T l W T l Lif &T l W T l Lif & M hi biliM hi biliTool Wear, Tool Life & Tool Wear, Tool Life & MachinabilityMachinability

By  S K MondalBy  S K Mondal

Tool FailureTool failure is two types1. Slow‐death: The gradual or progressive wearingg p g gaway of rake face (crater wear) or flank (flank wear) ofthe cutting tool or both.g2. Sudden‐death: Failures leading to premature end of the tool The sudden‐death type of tool failure is difficult topredict. Tool failure mechanisms include plasticpredict. Tool failure mechanisms include plasticdeformation, brittle fracture, fatigue fracture or edgechipping. However it is difficult to predict which ofpp g pthese processes will dominate and when tool failurewill occur.

Tool Wear( ) Fl kW(a) FlankWear(b) CraterWear( )(c) Chipping off of the cutting edge

lTool Wear Flank Wear: (Wear land)ReasonAb i b h d i l d i l i i h kAbrasion by hard particles and inclusions in the workpiece.Shearing off the micro welds between tool and workmaterialmaterial.Abrasion by fragments of built‐up‐edge ploughing

i h l f f h lagainst the clearance face of the tool.At low speed flank wear predominates.p pIf MRR increased flank wear increased.

Flank Wear: (Wear land)EffectFl k di l ff h di iFlank wear directly affect the component dimensionsproduced.Flank wear is usually the most common determinant oftool lifetool life.

Flank Wear: (Wear land)StagesFl k W i h f iFlankWear occurs in three stages of varying wear rates

Flank Wear: (Wear land)PrimarywearTh i h h h i d i i klThe region where the sharp cutting edge is quicklybroken down and a finite wear land is established.

Secondary wearyThe region where the wear progresses at a uniform rate.

Flank Wear: (Wear land)Tertiary wearTh i h d llThe region where wear progresses at a graduallyincreasing rate.In the tertiary region the wear of the cutting tool hasbecome sensitive to increased tool temperature due tobecome sensitive to increased tool temperature due tohigh wear land.R i di i d d b f h hiRe‐grinding is recommended before they enter thisregion.

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Tool life criteria ISO(A  i   id h  f fl k   (VB) i   h      (A certain width of flank wear (VB) is the most common criterion)Uniform wear: 0.3 mm averaged over all pastLocalized wear: 0 5 mm on any individual pastLocalized wear: 0.5 mm on any individual past

Crater wearMore common in ductile materials which produce

hcontinuous chip.

C h k fCrater wear occurs on the rake face.

At hi h d t d i tAt very high speed crater wear predominates

For crater wear temperature is main culprit and toolFor crater wear temperature is main culprit and tool

defuse into the chip material & tool temperature isdefuse into the chip material & tool temperature is

maximum at some distance from the tool tip.

Crater wear         Contd…..Crater depth exhibits linear increase with time.It increases with MRRIt increases with MRR.

Crater wear has little or no influence on cutting forcesCrater wear has little or no influence on cutting forces,work piece tolerance or surface finish.

Wear Mechanism1. Abrasion wear

2. Adhesion wear

3 Diffusion wear3. Diffusion wear

4. Chemical or oxidation wear

Why chipping off or fine cracks d l d h ddeveloped at the cutting edge

Tool material is too brittle

Weak design of tool, such as high positive rake angle

As a result of crack that is already in the toolAs a result of crack that is already in the tool

E i i h k l di f h lExcessive static or shock loading of the tool.

Notch WearNotch wear on the trailing edge is to a great extent an

id ti h i i h th ttioxidation wear mechanism occurring where the cutting

edge leaves the machined workpiece material in the feededge leaves the machined workpiece material in the feed

direction.

But abrasion and adhesion wear in a combined effect can

contribute to the formation of one or several notches.

List the important properties of cutting tool t i l d l i h h i i t tmaterials and explain why each is important.

