The relationship between cutting tool life (T ) in minutes and cutting speed (V) in feet/minute is expressed by Taylor’s equation: VTⁿ = K, where K is a constant. From this equation, it is possible to mathematically derive an equation to find the total tool life resulting in minimum unit cost. The equation is:

A metal machining company is evaluating three different types of cutting tool inserts for one of their high-volume NC turning operations. The specifications and cost information available for the inserts are as follows:

a. For each insert type, determine the tool life for minimum unit cost and the corresponding cutting speed.

b. Which insert type is preferred to maximize the metal removal rate (proportional to cutting speed), and hence the production rate?

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where = T-(+) (-1) Co T = tool life for minimum unit cost, minutes te tool change time, minutes c=cost per cutting edge, $/edge Co-cost of labor and overhead, $/minute n Taylor's tool life exponent