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).
Page of calculations for determining the arc of contact and number of teeth in contact for gears.
| Identifier | ExFiles\Box 136\1\ scan0317 | |
| Date | 12th April 1940 guessed | |
| -2- During the passage of a pair of tooth profiles into and out of contact this length MN is rolled off one base circle and on to another. Therefore the arc of contact measured on the base circle is MN. Measured on the pitch circle it is (MN / Cos. ø) and the number of teeth in contact is (MN / (Cos. ø pc)) where pc is the circular pitch. MN = MP + PN{Mr Northey} PN{Mr Northey} = LN - LP{Mr Lappin} LN = √(O2N2 - O2L2) = √((r₂+a₂)² - r₂²cos²ø) LP{Mr Lappin} = r₂ sin. ø ∴PN{Mr Northey} = √((r₂+a₂)² - r₂²cos²ø) - r₂ sin ø similarly MP = √((r₁+a₁)² - r₁²cos²ø) - r₁ sin ø MN = √((r₁+a₁)² - r₁²cos²ø) + √((r₂+a₂)² - r₂²cos²ø) - (r₁+r₂) sin ø and number of teeth in contact: = (1 / (Cos ø pc)) { √((r₁+a₁)² - r₁²cos²ø) + √((r₂+a₂)² - r₂²cos²ø) - (r₁+r₂)sinø } | ||