Lathe operations and machining time

Why it matters

The centre lathe is the parent of all machine tools, and turning is still the most common way to make shafts, pins, bushes and flanges. Estimating the spindle speed, number of passes and machining time correctly is how process plans, quotations and shop schedules are built.

Key ideas

Main parts of a centre lathe. Bed (rigid base with guideways), headstock (spindle, gearbox, chuck), tailstock (supports long work on a centre, carries drills and reamers), carriage (saddle, cross-slide, compound rest and tool post), apron (feed and thread-cutting mechanism with split nut), lead screw (for threading) and feed rod (for ordinary feeds). The size of a lathe is given by the swing (largest diameter over the bed) and the distance between centres.

Work-holding. Three-jaw self-centring chuck (round/hex stock, quick but limited accuracy), four-jaw independent chuck (irregular work, can be trued accurately), collets (bar stock, high accuracy), face plate (odd shapes), and between centres with a driving dog (long shafts, re-chucking without losing concentricity). Steady and follower rests support slender work against deflection.

Operations

• Straight (cylindrical) turning — tool fed parallel to the axis; reduces diameter.
• Facing — tool fed across the end, perpendicular to the axis; produces a flat end face.
• Taper turning — by swivelling the compound rest (short, steep tapers, hand feed), offsetting the tailstock (long, gentle tapers between centres), a taper-turning attachment, or a form tool (very short tapers). CNC lathes interpolate any taper.
• Parting (cut-off) and grooving — a narrow tool plunged radially.
• Drilling, boring and reaming — drill and reamer in the tailstock; boring bar on the carriage for internal diameters.
• Thread cutting — the lead screw drives the carriage so that it advances one pitch per spindle revolution.
• Knurling — a diamond or straight pattern rolled (not cut) into the surface for grip.
• Chamfering, eccentric turning, form turning, spinning.

Cutting parameters. Cutting speed V is the surface speed of the work at the cut; feed f is the tool advance per revolution; depth of cut d is the radial thickness removed in one pass (half the diameter reduction). Roughing uses large d and f with moderate V; finishing uses small d and f with higher V.

Allowances. Real machining time includes approach and over-travel (a few millimetres each) added to the length of cut, plus non-productive time for loading, measuring and tool changes.

Formulas

• N = 1000·V / (π·D) (N in rev/min; V in m/min; D in mm — use the diameter being cut, normally the larger)
• d = (D − D₁) / 2 (depth of cut per side for a single pass, mm)
• tm = (L + A + O) / (f·N) per pass (min; L length of cut, A approach, O over-travel, mm; f in mm/rev)
• Number of passes = total radial stock ÷ allowed depth per pass (rounded up).
• MRR = π·Dm·d·f·N ≈ 1000·V·f·d (mm³/min; Dm = mean diameter (D + D₁)/2)
• Facing at constant N from diameter D to the centre: tm = (D/2) / (f·N).
• Compound-rest taper: tan α = (D − d) / (2·l) (α = half taper angle; D, d end diameters; l taper length)
• Tailstock offset: s = L_job·(D − d) / (2·l) (L_job = total length of work between centres; s in mm)

Worked examples

Example 1 (standard). A 60 mm bar is turned to 55 mm over 150 mm in one pass at V = 90 m/min and f = 0.2 mm/rev, with 5 mm total approach and over-travel. Find N, the depth of cut, the machining time and the MRR.

1. N = 1000·V / (π·D) = 90 000 / (π × 60) = 477 rev/min.
2. d = (60 − 55)/2 = 2.5 mm.
3. tm = (L + A + O)/(f·N) = (150 + 5)/(0.2 × 477.5) = 155/95.49 = 1.62 min.
4. MRR = π·Dm·d·f·N = π × 57.5 × 2.5 × 0.2 × 477.5 = 43 125 mm³/min ≈ 43.1 cm³/min. (The quick estimate 1000·V·f·d = 45 000 mm³/min is a little high because it uses the outer diameter's speed.)

Example 2 (GATE level). (a) The end of a 200 mm diameter disc is faced from the outside to the centre at constant spindle speed. The cutting speed must not exceed 150 m/min and f = 0.25 mm/rev. Find the facing time. (b) A 300 mm long job between centres needs a taper from 50 mm to 40 mm diameter over a length of 100 mm. Find the tailstock offset, and the compound-rest angle if the taper were turned that way instead.

1. Highest speed is at the outer diameter: N = 1000 × 150/(π × 200) = 238.7 rev/min.
2. tm = (D/2)/(f·N) = 100/(0.25 × 238.7) = 1.68 min. (The cutting speed falls to zero at the centre — CNC lathes use constant surface speed to avoid this.)
3. Tailstock offset s = L_job·(D − d)/(2·l) = 300 × 10/(2 × 100) = 15 mm.
4. Compound rest: tan α = (D − d)/(2·l) = 10/200 = 0.05 → α = 2.86°.

Common mistakes

• Using the diameter in m with V in m/min without the 1000 factor (or vice versa) — N comes out 1000 times wrong.
• Taking the depth of cut as the full diameter reduction; it is half of it per pass.
• Forgetting approach and over-travel, or the number of passes, in time estimates.
• Using the tailstock-offset formula with the taper length instead of the whole job length.
• Computing facing time with the full diameter instead of the radius.
• Choosing the speed from the smaller diameter, so the tool overspeeds at the larger diameter.

For GATE PI

• NAT on spindle speed, machining time (single and multiple passes), MRR and cutting power (P = Fc·V).
• Facing time at constant N and at constant cutting speed; time for drilling/boring on a lathe.
• Taper turning: compound-rest angle and tailstock offset.
• MCQs on lathe parts, work-holding devices and which method suits which taper.

Quick check

1. V = 100 m/min, D = 50 mm. Spindle speed?
2. A 40 mm bar is turned to 34 mm with 1.5 mm cuts. How many passes?
3. L = 120 mm, f = 0.25 mm/rev, N = 400 rev/min, no allowances. Time per pass?
4. Which taper-turning method suits a long, gentle taper between centres?
5. What is knurling, and is it a cutting operation?

Answers: 1. 100 000/(π × 50) ≈ 637 rev/min. 2. Radial stock 3 mm ÷ 1.5 = 2 passes. 3. 120/100 = 1.2 min. 4. Tailstock offset (or a taper-turning attachment). 5. Rolling a pattern into the surface for grip — it is a forming, not a cutting, operation.