Dynamic analysis of geared rotor-bearing systems by the transfer matrix method

An analytical study of the dynamic characteristics of a geared rotor-bearing system by the transfer matrix method is presented. Rotating shafts of the system are modeled as Timoshenko beams with effects of shear deformation and gyroscopic moment taken into account. The gear mesh is modeled as a pair of rigid disks connected by a spring-damper set along the pressure line and the transmission error is simulated by a displacement excitation at the mesh. The transfer matrix of a gear mesh is developed. The coupled lateral-torsional vibration of a geared rotor-bearing system is studied. Natural frequencies and corresponding mode shapes, and whirl frequencies under different spin speeds are determined. In addition, steady-state responses due to the excitation of mass unbalance, geometric eccentricity and transmission error of gear mesh are obtained. Effect of the time-varying stiffness of the gear mesh is investigated.