The three-dimensional vibrations of an engine crankshaft system under firing conditions were investigated by simple modelling and analysis using the dynamic stiffness matrix method (DSMM). In the analyses, the authors took account of the dynamic behaviour 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 modelled by finite elements. Then the dynamic stiffness matrix (DSM) was derived in closed form for each constituent member.To eliminate the complicated finite element method (FEM) analysis for a cylinder block of complicated structure [1, 2], the authors 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 consisting 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 pulley, 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.
The modeling and analysis procedures with the dynamic stiffness matrix method described in Part 1 were applied to a crankshaft system, consisting of crankshaft, front pulley, flywheel, piston, and connecting rod, under firing conditions. For firing conditions, (7) one half of the reciprocating masses consisting of the piston, piston pin, and connecting rod small end, and (2) rotating masses of the connecting rod big end mass, were attached to the two ends of the crankpin, taking account of the rigidity of the connecting rod. The excitation forces were calculated from the gas force and the inertia force due to the reciprocating masses. By solving the equations of motion derived in the form of the dynamic stiffness matrix, we calculated the three-dimensional steady-state vibrations of the crankshaft system under firing conditions. A crankshaft system for a four-cylinder in-line automobile engine was used for the analysis. We calculated the influence of the mass and moments of inertia of the front pulley on the behavior of the crankshaft vibrations and the excitation induced at the crankjournal bearings. Calculated values were compared with experimental results.
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