Life equation for a turning operation:

As for minimum cost, decrease in T_l and T_d will increase the production rate. Increase in cutting speed will reduce T_c but it will increase the tool changing time per component (tool life decreases at higher cutting speed); a minimum time per component (TT) (or maximum production rate) will therefore result as can be given.

The profit rate (Pr) is expressed by

                                                             ------------- (6)

where, I is income per component excluding material cost and C is cost per component excluding material cost.

  -----------------(7)

The variables which reduce the cost per component and increase the production rate will increase the profit rate. In general, the speed for maximum profit rate will differ from those for minimum cost per component and maximum production rate.

The generalized tool life equation for a turning operation is given by

  ------------------(8)

where,

T = tool life in minutes,

V = cutting speed in m/min,

f  = feed in m/rev,

d = depth of cut in m, and

K, A, B = constants.

1/n, 1/n₁, 1/n₂ are exponents of speed, feed and depth of cut, respectively.

In the following analysis, it is assumed that machine tool, tool and work material have been selected. The three criteria discussed above will be applied only to a single pass turning operations.