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MECHANICS OF METAL CUTTING

The Final Shapes are Obtained

Achive parts with Desired Shapes, Dimensions & Surface Finish Quality

Two Category CUTTING & GRINDING

Most Common Cutting Operations TURNING & MILLING & DRILLING

MECHANICS OF ORTOGONAL CUTTING

Used Explain the General Mechanics of Metal Removal

Cutting Edge is Perpendicular to the Direction of Relative Tool-Workpiece Motion

To Acquire 3-D ( Oblique) Geometric and Kinematic Transforms Applied to

Ortogonal

b) Oblique cutting geometry

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Firstly, Chip Sticks to Rake Face then; Starts sliding over the Rake Face With Friction

Coefficient

Length of The Contact Zone Depends on CUTTING SPEED, TOOL GEOMETRY &

MATERIAL PROPERTøES

Primary Shear Zone Assumed as a THøN PLANE ( Ignore STRAIN-HARDENING )

CUTTING FORCE DIAGRAM

It is assumed that the cutting edge is sharp without a chamfer or radius and that the

deformation takes place at the infinitely thin shear plane.

The shear angle ( Ø

c

) angle between the direction of the cutting speed (V) and the

shear plane.

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Shear stress (Ĳs) and the normal stress (ıs) on the shear plane are constant

The resultant force (F) on the chip, applied at the shear plane, is in equilibrium to the

force (F) applied to the tool over the chip-tool contact zone on the rake face; an av-

erage constant friction is assumed over the chip-rake face contact zone.

From the force equilibrium, the resultant force (F) is formed from the feed (Ff) and

tangential (Ft) cutting forces

ȕa is average friction angle between the tool's rake face and the moving chip, and Į

r

is

the rake angle of the tool.

Power Spend on the Shear Plane

Ps = mc x cs ( Ts- Tr ) where mc metal removal rate

cs is coefficent of heat for workpiece material

Ts is Temperature rise on Shear Plane

Tr is Shop Temperature

The Average Friction Coefficent on the Rake Face

ȝa = tan(ȕa) = Fu / Fv where Fu is Friction Force

Fv is Normal Force

The prediction of temperature distribution at the tool-chip interface is very important

in determining the MAXIMUM SPEED that gives the most optimal MATERIAL

REMOVAL RATE without excessive tool wear.

The fundamental machinability study requires THE øDENTø)øCATøON OF A

MAXøMUM CUTTøNG SPEED VALUE that corresponds to the critical temperature

limit where the tool wears rapidly. By using the approximate solutions summarized

above, one can select a cutting speed that would correspond to a tool-chip interface

temperature (Tint) that lies just below the diffusion and melting limits of materials

present in a specific cutting tool.

a) Cutting Speed V = 4.61(m/d)

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b) Cutting Speed V = 47.3(m/d)

It is difficult to predict the SHEAR ANGLE AND STRESS øN THE SHEAR PLANE

and the average friction coefficient on the rake face using the standard material

properties obtained from tensile and friction tests. For an accurate and realistic

modeling, such fundamental parameters are identified from orthogonal cutting tests,

where the DEFORMED CHIP THICKNESS & FEED and TANGENIAL CUTTING

FORCES are measured using cutting tools with a range of rake angles.

The influence of uncut chip thickness and cutting speed is also considered by

conducting experiments over a wide range of feeds and cutting speeds.

Kte & Kfe : The Average Edge Force Coefficents

MECHANISTIC MODELLING OF CUTTTING FORCES

Shearing Force is Formulated as a Function of Measured Feed & Tangential Cutting

Force

In metal cutting literature the cutting parameter called specific cutting pressure or

tangential cutting force coefficient {Kt) is defined as

Kt [N/mm2] = Ĳs x cos ( ȕa – Į r ) / [ sin (øc) x cos(øc + ȕa - Į r) ]

Feed Force Constant

Kf [N/mm2] = Ĳs x sin ( ȕa – Į r ) / [ sin (øc) x cos(øc + ȕa - Į r) ]

The Specific Cutting Pressure is a function of the yield shear stress of the workpiece

(t

s

) material during cutting, the shear angle (øc), tool geometry (i.e., rake angle Į r),

and the friction between the tool and the chip (ȕa) only the tool geometry is known

beforehand.

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The friction angle depends on the lubrication used, the tool-chip contact area, and the

tool and workpiece materials.

