Set-over taper and M20 × 2.5 thread on a centre lathe
An adapter is turned from Ø60 mm MS bar on a centre lathe: a 1:10 taper on diameter over a 120 mm length (Ø60 down to Ø48), followed by an M20 × 2.5 external thread on the small end. The lathe has a 6 mm-pitch lead screw, a change-gear set of 30, 40, 50, 60, 80, 100 and 120 teeth, a compound rest graduated in degrees and minutes with 90 mm of slide travel, and a tailstock set-over of up to 20 mm on a 300 mm bed length. No taper turning attachment is fitted. The batch is 25 pieces. The turner plans to use tailstock set-over for the taper because it is quick, and to cut the thread in six passes starting with 0.5 mm radial depth. The taper is checked with a dial indicator on a surface plate and the thread with a GO/NO-GO ring gauge.
1. Calculate the set-over and the compound-rest angle, and justify which method should actually be used for this batch.
Read the worked answer
Angle. tan α = (D − d)/(2L) = (60 − 48)/(2 × 120) = 12/240 = 0.05 → α = 2.862° = 2°51′45″ (included angle 5°43′).
Set-over. Set-over = (bed length between centres/taper length) × (D − d)/2 = (300/120) × 6 = 15 mm, which is inside the 20 mm capacity.
Method judgement. The compound rest cannot do this job: the taper is 120 mm long and the slide travels only 90 mm, so the job would have to be re-set mid-cut, leaving a step and a mismatch. A taper attachment is not fitted, so set-over is the only power-feed option.
A 5°43′ included angle is within the practical range for set-over (roughly up to 8°), so the method is geometrically acceptable, but 15 mm is a large offset: the bar axis is tilted, the ends swing, centre holes wear and every piece must be re-set. Therefore set the tailstock with a dial indicator, not by trusting graduations; lubricate the centres; keep the bar overhang short; take light cuts; and verify each piece on the surface plate rather than relying on the set-over figure.
2. Work out the change gears for the 2.5 mm pitch and state the thread depth, core diameter, pitch diameter and the tapping drill for the mating nut.
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Gearing. Driver/driven = pitch to cut / lead-screw pitch = 2.5/6 = 5/12. Multiply by 10: 50 teeth on the spindle stud (driver), 120 teeth on the lead screw (driven), with any convenient idler to bridge and to give the correct hand.
Check: pitch cut = lead-screw pitch × driver/driven = 6 × 50/120 = 2.50 mm exactly, so no approximation error and no thread error accumulated per revolution.
Thread data (ISO metric, 60°).
- Depth of thread = 0.6134 × P = 0.6134 × 2.5 = 1.534 mm radial
- Core (minor) diameter = 20 − 2 × 1.534 = 16.93 mm
- Pitch diameter = 20 − 0.6495 × 2.5 = 18.38 mm
- Tapping drill for the nut = 20 − 2.5 = 17.5 mm
Note that the ring gauge accepts a thread whose pitch diameter, not core diameter, is within limits; if the tool has a rounded crest (as standard inserts do), the core diameter will measure larger than 16.93 mm and that is acceptable as long as the pitch diameter and flank angle are right.
3. Critique the six-pass plan starting at 0.5 mm radial depth, and explain how the half-nut should be engaged.
Read the worked answer
Depth distribution. Total radial depth is 1.534 mm. Six passes with progressively reducing depth work, for example 0.50 + 0.35 + 0.25 + 0.18 + 0.14 + 0.114 = 1.534 mm.
Critique. A 0.50 mm radial first pass on a 2.5 mm pitch means the full 60° flank is engaged over a long helix; the forces are high and on a slender small end the work can spring. A safer plan is 0.35 as the first pass with the missing depth redistributed (e.g. 0.35, 0.30, 0.25, 0.22, 0.20, 0.214) and a final light spring pass without in-feed to remove deflection. Too-light final passes cause rubbing and a torn flank, so keep the last cut at about 0.10–0.15 mm.
Half-nut engagement. The lead screw makes 6/2.5 = 2.4 work revolutions per turn, which is not a whole number, so the half-nut cannot be closed at random. Engagement repeats only every 5 lead-screw revolutions (= 30 mm of carriage travel = 12 work threads). Use the thread-chasing dial and always close on the same mark, or - better for a 20 mm thread - leave the half-nut engaged, reverse the spindle to return, and re-in-feed.