Hardness at high temperatures this provides longerHardness at high temperatures ‐ this provides longerlife of the cutting tool and allows higher cutting speeds.Toughness ‐ to provide the structural strength neededto resist impacts and cutting forcesto resist impacts and cutting forcesWear resistance ‐ to prolong usage before replacementdoesn’t chemically react ‐ another wear factorFormable/manufacturable can be manufactured in aFormable/manufacturable ‐ can be manufactured in auseful geometry

Tool Life CriteriaTool life criteria can be defined as a predeterminednumerical value of any type of tool deterioration whichnumerical value of any type of tool deterioration whichcan be measured.

Some of thewaysActual cutting time to failure.Volume of metal removedVolume of metal removed.Number of parts produced.p pCutting speed for a given timeLength of work machined.

Taylor’s Tool Life Equation based on Flank WearCausesCausesSliding of the tool along the machined surfaceTemperature rise

nVT CnVT C=Where, V = cutting speed (m/min)T   Time (min)T = Time (min)n = exponent depends on tool materialC = constant based on tool and work material and cutting condition.For IES, GATE, PSUs Page 3 of 49 Bhopal -2014

Values of Exponent ‘n’n = 0.08 to 0.2 for HSS tool= 0.1 to 0.15 for Cast Alloys

f bid l= 0.2 to 0.4 for carbide tool[IAS‐1999; IES‐2006][IAS 1999; IES 2006]

= 0.5 to 0.7 for ceramic tool5 7[NTPC‐2003]

Extended or Modified Taylor’s equation

i.e Cutting speed has the greater effect followed by feed g p g yand depth of cut respectively.

l fTool Life Curve

1. HSS    2. Carbide   3. Ceramic

Cutting speed used for different tool materials 

HSS (min) 30 m/min < Cast alloy < Carbide < Cemented carbide 150 m/min < Cermets < Ceramics or sintered oxide (max) 600 m/minm/min

Effect of Rake angle on tool life Effect of Clearance angle on tool lifeIf clearance angle increased it reduces flank wear butweaken the cutting edge so best compromise is 80 forweaken the cutting edge, so best compromise is 80 forHSS and 50 for carbide tool.

Effect of work piece on tool lifeWith hard micro‐constituents in the matrix gives poortool life.With larger grain size tool life is better.

Chip EquivalentEngaged cutting edgelengthChipEquivalent(q)

Planareaof cut=

I i d f lli h l

Planareaof cut

It is used for controlling the tool temperature.

• The SCEA alters the length of the engaged cutting

edge without affecting the area of cut. As a result, the

chip equivalent changed. When the SCEA is increased,

h h l d h f lthe chip equivalent is increased, without significantly

h i th tti fchanging the cutting forces.

I i di l i th l f th• Increase in nose radius also increases the value of the

chip equivalent and improve tool lifechip equivalent and improve tool life.

E i f t l ttiEconomics of metal cutting

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lFormula=n

o oV T COptimum tool life for minimumcost

⎛ ⎞⎛ ⎞1T T if T , & givento c c t m

m

C n C CC n

⎛ ⎞ −⎛ ⎞= +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

1 if & given

m

tt m

C n C CC

⎝ ⎠⎝ ⎠−⎛ ⎞= ⎜ ⎟

⎝ ⎠g

Optimum tool life for Maximum Productivity

t mmC n⎜ ⎟⎝ ⎠

p y(minimum production time)

1⎛ ⎞1T To cn

n−⎛ ⎞= ⎜ ⎟

⎝ ⎠

Units:Tc – min  (Tool changing time)c g gCt – Rs./ servicing or replacement (Tooling cost)cost)Cm – Rs/min (Machining cost)V – m/min (Cutting speed)

Tooling cost (Ct) = tool regrind cost + tool depreciation per service/ replacement

Machining cost (C )   labour cost + over head cost per Machining cost (Cm) = labour cost + over head cost per min

Minimum Cost Vs Production Rate

V V Vmax.production max.profit min. costV >V >V

Machinability‐DefinitionM hi bili b i l d fi d ‘ bili fMachinability can be tentatively defined as ‘ability ofbeing machined’ and more reasonably as ‘ease ofmachining’.

h f h h hSuch ease of machining or machining charactersof any tool‐work pair is to be judged by:y p j g y

Tool wear or tool lifeMagnitude of the cutting forcesSurface finishSurface finishMagnitude of cutting temperatureg g pChip forms.

