Dynamical analysis of the large mechanical systems containing subsystems

The modal synthesis method with reduction number DOF for the modelling of vibration and dynamic loads of the large coupled mechanical system is presented. The best-known reduction method (see[1]) used in linear dynamic problems consist in choosing lower undamped vibration mode shapes of whole system. The presented method is based on the system decomposition into subsystems joined by discrete couplings and on the choosing master mode shapes of the mutually uncoupled subsystems. The method is numericaly tested on the gearbox excited by kinematic transmission errors. Shafts with gears as one dimensional continuum subsystems and housing as a three dimensional continuum subsystem are discretizated by FEM. Model of the gearbox respects proportional damping of the subsystems, viscous damping in couplings (gear meshing and bearings) and gyroskopic effects caused by rotating of shafts.