Formulation of the equations of dynamic motion including the effects of variable inertia on the torsional vibrations in reciprocating engines, part I

Abstract The torsional vibration problem in reciprocating engines is described by linear differential equations with constant coefficients: that is to say that all the masses are constant, and all the damping forces are proportional to velocity. However, such a representation is only approximate since a crankshaft-connecting rod system is a vibrating system with varying inertia. The total effective inertia of the crank assembly varies twice during each revolution of the crankshaft. Large variations in inertia torques can give rise to the phenomenon of secondary resonance in the torsional vibration of modern marine diesel engines. In recent years several cases of fractures in the crankshafts of large multi-cylinder marine engine systems have been attributed to the phenomenon of secondary resonance. Simplified theories predicted these designs of diesel engines as safe in practice. In view of the importance of the subject of torsional vibration in engineering practice, the formulation of the equations of dynamic motion for a multi-cylinder engine, allowing for variable inertia, is given in the present paper.