Chapter 2
MECHANICS OF
METAL CUTTING
Prof. Dr. S. Engin KILIÇ
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
1
Content
 Terms and Definitions
 Chip Formation
 Cutting Forces and Force
Diagram
 Shear Angle
 Orthogonal Cutting
Geometry
 Mathematical Models
 Metal Removal Rate
 Power Requirement
 Examples
Photos from internet sites.
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
2
Terms and Definitions
Machining : Removal of
material in the form of
chips from the workpiece
by shearing with a sharp
tool.
Resultant Cutting Motion
in Cylindrical Turning
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
3
Terms and Definitions
Kalpakjian-Schmid, 2008
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
4
Terms and Definitions
Orthogonal Cutting
Oblique Cutting
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
5
Terms and Definitions
Oblique Cutting
(a)
Schematic illustration of cutting with an oblique tool.
(b) Top view, showing the inclination angle, i.
(c) Types of chips produced with different inclination
angles.
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
6
Terms and Definitions
Orthogonal Cutting Analogy in Turning (for k=00)
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
7
Terms and Definitions
Relative Motion
between tool and workpiece
Primary
motion
Secondary motion
Cutting motion
Feed motion
Cutting speed
Feed rate
Depth of cut
adjustment
Depth of cut
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
8
Chip Formation
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
9
Chip Formation
Shiny (burnished) surface on the tool
side of a continuous chip produced in
turning.
Basic types of chips produced in metal cutting and
their micrographs: (a) continuous chip with narrow,
straight primary shear zone; (b) secondary shear zone
at the tool-chip interface; (c) continuous chip with
built-up edge; (d) serrated (segmented or
nonhomogeneous) chip; and (e) discontinuous chip.
Source: After M.C. Shaw, P.K. Wright, and S.
Kalpakjian.
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
3/22/2016
ME 303 - Section 05a
10
Continuous Chip

Common in machining ductile materials
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
11
Discontinuous Chip




Machining brittle
materials
Small rake angle
Large depth of cut
Machining ductile
materials at


low cutting speed
high feed
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
12
Serrated Chip
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
13
Continuous Chip with BUE





Occurs in machining
ductile materials with
high friction at toolchip interface
Chip welds to tool face
Destroys accuracy and
surface finish
Increases tool wear
Can be reduced by


decreasing depth of cut
increasing cutting speed
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
14
Cutting Forces

n
a0
ac
Fc: tangential (main) cutting force
cutting
tool
Ft: thrust (feed) cutting force
Ff: frictional force on rake

 
n
s
Fr

n
Ft
Ff

n
Fs
Fc
Fn

cutting
tool
Fn: normal force on rake
Fs: shear force on shear plane
Fn : normal force on shear plane
s
Fr: resultant force
: shear angle
n: normal rake angle
Fn
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
15
Cutting Forces
F 2 r  Fc2  Ft 2  Fs2  Fn2s  Fn2  F f2
tan(  -  n ) =
Ft
Fc
Fs  Fc cos  - Ft sin 
Fns  Fc sin   Ft cos
F f  Fc sin  n + Ft cos  n
Fn  Fc cos  n - Ft sin  n
Ff
=
= tan 
Fn
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
16
Orthogonal Cutting Geometry
ac
a0
ls 

sin  cos   n 
ac
sin   cos   n 
a0
ac
 rc
a0
rc cos  n
tan  
1  rc sin  n
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
17
Theoretical Models

Only two of the simple thin shear-zone
models will be covered:


Ernst and Merchant’s model
Lee and Shaffer’s model
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
18
Ernst and Merchant Model
Common assumptions:
• Sharp tool tip  no rubbing
or ploughing between tool and
w.p.
• Two dimensional deformation
 no side spread
• Uniform stress distribution
on shear plane
• Resultant force on shear plane
equal and opposite to res.
force at chip-tool interface.
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
19
Main Assumption (EM Model)
Shear angle would take up such a value as to reduce
the work done in cutting to a minimum.
For given cutting conditions, work done in cutting is proportional
to Fc, it is necessary to develop an expression for Fc in terms of 
and then to obtain the value of  for which Fc is a minimum:
Fs  Fr cos     n 
 s Ac
Fs   s As 
sin 
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
20
Shear Angle (EM Model)
 s  shear strength of the work material on the shear plane
As  area of the shear plane
A c  cross - sectional area of the uncut chip
  mean angle of friction
 n  normal rake angle
 s Ac
1
Fc
Fr 
 0 to minimize Fc
sin  cos     n 

Fc  Fr cos   n 

 2     n 
 s Ac cos   n 
2
 Fc 
sin  cos     n 
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
21





Work material is rigid plastic.
Elastic strain is negligible.
Behaviour of work material is
independent of the rate of
deformation.
Temperature effects are
neglected.
Inertia effects are neglected.
Uniform stress distribution at the
chip-tool interface.
Stress
Lee and Shaffer’s Model
Strain
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
22
Main Assumptions (LS Model)


A slip-line field is formed in the triangular
plastic zone extending from the shear plane to
the interface between the tool and the chip
where no deformation takes place except for
the transmission of forces from tool-chip
interface to shear plane and for the material
being stressed to its yield point.
All the deformation takes place in the plane
(Shear Plane) extending from the tool cutting
edge to the point of intersection of the free
surfaces of the work and the chip.
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
23
Assumptions (Cont’d)




