THEORY OF METAL THEORY OF METAL CUTTINGCUTTING

PRODUCTION ENGINEERINGPRODUCTION ENGINEERING

Metal cuttingMetal cutting• It is the process of producing work piece by removing It is the process of producing work piece by removing

unwanted material from a block of metal, in the form of chips.unwanted material from a block of metal, in the form of chips.

SINGLE POINT CUTTING TOOL

Shank. It is main body of toolFlank. The surface below & adjacent to cutting edge is called flank of the tool.Face. The surface on which the chip slides is called is called face of the tool.Heel. It is the intersection of flank & base of the tool.Nose. It is the point where the side cutting edge & the end cutting edge intersect.Cutting edge. It is the edge on the face of tool which removes material from work piece.

Types of surfacesTypes of surfacesThree types of surfacesThree types of surfaces::1.The work surface1.The work surface

2.The machined surface2.The machined surface

3.Cuttting surface3.Cuttting surface

Designation of cutting ToolsDesignation of cutting Tools It means the designation of the shape of the part of cutting tool. Two system to It means the designation of the shape of the part of cutting tool. Two system to

designate the tool shape are:designate the tool shape are: 1.American Standards Association System (ASA)1.American Standards Association System (ASA) 2.Orthogonal rake system (ORS)2.Orthogonal rake system (ORS)

1. 1. ASA SYSTEMASA SYSTEM: : In this In this system, angles of the tool system, angles of the tool face, are defined in two face, are defined in two orthogonal planes, one orthogonal planes, one parallel to & the other parallel to & the other perpendicular to, axis of the perpendicular to, axis of the cutting tool, both planes cutting tool, both planes being perpendicular to the being perpendicular to the base of the tool.base of the tool.

Various tool anglesVarious tool anglesSide cutting edge angle (SCEA) Cs, also known as lead angle, is angle between the side cutting edge & the side of the tool shank.The complementary angle of SCEA is called “Approach angle”.End cutting edge angle (ECEA)It is the angle between the end cutting edge & a line normal to the tool shank.Side relief angle (SRA)It is angle between the portion of the side flank immediately below the side cutting edge & a line perpendicular to the base of the tool.

Cont…..Cont…..End relief angle( ERA) It is the angle between the portion of the end flank immediately below the end cutting edge & a line perpendicular to the base of the tool & measured at right angle to the end flank.Back rake angle (BR)αb It is the angle between the face of the tool & a line parallel to the base of the tool & measured in a plane through the side cutting edge. This angle gives the slope of the face of the tool from the nose towards the shank.Side rake angle (SR) αs it is the angle between the tool face & a line parallel to the base of the tool & measured in a plane perpendicular to base & the side cutting edge. This angle gives the slope of the face of the tool from the cutting edge

Nose radius it is favorable to long tool life & good surface finish. The use of following values for nose radius is recommended: R=0.4 mm, for delicate components > 1.5mm for heavy depth of cut =0.4 to 1.2 mm for disposable carbide inserts =1.2 to 1.6 mm for heavy duty inserts

Tool Designation it is given in the order given as BRA, SRA, ERA,SRA, ECEA, SCEA, Nose radius that is αb –αs –θe –θs –Ce -Cs -R

Orthogonal rake system (ORS)Orthogonal rake system (ORS)In this system the planes for designating tools are the planesContaining the principal or side cutting edge & the plane normal to it. Plane NN is known as orthogonal plane. we have following angles:Side relief angle γ,side rake angle α,wedge & cutting angle

Tool designation under ORSBack rake, side rake, side relief, end relief, end cutting edge angle, approach angle, nose radius i- α- γ- γ1-Ce-λ-R

Methods of machiningMethods of machiningTwo methods of metal cutting,1.Orthogonal cutting or 2D cutting2.Oblique cutting or 3D cutting

Types of chips

Determination of shear angleDetermination of shear angleThe cutting tool is completely defined by rake angle The cutting tool is completely defined by rake angle αα & the & the

clearance angle clearance angle γγ & following assumptions are made & following assumptions are made1.The tool is perfectly sharp.1.The tool is perfectly sharp.2.The primary deformation takes place in a very thin zone 2.The primary deformation takes place in a very thin zone

adjacent to the shear plane AB,adjacent to the shear plane AB,3.There is no side flow of the chip.3.There is no side flow of the chip.Shear angle Ø, is defined as angle made by the shear Shear angle Ø, is defined as angle made by the shear

plane, with the direction of tool travel.plane, with the direction of tool travel. t= uncut chip thicknesst= uncut chip thickness tc= chip thickness after metal is cut tc= chip thickness after metal is cut r=t/tc is called the cutting ratior=t/tc is called the cutting ratio ç =1/r is called the chip reduction factorç =1/r is called the chip reduction factor

