The existence of cutting rate-tool life (R-T) characteristic functions for material removal operations is introduced in this paper. This new concept enables a comprehensive development of a theory for economic optimization encompassing commonly used criteria of cost, production rate, and profit rate in machining when more than one cutting variable is involved. The theory provides conditions for the existence of economic optima, all of which must lie on the R-T characteristic curve for a given operation. The analysis of the theory is carried out for one and two independent cutting variables. For these two cases, it is proven that the locus of the tangent points of constant cutting rate and constant tool life curves describes the R-T characteristic curve, and also that the tool life is maximum along a given constant cutting rate curve at the point of tangency and vice versa. This geometric interpretation provides useful application of the concept as shown in Part 2.

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