Intrinsic physical relationships between rotor modal shapes and instantaneous vibrational energy flow transmission characteristics: Theoretical and numerical analysis and application

The modal vibration of the rotor is the main cause of excessive vibration of the aero-engine overall structure. To attenuate the vibration of the rotor under different modal shapes from the perspective of energy control, the intrinsic physical relationships between rotor modal shapes and instantaneous vibrational energy flow transmission characteristics is derived from the general equation of motion base on the structural intensity method. A dual-rotor-support-casing coupling model subjected to the rotor unbalanced forces is established by the finite element method in this paper. The transmission, conversion and balance relationships of the vibrational energy flow for the rotors in the first-order bending modal shape, the conical whirling modal shape and the translational modal shape are analyzed, respectively. The results show that the vibrational energy flow transmitted to the structure can be converted into the strain energy, the kinetic energy and the energy dissipated by the damping of the structure. The vibrational energy flow transmission characteristics of rotors with different modal shapes are quite different. Especially for the first-order bending modal shape, the vibrational energy flow and the strain energy are transmitted and converted to each other in the middle part of the rotor shaft, resulting in large deformation at this part. To attenuate this harmful vibration, the influences of grooving on the shaft on the first-order bending vibration are studied from the perspective of transmission control of vibrational energy flow. This study can provide theoretical references and guidance for the vibration attenuation of the rotors in different modal shapes from a more essential perspective.