Chatter, Taper and a Micrometer With a Zero Error
On a centre lathe, a 45 mm diameter mild steel bar 300 mm long is to be turned to 40.00 ± 0.05 mm over a 200 mm length, then chamfered 1.5 mm × 45°. The job is set in a 3-jaw chuck with no tailstock support, spindle speed 480 rpm, feed 0.25 mm/rev, and a high-speed steel tool with a visibly worn nose. The coolant pump is not working. After the first pass the diameter measures 40.42 mm at the chuck end and 40.36 mm at the free end on a micrometer that reads 0.03 mm when the anvils are closed; nobody checked the zero before measuring. The surface shows evenly spaced chatter marks along the whole length.
1. Correct the readings for the micrometer error, state the true taper, and decide what finishing allowance remains and whether the part can still be saved.
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Zero error: the micrometer reads 0.03 mm with the anvils closed, so every reading is 0.03 mm too large. Corrected readings = reading − 0.03 mm.
- Chuck end: 40.42 − 0.03 = 40.39 mm
- Free end: 40.36 − 0.03 = 40.33 mm
- True taper = 0.06 mm over 200 mm (0.03 mm per 100 mm).
Allowance: to reach 40.00 mm the diameters must be reduced by 0.39 mm and 0.33 mm, i.e. a radial depth of cut of about 0.17–0.20 mm, or roughly 0.35 mm on diameter at the worst section.
Can it be saved? Yes, but not in one pass with a worn tool at 0.25 mm/rev - that is a roughing cut and the chatter marks would remain. Plan on one roughing pass of about 0.25 mm on diameter and a finishing pass of 0.08–0.10 mm on diameter with a freshly ground tool, low feed and coolant, then measure again. Leave the 1.5 × 45° chamfer for last so it is not cut twice.
2. Diagnose the chatter and the taper, giving the reason for each and ranking the causes by contribution.
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Chatter - likely combined causes, ranked:
- Workpiece rigidity: overhang-to-diameter ratio is about 300/45 ≈ 6.7, and there is no tailstock support. Above roughly 3–4 × D, a slender bar deflects and regenerates vibration.
- Worn tool nose: a dull tool increases cutting force and rubs instead of cutting, feeding energy into the vibration.
- Speed too high for HSS in mild steel: cutting speed = πDN/1000 = π × 0.045 × 480/1000 ≈ 68 m/min, roughly double the 30–40 m/min normally used for HSS in MS.
- No coolant - built-up edge and thermal growth add to the instability.
Taper: a deflection taper (bar springs away most at the free end) plus possible tailstock/headstock misalignment or bed twist. The 0.06 mm over 200 mm pattern - smaller at the free end - is consistent with deflection and tool push-off, not with a badly worn bed, which would show a step or a hollow.
Diagnosis order matters: support the work first, then sharpen the tool and slow down; only then check machine alignment with a test bar, because a deflection taper masks alignment truth.
3. Write the corrected process plan (speed, feed, support, measurement) for the finishing operation.
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- Support: fit a revolving centre in a drilled and chamfered end; this alone removes most of the 0.06 mm deflection taper. Check the centre runs true.
- Speed: target 30–35 m/min for HSS in MS → N = 1000 × 32 ÷ (π × 40) ≈ 255–280 rpm, so reset from 480 rpm to about 270 rpm.
- Tool: regrind or replace the HSS bit - correct side and back rake, small nose radius, sharp edge. A sharp tool at low feed gives the surface finish; the worn tool cannot.
- Roughing pass: 0.25 mm on diameter, feed 0.2 mm/rev, with coolant restored (repair or use a brush-and-can supply and record the pump defect on the maintenance card).
- Finishing pass: 0.08–0.10 mm on diameter, feed 0.05–0.08 mm/rev, high speed within the HSS limit, coolant on. Spring passes (one cut at the same setting) help if deflection persists.
- Measure: zero the micrometer with the anvils closed, record the error, then measure at three positions and two diameters 90° apart to catch ovality. Cross-check with a vernier or snap gauge.
- Chamfer 1.5 × 45° last, then deburr and mark the part before it leaves the machine.