Excitation characteristic and dynamic response of misalignment of flexible rotor system with three supportings

Equivalent stiffness is introduced for the first time into dynamics analysis of the problem of bearing misalignment of flexible rotor system with three supportings, based on comprehensive consideration of the characteristics of rotor structure and load. Nonlinear stiffness of the rotor shaft with bearing misalignment can then be described quantitatively. Mathematical descriptions of the misalignment excitation of multi-span flexible rotor are obtained, and the mechanical modeling for the flexible rotor with bearing misalignment is established. The solution method for the governing equations for the rotor system with bearing misalignment is established based on Lagrange energy method, and the vibration characteristics of the rotor system is studied. The results show that the bearing misalignment leads to nonlinearity of the coupling's stiffness, resulting in 2 times frequency excitation load and extra unbalanced load. The 2 times frequency component is one typical feature of the rotor system with bearing misalignment. The 2 times frequency component increases rapidly with the increase of bearing misalignment, and the 1 times frequency component remains the same. The vibration response of the rotor shows a trend of “increasing slowly first, and then reducing quickly with the increase of rotation frequency”, and turns to be more obvious with the increase of the nonlinear stiffness and unbalance.