Machinability‐‐‐‐‐‐‐‐‐‐‐‐‐Contd…….M hi bilit ill b hi h h tti fMachinability will be high when cutting forces,temperature, surfaces roughness and tool wear are less,t l lif i l d hi id ll if d h ttool life is long and chips are ideally uniform and short.

The addition of sulphur lead and tellurium to non‐The addition of sulphur, lead and tellurium to non‐ferrous and steel improves machinability.S l h i dd d t t l l if th i ffi i tSulphur is added to steel only if there is sufficientmanganese in it. Sulphur forms manganese sulphidehi h i t i l t d h d t i t lwhich exists as an isolated phase and act as internal

lubrication and chip breaker.If insufficient manganese is there a low melting ironsulphide will formed around the austenite grainboundary. Such steel is very weak and brittle.

Free Cutting steelsAddition of lead in low carbon re‐sulphurised steels andalso in aluminium copper and their alloys help reducealso in aluminium, copper and their alloys help reducetheir τs. The dispersed lead particles act as discontinuityand solid lubricants and thus improve machinability byand solid lubricants and thus improve machinability byreducing friction, cutting forces and temperature, tool

d BUE f iwear and BUE formation.It contains less than 0.35% lead by weight .35 y gA free cutting steel containsC % Si % M % P % S % Pb %C‐0.07%, Si‐0.03%, Mn‐0.9%, P‐0.04%, S‐0.22%, Pb‐0.15%

Machinability Index Or    Machinability Rating

The machinability index KM is defined byKM = V6 /V6 RKM = V60/V60R

Where V60 is the cutting speed for the target materialh l lif f 6 i V i h f hthat ensures tool life of 60 min, V60R is the same for thereference material.If KM > 1, the machinability of the target material isbetter that this of the reference material and vice versabetter that this of the reference material, and vice versa

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Role of microstructure on MachinabilityC   i  l d    l   l   f Coarse microstructure leads to lesser value of τs.

Therefore, τs can be desirably reduced byP  h    lik   li   f  lProper heat treatment like annealing of steelsControlled addition of materials like sulphur (S), lead p ( ),(Pb), Tellerium etc leading to free cutting of soft ductile metals and alloysmetals and alloys.

Brittle materials are relatively more machinable.

ff f l k l ( )Effects of tool rake angle(s) onmachinabilitymachinability

As Rake angle increases machinability increases.

But too much increase in rake weakens the cutting edge.

Effects of Cutting Edge angle(s) on machinabilitymachinability

Th i ti i th tti d l d t ff tThe variation in the cutting edge angles does not affect

cutting force or specific energy requirement for cuttingcutting force or specific energy requirement for cutting.

Increase in SCEA and reduction in ECEA improvesIncrease in SCEA and reduction in ECEA improves

surface finish sizeably in continuous chip formation

hence Machinability.

Effects of  clearance angle on machinability

Inadequate clearance angle reduces tool life and surfacefinish by tool – work rubbing, and again too largeclearance reduces the tool strength and tool life hencegmachinability.

Effects of Nose Radius on machinabilityProper tool nose radiusing improves machinability tosome extent throughsome extent throughincrease in tool life by increasing mechanical strength

d d i h l iand reducing temperature at the tool tipreduction of surface roughness, hmaxg , max

2fmax 8

fhR

=max 8R

Surface RoughnessIdeal Surface ( Zero nose radius)

fPeak to valley roughness (h) =tan cot

fSCEA ECEA+

and (Ra) = ( )4 4h f

SCEA ECEA=a

Practical Surface ( with nose radius = R)( )4 4 tan cotSCEA ECEA+

2 2

ah and R8 18 3f fR R

= =a8 18 3R RChange in feed (f) is more important than a change in nose radiusg ( ) p g(R) and depth of cut has no effect on surface roughness.

