TIME-VARYING LATERAL RESPONSE OF A MARINE SHAFTING SYSTEM WITHIN A STERN BEARING (HYDRODYNAMIC, JOURNAL, VIBRATION, DYNAMIC, TRAJECTORY)

A new direct iterative method for obtaining the time-varying lateral behavior of a statically indeterminate marine shafting system within its stern, hydrodynamic journal bearing is described. A modified Newmark's method is used to step in time. At each integration time step, an optimization technique iterates between the shafting system and the oil film analyses until a quasi-equilibrium is achieved. The three-dimensional shafting system structural analysis and the two-dimensional oil film hydrodynamic analysis utilize the finite element method. Rectangular, linear elements employing the "hourglass control" method are used for the construction of the oil film fluidity matrix. The bearing housing is modeled as a rigid body supported in two planes by linear springs. The exciting forces are due to a propeller operating in a spatially nonuniform wake field. The effect on the shafting dynamics of the oil filled stern tube, which surrounds a region forward of the stern tube bearing, is examined. Numerical examples are used to verify the method and the algorithm. A comprehensive ship example illustrates the usefulness of the present simulation. A physically reasonable periodic trajectory, reaching 25 percent of the clearance, and the corresponding periodic hydrodynamic bearing resultant forces and moments are achieved after about one shaft revolution.