ContCont……The shear angle can be determined by following ways:The shear angle can be determined by following ways:(a)(a) tantanØ =rcosØ =rcosαα/1-r sin/1-r sinαα

(b)(b) If length of cut is l & length of chip is lc, thenIf length of cut is l & length of chip is lc, then r=lc/l =t/tcr=lc/l =t/tc after putting r in above equation, we can get Ø.after putting r in above equation, we can get Ø.(c) If length of cut is not known, then by weighing a known (c) If length of cut is not known, then by weighing a known

length of chip.length of chip. Wc=plbt ,therefore l=Wc/pbtWc=plbt ,therefore l=Wc/pbt(d) If chip & work piece velocities Vc & V are known(d) If chip & work piece velocities Vc & V are known r=t/tc=Vc/Vr=t/tc=Vc/V

Cont…Cont…The shearing process in metal cutting can be represented The shearing process in metal cutting can be represented

by a simple modelby a simple model shear strain can be given as shear strain can be given as

s=distance sheared/thickness of zones=distance sheared/thickness of zone

=AB/OC=AB/OC

=Cot =Cot Ø+ tan(Ø-Ø+ tan(Ø-αα))

VelocitiesVelocities Three kinds of velocities are involved in metal cutting :Three kinds of velocities are involved in metal cutting :1.The velocity of tool relative to work piece, V is called 1.The velocity of tool relative to work piece, V is called

cutting speedcutting speed2.The velocity of the chip relative to the work, Vs is called 2.The velocity of the chip relative to the work, Vs is called

shear velocity.shear velocity.3.The velocity of the chip up the face of tool, Vc is called 3.The velocity of the chip up the face of tool, Vc is called

chip velocity.chip velocity. r= Vc/v=t/tcr= Vc/v=t/tc From the figureFrom the figureVs/V=CosVs/V=Cosαα/cos(Ø-/cos(Ø-αα))Vc/V=sinØ/cos(Ø-Vc/V=sinØ/cos(Ø-αα)) s=Vs/tss=Vs/ts max. value of ts =.025mmmax. value of ts =.025mm

Determination of under formed chip thicknessDetermination of under formed chip thicknessFrom the figureFrom the figure t=fsint=fsinλλ & b=d/sin & b=d/sinλλ for drilling operation, tool hasfor drilling operation, tool has 2 cutting edges, thus2 cutting edges, thus t=f/2*sint=f/2*sinλλ

In fig (c) where In fig (c) where λλ=90deg.=90deg. & Ce is not 0& Ce is not 0 t=f & b=dt=f & b=d& width of cut=depth of cut& width of cut=depth of cutSuch a case is calledSuch a case is called““Restricted Orthogonal cutting”Restricted Orthogonal cutting”

Force relationsForce relationsWhen a cut is made, the forces acting on the chip are:When a cut is made, the forces acting on the chip are:1.Force Fs, which is resistance to the shear of the metal 1.Force Fs, which is resistance to the shear of the metal

forming the chip. it acts along the shear plane.forming the chip. it acts along the shear plane.2.Force Fn normal to the shear plane.2.Force Fn normal to the shear plane.3.Force N at the tool chip interface acting normal to the 3.Force N at the tool chip interface acting normal to the

cutting face of the tool& is provided by the tool.cutting face of the tool& is provided by the tool.4.Force F is the frictional resistance of the tool acting on 4.Force F is the frictional resistance of the tool acting on

the chip. It acts downward against the motion of the chip the chip. It acts downward against the motion of the chip as it glides upward along the tool face.as it glides upward along the tool face.

