1. Forces and Mechanics of Cutting
Why should we know?
Power requirement for the machine tool can be calculated
Design of stiffness, etc. for the machine tolerances
Whether workpiece can withstand the cutting force

3. Ernst and Merchant (1941) did the first scientific analysis
Normal = N
Along the tool = F
FC and FT along and normal to cutting along the direction of tool movement with velocity, ‘v’.
(1)
(2)

4. (3)
(4)
(5)
(6)
(7)
(8)
(9)

5. We can measure FC and FT using force dynamometer.
FS, FN, F, and N can be found.
FS and FN from equations 5 & 6.
F and N from 3 & 4
( friction angle)
Eq. 10

6. Cutting Force FC depends on
FC increases as t0 increases
FC decreases as rake angle increases and as speed increases
Why FC is affected by speed:
As speed goes up, shear angle goes up, and friction reduces.
Forces can also be affected by the nose radius. Large nose radius increases force. (Blunt tool)

7. Large nose radius can create positive rake angle and cause rubbing and create plastic deformation.

10. Coefficient of friction in metal cutting range from 0.5 to 2.0
Shows how high friction can rise on the chip-tool interface
Forces on the tool tip are very high because of small contact area.

11. Stresses Average shear stress Average normal stress
The area where the stress acts (area of shear plane)
AS can be increased by increasing t0.
is independent of rake angle
decreases with increase in rake angle.

12. Problems in finding stresses on the rake face:
Consequently, normal stress in the shear plane has no effect on the magnitude of shear stress.
Problems in finding stresses on the rake face:
Hard to find the contact on the rake face.
Stresses in practice is not uniformly distributed on the rake face.

14. Shear-angle relationship
Let’s take friction angle as
Assume is independent of
Differentiate with respect to and equate to 0 (zero).
In the previous slides we
called this l

15. The equation (A) shows that
If decreases and/or increases then decreases.
In practice this analysis is corrupted because of several reasons like:
Shear stress is effected by normal stresses.
is effected by etc.
(see graph 8.19)
(A)

17. Specific Energy Total power = FCV If width of unit = ‘W’
Total energy/unit volume of material removal.
Frictional specific energy:

18. Power required to shear along the plane
As uf increases, shear angle decreases, and hence us goes up directly.
Thus friction plays an important part in metal cutting.

21. Problem
t0=0.005 in, V=400 ft/min, α=10o, w=0.25, tc=0.009, Fc=125 lb, Ft=50 lb.
What % of total energy is consumed in friction?

22. Summary Velocity triangle Merchants circle
Compute Forces and obtain Fs, Fn etc based on measuring Fc and Ft (Equations 1 to 10 of this slide set)
Calculate Shear stress and normal Stress
Specific energy
Shear angle relationships
Relationships between rake angle, velocity, shear angle and cutting force
Effect on Ft due to –ve and +ve rake angle.