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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).
Analysis of engine vibration, comparing 12 and 6 cylinder engines and the effects of gas and inertia on B.60 torsionals.

Identifier  ExFiles\Box 132\2\  scan0187
Date  26th October 1940 guessed
  
4.

A flat 12 cyl. 2 stroke is not really a practical proposition since two cylinders have to be fired at the same time. This causes a very bad 3/rev. vibration, giving ± 1º amplitude at 2500 R.P.M. and ± 2º at 3400 R.P.M. On the 4 stroke engine there is no 3/rev. vibration.

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5. The separate effect of gas and inertia on B.60 torsionals.

6, 5½, 5, 4½, 3½ orders are due to gas pressure alone.
4th and 3rd orders are due to gas and inertia.
2nd order is due to inertia alone.

The proportion in which gas and inertia are represented in the 4th and 3rd orders is best seen by reference to SHEET 5.

It may be pointed out, however, that gas and inertia effects are added algebraically to obtain the resultant effect.

½º amplitude due to gas and ½º amplitude due to inertia does not necessarily mean 1º amplitude due to gas plus inertia. Thus the 3rd order vibration due to inertia only is slightly worse than that obtained when the engine is under load.

In reply to your query "Would inertia still be a predominating factor if maximum m.e.p. could be maintained at 5000 R.P.M." we calculate that under these conditions the 3/rev. amplitude would actually be reduced to ± 9.65º. It is ± 10.55º under normal gas plus inertia conditions, and ± 10.9º due to inertia only.

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6. The fundamental frequency of 12 cylinder and 6 cylinder crankshafts.

The natural frequency of the 6 cylinder crankshaft under consideration is approximately 22% higher than that of the 12 cylinder - 15150 vib/min. against 12440 vib/min.

As you point out, the inertia masses of the 12 cylinder are twice those of the 6 cyl., but there is not the corresponding difference in stiffness. Both shafts have 2.75" journals - the 6 cylinder with 3/16" greater depth of metal - and the main bearing lengths are about the same.

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