Section 13. qxd

BASIC MECHANICS OF METAL CUTTING
The basic mechanics of chip-type machining processes (Fig. 13.4.1) are
shown, in simplest two-dimensional form, in Fig. 13.4.2. A tool with a
certain 
rake angle
a
(positive as shown) and 
relief angle
moves along the
surface of the workpiece at a depth 
t
1
.
The material ahead of the tool is
sheared continuously along the 
shear plane,
which makes an angle of 
f
with the surface of the workpiece. This angle is called the 
shear angle
and, together with the rake angle, determines the chip thickness 
t
2
.
The
ratio of 
t
1
to 
t
2
is called the 
cutting ratio 
r.
The relationship between the
shear angle, the rake angle, and the cutting ratio is given by the equa-
tion tan 
f
r
cos 
a
/(1 
r
sin 
a
). It can readily be seen that the shear
angle is important in that it controls the thickness of the chip. This, in
turn, has great influence on cutting performance. The 
shear strain
that
the material undergoes is given by the equation 
g
cot 
f
tan (
f
a
).
Shear strains in metal cutting are usually less than 5.
13.4
MACHINING PROCESSES AND MACHINE TOOLS
by Serope Kalpakjian
Fig. 13.4.1
Examples of chip-type machining operations.
Tool
Straight turning
Drilling
Boring and 
internal geooving
Threading
Investigations have shown that the shear plane may be neither a plane
nor a narrow zone, as assumed in simple analysis. Various formulas
have been developed which define the shear angle in terms of such fac-
tors as the rake angle and the friction angle 
b
.
(See Fig. 13.4.3.)
Because of the large shear strains that the chip undergoes, it becomes
hard and brittle. In most cases, the chip curls away from the tool. Among
possible factors contributing to chip curl are nonuniform normal stress
distribution on the shear plane, strain hardening, and thermal effects.
Regardless of the type of machining operation, some basic types of
chips or combinations of these are found in practice (Fig. 13.4.4).