Torsional Vibrations in Reciprocating Engine Shafts

It is well known that, in the case of reciprocating engines, there are certain critical speeds of running at which the torsional vibrations in the shaft become large in amplitude and introduce an element of danger into the system. Fairly simple methods have been devised for the practical calculation, from the constants of the machinery, of the location of these critical speeds. In these methods, the reciprocating parts of the engine are replaced by an “equivalent mass” which is assumed to contribute to the elastic vibrations of the shaft in exactly the same way as do the actual, rather complicated, system of crank, connecting-rod, piston and piston-rod. It is the main purpose of this paper to examine the correctness of this equivalence. In two particular cases examined by the author, the automatic records of the shaft vibrations at about a critical speed showed a large amplitude at the expected point, but the period of the vibration was twice that anticipated. This anomaly is examined on p.116 and the conditions of its existence exhibited.