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Bevel Pinion with a No. 6 Cutter, Filed at the Small End (Brown & Sharpe 1911)
Forge

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Forge

27. October 2026NO
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Bevel Pinion with a No. 6 Cutter, Filed at the Small End (Brown & Sharpe 1911)

The same 12-tooth, 8-pitch pinion as Brown & Sharpe's worked example, but cut the way their own shop did it: with a No. 6 cutter instead of the No. 8 they sell for it, cut to the right thickness at the large end, then filed well round at the small end. They did this only for a 12-tooth pinion running with a gear two or three times its size. Source: Brown & Sharpe, Practical Treatise on Gearing (1911), Fig. 23 example, Part I ch. IX–X, Part II ch. III and the set-over table p. 58. The blank sizes are our arithmetic with their rules; the steel and bore are ours. Picture: their Fig. 23.
Advanced
1 day

Instructions

1

Work out and turn the blank

Pitch diameter 12 ÷ 8 = 1.500 in. Angle of edge 26° 34′ and angle of face 59° 11′ (Brown & Sharpe's figures for every 12 and 24 tooth pair). Diameter increment = cos 26° 34′ × 0.250 = 0.224 in, so turn the steel blank to 1.72 in outside diameter. Face ½ in long. Try both angles with a protractor against the end of the hub.

Materials for this step:

Mild Steel BarMild Steel Bar1 length for one blank

Tools needed:

Metal LatheMetal Lathe
Lathe Cutting ToolLathe Cutting Tool
ProtractorProtractor
MicrometerMicrometer
2

Choose the cutter

Twice the back cone radius × 8 comes to about 13, which would call for a No. 8, but take a No. 6, 8-pitch bevel gear cutter (17 to 20 teeth), as Brown & Sharpe's own shop did for this pinion. Measure its thickness Tc at the pitch line, 0.145 in from its tip.

Tools needed:

Bevel Gear CutterBevel Gear Cutter
Gear Tooth Vernier CaliperGear Tooth Vernier Caliper
3

Set the head at 22° 18′

Apex distance = sec 26° 34′ × 1.5 = 1.677 in. Angle increment: tan = sin 26° 34′ ÷ 6, giving 4° 16′. Set the dividing head to the cutting angle 26° 34′ − 4° 16′ = 22° 18′ and index 12 spaces. Depth at the large end 0.270 in.

Tools needed:

Milling MachineMilling Machine
Dividing HeadDividing Head
Bevel Gear CutterBevel Gear Cutter
4

Set over and cut one side

Apex distance ÷ face = 3.35; we take the nearest column, 3¼, where a No. 6 cutter has the factor .318. Set-over = Tc ÷ 2 − .318 ÷ 8 = Tc ÷ 2 − 0.040 in. Set off centre by that amount, take up backlash, and cut round all 12 spaces.

Tools needed:

Milling MachineMilling Machine
Dividing HeadDividing Head
Bevel Gear CutterBevel Gear Cutter
5

Set over the other way and trim

Set over the same amount the other side, line the cutter up with the space at the small end, take a trial cut, and rotate toward the cutter until the tooth is right at the faces of the large end: 0.196 in at the pitch line (0.138 in at the small end). Check with the gear tooth vernier, then cut round.

Tools needed:

Milling MachineMilling Machine
Dividing HeadDividing Head
Bevel Gear CutterBevel Gear Cutter
Gear Tooth Vernier CaliperGear Tooth Vernier Caliper
6

File the small ends

The No. 6 cuts the tooth sides with a longer curve than the No. 8, so expect considerable filing: round the teeth over at the small ends, without filing them thinner at the pitch line.

Tools needed:

Fine FileFine File

Materials

1

Tools Required

9

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