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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Calculations and diagrams for gear hobbing, including setup, modification, and teeth contact.

Identifier  ExFiles\Box 136\5\  scan0345
Date  15th January 1940 guessed
  
TO FIND THE EXTREME END POSITION FOR SETTING A HOB WHEN CUTTING SPUR GEARS.

Fig. #5

Rь = BASE RAD.
R = PITCH RAD.
R₀ = OUTSIDE RAD.
C = DISTANCE BELOW PITCH LINE ON HOB TO LAST POINT OF CONTACT
Φ = PRESSURE ANGLE

Cos α = Rь / R₀
C = R₀ Cos(α - Φ) - R
D = R₀ Sin(α - Φ)

*F MUST BE SUBSTANTIALLY LARGER THAN D TO PROVIDE PROPER STRENGTH OF LAST TOOTH

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TO FIND START OF MODIF. ON HOB FOR KNOWN MODIF. OF GEAR

Fig. #6

Φ = PRESSURE ANGLE
R = PITCH RAD
Rь = BASE RAD.
A = RAD. TO START OF MODIFICATION ON GEAR
H = DISTANCE BELOW PITCH LINE WHERE SECOND ANGLE STARTS ON HOB FOR MODIFICATION OF GEAR

Cos β = Rь / A
δ = β - Φ
H = A · COS δ - R

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TO FIND Nº OF TEETH IN CONTACT

Fig #7

Φ = PRESSURE ANGLE
C = CENTER DISTANCE
R₁ = PITCH RAD. OF PINION
R₂ = PITCH RAD. OF GEAR
(Rь)₁ = BASE RAD. OF PINION
(Rь)₂ = BASE RAD. OF GEAR
(R₀)₁ = OUTSIDE RAD. OF PINION
(R₀)₂ = OUTSIDE RAD. OF GEAR
Pₙ = NOR. CIR. PITCH AT BASE
Y = Nª OF TEETH IN CONTACT

Y = (√(R₀)₁² - (Rь)₁² + √(R₀)₂² - (Rь)₂² - C · Sin Φ) / Pₙ

For External Gears
  
  


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