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12.4 Single Variable Searches


• For simple single value problems use derivatives and find the maxima/minima.


12.4.1 Example Problem


• As with most engineering problems we want to get the highest return, with the minimum investment. In this case we want to minimize costs, while increasing cutting speeds.


• EFFICIENCY will be the key term - it suggests that good quality parts are produced at reasonable cost.


• Cost is a primarily affected by,

- tool life

- power consumed


• The production throughput is primarily affected by,

- accuracy including dimensions and surface finish

- mrr (metal removal rate)


• The factors that can be modified to optimize the process are,

- cutting velocity (biggest effect)

- feed and depth

- work material

- tool material

- tool shape

- cutting fluid


• We previously considered the log-log scale graph of Taylor’s tool life equation, but we may also graph it normally to emphasize the effects.



• There are two basic conditions to trade off,

- Low cost - exemplified by low speeds, low mrr, longer tool life

- High production rates - exemplified by high speeds, short tool life, high mrr

*** There are many factors in addition to these, but these are the most commonly considered




• A simplified treatment of the problem is given below for optimizing cost,





• We can also look at optimizing production rates,



• We can now put the two optimums in perspective,



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