# Merchant’s Circle Diagram

In orthogonal cutting when the chip flows along the orthogonal plane, πO, the cutting force (resultant) and its components PZ and PXY remain in the orthogonal plane. Fig is schematically showing the forces acting on a piece of continuous chip coming out from the shear zone at a constant speed. That chip is apparently in a state of equilibrium.

The circle(s) drawn taking R or R1 as diameter is called Merchant’s circle which contains all the force components concerned as intercepts. The two circles with their forces are combined  into one circle having all the forces contained in that as shown by the diagram called Merchant’s Circle Diagram (MCD)
The significance of the forces displayed in the Merchant’s Circle Diagram are :

PS – the shear force essentially required to produce or separate the chip from the parent body by shear

Pn – inherently exists along with PS
F – friction force at the chip tool interface
N – force acting normal to the rake surface
PZ – main force or power component acting in the direction of cutting velocity
$P_{xy}=\bar{P_{x}}+\bar{P_{y}}$
The magnitude of PS rovides the yield shear strength of the work material the nature and degree of p under the cutting condition. The values of F and the ratio of F and N indicate interaction like friction at the chip-tool interface. The force components PX, PY, PZ are generally obtained by  direct measurement. Again PZ helps in determining cutting power and specific energy requirement. The force components are also required to design the cutting tool and the machine tool.