Maximum shear stress throughout the zone is s, shear
stress on the shear plane and two directions of this
max. shear stress are indicated by two orthogonal sets
of lines (slip lines).
Top surface of the triangular plastic zone then becomes
a free surface across which no stresses are transmitted.
Therefore between this surface and the max. shear
stress plane (shear plane) there is an angle of /4.
Principal stresses act on the chip-tool interface
(secondary def. Zone) at angles  and +/2.
Directions of max. shear stress lie at  /4 to the dir. of
principal stress
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
3/22/2016
ME 303 - Section 05a
24
Lee-Shaffer Theory (Cont’d)

n
45o
Sh
=
e
45o
ipT
1

2 = 90o

2
45o 

2
Fr
1
1
ea
rP
lan
Ch
e
rfac
u
S
Free
)
s
s
e
(Str
Sl
ip
Li
ne
s
2
oo
l In
ter
fac
e
max
90o n
Hence,  n /4
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
25
Metal Removal Rate
ac
w = v.f.d
d
where,
w: metal removal rate
v: cutting speed
f: feed rate
cutting conditions
d: depth of cut
Ac: f.d = undeformed chip cross sectional area
ac
k
f
f
ac = f cosk
k:Side Cutting Edge Angle
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
26
Power Requirement
E: Energy required to remove unit volume of chips
or
Resistance to cutting force
 GJ 
E   3  or GPa
m 
 GJ   GN  m   GN 
 m 3    m 3    m 2   GPa
E Specific cutting energy  Energy to remove unit volume of chips
or
E Specific cutting pressure  Force to produce chips with unit cross
sectional area
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
27
Power Requirement
E is used to calculate the power requirement
Power = E . w
where E = specific cutting energy {GJ/m3}
w = chip removal rate {mm3/sec}
 10 9 J 
 10 -9 m3 
Power = E 
. w
= E w W 
 m3 
 sec 
“E w” is the power required at the spindle
Motor power
P = (Ew/)
where  is the transmission efficiency of the
machine tool
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
28
Power Requirement
Power required at the spindle:
P = Fc v = E w
where
Fc v = E v f d
Fc = cutting force
v = cutting speed
w = chip removal rate = v f d
E = spec. cut. energy
E = (Fc/fd)
E is a function of material property and the undeformed chip thickness
If Eo is the specific cutting energy for an undeformed chip thickness of 1 mm,
then the specific cutting energy for a chip thickness ac :
E = Eo . (ac )
=>
so
ac
E
E = Power / Material Removal Rate
E = (Fc.v) / (v.f.d)
where ac = f . cos k
 E = (Fc . cos k) / (ac . d)
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
29
Power Requirement
log E
log E1

logE2
log a
c1
log a
log a
c2
c
- = ln (E1/E2) / ln (ac1/ac2)
E1/E2 = (ac1/ac2) -
 ranges between 0.2 - 0.4
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
30
Power Requirement
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
3/22/2016
ME 303 - Section 05a
31
Power Requirement
EXAMPLE:
For an orthogonal cutting operation where v= 36 m/min f= 0.25 mm/rev it was found E = 3.8
(W-sec/mm3) (m/min). If the power available at the spindle = 5 hp, find the maximum metal
removal rate and corresponding depth of cut. Note that 1 hp = 746 W.






 mm3 
Power 5 x746
W
w


  982 

E
3.8  W
 s 
3 
mm


s 

 N  m
5 x746 
Power
 s   6216 N
F

36  m 
v
60  s 
 mm3 
982 

w
 s 
d

 6.55mm
vf 36 x103  mm 
x0.25mm
60  s 
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
32
Specific Cutting Energy
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
33
Problem 1
In an orthogonal cutting test on mild steel, the following results
were obtained:
ac= 0.25 mm
a0= 0.75 mm
d = 2.5 mm
Fc = 900N
Ft = 450N
n = 100
a) Calculate the mean angle of friction on the tool rake
b) Calculate the cutting ratio
c) Calculate the shear angle
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
34
Problem 2
For an orthogonal turning operation it was found that
power consumption of lathe when idle
= 325 W
power consumption of lathe when cutting = 2580 W
For the following conditions:
spindle speed, N = 124 rpm;
cutting speed, v = 24.5 m/min
depth of cut, d = 3.8 mm;
feed rate, f = 0.2 mm/rev
Find:
a) specific cutting energy of the work material,
b) torque at the spindle,
c) cutting force,
d) specific cutting energy for 1 mm undeformed chip thickness
assuming = 0.4.
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
35
Problem 3
25 mm holes will be drilled on a steel workpiece, having a
hardness of Rc=45 {specific cutting energy, E = 77 W/(cm3/min)}
using an HSS twist drill at the following conditions:
cutting speed, v = 24.5 m/min
feed rate, f = 0.2mm/rev
Find:
a) the motor power if the efficiency of the transmission is 85%,
b) torque required.
MFGE 307 THEORY OF MANUFACTURING TECHNOLOGY II
36