The shear stress in the shear plane is also still in question with the present knowledge

of the cutting process. If the shear plane is assumed to be a thick zone, which is more

realistic than having a thin shear plane, there will be a work hardening, and the shear

stress will be larger than the workpiece material's original yield shear stress measured

from pure torsion or tensile tests. The temperature variation in the shear and the

friction zones will also affect the hardness of the workpiece material; therefore the

shear stress in the primary deformation zone will vary.

The shear yield stress varies as a function of chip thickness as well due to varying

strain hardening of the material being machined. Hence, it is customary to define the

cuttingforces mechanistically as a taction of cutting conditions and the cutting

constants (Ktc) and (Kfc)

Ft = Ktcbh + Kteb

Ff = Kfcbh + Kfeb

THEORETICAL PREDICTION OF SHEAR ANGLE

Some of the most fundamental models, which assume a perfect rigid plastic workpiece

material without any strain hardening, are briefly presented in this section. These

models assume that the shear plane is thin; that the shear stress in the shear plane is

equivalent to the yield shear stress of the material; and that the average friction is

found from friction tests between the tool and workpiece materials, leaving only the

shear angle as unknown. There have been two fundamental approaches to predict the

shear angle as follows.

a) Maximum Shear Stres Principle

Based on the maximum shear stress principle (i.e., shear occurs in the direction

of maximum shear stress).

The resultant force makes an angle (øc + ȕa - Į r) with the shear plane , and the

angle between the maximum shear stress and the principal stress (i.e., the

resultant force) must be ɉ /4.

Shear angle relation is obtained:

øc = ɉ /4 – (ȕa - Į r)

b) Minumum Energy Principle

Taking the PArtial Derivative of Cutting Power

øc = ɉ /4 – (ȕa - Į r) / 2

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MECHANICS OF OBLIQUE CUTTING

The cutting velocity (V) is perpendicular to the cutting edge in orthogonal cutting,

whereas in oblique cutting, it is inclined at an acute angle i to the plane normal to the

cutting edge.

OBLIQUE CUTTING GEOMETRY

A plane normal to the cutting edge and parallel to the cutting velocity V is defined as

the normal plane or P

n

.

Shear deformation is plane strain without side spreading, the shearing and chip motion

are identical on all the normal planes parallel to the. cutting speed V and perpendicular

to the cutting edge.

Velocities of cutting (V), shear (V

s

), and chip (V

c

) are all perpendicular to the cutting

edge, and they he in the velocity plane (P

v

) parallel to or coincident with the normal

plane (P

n

). The resultant cutting force F, along with the other forces acting on the

shear and chip-rake face contact zone

There is no CUTTING FORCE in THøRD DøRECTION

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Most analyses assume that the mechanics of oblique cutting in the normal plane are

equivalent to that of orthogonal cutting; hence all velocity and force vectors are

projected on the normal plane.

The sheared chip moves over the rake face plane with a chip flow angle n measured

from a vector measured from a vector on the rake face but normal to cutting edge

Geometry of Oblique Cutting Process

Tan Ș = [tan (i) cos ( øc – Į n ) – cos (Į n) x tan (øi)] / sin (øn)

5 Unknown angles that describe the mechanics of oblique cutting

Resultant Force Directions ( șn , și )

Shear Velocity Directions( øn , øi )

Chip Flow ( Ș )

However, direct analytical solution of the equations are rather difficult; hence they are

solved by employing an iterative numerical method. The iterative solution is started by

assuming an initial value for the chip flow angle (i.e., r} = i)

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Input Angles – Geometric Relations

PREDICTION OF CUTTING FORCES

There Components

Ft (Tangential Force)

Ff (Feed Force)

Fr (Radial Force)

They are expressed as a Function of

Yield Stres

Resultant Force Direction

Oblique Angle ( i )

Oblique Shear Angle (øn , øi )

Corresponding Cutting Constants

Ktc

Kfc

Krc

PRATICAL APPROACHES

Evaluate the shear angle (øc), average friction angle (ȕa), and shear yield stress (Ĳs)

from orthogonal cutting tests.

The orthogonal shear angle is equal to the normal shear angle in oblique cuttingthe

normal rake angle is equal to the rake angle in orthogonal cutting (Įr = Įn); the chip

flow angle is equal to the oblique angle (Ș= i)

The friction coefficient (ȕa) and shear stress (Ĳs) are the same in both orthogonal and

oblique cutting operations for a given speed, chip load, and tool-work material pair.

Predict the cutting forces using the oblique cutting

Many practical oblique cutting operations, such as turning, drilling, and milling, can

be evaluated using the oblique cutting mechanics procedure outlined above.

MECHANICS OF TURNING PROCESS

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