The author presents a mathematical analysis of the geometry and mechanics of the metal-cutting process, covering two common types of geometry which occur in cutting. This analysis offers a key for the study of engineering problems in the field of metal cutting in terms of such fundamental quantities as strain, rate of shear, friction between chip and tool, shear strength of the metal, work done in shearing the metal and in overcoming friction, etc. The two cases covered are, in essence, that of a straight-edged cutting tool moving relative to the work-piece in a direction perpendicular to its cutting edge, termed “orthogonal cutting,” and that of a similar cutting tool so set that the cutting edge is oblique to the direction of relative motion of tool and work, termed “oblique cutting.” Equations are developed which permit the calculation of such quantities as those just enumerated from readily observable values. The theoretical findings are particularly applicable and significant in the case of present-day high-speed machining operations with sintered-carbide tools.

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