Turning a batch of EN8 shafts against a shift deadline
A batch of 200 EN8 shafts must be turned from Ø50 mm bar to Ø44 mm over a length of 300 mm on a centre lathe. Surface finish must be Ra 1.6 µm and the diameter tolerance is ±0.05 mm. The process sheet specifies a carbide insert with 0.8 mm nose radius, cutting speed 120 m/min, feed 0.20 mm/rev and depth of cut 2.0 mm per pass. The lathe has a stepless spindle drive; the operator sets 760 rpm. Handling and gauging take 1.2 min per piece. After the first ten pieces the operator reports chatter marks on the second pass, a taper of 0.06 mm over the length, and Ra of about 3.2 µm. The tool is set with 55 mm overhang from a 25 mm square shank, the workpiece is held in a three-jaw chuck only, and the coolant nozzle is blocked. Two 8-hour shifts are available before the assembly line stops.
1. Calculate the cycle time per piece and decide whether two 8-hour shifts are enough to complete the batch.
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Spindle speed check: N = 1000V/(πD) = 1000 × 120/(π × 50) = 764 rpm. The set 760 rpm is consistent, so cutting speed is correct at the largest diameter (it rises slightly as the bar is reduced, which is normal).
Radial stock to remove = (50 − 44)/2 = 3 mm. At 2.0 mm depth of cut per pass, 3/2 = 1.5, so two passes are needed: one at 2.0 mm and a finishing pass at 1.0 mm.
Feed rate: f_rate = f × N = 0.20 × 760 = 152 mm/min.
Machining time per pass: t = L/f_rate = 300/152 = 1.97 min.
Two passes: 1.97 × 2 = 3.95 min.
Add handling and gauging: 3.95 + 1.2 = 5.15 min per piece.
Batch time: 200 × 5.15 = 1030 min = 17.2 h (about 86% efficiency disregarded).
Available time: 2 × 8 × 60 = 960 min (16 h), and that assumes zero tool changes, no break, no warm-up, and 100% availability - unrealistic. So the batch will not finish in two shifts; with a realistic 85% utilisation the available cutting time is about 816 min against 1030 min required, a shortfall of over 3.5 hours. Plan either a third partial shift/overtime, or a process change to raise the removal rate.
2. Diagnose the chatter, the 0.06 mm taper and the Ra 3.2 µm from the evidence given, ranking the causes by likelihood.
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Chatter on the second pass - most likely workpiece deflection plus tool overhang. The bar is 300 mm long and finishes at Ø44 mm, so length/diameter = 300/44 ≈ 6.8, which is slender. Held in a three-jaw chuck only, with no tailstock support, the free end deflects under radial force. The second pass is at 1.0 mm depth on an already-reduced, less stiff bar, which is exactly when chatter appears. The 55 mm tool overhang from a 25 mm shank is about 2.2 × shank height; the usual rule is to keep overhang below about 1.5 × shank height, so the tool is also a compliant element.
Taper of 0.06 mm - same root cause. Deflection is greatest at the free end and least at the chuck, so the bar machines oversize at the tail end. A worn or mis-set tailstock, a bell-mouthed chuck jaw seat, and bed wear near the headstock can add to this, but with a slender unsupported bar, deflection is the first suspect. Note 0.06 mm also exceeds the ±0.05 mm tolerance, so the parts are already non-conforming on size, not just finish.
Ra 3.2 µm - chatter, not feed. With a 0.8 mm nose radius at 0.20 mm/rev, the theoretical roughness is only around 1.6 µm (Ra ≈ f²/32r = 0.04/25.6 mm ≈ 1.6 µm). A measured 3.2 µm therefore points to vibration, plus the blocked coolant nozzle causing built-up edge and smearing, and possibly a dull insert. Feed alone would not explain it.
3. Recommend the changes needed to hold Ra 1.6 µm and ±0.05 mm within the deadline, and show the effect on output.
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Rigidity first - this is a setup problem, not a speed problem.
- Support the free end with a revolving centre in a drilled centre hole (or use a fixed steady if the centre is not practical). This alone removes most of the deflection and taper.
- Reduce tool overhang from 55 mm to about 30–35 mm, or move to a 32 mm shank holder. Check the insert edge and index it if worn.
- Restore coolant flow; clear the nozzle and confirm it reaches the cutting zone, since built-up edge is contributing to the poor finish.
- Make the first pass the deep one, 2.5 mm, and the finishing pass 0.5 mm - a light finishing cut with a sharp edge gives better finish than a 1.0 mm cut on a vibrating bar, and 0.5 mm avoids rubbing.
- For the finishing pass, raise speed to about 160–180 m/min and drop feed to 0.10 mm/rev. Theoretical Ra then becomes f²/32r = 0.01/25.6 mm ≈ 0.4 µm, leaving margin for real-world vibration.
Output effect: finishing pass time rises (at 0.10 mm/rev and 900 rpm, feed rate 90 mm/min, 300/90 = 3.3 min against 1.97). Total per piece becomes 1.97 (rough) + 3.3 (finish) + 1.2 (handling) ≈ 6.5 min, i.e. 1300 min = 21.7 h for the batch.
Judgement: the corrected process is slower, so the deadline cannot be met on one lathe with a stable, in-tolerance finish. The honest options are to release a third shift, split the batch across two lathes, or re-negotiate the delivery - not to chase the deadline by running unsupported and shipping parts with 0.06 mm taper and Ra 3.2 µm.