Cutting fluidCutting fluidThe cutting fluid acts primarily as a coolant and

dl l b i t d i th f i ti ff t tsecondly as a lubricant, reducing the friction effects atthe tool‐chip interface and the work‐blank regions.Cast Iron: Machined dry or compressed air, Soluble oilfor high speed machining and grindingfor high speed machining and grindingBrass: Machined dry or straight mineral oil with ori h EPAwithout EPA.

Aluminium: Machined dry or kerosene oil mixed withymineral oil or soluble oilStainless steel and Heat resistant alloy: HighStainless steel and Heat resistant alloy: Highperformance soluble oil or neat oil with high

i i h hl i d EP ddi iconcentration with chlorinated EP additive.

IAS 2009 MainIAS ‐2009 MainWhat are extreme‐pressure lubricants?What are extreme pressure lubricants?

[ 3 – marks]Wh hi h d bbi iWhere high pressures and rubbing action areencountered, hydrodynamic lubrication cannot be

i i d E P (EP) ddi i bmaintained; so Extreme Pressure (EP) additives must beadded to the lubricant. EP lubrication is provided by a

b f h i l h bnumber of chemical components such as boron,phosphorus, sulfur, chlorine, or combination of these.Th d i d b h hi hThe compounds are activated by the higher temperatureresulting from extreme pressure. As the temperaturei EP l l b i d lrises, EP molecules become reactive and releasederivatives such as iron chloride or iron sulfide andf lid i iforms a solid protective coating.

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Metal FormingMetal FormingSh t M t l O tiSheet Metal OperationP d  M llPowder Metallurgy

By  S K MondalBy  S K Mondal

Four Important forming techniques are:Rolling 

Forgingg g

ExtrusionExtrusion

D iDrawing

TerminologyTerminologySemi‐finished productI i h fi lid f f lIngot: is the first solid form of steel.Bloom: is the product of first breakdown of ingot has squarep g qcross section 6 x 6 in. or largerBillet: is hot rolled from a bloom and is square 1 5 in on aBillet: is hot rolled from a bloom and is square, 1.5 in. on aside or larger.Sl b i th h t ll d i t bl t lSlab: is the hot rolled ingot or bloom rectangular crosssection 10 in. or more wide and 1.5 in. or more thick.

slabIngot Bloom Billet

TerminologyMill product

Plate is the product with thickness > 5 mm

Sheet is the product with thickness < 5 mm and width > 600

mmmm

Strip is the product with a thickness < 5 mm and width <Strip is the product with a thickness < 5 mm and width <

600 mm

Plastic DeformationDeformation beyond elastic limits.

Due to slip, grain fragmentation, movement of atoms p, g g ,

and lattice distortion.and lattice distortion.

Recrystallisation Temperature (Rx)“Th i i hi h h l d“The minimum temperature at which the completedrecrystallisation of a cold worked metal occurs within aspecified period of approximately one hour”.Rx decreases strength and increases ductilityRx decreases strength and increases ductility.If working above Rx, hot‐working process whereas

ki b l ld kiworking below are cold‐working process.It involves replacement of cold‐worked structure by at vo ves ep ace e t o co d o ed st uctu e by anew set of strain‐free, approximately equi‐axed grains toreplace all the deformed crystals Contdreplace all the deformed crystals. Contd.

Rx depends on the amount of cold work a material has

already received. The higher the cold work, the lower

ld b hwould be the Rx.

Rx varies between 1/3 to ½ melting paintRx varies between 1/3 to ½ melting paint.

Rx = 0 4 xMelting temp (Kelvin)Rx = 0.4 x Melting temp. (Kelvin).

Rx of lead and Tin is below room temp.p

Rx of Cadmium and Zinc is room temp.

Rx of Iron is 450oC and for steels around 1000°C

Finer is the initial grain size; lower will be the RxContd.

hGrain growthGrain growth follows complete crystallization if the materials left at elevated temperatures.p

Grain growth does not need to be preceded by recovery and ll ll l ll lrecrystallization; it may occur in all polycrystalline materials.

