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).
Technical document detailing the calculation of the arc of contact for gear teeth.
| Identifier | ExFiles\Box 136\2\ scan0255 | |
| Date | 15th 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 an-other. Therefore the arc of contact measured on the base circle is MN. Measured on the pitch circle it is (MN / Cos. φ) and the number of teeth in contact is (MN / (Cos. φ 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 - r2²cos²φ) LP{Mr Lappin} = r2 sin. φ ∴PN{Mr Northey} = √((r2+a2)² - r2²cos²φ) - r2 sin φ similarly MP = √((r1+a1)² - r1²cos²φ) - r1sin φ MN = √((r1+a1)² - r1² cos² φ) + √((r2+a2)² - r2²cos² φ) - (r1+r2) sin φ, and number of teeth in contact: = (1 / (Cos φ pc)) * [√((r1+a1)² - r1²cos²φ) + √((r2+a2)² - r2²cos²φ) - (r1+r2)sinφ] | ||