THEORY OF METAL
MACHINING
1.
2.
3.
4.
Overview of Machining Technology
Theory of Chip Formation in Metal Machining
Force Relationships and the Merchant Equation
Cutting Temperature

(Video) CNC Lathe
https://www.youtube.com/watch?v=MwgobIVj4fU
Material Removal Processes
 A family of shaping operations, the common feature of
which is removal of material from a starting work part so
the remaining part has the desired geometry
 Machining – material removal by a sharp cutting tool,
e.g., turning, drilling, milling
 Abrasive processes – material removal by hard,
abrasive particles, e.g., grinding
 Nontraditional processes - various energy forms other
than sharp cutting tool to remove material, e.g.,
mechanical, electromechanical, thermal, & chemical
energy forms
 The family
tree of
material
removal
processes
Machining
 Cutting action involves shear deformation of work
material to form a chip
 As chip is removed, new surface is exposed: (a) positive and
(b) negative rake tools
Advantages of Machining



Variety of work materials can be machined
 Most frequently used to cut metals
Variety of part shapes and special geometric features
possible:
 Screw threads
 Accurate round holes
 Very straight edges and surfaces
Good dimensional accuracy and surface finish
 Achieve tolerances of +/- .001 in
 Achieve roughness values less than 16 microinches
Disadvantages of Machining
 Wasteful of material
 Chips generated in machining are wasted material
 At least in the unit operation
 Chips are usually recycled
 Time consuming
 A machining operation generally takes longer to shape
a given part than alternative shaping processes such
as casting and forming
Machining in the
Manufacturing Sequence
 Generally performed after other basic manufacturing
processes, such as casting, forging, and bar drawing
 Other processes create the general shape of the
starting work part
 Machining provides the final shape, dimensions,
finish, and special geometric details that other
processes cannot create
Machining Operations
 Most important machining operations:
 Turning
(Video) Shaping Machine
 Drilling
https://www.youtube.com/watch?v=Omsyy-RiaqU&t=1s
 Milling
(Video) Planing Machine
https://www.youtube.com/watch?v=W8-_9ziKiao&t=1s
 Other machining operations:
 Shaping and Planing (Video) Broaching
https://www.youtube.com/watch?v=rAJx-6SLdP0
 Broaching
(Video) Band Sawing Machine
https://www.youtube.com/watch?v=AwPmhsjYuck&t=2s
 Sawing
(Video) Circular Sawing Machine
https://www.youtube.com/watch?v=mlrxKJW5i8Y&t=1s
Turning
 Single point cutting tool removes material from a rotating
workpiece to form a cylindrical shape
Drilling
 Used to create a round
hole, usually by means of
a rotating tool (drill bit)
with two cutting edges
Milling
 Rotating multiple-cutting-edge tool is moved across work
to cut a plane or straight surface
 Peripheral milling: cutter axis parallel to surface being milled
 Face milling: cutter axis is perpendicular to surface being milled
Cutting Tool Classification
1. Single-Point Tools
 One dominant cutting edge
 Point is usually rounded to form a nose radius
 Turning uses single point tools
2. Multiple Cutting Edge Tools
 More than one cutting edge
 Motion relative to work achieved by rotating
 Drilling and milling use rotating multiple cutting edge
tools
Cutting Tools
 (a) Single-point tool showing rake face, flank, and tool point
 (b) Helical milling cutter, representative of tools with multiple
cutting edges
Machine Tool
 A power-driven machine that performs a machining
operation, including grinding
 Functions in machining:
 Holds work part
 Positions tool relative to work
 Provides power at speed, feed, and depth that
have been set
 The term also applies to machines that perform metal
forming operations
Cutting Conditions in
Machining
 Three dimensions of
a machining process
 Cutting speed v :
primary motion
 Feed f :
secondary motion
 Depth of cut d :
penetration of tool
below original
work surface
Cutting Conditions in
Machining
 For certain operations (e.g., turning), material removal rate
RMR can be computed as
RMR = v f d
where
v = cutting speed (in/s)
f = feed (in)
d = depth of cut (in)
RMR = removal rate (in3/s)
Roughing vs. Finishing Cuts
 In production, several roughing cuts are usually taken on a
part, followed by one or two finishing cuts
 Roughing - removes large amounts of material from
starting work part
 Some material remains for finish cutting
 High feeds and depths, low speeds
 Feeds of .015 - .050 in/rev, & depths of .100 - .750 in
 Finishing - completes part geometry
 Final dimensions, tolerances, and finish
 Low feeds and depths, high cutting speeds
 Feeds of .005 - .015 in/rev, & depths of .030 - .075 in
Orthogonal Cutting Model
 Orthogonal cutting uses a wedge-shaped tool in which the
cutting edge is perpendicular to the direction of speed motion
as the tool is forced into the work material
 Simplified 2-D model of machining that describes the mechanics
of machining fairly accurately
Chip Thickness Ratio
 Chip thickness ratio
to
r 
tc
where
r = chip thickness ratio
to = thickness of the chip prior to chip formation
tc = chip thickness after separation
 Chip thickness after cut is always greater than before, so
chip ratio is always less than 1.0
Shear Plane Angle
 Based on the geometric parameters of the orthogonal
model, the shear plane angle  can be determined as:
r cos 
tan  
1  r sin
where
r = chip thickness ratio
 = rake angle
Shear Strain
 Shear strain in machining can be computed from the
following equation, based on the preceding parallel plate
model
 = tan( - ) + cot 
where
 = shear strain
 = shear plane angle
 = rake angle of cutting tool
Example:
Orthogonal Cutting
 In a machining operation that approximately orthogonal cutting, the
cutting tool has a rake angle α = 10°. The chip thickness before the
cut to = 0.50 mm and the chip thickness after the cut tc = 1.125 mm.
Calculate the shear plane angle and the shear strain in the
operation.
 The chip thickness ratio:
r = to / tc = 0.50 / 1.125 = 0.444
 The shear plane angle:
tan  = (r cosα) / (1-r sinα)
= (0.444 cos10) / (1-0.444 sin10)
= 0.4738
 = 25.4°
 The shear strain:
 = tan( - ) + cot 
= tan(25.4-10) + cot25.4
= 2.386
Actual Chip Formation
 More realistic view
of chip formation,
showing shear
zone rather than
shear plane
 Also shown is the
secondary shear
zone resulting
from tool-chip
friction
Four Basic Types of Chip in
Machining
1.
2.
3.
4.
Discontinuous chip
Continuous chip
Continuous chip with Built-up Edge (BUE)
Serrated chip
Discontinuous Chip
 Brittle work materials
 Low cutting speeds
 Large feed and depth of
cut
 High tool-chip friction
Continuous Chip
 Ductile work materials
 High cutting speeds
 Small feeds and depths
 Sharp cutting edge
 Low tool-chip friction
Continuous with Built-Up Edge
 Ductile materials
 Low-to-medium cutting
speeds
 Tool-chip friction causes
portions of chip to
adhere to rake face
 BUE forms, then breaks
off, cyclically
Serrated Chip
 Semicontinuous - sawtooth appearance
 Cyclical chip forms
with alternating high
shear strain then low
shear strain
 Associated with
difficult-to-machine
metals at high cutting
speeds
Forces Acting on Chip
 Friction force F and Normal force to friction N
 Shear force Fs and Normal force to shear Fn
Resultant Forces
 Vector addition of F and N = resultant R
 Vector addition of Fs and Fn = resultant R'
 Forces acting on the chip must be in balance:
 R' must be equal in magnitude to R
 R’ must be opposite in direction to R
 R’ must be collinear with R
Cutting Force and Thrust
Force
 F, N, Fs, and Fn
cannot be directly
measured
 Forces acting on the
tool that can be
measured
 Cutting force Fc and
Thrust force Ft
Forces in Metal Cutting
 Equations to relate the forces:
F = Fc sin + Ft cos
N = Fc cos - Ft sin
Fs = Fc cos - Ft sin
Fn = Fc sin + Ft cos
 Based on these calculated
force, shear stress and
coefficient of friction can be
determined
F
 s
As
F

