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 for beam deflection and reaction forces related to crankpin and balance weight loads on a journal.
| Identifier | ExFiles\Box 115\2\ scan0383 | |
| Date | 10th January 1939 guessed | |
| - 5 - A further assumption which was included in the previous calculation is that torsion effects which tend to misalign the journal centres do not occur at the end throws. This is practically true for No.7 but not for No.1. throw. No.7 is the journal mainly under consideration as it is the one which has given the most trouble. [Diagram of a cantilever beam with reaction R at one end, force F at distance b, and total length l=a+b] - EI d²y/dx² = Rx - F[x-b] ∴ - EI dy{F R Danby}/dx = Rx²/2 - F/2[x-b]² + A let a+b = l. if x = l, dy{F R Danby}/dx = 0 ∴ Rl²/2 - Fa²/2 + A = 0. - EI dy{F R Danby}/dx = Rx²/2 - F/2[x-b]² + Fa²/2 - Rl²/2 - EI y = Rx³/6 - F/6[x-b]³ + Fa²x/2 - Rl²x/2 + B. if x=0 y=0 ∴ B=0 x=l y=0 ∴ Rl³/6 - Fa³/6 + Fa²l/2 - Rl³/2 = 0. ∴ Fa²l/2 - Fa³/6 = Rl³/3 ∴ R = Fa²/(2l³) (3l-a). - EI dy{F R Danby}/dx |x=0 = Fa²/2 - Rl²/2 = Fa²/2 - Fa²/4l {3l-a} = Fa²/4l {2l+a-3l} ∴ EI dy{F R Danby}/dx = Fa²/4l {l-a} where a = 2.812 l = 5.025 for crankpin load. and a = 4.338 l = 5.025 for balance weight load. EI = 7.56x10⁶ in plane of webs 14.53 x10⁶ " " L | ||