unit 1 metal cutting and chip formation - IGNOU

Theory of Metal Cutting
14
Figure 1.10 : (a) Force Components Acting on a Chip; and (b) Free Body Diagram of a Chip
Figure 1.11 shows a composite diagram in which the two force triangles of
Figure 1.10, have been superimposed by placing the two equal forces R and R ' together.
Since the angle between Fs and Fn is a right angle, the intersection of these forces lies on
the circle with diameter R as shown. Also, F and N may be replaced by R to form the
circle diagram (Figure 1.11).
Figure 1.11 : Force Circle Diagram
The horizontal cutting force Fc and vertical force Ft can be measured in a machining
operation by the use of a force dynamometer. The electric strain gauge type of transducer
is used in the dynamometer. After Fc and Ft are determined, they can be laid off as in
Figure 1.11 and their resultant is the diameter of the circle. The rake angle α can be laid
off, and the forces F and N can then be determined. The shear plane angle φ can be
measured approximately from a photomicrograph or by measuring tc and tu, or length of
chip and corresponding length of unmachined chip (discussed elsewhere).
From Figure 1.11, the following vector Eqs. can be written
ρ ρ ρ
R'
= F + N
ρ ρ ρ ρ ρ ρ
R = Fs
+ Fn
= Fc
+ Ft
= R'
Merchant represented various forces in a force circle diagram in which tool and reaction
forces have been assumed to be acting as concentrated at the tool point instead of their
actual points of application along the tool face and the shear plane. The circle has the
diameter equal to R (or R') passing through tool point.
After Fc, Ft, α and φ are known, all the component forces on the chip may be determined
from the geometry. For instance, the average stress on the shear plane can be determined
by using force Fs and the area of the shear plane. Another useful quantity is the
coefficient of friction (μ) between the tool and chip. Using force circle diagram, it can be
shown that