It is easily shown that It is easily shown that

F=Fc sinF=Fc sinαα+Ft cos+Ft cosαα N=Fc cosN=Fc cosαα-Ft sin-Ft sinαα

Cont…Cont…ζζs=s=Fcsec(Fcsec(ββ--αα).cos(Ø+).cos(Ø+ββ--

αα).sinØ).sinØ btbtMax. shear stressMax. shear stress,,

δ δ ζζs s = 0= 0δδØØTherefore Ø=45deg.+Therefore Ø=45deg.+αα/2-/2-ββ/2/2For practical purposes Ø has been For practical purposes Ø has been

suggestedsuggested

Ø=Ø=αα, for , for αα>15 deg>15 deg Ø=15 deg. for Ø=15 deg. for αα <15 deg. <15 deg.

Theory of lee & ShafferTheory of lee & Shaffer They applied the theory of plasticity for an ideal rigid plastic They applied the theory of plasticity for an ideal rigid plastic

material,for analyzing the problem of orthogonal meta cutting.material,for analyzing the problem of orthogonal meta cutting. Ø=Ø=ΠΠ/4-(/4-(ββ--αα))

Cutting powerIt is the product of cutting speed, V, & the cutting force Fc E=Fc*VPower assumed in cutting ,Pc=Fc*V kw 60*102 V=ΠDN/60*1000 m/s Fc=C dxf yV n The values for constants areC=300, x=1,y=.75, n=-0.15

A) hot rolled 0.2% C-steelA) hot rolled 0.2% C-steel Fc=162.4f Fc=162.4f 0.850.85 d d 0.980.98kgfkgf b) 18 -8 stainless steelb) 18 -8 stainless steel Fc=196.7 f Fc=196.7 f .85.85 d d .96.96 kgf kgfc) Yellow brass c) Yellow brass Fc=123.6 f Fc=123.6 f 0.810.81 d d .96.96 kgf kgf constant C is given asconstant C is given as =60.2 for BHN 126=60.2 for BHN 126 =111.6 for BHN 181 =111.6 for BHN 181 =131.1 for BHN 241=131.1 for BHN 241 d & f are in mm.d & f are in mm.

Power needed to make particular cut:Power needed to make particular cut: power=dfVC, wattspower=dfVC, watts

For negative rake cutting, increase value of C by 50%.For negative rake cutting, increase value of C by 50%.

Metal removal ratesMetal removal rates it is expressed as mm3/min.it is expressed as mm3/min. for a single point tool, MMRfor a single point tool, MMR = Ac V= Ac VWhere Where Ac =cross sectional area of uncut chipAc =cross sectional area of uncut chip == b* t b* t

Energy consideration in metal cuttingEnergy consideration in metal cuttingTotal energy consists of two main parts:Total energy consists of two main parts: shear energy, Esshear energy, Es friction energy, Effriction energy, Ef E=Es+EfE=Es+EfThe energy per unit time divided by volume removed The energy per unit time divided by volume removed Per unit time, is known as specific energy.Per unit time, is known as specific energy. Total specific energy, e=E/btV=Fc/bt N/mmTotal specific energy, e=E/btV=Fc/bt N/mm22 Specific shear energy, eSpecific shear energy, e s s=Es/btV=FsVs/btV=Es/btV=FsVs/btV

Specific friction energy, eSpecific friction energy, eff=Ef/btV =FVc/btV=Ef/btV =FVc/btV

Now Vs/V=CosNow Vs/V=Cosαα/Cos(Ø-/Cos(Ø-αα)) Vc/V=t/tc=rVc/V=t/tc=r put values of Vs/V & Vc/V in e value & get the result.put values of Vs/V & Vc/V in e value & get the result.

Oblique cutting Oblique cutting nncc is chip flow angle is chip flow angle

ααnn=normal rake angle=normal rake angle

ααee=effective rake angle=effective rake angle

i=0, i=0, ααnn will be equal to will be equal to αα

From the geometryFrom the geometrysin sin ααee=sin=sin22i+cosi+cos22isin isin ααnn

Tool wear & tool lifeTool wear & tool lifeTool wear may be classified asTool wear may be classified as a)a) Flank wearFlank wearb)b) Crater wear on tool faceCrater wear on tool facec)c) Chipping off cutting edgeChipping off cutting edged)d) Localized wearLocalized wear

Tool lifeTool lifeTheThe total cutting time accumulated before tool failure occurs is total cutting time accumulated before tool failure occurs is

termed as tool life. The most commonly used criteria for termed as tool life. The most commonly used criteria for measuring the tool life are:measuring the tool life are:

1.Total destruction of tool when it ceases to cut1.Total destruction of tool when it ceases to cut2.A fixed size of wear land on the tool flank. Tool life is taken 2.A fixed size of wear land on the tool flank. Tool life is taken

as 0.038 or 0.076mm wear land on the flank for finishing. as 0.038 or 0.076mm wear land on the flank for finishing.

