Lathe Batch: Micrometer Zero Error, Taper and Tool Drift
A batch of 20 mild steel shafts is being turned on a centre lathe to 25.00 mm ±0.03 mm. The operator uses a carbide tool at 600 rpm and 0.2 mm/rev without coolant. The micrometer, when closed on its anvils, reads 0.01 mm. Measurements on the first three shafts, taken near the chuck, are 25.06, 25.07 and 25.08 mm. Shaft 10 measures 25.11 mm near the chuck and 25.04 mm at the tailstock end. The surface finish on the last few shafts is torn and bright. The operator proposes to keep turning and 'just hit the last few with emery cloth' before inspection. The customer will sample three shafts and reject the batch if any dimension is outside tolerance.
1. Correct the micrometer readings for zero error and decide the status of the first three shafts and of shaft 10 against the tolerance. Show your calculations and state the limits.
Read the worked answer
Zero error: the micrometer reads +0.01 mm when closed, so actual = reading − 0.01 mm.
| Shaft | Reading near chuck | Corrected | Status |
|---|---|---|---|
| 1 | 25.06 | 25.05 | oversize by 0.02 |
| 2 | 25.07 | 25.06 | oversize by 0.03 |
| 3 | 25.08 | 25.07 | oversize by 0.04 |
| 10 near chuck | 25.11 | 25.10 | oversize by 0.07 |
| 10 near tailstock | 25.04 | 25.03 | at upper limit |
Tolerance limits: 24.97 to 25.03 mm. None of the first three is within tolerance; all are oversize. Shaft 10 is tapered by 0.07 mm over the measured length: the chuck end is 0.07 mm above nominal +0.03, while the tailstock end is exactly at the upper limit. The batch is not capable as run. The trend from 25.05 to 25.10 over ten parts (0.05 mm) is consistent with progressive tool wear, and the taper is a separate alignment problem.
2. Evaluate the operator's emery-cloth proposal and describe the correct measurement and inspection approach for this batch.
Read the worked answer
Emery cloth is not a size-correction process. Hand polishing can remove a few micrometres unevenly, round the edges and leave abrasive grit embedded in the surface; it cannot reliably remove 0.02–0.07 mm and hold a ±0.03 mm tolerance. It may improve appearance but will not make the batch conform, and the customer samples three shafts, so hiding one bad part is not a strategy.
The correct approach:
- Stop and re-set the machine: tailstock alignment, tool height, coolant, speed/feed.
- Take a trial cut on a scrap piece or first-off, measure after it has cooled, and set the tool offset from that.
- Use a finish pass with a sharp tool and a small depth of cut; allow a spring pass if needed.
- Measure each shaft with the micrometer at three positions (near chuck, middle, tailstock) and in two directions at 90° to detect ovality.
- Record the zero error and re-check the micrometer against a gauge block or standard; a 0.01 mm zero error is enough to scrap a batch at this tolerance.
- Segregate the 20 shafts; rework only if there is enough material, otherwise scrap. Do not mix corrected and uncorrected parts.