Taylor Tool Life Versus Delivery Deadline
A CNC lathe must turn 300 identical mild-steel shafts from 200 mm diameter bar to 180 mm diameter over a 300 mm length in one pass. Feed is 0.25 mm/rev. At a cutting speed of 120 m/min the tool life is 20 min; the Taylor exponent is 0.25. Tool change takes 1.5 min; machine and operator cost is ₹900/h; each cutting edge costs ₹450. The customer requires the batch within 30 machining hours. The foreman proposes raising the speed to 160 m/min to 'save time'. Overtime is available at an additional ₹450/h if the normal 30-hour window is exceeded. You must decide whether to run at 120 m/min with overtime, at 160 m/min, or at some intermediate speed, considering both cost and delivery.
1. Compute machining time per piece, tool life, tool changes per piece, and total time per piece at 120 and 160 m/min.
Read the worked answer
At 120 m/min: N=1000V/(πD)=1000×120/(π×200)=191 rpm. Time/pc=L/(fN)=300/(0.25×191)=6.28 min. Taylor: T=20 min, so edges/pc=20/6.28=3.18; tool-change time/pc=1.5/3.18=0.47 min; total=6.75 min/pc. At 160 m/min: N=255 rpm; time=4.71 min; T=20(120/160)^(1/0.25)=20(0.75)^4=6.33 min; edges/pc=6.33/4.71=1.34; change=1.5/1.34=1.12 min; total=5.83 min/pc.
2. Compare the batch cost at 120 m/min with overtime and at 160 m/min.
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Batch time at 120: 300×6.75=2025 min=33.75 h; overtime=3.75 h; overtime cost=3.75×450=₹1,688. Cost/pc: machining=6.75×15=₹101.25; tool=450/3.18=₹141.5; total=₹242.8; batch=300×242.8=₹72,840; plus overtime=₹74,528. At 160: batch=300×5.83=1749 min=29.15 h, no overtime. Cost/pc: machining=5.83×15=₹87.45; tool=450/1.34=₹335.8; total=₹423.3; batch=₹126,990. The 160 m/min plan is much more expensive because tool consumption dominates.
3. Determine an intermediate speed that meets 30 hours without overtime, and recommend a final plan.
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To meet 30 h without overtime, total time/pc must be ≤30×60/300=6.00 min. At 150 m/min: N=239 rpm; time=5.03 min; T=20(120/150)^4=8.19 min; edges/pc=1.63; change=0.92 min; total=5.95 min; batch=1785 min=29.75 h. Cost/pc=5.95×15+450/1.63=₹89.3+₹276.1=₹365.4; batch=₹109,620. This meets delivery but costs about ₹35,000 more than 120 m/min plus overtime. Recommendation: run at 120 m/min and authorize 3.75 h overtime, provided the 30-hour window is a customer requirement and overtime is permitted; if overtime is not permitted, use about 150 m/min, not 160, because 160 wastes tools for no delivery benefit.