In contrary to recovery and recrystallization, driving force  In contrary to recovery and recrystallization, driving force  for this process is reduction in grain boundary energy.

In practical applications, grain growth is not desirable.

Incorporation of impurity atoms and insoluble second phase Incorporation of impurity atoms and insoluble second phase particles are effective in retarding grain growth.

Grain growth is very strongly dependent on temperature.

Strain HardeningStrain HardeningWhen metal is formed in cold state there is noWhen metal is formed in cold state, there is no

recrystalization of grains and thus recovery fromy g y

grain distortion or fragmentation does not take

place.

As grain deformation proceeds, greater resistance

t thi ti lt i i d h d dto this action results in increased hardness and

strength i.e. strain hardening.strength i.e. strain hardening.

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St i H d iStrain HardeningStrain hardening (cold Working)Strain hardening (cold Working)

no Kσ ε=

Strain rate effect (hot Working)

o

( g)

mo Cσ ε=o

VelocityPlaten1 vdhWhere heightousInstantane

VelocityPlaten1===

hv

dtdh

hε

ll b lMalleabilityMalleability is the property of a material whereby it can

b h d h ld b h llbe shaped when cold by hammering or rolling.

A ll bl i l i bl f d i l iA malleable material is capable of undergoing plastic

deformation without fracturedeformation without fracture.

A malleable material should be plastic but it is notA malleable material should be plastic but it is not

essential to be so strong.g

Lead, soft steel, wrought iron, copper and aluminium are

some materials in order of diminishing malleability.

Cold WorkingCold WorkinggW ki  b l   li i  Working below recrystalization temp.

d f ld kAdvantages of Cold Working1. Better accuracy, closer tolerances

2. Better surface finish

3. Strain hardening increases strength and hardness

4. Grain flow during deformation can cause desirable

directional properties in productdirectional properties in product

5 No heating of work required (less total energy)5. No heating of work required (less total energy)

d f ld kDisadvantages of Cold Working1. Equipment of higher forces and power required

S f   f  t ti   k  i   t b  f   f  l   d 2. Surfaces of starting work piece must be free of scale and 

dirt

3. Ductility and strain hardening limit the amount of forming 

that can be done

4. In some operations, metal must be annealed to allow 

further deformationfurther deformation

5. Some metals are simply not ductile enough to be cold 5 p y g

worked.

Hot WorkingHot Working

Working above recrystalization tempWorking above recrystalization temp.

Advantages of Hot Working1. The porosity of the metal is largely eliminated.2 The grain structure of the metal is refined2. The grain structure of the metal is refined.3. The impurities like slag are squeezed into fibers anddi ib d h h h ldistributed throughout the metal.4. The mechanical properties such as toughness,4 p p g ,percentage elongation, percentage reduction in area, andresistance to shock and vibration are improved due toresistance to shock and vibration are improved due tothe refinement of grains.

Dis‐advantages of Hot Working1. It requires expensive tools.2 It produces poor surface finish due to the rapid2. It produces poor surface finish, due to the rapidoxidation and scale formation on the metal surface.

D h f fi i h l l3. Due to the poor surface finish, close tolerancecannot be maintained.

Mi St t l Ch i H tMicro‐Structural Changes in a Hot Working Process (Rolling)Working Process (Rolling)

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Annealing•Annealing relieves the stresses from cold working – threestages: recovery recrystallization and grain growth

g

stages: recovery, recrystallization and grain growth.•During recovery, physical properties of the cold‐worked

i l d i h b bl h imaterial are restored without any observable change inmicrostructure.

Warm FormingDeformation produced at temperatures intermediate to

h d ld f k fhot and cold forming is known as warm forming.

C d ld f i i d l d iCompared to cold forming, it reduces loads, increase

material ductilitymaterial ductility.

Compared to hot forming it produce less scaling andCompared to hot forming, it produce less scaling and

decarburization, better dimensional precision andp

smoother surfaces.

h lIsothermal FormingDuring hot forming, cooler surfaces surround a hotter

interior and the variations in strength can result in noninterior, and the variations in strength can result in non‐

uniform deformation and cracking of the surface.