N
Shear Stress
 Shear stress acting along the shear plane

Fs
As
where As = area of the shear plane
As 
t ow
sin 
 Shear stress  equals shear strength S of work material
during cutting
Coefficient of Friction
 Coefficient of friction between tool and chip
F

N
 Friction angle related to coefficient of friction as
  tan 
The Merchant Equation
 Of all the possible angles at which shear deformation can occur,
the work material will select a shear plane angle  that minimizes
energy
  45 

2


2
 Derived by Eugene Merchant
 Based on orthogonal cutting,
but validity extends to 3-D machining
 To increase shear plane angle ( )
 Increase the rake angle (α)
 Reduce the friction angle (β) or the coefficient of friction (μ)
Example:
Shear Stress in Machining
 In a machining operation that approximately orthogonal cutting, the
cutting tool has a rake angle α = 10° and shear plane angle  =
25.4°. The chip thickness before the cut to = 0.50 mm and the chip
thickness after the cut tc = 1.125 mm. Also Fc = 1559 N and Ft =
1271 N. The width of the orthogonal cutting operation w = 3.0 mm.
Determine the shear strength of the work material.
 The shear force:
Fs = Fc cos - Ft sin
= 1559(cos25.4)-1271(sin25.4) = 863 N
 The shear plane area:
 The shear stress:
As = tow / sin
= (0.5)(3.0) / sin25.4 = 3.497 mm2
 = S = Fs / As
= 863 / 3.497 = 247 N/mm2 = 247 MPa
Example:
Estimating Friction Angle
 In a machining operation that approximately orthogonal cutting, the
cutting tool has a rake angle α = 10° and shear plane angle  =
25.4°. Determine the friction angle and the coefficient of friction.
 Using the Merchant equation:
 The friction angle:
  45 

2


2
β = 2(45) + α - 2
= 2(45) + 10 – 2(25.4) = 49.2°
 The coefficient of friction:
μ = tan β
= tan(49.2) = 1.16
Effect of Higher Shear Plane
Angle
 Higher shear plane angle  with a resulting lower shear plane area
 Smaller shear plane angle  with a corresponding larger shear
plane area
Cutting Temperature
 Approximately 98% of the energy in machining is converted into
heat
 This can cause temperatures to be very high at the tool-chip
 The remaining energy (about 2%) is retained as elastic energy
in the chip
 High cutting temperatures result in the following:
 Reduce tool life
 Produce hot chips that pose safety hazards to the
machine operator
 Can cause inaccuracies in part dimensions due to
thermal expansion of work material