Screw Threads and Gear manufacturing Methods

(a) Production of screw threads

Machining (cutting):

• Single-point cutting on a lathe: a tool ground to the thread form is moved along the work by the lead screw; several passes. Gives any pitch and size, accurate, but slow.
• Taps and dies: internal threads are cut by tap, external by die, in one pass or a few; fast for small sizes.
• Thread milling: a rotating multi-tooth cutter, used for large threads, and for worms and lead screws; CNC thread milling is done by helical interpolation.
• Thread chasing, whirling.

Thread rolling: the blank is pressed between hardened dies (flat reciprocating or round rolling dies) and the thread is formed by plastic deformation (cold). No chips; the grain follows the thread contour, and the surface is work hardened and smooth. Gives higher strength and much better fatigue life, very high production rate, but only for ductile materials and a limited hardness, with the die cost.

Thread grinding: a wheel dressed to the thread form grinds the thread, either by traverse (single rib wheel) or plunge (multi-rib wheel). It gives the highest accuracy and finish and can cut hardened material (gauges, lead screws, ball screws) but costs more and is slow.

(b) Change gears

For thread cutting the work (spindle) and the lead screw are linked by a gear train so that the carriage moves one pitch of the job per revolution of the work:

$$\frac{\text{Pitch of job}}{\text{Pitch of lead screw}} = \frac{\text{Driver (on spindle)}}{\text{Driven (on lead screw)}}$$ $$\frac{2.5}{6} = \frac{5}{12} = \frac{25}{60}$$

The driver on the spindle stud has 25 teeth and the driven gear on the lead screw has 60 teeth (a simple train, gears available in steps of 5 teeth). A compound train, e.g. $\frac{25}{50}\times\frac{40}{48}$, gives the same ratio $5/12$ if the exact simple gears are not available.

Answer: driver 25 teeth, driven 60 teeth (ratio 5/12).

(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.