Dynamic modeling of spur gear system under marine ship heaving-pitching motion

Sea waves often result in multi-freedom motions of ships, and affect the stability of marine gear systems. This study presents a novel dynamic modeling method for spur gear system considering the influence of marine ship heaving-pitching motion and investigates the spur gear dynamics. An excitation transmission path from wave to gear is illustrated and incorporated into the gear dynamic model. The hydrodynamic force is analyzed and the hull heaving-pitching motion is solved using the New Strip Method (NSM). Considering the time-varying meshing stiffness, transmission error, and tooth side clearance, the motion differential equation of the spur gear system impacted by the heaving-pitching coupling motion of the hull is established. The influences of key wave and navigation parameters on gear dynamics are analyzed. The results show that ship heaving-pitching motion causes additional stiffness and damping excitation, and leads to typical nonlinear phenomena of the spur gear system in a marine ship, such as period, quasi-period, and chaos, and causes a sharp increase in the meshing impact amplitude up to a maximum of 36.81%. The changes in wave frequency, the hull's heading angle, and hull's speed have a significant impact on gear dynamics, whereas the wave amplitude has less of an impact.