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Gear manufacturing and simple indexing

Short answer

Gear manufacturing methods include casting, forming, machining, and finishing. Hobbing generates teeth continuously with higher accuracy and speed, while form milling cuts one tooth at a time with a form cutter and requires indexing. For module 3 mm, 34 teeth: outside diameter = 108 mm, tooth depth = 6.75 mm. Simple indexing: 1 full turn plus 3 holes on the 17-hole circle.

Name the methods of manufacturing gears and compare gear hobbing with form milling. A spur gear of module 3 mm and 34 teeth is to be cut on a milling machine using the dividing head (ratio 40:1). Find (a) the outside diameter and tooth depth, and (b) the indexing for each tooth by simple indexing, using the Brown and Sharpe plate holes 15, 16, 17, 18, 19 and 20.

Gear manufacturing methods

  • Casting (sand casting, die casting) for rough gears.
  • Forming: powder metallurgy, extrusion, cold rolling of gears.
  • Machining: milling with a form cutter, gear shaping, gear hobbing, gear planing, broaching.
  • Finishing: shaving, grinding, lapping, honing.

Hobbing versus form milling

Form millingHobbing
A form (disc) cutter cuts one tooth space at a timeA hob (worm-like cutter) cuts continuously; the teeth are generated by rolling
Needs an indexing head; each cutter profile serves a range of tooth numbers, so it is slightly inexactHigher profile accuracy; one hob cuts all gears of the same module
Slow; for single parts or small lotsFast; for large production
Only spur and helical gearsSpur, helical gears and worm wheels

(a) Gear dimensions

Do=m(z+2)=3×36=108 mmTooth depth=2.25m=6.75 mmPitch circle diameter=mz=102 mm\begin{aligned} D_o &= m(z+2) = 3\times 36 = 108\ \text{mm} \\ \text{Tooth depth} &= 2.25m = 6.75\ \text{mm} \\ \text{Pitch circle diameter} &= mz = 102\ \text{mm} \end{aligned}

A module 3 involute cutter for the 26 to 34 teeth range is used: No. 4 in the Brown and Sharpe 8-cutter numbering (No. 5 in the metric module cutter numbering, which runs the other way).

(b) Indexing

Simple indexing with a 40:1 worm gear:

Index crank turns=40z=4034=1634=1317\text{Index crank turns} = \frac{40}{z} = \frac{40}{34} = 1\frac{6}{34} = 1\frac{3}{17}

So after cutting each tooth, turn the crank by 1 full turn plus 3 holes in the 17-hole circle (set the sector arms to 3 spaces).

Answer: outside diameter = 108 mm, tooth depth = 6.75 mm; indexing = 1 full turn + 3 holes on the 17-hole circle.

✓ Answer checked by Claude Opus 5.5 (high effort)

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