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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 ToolWorkpiece Motion
To Acquire 3D ( 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 STRAINHARDENING )
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 chiptool contact zone on the rake face; an av
erage constant friction is assumed over the chiprake 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 toolchip 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 toolchip 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 toolchip 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 chiprake 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 toolwork 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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