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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).
Comparison of 6/rev vibration amplitude between a flat 12-cylinder engine and a B.60 engine.

Identifier  ExFiles\Box 132\2\  scan0185
Date  26th October 1940
  
2.

In Rm.{William Robotham - Chief Engineer}8/ML.26.10.40 you ask for the following information:-

1. The amplitude of the 6/rev. vibration on the flat 12 cylinder engine in relation to the same vibration on B.60.

Sheets 1 & 4 - These amplitudes are almost identical in the calculations which have been made.

As would be expected the resultant harmonic torque (Σα) is about twice as great for the flat 12 as for B.60. This is because the crankshaft gets a kick from a cylinder every cycle instead of every other cycle.

The amplitude (αs) at the free end of the crankshaft is proportional to

the resultant harmonic torque / the effective moment of inertia of the system referred to the free end of the crankshaft. = √ ( Σα / ΣJα² )

On the 12 cylinder engine there are two sets of reciprocating parts at each crankpin, therefore Σ Jα² for the 12 is almost twice that for the 6 cylinder engine.

Hence the crankshaft amplitude is the same for both engines. This happens for harmonics occurring when gas pressure is relatively important, as in the case of the 6/rev. At higher speeds the inertia effect of the double set of reciprocating parts on the 12 cylinder gains supremacy. The amplitude αs is also proportional to √TN where TN is the resultant component of tangential effort. Thus, when TN is solely due to inertia, the amplitude of the 12 cylinder crankshaft should be √2 times that of the 6.

This is borne out with reference to the 2nd order vibrations.
  
  


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