-9.
3) Beddoes, J. and Bibbly M.J., Principles of metal manufacturing process, 1999,
Arnold, ISBN 0-470-35241-8.
4) Suranaree University of Technology; 2007; Chapter 3 - Rolling of metals;
http://eng.sut.ac.th/metal/images/stories/pdf/03_Rolling%20of%20metals.pdf
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http://en.wikipedia.org/wiki/Rolling_%28metalworking%29
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Department of Production Engineering;
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Metallurgy.
8) NPTEL; 2015; Hot rolling and rolling defects – nptel;
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5.pdf
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http://thelibraryofmanufacturing.com/metal_rolling.html
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http://www.engr.mun.ca/~adfisher/3941/Ch13_Metal-Rolling.pdf
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processes/metal-forming-processes/rolling/