An NC lathe cuts two passes across a cylindrical workpiece under automatic cycle. The operator loads and unloads the machine. The starting diameter of the work is 3.00 in and its length = 10 in. The work cycle consists of the following steps (with element times given in parentheses where applicable):
(1) Operator loads part into machine, starts cycle (1.00 min);
(2) NC lathe positions tool for first pass (0.10 min);
(3) NC lathe turns first pass (time depends on cutting speed);
(4) NC lathe repositions tool for second pass (0.4 min);
(5) NC lathe turns second pass (time depends on cutting speed); and
(6) Operator unloads part and places in tote pan (1.00 min).
In addition, the cutting tool must be periodically changed. This tool change time takes 1.00 min. The feed rate = 0.007 in/rev and the depth of cut for each pass = 0.100 in. The cost of the operator and machine = $39/hr and the tool cost = $2/cutting edge. The applicable Taylor tool life equation has parameters: n = 0.26 and C = 900 (ft/min). Determine
(a) the cutting speed for minimum cost per piece,
(b) the average time required to complete one production cycle,
(c) cost of the production cycle.
(d) If the setup time for this job is 3.0 hours and the batch size = 300 parts, how long will it take to complete the batch?