The Mechanics of the Simple Shearing Process During Orthogonal Machining

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Abstract
In the orthogonal machining operation, a continuous chip is often produced by the simple shearing process, which is characterized by the existence of a shear line extending from the tip of the tool to the intersection of the free surfaces of the workpiece and chip. Chip formation by this process is analyzed, and analytical expressions are developed for the force required to machine a given material with a tool having a prescribed coefficient of friction. It is found that when the friction angle is less than the rake angle, the solution is obtained by seeking the condition for which the machining force is a minimum. However, for the more common case, when the friction angle is greater than the rake angle, the solution is obtained by seeking the machining force for which there exists a limiting stress distribution within the chip. Both these solutions are developed from a common foundation. Expressions also are derived for the chip-thickness ratio, as well as for the deformation to be expected when an initially squared grid is embedded in the material being cut.

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