Forces and Mechanics of Cutting

Forces and Mechanics of Cutting:

1. Power requirement for the machine tool can be calculated

2. Design of stiffness, etc. for the machine tolerances

3. Whether workpiece can withstand the cutting force

• Ernst and Merchant (1941) did the first 

scientific analysis

– Normal = N

– Along the tool = F

                                    F/N=µ

• FC and FT along and normal to cutting along 

the direction of tool movement with velocity, ‘v’.

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

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)

Large nose radius can create positive rake 

angle and cause rubbing and create plastic 

deformation.

• 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.

• 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.

                                        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.