For temp.‐sensitive materials deformation is performed

under isothermal conditions.

Th di li b h d h k iThe dies or tooling must be heated to the workpiece

temperature, sacrificing die life for product quality.p , g p q y

Close tolerances, low residual stresses and uniform metal

flow.

RollingRollingg

By  S K MondalBy  S K Mondal

RollingDefinition: The process of plastically deforming metal

b b llby passing it between rolls.

M id l d hi h d i d l lMost widely used, high production and close tolerance.

F i ti b t th ll d th t l fFriction between the rolls and the metal surface

produces high compressive stressproduces high compressive stress.

Hot‐working (unless mentioned cold rolling.Hot working (unless mentioned cold rolling.

Metal will undergo bi‐axial compression.g p

Hot RollingDone above the recrystallization temp.

Results fine grained structure.

S f lit d fi l di i l tSurface quality and final dimensions are less accurate.

Breakdown of ingots into blooms and billets is done byBreakdown of ingots into blooms and billets is done by

hot‐rolling. This is followed by further hot‐rolling intog y g

plate, sheet, rod, bar, pipe, rail.

Hot rolling is terminated when the temp. falls to about

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Cold RollingDone below the recrystallization temp..

Products are sheet, strip, foil etc. with good surface

fi i h d i d h i l h i h lfinish and increased mechanical strength with close

product dimensionsproduct dimensions.

Performed on four‐high or cluster‐type rolling millsPerformed on four high or cluster type rolling mills.

(Due to high force and power)( g p )

Ring RollingRing rolls are used for tube rolling, ring rolling.

As the rolls squeeze and rotate, the wall thickness is

d d d h di f h i ireduced and the diameter of the ring increases.

Sh d ll b d t d id i t fShaped rolls can be used to produce a wide variety of

cross‐section profilescross section profiles.

Ring rolls are made of spheroidized graphite bainitic andRing rolls are made of spheroidized graphite bainitic and

pearlitic matrix or alloy cast steel base.

Sheet rollingIn sheet rolling we are only attempting to reduce the

h k f lcross section thickness of a material.

Roll Forming Roll BendingA continuous form of three‐point bending is roll

bending, where plates, sheets, and rolled shapes can

be bent to a desired curvature on forming rolls.

Upper roll being adjustable to control the degree of

tcurvature.

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Shape rolling Pack rollingPack rolling involves hot rolling multiple sheets of

l h l f lmaterial at once, such as aluminium foil.

A hi f id fil h i ldiA thin surface oxide film prevents their welding.

Thread rollingUsed to produce threads in substantial quantities.

This is a cold‐forming process in which the threads are

f d b lli h d bl k b h d d diformed by rolling a thread blank between hardened dies

that cause the metal to flow radially into the desiredthat cause the metal to flow radially into the desired

shape.p

No metal is removed, greater strength, smoother, harder,g g

and more wear‐resistant surface than cut threads.

Thread rolling                    contd….Major diameter is always greater than the diameter of the

bl k (blank (

Bl k di i li l l h h i h di fBlank diameter is little larger than the pitch diameter of

the threadthe thread.

Restricted to ductile materialsRestricted to ductile materials.

Manufacture of gears by rollingThe straight and helical teeth of disc or rod type external

l f ll d d d d lsteel gears of small to medium diameter and module are

generated by cold rollinggenerated by cold rolling.

High accuracy and surface integrityHigh accuracy and surface integrity.

Employed for high productivity and high quality (costlyEmployed for high productivity and high quality. (costly

machine))

Larger size gears are formed by hot rolling and then

finished by machining.

