MECHANICS OF METAL CUTTING

Topics to be covered

Inroduction to Machining Technology Cutting Models Turning Forces Merchants Circle Power & Energies

Elements of Metal Cutting

Tool

Workpiece

Chip

Heat Generation Zones

(Dependent on sharpnessof tool)

(Dependent on )

(Dependent on

10%

30%

60%

Tool TerminologyTool Terminology

Side relief angle

Side cutting edge angle(SCEA)

Clearance or end relief angle

Back Rake(BR),+

Side Rake (SR), +

End Cuttingedge angle(ECEA)

Nose Radius

TurningCutting edge

FacingCutting edge

Cutting Geometry

Material Removal RateMRR vfd

Roughing(R)

f 0.4 1.25mm / rev

d 2.5 20mm

Finishing(F)

f 0.125 0.4mm / rev

d 0.75 2.0mm

vR vF

Cutting Models

ORTHOGONAL GEOMETRY OBLIQUE GEOMETRY

Tool

workpiece

Tool

workpiece

Assumptions(Orthogonal Cutting Model)

The cutting edge is a straight line extending perpendicular to the direction of motion, and it generates a plane surface as the work moves past it.

The tool is perfectly sharp (no contact along the clearance face).

The shearing surface is a plane extending upward from the cutting edge.

The chip does not flow to either side The depth of cut/chip thickness is constant uniform

relative velocity between work and tool Continuous chip, no built-up-edge (BUE)

Orthogonal Cutting

r to

tc

ls sinls cos( )

tan r cos

1 rsin

AC

BD

AD DC

BDtan( ) cot

F t

FC

Fr

DIRECTION OF ROTATION

WORKPIECE

CUTTING TOOL

DIRECTION OF FEED

Velocity of Tool relative to workpiece V

Longitudinal 'Thrust' Force (27%)

Radial Force (6%)

Tangential 'Cutting' Force (67%)

‘Turning’ Forces For Orthogonal Model

End view section 'A'-'A'Note: For the 2D Orthogonal Mechanistic Model we will ignore the radial component

Ft

'A' 'A'

cF

FL

FC

Fr

DIRECTION OF ROTATION

WORKPIECE

CUTTING TOOL

DIRECTION OF FEED

Velocity of Tool relative to workpiece V

Longitudinal Force

Radial Force ‘Thrust’ Force

Tangential Force 'Cutting' Force

‘Facing’ Forces For Orthogonal Model

End view

Note: For the 2D Orthogonal Mechanistic Model we will ignore the Longitudinal component

'Turning' Terminology

N is the speed in rpmD is the diameter of the

workpiecef is the feed (linear

distance/rev)d is the depth of cutV is the surface speed

= DN

Standard Terms

Beware, for turning: In the generalized orthogonal model depth of cut (to) is f (the feed), and width of cut (w) is d (the depth of cut)

N

D

d mm

feed (mm/rev)

Tool

Workpiece

rpm

Orthogonal Cutting Model (Simple 2D mechanistic model)

Mechanism: Chips produced by the shearing process along the shear plane

t 0

+

Rake Angle

Chip

Workpiece

Clearance AngleShear Angle

t c

depth of cut

Chip thickness

Tool

Velocity V

tool

tool

Cutting Ratio(or chip thicknes ratio)

As Sin =to

ABand Cos-) =

tc

AB

Chip thickness ratio (r) =t0

tc=

sincos( )

tc

to

A

B

Chip

Workpiece

Experimental Determination ofCutting Ratio

Shear angle may be obtained either from photo-micrographs or assume volume continuity (no chip density change):

Since t0w 0L0 = tcw cLc and w 0=w c (exp. evidence)

Cutting ratio , r = t 0tc

= L cL0

i.e. Measure length of chips (easier than thickness)

w

tL

0

0

0

wc

Lc

ct

Shear Plane Length

and Angle

Shear plane length AB =t0

sinShear plane angle () = Tan

-1 rcos1-rsin

or make an assumption, such as adjusts to minimize cutting force: = 45

0+ /2 - /2 (Merchant)

t c

to

A

B

Chip

tool

Workpiece

Velocities(2D Orthogonal

Model)

Velocity Diagram

From mass continuity: Vto = V ctc

From the Velocity diagram:

V s = Vcos

cos( )

V c = Vr and V c = Vsin

cos( )

(Chip relative to workpiece)

V = Chip Velocity (Chip relative to tool)

