Simple modelling and analysis for crankshaft three-dimensional vibrations under firing conditions

The three-dimensional vibrations of an engine crankshaft system under running conditions were investigated by simple modeling and analysis by dynamic stiffness matrix method. In the analyses, we took account of the dynamic behavior of cylinder block, oil film, and torsional damper. To simplify the analyses, the crankshaft was idealized by a set of jointed structures consisting of simple round rods and simple beam blocks of rectangular cross-section. The main journal bearings were idealized by a set of linear springs and dash-pots, and the flywheel was idealized by FEM model. Then the dynamic stiffness matrix was derived in closed form for each constituent member. To eliminate the complicated FEM analysis for a cylinder block of complicated structure[1,2], we derived the dynamic stiffness matrix from the inverse matrix of the compliance matrix. Here, the compliance matrix was derived in analytical form from the modal parameters obtained from a series of hammering tests. Finally, the dynamic stiffness matrix was constructed for the total engine system which consists of the crankshaft system and the cylinder block. The three-dimensional vibrations of the crankshaft system and cylinder block surface vibrations near the main bearings under firing conditions were calculated for an automobile diesel engine, in which five kinds of solid pulleys, each with different masses and moments of inertia, and a torsional damper were attached to the crankshaft. The calculated results were compared with the experimental results.