Abstract
The analysis of torsional vibrations in the running gear of reciprocating engine systems is normally carried out by neglecting the variation in inertia torques of the system arising from the motion of the reciprocating parts. When the variable inertia effect is allowed for the equation of motion taking into account the effect is non-linear. Assuming small displacements, the equation can be linearized to predict important characteristics of the motion. Such an equation when solved by numerical methods using a digital computer predicts the regions of instability and the manner in which the amplitude and frequency vary with the speed of rotation of the engine. The responses of the system show a modulation of amplitude and frequency at definite rotational speeds. The occurrence of such a modulation in amplitude and frequency is established by use of the process given by Wentzel, Kramers, Brillouin, and Jeffreys generally known as the WKBJ approximation. The method of variation of parameters and the WKBJ approximation are used to determine the time responses of the system as an independent verification of the numerical methods although this method is applicable only in a limited range of the engine speed for the specific ratio of the equivalent inertia of the reciprocating parts to the total equivalent inertia of the system. The first order term in the equation, the forcing term which represents the outer impulse from the reciprocating parts and the variable part of the elastic term are investigated for their effect on the waveforms of the responses of the system. Further investigations of the effect of external excitations on the characteristics of the motion are carried out which explain the cause of failure in some multi-cylinder engines due to secondary resonance. Various other characteristics of the variable inertia system and the complete solutions of the equation of motion including damping are explored in the present work. Theoretical results are compared with solutions of the equation obtained from an analogue computer. A discussion of results obtained by measurements on an engine in service with suspected secondary resonance and some actual cases of crankshaft failures in practice is included.