7.4 Single Variable Searches

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

7.4.1 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,