To simplify the analysis of the three-dimensional vibrations of automobile engine crankshafts under firing conditions, the crankshaft was idealized by a set of jointed structures consisting of simple round rods and simple beam blocks of rectangular cross-section. The front pulley, timing gear, and the fly-wheel were idealized by a set of masses and moments of inertia. The main journal bearings were idealized by a set of linear springs and dash-pots. For each constituent member, the dynamic stiffness matrix was derived (in closed form) from the transfer matrix. Then the dynamic stiffness matrix for the total crankshaft system was constructed, and the natural frequencies and mode shapes were calculated. The modeling and analysis procedures were applied to the analysis of free vibrations of four kinds of crankshafts: single cylinder, three-cylinder in-line, four-cylinder in-line, and V-six engines. The different coupling behavior of the three-dimensional vibrations in the planar-structure and the solid-structure crankshaft is discussed, and the influence of the bearing oil film stiffness on the crankshaft natural frequency is also analyzed.

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