Fig. Production of teeth of spur gears by rolling

llRoll piercing It is a variation of rolling called roll piercing.The billet or round stock is rolled between two rolls,,both of them rotating in the same direction with theiraxes at an angle of 4.5 to 6.5 degree.axes at an angle of 4.5 to 6.5 degree.These rolls have a central cylindrical portion with thesides tapering slightly There are two small side rollssides tapering slightly. There are two small side rolls,which help in guiding the metal.Because of the angle at which the roll meets the metal,it gets in addition to a rotary motion, an additionalaxial advance, which brings the metal into the rolls.This cross‐rolling action makes the metal friable at thegcentre which is then easily pierced and given acylindrical shape by the central‐piercing mandrel.cylindrical shape by the central piercing mandrel.

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Planetary millConsist of a pair of heavy backing rolls surrounded by a largeConsist of a pair of heavy backing rolls surrounded by a largenumber of planetary rolls.Each planetary roll gives an almost constant reduction to theEach planetary roll gives an almost constant reduction to theslab as it sweeps out a circular path between the backing rollsand the slab.As each pair of planetary rolls ceases to have contact with thework piece, another pair of rolls makes contact and repeath d ithat reduction.The overall reduction is the summation of a series of smalld ti b h i f ll Th f th l t illreductions by each pair of rolls. Therefore, the planetary mill

can reduce a slab directly to strip in one pass through themillmill.The operation requires feed rolls to introduce the slab intothe mill, and a pair of planishing rolls on the exit to improvethe mill, and a pair of planishing rolls on the exit to improvethe surface finish.

Camber

Camber can be used to correct the roll deflection (at onlyone value of the roll force).

Lubrication for RollingHot rolling of ferrous metals is done without a lubricant.

Hot rolling of non‐ferrous metals a wide variety of

d d il l i d f id dcompounded oils, emulsions and fatty acids are used.

C ld lli l b i t t l bl il lCold rolling lubricants are water‐soluble oils, low‐

viscosity lubricants such as mineral oils emulsionsviscosity lubricants, such as mineral oils, emulsions,

paraffin and fatty acids.p y

Defects in Rollingf hDefects What is Cause

Surface Scale, rust, Inclusions andSurfaceDefects

Scale, rust,scratches, pits,cracks

Inclusions andimpurities in thematerialscracks materials

Wavy edges Strip is thinner Due to roll bendingalong its edgesthan at its centre.

edges elongates moreand buckle.

Alligatoring Edge breaks Non‐uniformdeformationdeformation

Geometry of Rolling Process DraftT l  d i    “d f ”  k  i   lliTotal reduction or “draft” taken in rolling.

h h h 2 (R R ) D (1 )Δ 0 fh = h - h = 2 (R - R cos ) = D (1 - cos )Δ α α

Usually, the reduction in blooming mills is about 100 y, gmm and in slabbing mills, about 50 to 60 mm.

Maximum Draft PossibleMaximum Draft Possible

( ) 2hΔ R( ) 2maxhΔ = Rμ

Torque and PowerTh i i i ll i fThe power is spent principally in four ways1) The energy needed to deform the metal.) gy2) The energy needed to overcome the frictional force.) Th l i h i i d i i3) The power lost in the pinions and power‐transmissionsystem.4) Electrical losses in the various motors and generators.

Remarks: Losses in the windup reel and uncoiler mustpalso be considered.

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Torque and Power

Will bWill bediscusseddiscussedin class

[For IES Conventional Only][For IES Conventional Only]

Assumptions in RollingR ll i h i id li d1. Rolls are straight, rigid cylinders.

2. Strip is wide compared with its thickness, so that nop p ,widening of strip occurs (plane strain conditions).

3 The arc of contact is circular with a radius greater than3. The arc of contact is circular with a radius greater thanthe radius of the roll.

