Milling: cutters, operations and indexing

Why it matters

Milling makes flat faces, slots, pockets, keyways, gear teeth and free-form surfaces, and it is the main process on machining centres. Because a milling cutter has many teeth each taking a short, interrupted cut, the feeds, chip thickness and machining time are worked out differently from turning — and dividing-head indexing is still the classic way to space slots and teeth.

Key ideas

Machines. Column-and-knee (horizontal and vertical), universal (table swivels for helical work), bed-type and planer-type (heavy work), and CNC machining centres with automatic tool changers.

Cutters

• Plain (slab) mill — teeth on the periphery, axis parallel to the work surface; for wide flat surfaces on a horizontal machine.
• Side-and-face, staddle and gang mills — several cutters on one arbor to mill faces and steps together.
• Face mill — inserted teeth on the face and periphery, axis perpendicular to the surface; the main tool for flat faces.
• End mill — slots, pockets, shoulders and profiles; ball-nose end mills for 3D surfaces.
• Form cutters (gear cutters, convex/concave), slitting saws, T-slot, Woodruff key and dovetail cutters, fly cutters.

Up (conventional) vs down (climb) milling

• Up milling: cutter rotation opposes the feed at the contact. Chip thickness starts at zero and grows to a maximum; the tooth rubs before it bites, and the cutting force tends to lift the work. Safe on machines with backlash in the feed screw; preferred for scaly or hard-skinned work (the tooth starts under the scale).
• Down milling: rotation is in the direction of feed. The chip starts thick and ends thin, there is no rubbing, the force presses the work onto the table, finish and tool life are better. It needs a rigid machine with a backlash eliminator (ball screws on CNC), otherwise the cutter pulls the table in and can break.

Feed terms. Feed per tooth fz (mm/tooth), feed per revolution fz·Z (mm/rev), and table feed fm = fz·Z·N (mm/min). Feeds on milling machines are set as fm.

Chip thickness in slab milling varies along the arc of contact; its maximum is t_max = 2·fz·√(d/D) (for d ≪ D). This, not fz, governs the load per tooth.

Indexing with a dividing head. The worm-and-wheel ratio is usually 40:1, so 40 crank turns rotate the work once.

• Direct indexing — a plate on the spindle (e.g. 24 holes) for simple divisions.
• Simple (plain) indexing — crank turns = 40/n; the fractional part is taken on a hole circle of the index plate (Brown & Sharpe plates: 15, 16, 17, 18, 19, 20 / 21, 23, 27, 29, 31, 33 / 37, 39, 41, 43, 47, 49 holes).
• Angular indexing — one crank turn = 360°/40 = 9° of work rotation, so crank turns = θ/9° (θ in degrees).
• Differential indexing — for numbers (e.g. many primes above 50) not available by simple indexing; the index plate is driven through change gears so it rotates while cranking.

Formulas

• N = 1000·V / (π·D) (cutter speed, rev/min; V in m/min; D cutter diameter in mm)
• fm = fz·Z·N (table feed, mm/min; Z = number of teeth)
• MRR = w·d·fm (mm³/min; w width of cut, d depth of cut, mm)
• Slab (peripheral) milling approach: A = √(d·(D − d)); time tm = (L + A + O) / fm
• Face milling, full clearance at both ends (cutter centre on the work centre line): A = O = D/2; tm = (L + D) / fm
• t_max = 2·fz·√(d/D) (maximum uncut chip thickness, slab milling, mm)
• Simple indexing: crank turns = 40 / n; angular indexing: crank turns = θ / 9°

Worked examples

Example 1 (standard). A 300 mm long, 80 mm wide steel block is slab milled with a 100 mm diameter, 8-tooth HSS cutter at V = 30 m/min, fz = 0.1 mm/tooth, depth d = 4 mm, over-travel 2 mm. Find N, fm, machining time, MRR and t_max.

1. N = 1000·V/(π·D) = 30 000/(π × 100) = 95.5 rev/min.
2. fm = fz·Z·N = 0.1 × 8 × 95.5 = 76.4 mm/min.
3. A = √(d(D − d)) = √(4 × 96) = 19.6 mm.
4. tm = (L + A + O)/fm = (300 + 19.6 + 2)/76.4 = 4.21 min.
5. MRR = w·d·fm = 80 × 4 × 76.4 = 24 450 mm³/min.
6. t_max = 2·fz·√(d/D) = 2 × 0.1 × √0.04 = 0.04 mm — much smaller than fz.

Example 2 (GATE level). (a) A 400 mm long, 100 mm wide face is face milled with a 125 mm diameter, 10-insert face mill (centre on the work centre line) at V = 120 m/min, fz = 0.15 mm, depth 3 mm. Find the time for one pass with full clearance, and the MRR. (b) Using a 40:1 dividing head, find the indexing for 46 equal divisions and for an angle of 7°30′.

1. N = 120 000/(π × 125) = 305.6 rev/min; fm = 0.15 × 10 × 305.6 = 458.4 mm/min.
2. tm = (L + D)/fm = (400 + 125)/458.4 = 1.15 min.
3. MRR = 100 × 3 × 458.4 = 137 500 mm³/min (137.5 cm³/min).
4. Indexing 46: 40/46 = 20/23 → 20 holes on the 23-hole circle per division.
5. Angle 7°30′ = 7.5°: 7.5/9 = 5/6 = 15/18 → 15 holes on the 18-hole circle.

Common mistakes

• Writing fm = fz·N (forgetting Z) or treating fz as mm/rev.
• Leaving out the approach distance, which can be a large share of a short cut.
• Using the turning MRR formula; in milling MRR = w·d·fm.
• Saying down milling is always better — it needs a backlash-free feed drive and is poor on scaly castings.
• Indexing with 40/n but choosing a hole circle that is not a multiple of the reduced denominator.
• Taking fz as the chip thickness; in slab milling t_max = 2fz√(d/D) is much smaller.

For GATE PI

• NAT on table feed, MRR and machining time for slab, face and end milling (with approach distance).
• Maximum uncut chip thickness in slab milling; power from specific energy and MRR.
• Simple and angular indexing on a 40:1 dividing head.
• MCQs on up vs down milling, cutter types and their uses.

Quick check

1. fz = 0.1 mm, Z = 4, N = 600 rev/min. Table feed?
2. D = 50 mm, V = 80 m/min. Cutter speed?
3. Simple indexing for 24 divisions?
4. Which milling method pushes the work down onto the table?
5. Slab milling, D = 100 mm, d = 1 mm: approach distance?

Answers: 1. 240 mm/min. 2. 80 000/(π × 50) ≈ 509 rev/min. 3. 40/24 = 1⅔ turns = 1 turn + 12 holes on an 18-hole circle. 4. Down (climb) milling. 5. √(1 × 99) ≈ 9.95 mm.