In Part 1 of this paper, two tool-life equations are derived, one limited equation and one general tool-life equation, between the variables cutting speed, chip equivalent, and tool life. The chip equivalent, introduced by Woxén, is a well-defined function of feed, depth of cut, nose radius, and side-cutting-edge angle. The limited equation takes into account the variation of Taylor’s exponent n with the value of the chip equivalent, but the equation is only valid within certain limits of cutting speed and chip equivalent. A general equation is then derived on the basis of the limited equation. In Part 2 an expression called the productivity is derived. This relationship is valid for either maximum production or minimum cost and, combined with the general, hyperbolic, tool-life equation, it is used to investigate the optimum combination of tool-life, cutting speed, and chip equivalent.

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