4. The material is rigid perfectly plastic (constant yieldstrength).st e gt ).

5. The co‐efficient of friction is constant over the tool‐k i t fwork interface.

Stress Equilibrium of an Element in Rolling

Considering the thickness of the element perpendicular tothe plane of paper to be unity We get equilibriumthe plane of paper to be unity, We get equilibriumequation in x‐direction as,- σ h + (σ +dσ ) (h + dh) - 2pR dθ sin θ x x x

x+ 2 τ R dθ cos θ = 0

xFor sliding friction, τ = μp Simplifying and neglecting d d t i d 1 tθ θ θ≅

( )second order terms, sin and cos 1, we get

xd hθ θ θ

σ≅ =

( ) 2 ( )x pRd

θ μθ

= ∓

'0 0

23xp σ σ σ− = =

( ) ( )'0

3

2d h p pRσ θ μ⎡ ⎤− =⎣ ⎦ ∓( ) ( )0 2h p pRdd p

σ θ μθ⎡ ⎤⎣ ⎦

⎡ ⎤⎛ ⎞

∓

( )'0 '

0

1 2d ph pRd

σ θ μθ σ⎡ ⎤⎛ ⎞

− =⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦

∓0

' d p phσ

⎝ ⎠⎣ ⎦⎛ ⎞

+ −⎜ ⎟ ( ) ( )'1 2d h pRσ θ μ⎛ ⎞

=⎜ ⎟ ∓0 ' '0 0

hd

σθ σ σ

+ −⎜ ⎟⎝ ⎠

( ) ( )01 2h pRd

σ θ μθ

=⎜ ⎟⎝ ⎠

∓

'0

'

Due to cold rolling, increases as h decreases,σ'0thus nearly a constant and itsderivative zero. h

dσ

( )( )

'0/ 2

d p Rdσ

θ θ μ= ∓( )

( )

'0

2

/p hθ μ

σ= ∓

( )( )

2

'

2 1 cos

/f fh h R h R

d

θ θ= + − ≈ +

( )( ) ( )0

2'

/ 2/

d p R dh Rp

σθ μ θ

θσ=

+∓

( )0/

Integrating both sidefh Rp θσ +

( )'

Integrating both side2ln / R dp θ θσ 2 ( )R d I II sayμ θ∫ ∫∓ ∓( )0ln /f

ph

σ =+ 2 2 ( )

f

d I II sayR h R

μ θθ θ

=+∫ ∫∓ ∓

22Rθdθ 2Rθdθ 2θdθ hI ln

h h / R Rh Rθ⎛ ⎞= = = = ⎜ ⎟+ ⎝ ⎠∫ ∫ ∫

f

2f

h h / R Rh RθhNow h / R θ

+ ⎝ ⎠

= +Now h / R θR

d h θ

= +

⎛ ⎞d hor 2θdθ R

R

⎛ ⎞ =⎜ ⎟⎝ ⎠

2f

2RμII dθh Rθ

=+∫

f

22μ dθ

h / R θ= ∫ 2

f

1

h / R θR R

+

⎛ ⎞⎜ ⎟

∫

1

f f

R R2μ .tan .θh h

−⎛ ⎞

= ⎜ ⎟⎜ ⎟⎝ ⎠

( ) − ⎛ ⎞⎛ ⎞∴ = +⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

' 10

h R Rln p / σ ln 2μ .tan .θ lnCR h h

∓( ) ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎛ ⎞⎜ ⎟

f f

' μH

R h hhC ∓⎛ ⎞∴ = ⎜ ⎟

⎝ ⎠⎛ ⎞

μH0p Cσ e

R∓

− ⎛ ⎞= ⎜ ⎟⎜ ⎟

⎝ ⎠

1

f f

R Rwhere H 2 .tan .θh h⎝ ⎠=

f fh hNow at entry ,θ α

= ∝

=0Hence H H with θ replaced by in above equation

At exit θ 0=

= '0

At exit θ 0Therefor p σ

−⎛ ⎞= ⎜ ⎟

⎝ ⎠oμH' o

0hIn theentryzone, p C.σ eR⎜ ⎟

⎝ ⎠0y , p

RR

= oμH

o

Rand C .eh

( )−= 0

o

μ H H'0

hp σ . e00

p σ . eh

I th it⎛ ⎞

In the exit zoneh⎛ ⎞

= ⎜ ⎟⎝ ⎠

' μH0

f

hp σ .eh⎝ ⎠f

At theneutral po int aboveequationswill givesameresults

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