Effect of Damping on Parametrically Excited Torsional Vibrations of Reciprocating Engines Including Gas Forces

In recent years, several cases of secondary resonance have been found in torsional vibrations of crankshaft systems. In some reciprocating large marine diesel engine systems, these effects have been a contributing factor of catastrophic failures. In these instances, design based on invariable inertia characteristics of the systems and using constant damping could not project the existence of adverse situations that led to excessively large motions. Most of the mathematical models considered thus far either give limited information on the effects of damping or restrict the analysis to an undamped variable inertia system with gas forces to avoid complexities. As a result, these models do not highlight all the consequences of such motion. This paper presents the equation of motion with key nondimensional parameters to include both damping and external excitations in order to predict the complete response of an equivalent single-cylinder engine system. Additionally, the nondimensional mathematical model presented in this paper allows development of design charts and brings the analysis closer to becoming an effective design tool. This model extends the previous analytical model by the author (2001) to include the effects of damping and gas forces acting on the system and captures many of the important concepts of time-dependent inertia systems. The complex waveform responses are examined within the range of engine speeds at which inexplicable crankshaft failures are known to have occurred. The investigations are conducted to study the interaction of secondary resonance effects with harmonic excitations for variation in damping and inertia ratios. These studies show that the observed effect is a natural physical phenomenon arising from the variable inertia characteristics of the system, and under certain circumstances it can have a serious impact on torsional vibration. The conclusions reached in this paper differ from those of Draminsky (1961) and Hesterman and Stone (1994). Comments on these differences are also included.