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).
Analysis of engine vibration amplitudes and torque settings for constant friction dampers, comparing 6 and 12 cylinder engines.
| Identifier | ExFiles\Box 124\2\ scan0298 | |
| Date | 17th February 1941 | |
| Rm{William Robotham - Chief Engineer}/TAS.{T. Allan Swinden}4/ST.17.2.41 - 3 - where α = relative amplitude at each crank corresponding to unit deflection at the free end, ΣJα² = moment of inertia of the entire system referred to the free end of the crankshaft, Tɴ = resultant tangential effort at any one crank and ω = phase velocity of vibration. Therefore αs = constant x √( (Tɴ Σα) / (w²ΣJα²) ) or actual amplitude is proportional to √( (Σα) / (ΣJα²) ) and to √(Tɴ) The expression was split up into these two parts because the first shows that the 6th order vibration in the 12 cylinder, far from being twice the amplitude of that on the 6 cylinder, can be expected to be about the same. The second part shows that at higher speeds when Tɴ is solely due to inertia, and therefore twice as great for the 12 cylinder (2 cylinders/crank) as for the 6 cylinder, the amplitude of the former should be √2 times that of the latter. Referring to sheets 1 and 4 of our memo 2nd order max. amplitude of the 12 cyl. / 6 cyl. = 9.2 / 6.95 = 1.33 This is not an ideal comparison because of slightly different natural frequencies, but the order of magnitude is correct. B. The following expression was given for the optimum torque setting of a constant friction damper - 1.11 ΣαARTɴ where A = piston area R = crank radius. This expression hinges upon two expressions evolved both by Tuplin (Torsional Vibration p.211) and Den Hartog (Mechanical Vibrations p.234), and correlated by Ker Wilson in his paper on Torsional Vibration, Proc. I.A.E. February 1936. | ||