Slender Shaft Chatter and Mid-Span Undersize on a Manual Lathe
A 1045 cold-drawn shaft 600 mm long must finish at Ø36.00 ±0.02 mm with Ra 1.6 µm. It is held in a 3-jaw chuck with about 45 mm in the jaws and supported at the tailstock with a live centre; no steady rest is used. Roughing leaves 0.8 mm on diameter (Ø36.80). The operator takes a 0.40 mm depth cut with a CNMG 432 insert (0.8 mm nose radius) at 180 m/min and 0.25 mm/rev, expecting to finish at nominal size. After the pass, the middle of the shaft shows visible chatter and micrometer readings are 36.018 mm near the chuck, 35.982 mm at mid-span, and 36.010 mm near the tailstock. Surface finish is Ra 3.2 µm. The operator plans another 0.10 mm depth pass to clean up the chatter, then polish. The lathe top speed is 2000 rpm, and a steady rest is available but not mounted.
1. Explain what the three micrometer readings indicate and whether the fault is tailstock misalignment or workpiece deflection. Show your reasoning.
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Reasoning: The readings are 36.018 mm at the chuck, 35.982 mm at mid-span and 36.010 mm at the tailstock. The middle is low and both ends are near nominal, which is a symmetric barrel-shaped error. Tailstock misalignment produces a monotonic taper from one end to the other, for example 36.018 at the chuck and 35.982 at the tailstock, not a low middle. The length-to-diameter ratio is 600/36 ≈ 16.7, well above the roughly 10:1 point where a tailstock alone stops being enough support. The radial cutting force pushes the workpiece away from the tool most at mid-span, where stiffness is lowest. Chatter then makes the effective depth of cut vary, so mid-span is both undersize and rough.
Conclusion: the fault is workpiece deflection and compliance, not tailstock offset. Check tailstock alignment separately with a test bar, but do not correct this part by offsetting the tailstock.
2. State whether another cut is permissible on this part. Then recommend changes to speed, feed, depth of cut and support for the next part. Calculate the spindle speed at Ø36 for 200 m/min.
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No further cut is permissible on this part. The minimum size is 35.98 mm and mid-span is 35.982 mm, only 0.002 mm above the limit. A 0.10 mm depth cut removes 0.20 mm on diameter, so the shaft would finish near 35.78 mm and be scrap. Even polishing risks going below 35.98 mm because there is almost no stock left.
For the next part, calculate speed first: n = 1000Vc/(πD) = 1000 × 200/(π × 36) = 1768 rpm, within the 2000 rpm limit. Radial force is roughly proportional to feed × depth of cut. The current finishing index is 0.25 × 0.40 = 0.10. A proposed 0.10 mm/rev and 0.25 mm depth gives 0.025, about 25% of the original force, so deflection should fall from about 0.036 mm to roughly 0.009 mm before support is added. Use a 0.4 mm nose radius insert, positive rake and a sharp edge. Rough to within 0.3-0.4 mm on diameter, mount a steady rest at mid-span with a bronze tip or cathead, indicate the journal to 0.02 mm, then finish at 0.25-0.30 mm depth, 0.10 mm/rev and 200 m/min, followed by one spring pass at the same setting.
3. What inspection would you perform before accepting a shaft from this process, and why is polishing after a chatter pass not acceptable?
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Measure at six stations along the length and at 0°, 90°, 180° and 270° at each station with a 0.001 mm micrometer. Check roundness and lobing on V-blocks with a lever indicator, and check straightness on a surface plate with a roller or dial indicator. Compare the surface with a roughness specimen or use a profilometer against Ra 1.6 µm. Check for chatter witness marks and for a work-hardened or overheated layer.
Polishing after a chatter pass is not acceptable because it removes the peaks but leaves the waviness and the cold-worked or heat-affected layer. It also removes size from a part that has almost no stock left. A polished chatter mark can still fail a surface-finish requirement and may relax or distort after the final size is set. Acceptance requires size, taper, roundness, Ra 1.6 µm and no visible chatter.