Contact nonlinear analysis for the under-platform dampers of blade based on a frictional energy dissipation model

The under-platform dampers of blade in an aero-engine can reduce the vibration through friction energy dissipation, which is generally regarded as a kind of foundation vibration model subjected to fluctuant pressure. The possible unstable air-flow and complex changes in aero-engine's speed at service result in the consequence that the tangential pressure originated from blade vibration as well as the centrifugal force applied on the foundation vibration model appear fluctuating. These fluctuant parameters are often assumed in the sinusoidal form. Meanwhile, the frequency ratio and phase difference between them also change during the operation process. To explore the effects of the changes in frictional energy dissipation and nonlinear contact response, a differential equation for a frictional energy model with the vibrational foundation is deduced and proposed in this paper. The equation integrates the complex condition of friction into a simple differential form, through which the hysteresis characteristic for different frequency ratios and phase differences are calculated precisely and efficiently. Additionally, the amplitude-frequency characteristics of the relative displacement between the contact surfaces of the proposed model are further investigated. This study can provide a reference for dynamic tribology design of the under-platform damper for engineering.