Gear manufacturing methods and indexing

(a) Methods of gear manufacture

1. Forming/shaping from material: casting (sand, die, investment), powder metallurgy, forging, cold rolling, extrusion and stamping (thin gears) - low cost for large quantity but lower accuracy.
2. Machining (cutting):
   • Form milling: a form cutter (one of a set of 8 cutters for each module, numbered by tooth number range) cuts one tooth space at a time; the work is indexed in a dividing head. Slow and less accurate.
   • Generating: a tool and work move relative to each other as if a pair of gears (hobbing, gear shaping by pinion or rack cutter) - accurate, with one cutter for all tooth counts of one module.
3. Finishing: shaving, grinding, lapping, burnishing to improve accuracy and finish.

Gear hobbing: the hob is a worm-like cutter with gashes forming cutting teeth. Hob and gear blank rotate in a fixed speed ratio (as worm and wheel), and the hob is fed across the face of the blank. For a single-start hob and $z$ teeth, the blank turns $1/z$ revolution for each revolution of the hob. Tooth form is generated by the successive cuts.

Advantages: continuous cutting and high production rate; one hob cuts all gears of the same module and pressure angle; good accuracy; can cut spur, helical, worm wheels (not internal gears or gears near shoulders).

(b) Indexing and gear dimensions

Simple indexing with 40:1 dividing head: the crank turns per division

$$n = \frac{40}{z}$$

For $z = 24$:

$$n = \frac{40}{24} = 1\frac{2}{3} = 1 + \frac{10}{15}$$

One full turn and 10 holes in a 15-hole circle (or 20 holes in a 30-hole circle).

For $z = 37$:

$$n = \frac{40}{37} = 1\frac{3}{37}$$

One full turn and 3 holes in a 37-hole circle.

Gear dimensions (module $m = 3$ mm, $z = 24$):

Answer: 1 turn + 10 holes on the 15-hole circle (24 teeth); 1 turn + 3 holes on the 37-hole circle (37 teeth); PCD 72 mm, OD 78 mm, depth 6.75 mm, circular pitch 9.42 mm.