Taylor formula between cutting speed & tool life,Taylor formula between cutting speed & tool life, VTVT n n=C=C V is cutting speed, T is time for the flank wear to V is cutting speed, T is time for the flank wear to

reach a certain dimension, C is constant & n is reach a certain dimension, C is constant & n is exponent depends upon the cutting conditions. exponent depends upon the cutting conditions.

n=0.1 to 0.15 for HSS toolsn=0.1 to 0.15 for HSS tools =0.2 to 0.4 for carbide tools =0.2 to 0.4 for carbide tools =0.4 to 0.6 for ceramic tools =0.4 to 0.6 for ceramic tools

Economics of metal cuttingEconomics of metal cuttingTotal cost of cutting a unit volume of metal=cost of Total cost of cutting a unit volume of metal=cost of

machining metal per unit volume of metal cut+ cost machining metal per unit volume of metal cut+ cost of replacing tools per unit volume of metal cut.of replacing tools per unit volume of metal cut.

let Cm=machining cost per minutelet Cm=machining cost per minute Ct =tooling costCt =tooling costOptimum total cost,Optimum total cost, V=C {Cm*n/Ct(1-n)}V=C {Cm*n/Ct(1-n)}nn

VV00=C/{Tc(1-n/n)}=C/{Tc(1-n/n)}nn

TT00=Tc(1-n/n)=Tc(1-n/n)

MachineabilityMachineability1.1.The ease with which it could be machinedThe ease with which it could be machined2.The life of tool before tool failure2.The life of tool before tool failure3.The quality of the machined surface3.The quality of the machined surface4.The power consumption per unit volume of material 4.The power consumption per unit volume of material

removed.removed. Machineability index,%Machineability index,% ==cutting speed of material for 20 min tool life *100cutting speed of material for 20 min tool life *100 cutting speed of free cutting steel for 20 min tool lifecutting speed of free cutting steel for 20 min tool lifeMachineability index for common materials Machineability index for common materials

C- steel =65 copper = 70C- steel =65 copper = 70 C- 45 steel =60 brass =180C- 45 steel =60 brass =180 stainless steel =25 Al alloys=300-1500stainless steel =25 Al alloys=300-1500

Surface roughnessSurface roughnessThe quality of the surface produced during machining The quality of the surface produced during machining

process will depend upon:process will depend upon:1.1. Tool geometry & feed rateTool geometry & feed rate2.2. Irregularities in machining processIrregularities in machining process Irregularities include:Irregularities include:1.Occurance of B.H.U1.Occurance of B.H.U2.Occurrence of vibration & chatter2.Occurrence of vibration & chatter3.Deflection of the tool or workpiece3.Deflection of the tool or workpiece4.Inaccuracies in movements of spindles , slides & feed 4.Inaccuracies in movements of spindles , slides & feed

mechanism of machine toolmechanism of machine tool5.Formation of discontinuous chip when cutting brittle 5.Formation of discontinuous chip when cutting brittle

materialsmaterials6. Flow of chips on machined surface 6. Flow of chips on machined surface

Ideal surface roughnessIdeal surface roughness The surface roughness produced will depend entirely The surface roughness produced will depend entirely

on tool geometry such a surface roughness is on tool geometry such a surface roughness is called ideal surface roughness.called ideal surface roughness.

sum of all area above & sum of all area above & Ra= Ra= below the mean linebelow the mean line sampling lengthsampling length

Two areas are equal Two areas are equal

Ra=2/f(area 1)=h/4Ra=2/f(area 1)=h/4 where h is height of where h is height of Geometry of the surface Geometry of the surface roughnessroughness h=fh=f22/8R Therefore,/8R Therefore, Ra=fRa=f22/18/18√3.R√3.R

Natural surface roughnessNatural surface roughnessSurface roughness obtained will depend upon the Surface roughness obtained will depend upon the

combined effect of tool geometry & the contributing combined effect of tool geometry & the contributing factors , such a surface roughness is called natural factors , such a surface roughness is called natural surface roughness.surface roughness.