Question

Write an executive summary on Ernst-Merchant Chip Formation theory and its practical applications in machining industries. (Hints: draw the free-body diagram and the force circle at the cutting edge, label all important parameters, explain the theory based on the minimum cutting force; show its importance on energy consumption and economy in mass production. (2 pages, single space, single column); use an abstract, divide the paper in headings and subheadings, and a conclusion or final remarks (summing up).

Answer 1

fi=(pi/4) - (1/2)(tau - alfa)- the basic relation from Merchant theory of metal cutting.

Conditions for the relationship above to be true:

fi- shear angle which it is adjusting itself to result minimum work
tau- friction angle which is independent of fi and is constant
the edge of the tool is sharp
the distribution of the shear force and normal stress is uniform, in the shear plane
the part material is rigid and plastic
the width of the generated chip is constant

After experimental work, the relationship above was found to be over estimated, so that Merchant modified it and the result was another relationship:

2*fi +tau - alfa=C, C being the machining constant. In order to C<PI/2, grain size and the micro structure has to remain constant after the material is manufactured.

The normal force Fn, which is acting in a direction perpendicular to the shear plane, is changing due to the deformations and frictions.The normal stress affects the shear stress, in the shear's direction.

theres a lot of practical appication of ernst and merchant theory in machining industries:

1> design of machine stiffness for machine tolerance.

2>whether workpiece can withstand cutting force predicted.

3>in studying behaviour and machinability of material.

4>estimation of power consumption in cutting.