ART
BEAUTY & WELLNESS
CRAFT
CULTURE & HISTORY
ENTERTAINMENT
ENVIRONMENT
FOOD & DRINKS
REVERSE ENGINEERING
SCIENCES
SPORTS
TECHNOLOGY
WEARABLES
Mitre Gears: a 1:1 Bevel Pair Cut on the Milling Machine (Brown & Sharpe 1911)
Two equal bevel gears on shafts at right angles are mitre gears, and one cutter cuts both. A rotary cutter can only be right for one end of a bevel tooth, so Brown & Sharpe cut each space twice, set off centre to each side, then file the small ends round. Every figure here comes from their rules, worked out for a pair of 16 teeth, 8 pitch.
Source: Brown & Sharpe, Practical Treatise on Gearing (1911), Part I ch. IX–X and Part II ch. III; set-over table p. 58. The tooth count, pitch, face width, steel and bore are ours, and so is the arithmetic. Picture: Brown & Sharpe's Fig. 24.
Advanced
2 days
Instructions
1
1
Work out and turn two blanks
Work out and turn two blanks
Ours: 16 teeth, 8 pitch, so pitch diameter 2.000 in. Mitre gears have a 45° centre angle (tangent 16/16). Diameter increment = cos 45° × working depth 0.250 = 0.177 in. Apex distance 1.414 in. Angle increment: tan = sin 45° ÷ 8, giving 5° 03′; cutting and face angle 45° − 5° 03′ = 39° 57′. Turn two blanks from steel to 2.18 in outside diameter, with the angle of edge 45° and the angle of face 39° 57′, tried with a protractor against the end of the hub. Face length ⅜ in (ours; no more than a third of the 1.414 in apex distance). Bore and hub are ours.
Materials for this step:
Mild Steel Bar1 length for two blanksTools needed:
Metal Lathe
Lathe Cutting Tool
Protractor
Micrometer2
2
Choose the cutter
Choose the cutter
Back cone radius 1.414 in: twice that × 8 pitch = 22.6 teeth, so a No. 5, 8-pitch bevel gear cutter (21 to 25 teeth). One cutter does both gears. Measure its thickness Tc at the pitch line, 0.145 in (1.157 ÷ 8) from its tip.
Tools needed:
Bevel Gear Cutter
Gear Tooth Vernier Caliper3
3
Set the head and the depth
Set the head and the depth
Mount the blank on the dividing head, set to the cutting angle of 39° 57′, to index 16 spaces. Set the depth at the large end to the working depth plus clearance, 0.270 in. Clearance stays the same at the small end.
Tools needed:
Milling Machine
Dividing HeadBevel Gear Cutter4
4
Set over and cut one side of every tooth
Set over and cut one side of every tooth
Set-over: apex distance ÷ face = 1.414 ÷ 0.375 = 3.77, so use the 3¾ column, where a No. 5 cutter has the factor .293. Set-over = Tc ÷ 2 − .293 ÷ 8 = Tc ÷ 2 − 0.037 in. Set the work off centre by that amount to one side, taking up backlash. Run the cutter through, indexing round all 16 spaces.
Tools needed:
Milling MachineDividing HeadBevel Gear Cutter5
5
Set over the other way and trim to thickness
Set over the other way and trim to thickness
Set over by the same amount on the other side of centre and rotate the blank to line the cutter up with the space at the small end. Take a trial cut, then rotate the blank toward the cutter until the tooth is right: 0.196 in thick at the large end and 0.144 in at the small end. Check both ends with the gear tooth vernier. Right at the large end but thick at the small end means too much set-over; the other way round, too little.
Tools needed:
Milling MachineDividing HeadBevel Gear CutterGear Tooth Vernier Caliper6
6
Cut round, then make the second gear
Cut round, then make the second gear
Cut the second side of every tooth with that setting. Cut the second blank the same way with the same cutter.
Tools needed:
Milling MachineDividing HeadBevel Gear Cutter7
7
File the small ends
File the small ends
Round the teeth over at the small ends with a file, where the cutter could not. Do not file them thinner at the pitch line.
Tools needed:
Fine FileMaterials
1- 1 length for two blanksPlaceholder
This blueprint makes
CC0 Public Domain
This blueprint is released under CC0. You are free to copy, modify, distribute, and use this work for any purpose, without asking permission.
Support the Maker by purchasing products through their Blueprint where they earn a Maker Commission set by Vendors, or create a new iteration of this Blueprint and include it as a connection in your own Blueprint to share revenue.