L 9.1 Velocity Relationship

The relationship of different velocities for Orthogonal Cutting is shown in Fig. 9.1. Let the velocities  depicted in the diagram, be as follows: 

Vc= Velocity of the tool relative to work, or the Cutting Velocity. 

Vf = Velocity of chip flow relative to the tool, or the Chip flow velocity. 

Vs = Velocity of displacement of the chip along the shear plane relative to work, or the Velocity of Shear. 

Of the above three Velocities, the Cutting velocity Vc is always known. The other two can be computed with its help of the following relations, which refer to the velocity diagram shown on the right-hand side in Fig. 9.1. 

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Fig. 9.1 Velocity relationships. 

From standard trigonometrical ratios, we get: 

6 

From these relations the values of Vf  and Vs   can be derived in terms of the known velocity Vc as follows: 

5 

But, it has already been shown in equation (L8-6) that: 

4 

Therefore, by substituting this value in equation (2), we get: 

3 

The same relationship can also be derived by equating the two volumes of material, which are equal in Orthogonal Cutting, such as : 

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