L 15.1 Theory of Ernst & Merchant

This story is suggested in 1941 based on the “principle of minimum energy consumption”. 

  1. Cutting velocity always remains constant. 

  1. The cutting edge of the tool remains sharp throughout cutting and there is no contact between the workpiece and tool flank. 

  1. There is no sideways flow of chip. 

  1. Only continuous chip is produced. 

  1. There is no built-up Edge. 

  1. No consideration is made of the inertia force of the chip. 

  1. The behaviour of chip is like that of a free-body which is in the state of a stable equilibrium due to the action of two resultant forces which are equal opposite and collinear. 

The basis of Ernst and Merchant theory was this suggestion that the shear angle would take up such a value as to reduce the work one in cutting a minimum. For this, is necessary to develop an expression for cutting force in terms of shear angle and then obtain the value of shear angle for which cutting force is a minimum. 


From Fig. 15.1 


where

τs = shear strength of the work material on the shear plane

As = area of the shear plane

Ao = cross-sectional area of the uncut chip

τ = mean angle of friction between chip and tool (given by merchant F/ N)

α = working normal rake

From Equation (1) and Equation (2):


Now by geometry: 

Hence from Equation (3) and Equation (4): 

Equation (5) may now be differentiated with respect to Shear Angle and equated to zero to find the value of Shear Angle for which Fc is a minimum. The required value is given by