Tool

Workpiece

Chip

Vs V = Cutting Velocity

(Tool relative to workpiece)

Shear Velocity

c

Vs

Vc

V

Cutting Forces(2D Orthogonal Cutting)

Free Body Diagram

Generally we know:Tool geometry & typeWorkpiece material

and we wish to know:F = Cutting ForceF = Thrust ForceF = Friction ForceN = Normal ForceF = Shear ForceF = Force Normal

to Shear

c

t

s

n

Tool

Workpiece

Chip

Dynamometer

R

R

R

R

FcFt

sF

FnN

F

Force Circle Diagram(Merchants Circle)

R

Ft

Fc

Tool

F

N

Fs

Fn

Results fromForce Circle Diagram

(Merchant's Circle)

Friction Force F = Fcsin + Ftcos

Normal Force N = Fccos - Ftsin

Shear Force Fs = Fccos - Ftsin

= F/N and = tan typically 0.5 - 2.0)

Force Normal to Shear plane Fn = Fcsin + Ftcos

Forces on the Cutting Tool

and the workpiece

Importance: Stiffness of tool holder, stiffness of machine, and stiffness of workpiece must be sufficient to avoid significant deflections (dimensional accuracy and surface finish)

Primary cause: Friction force of chip up rake face + Shearing force along shear plane

Cutting speed does not effect tool forces much (friction forces decrease slightly as velocity increases; static friction is the greatest)

The greater the depth of cut the greater the forces on the tool Using a coolant reduces the forces slightly but greatly

increases tool life

Stresses On the Shear plane:

Normal Stress = s = Normal Force / Area =Fn

AB w=

Fnsintow

Shear Stress = s = Shear Force / Area =Fs

AB w=

Fssintow

On the tool rake face: = Normal Force / Area = N

tc w(often assume tc = contact length)

= Shear Force / Area = Ftc w

Note: s = y = yield strength of the material in shear

Power

•Power (or energy consumed per unit time) is the product of force and velocity. Power at the cutting spindle:

•Power is dissipated mainly in the shear zone and on the rake face:

•Actual Motor Power requirements will depend on machine efficiency E (%):

Cutting Power Pc = FcV

Power for Shearing Ps = FsVs

Friction Power Pf = FVc

Motor Power Required =Pc

Ex 100

Material Removal Rate (MRR)

Material Removal Rate (MRR) = Volume RemovedTime

Volume Removed = Lwto

Time to move a distance L = L/V

Therefore, MRR =Lwto

L/V= Vwto

MRR = Cutting velocity x width of cut x depth of cut

Specific Cutting Energy(or Unit Power)

Energy required to remove a unit volume of material (often quoted as a function of workpiece material, tool and process:

Ut = EnergyVolume Removed

= Energy per unit timeVolume Removed per unit time

Specific Energy for shearing Us =FsVs

Vwto

Specific Energy for friction Uf =FVc

Vwto= Fr

wto

Ut =Cutting Power (Pc)

Material Removal Rate (MRR)=

FcVVwto

=Fc

wto

Specific Cutting EnergyDecomposition

1. Shear Energy/unit volume (Us)(required for deformation in shear zone)

2. Friction Energy/unit volume (Uf)(expended as chip slides along rake face)

3. Chip curl energy/unit volume (Uc)(expended in curling the chip)

4. Kinetic Energy/unit volume (Um)(required to accelerate chip)

Ut = Us + Uf +Uc +Um

Specific Cutting EnergyRelationship to Shear strength of Material

SHEAR ENERGY / UNIT VOLUME Specific Energy for shearing Us =

FsVs

Vwto

FRICTION ENERGY / UNIT VOLUME

Specific Energy for friction Uf =FVc

Vwto= Fr

wto= F

wtc=

APPROXIMATE TOTAL SPECIFIC CUTTING ENERGY

Ut = Us + Uf = s+ y1+)

U s =scos

sin cos( )= s.

Relation between Pressure and Cutting velocity

Effect of Rake angle on Cutting Force

Average Unit Horsepower Values of Energy per unit volume

Typical Orthogonal Model Violations

• Geometry and form Violations (i.e. non zero angles of inclination, not sharp - radiused end)

• Shear takes place over a volume (not a line or plane)

• Cutting is never a purely continuous process (cracks develop in chip; material not homogeneous)

• 'Size Effect' - larger stresses are required to produce deformation when the chip thickness is small (statistical probability of imperfection in the shear zone)

• BUE - some workpiece material 'welds' to the tool face (cyclic in nature)