In turbomachinery applications, thin-walled gears are cyclic symmetric structures and often subject to dynamic meshing loading which may result in high cycle fatigue (HCF) of the thin-walled gear. To avoid HCF failure, ring dampers are designed for gears to increase damping and reduce resonance amplitude. Ring dampers are installed in the groove. They are held in contact with the groove by normal pressure generated by interference or centrifugal force. Vibration energy is attenuated (converted to heat) by frictional force on the contact interface when the relative motion between ring dampers and gears takes place. In this article, a numerical method for the prediction of friction damping in thin-walled gears with ring dampers is proposed. The nonlinear damping due to the friction is expressed as equivalent mechanical damping in the form of vibration stress dependence. This method avoids the forced response analysis of nonlinear structures, thereby significantly reducing the time required for calculation. The validity of this numerical method is examined by a comparison with literature data. The method is applied to a thin-walled gear with a ring damper and the effect of design parameters on friction damping is studied. It is shown that the rotating speed, geometric size of ring dampers and friction coefficient significantly influence the damping performance.

The mistuning effects on the aero-elastic stability of axial compressor rotor blades have been investigated by employing aero-elastic eigenvalue method. An axial compressor rotor suffered from flutter failure has been analyzed with four intentional mistuning patterns and their sensitivities to random mistuning. Through a comparison of four intentional mistuning patterns, the mistuning mechanism of improving aero-elastic stability may be understood from the combining effects of frequency offset and the destruction of periodicity by the introduction of mistuning. Increasing the amount of alternate mistuning cannot provide any additional improving effects on the aero-elastic stability when the mistuning amount reaches a critical value. However, the further mistuning effects can be obtained by placing several groups (isolation zone) with additional frequency offset relative to the alternately mistuned system. The random mistuning can always improve the aero-elastic stability of the tuned system. However, for the intentionally mistuned system, the inclusion of random mistuning with a small level may weaken the improving effects of intentional mistuning and even makes the system unstable.

The gear is a cyclic symmetric structure, and each tooth is subjected to a periodic mesh force. These mesh forces have the same phase difference tooth by tooth, which can excite gear vibrations. The mechanism of additional axial force caused by gear bending is shown and examined, which can significantly affect the stability of a self-excited thin spur gears vibration. A mechanical model based on energy balance is then developed to predict the contribution of additional axial force, leading to the proposed numerical integration method for vibration stability analysis. By analyzing the change in the system energy, the occurrence of the self-excited vibration is validated. A numerical simulation is carried out to verify the theoretical analysis. The impacts of modal damping, contact ratio, and the number of nodal diameters on the stability boundaries of the self-excited vibration are revealed. The results prove that the backward traveling wave of the driven gear as well as the forward traveling wave of the driving gear encounter self-excited vibration in the absence of sufficient damping. The model can be used to predict the stability of the gear self-excited vibration.