Dynamics Of Turbine Blades With Under-platform Dampers Considering The Bladed Disc's Rotation And The Normal Pressure Distribution

The Turbine blade is an essential component of aero-engines,and the high cycle fatigue failure of the turbine blades caused by its vibration is one of the leading causes of aero-engine incidents.At present,blade vibration reduction has been an important area in design of the turbine blades in aero-engines.As the under-platform damper has a simple structure and is not sensitive to temperature,it was widely used to reduce the vibration of the turbine blades.It has been proved that in engineering and studies attaching under-platform dampers to turbine blades can effectively reduce the blades vibration.Recently,there have been many studies on the design of under-platform dry friction dampers.However,the study involves dynamics,tribology and other aspects,and the dry friction damping is of complex nonlinearity.There are still some problems that need to be studied in depth,especially the modeling and the solution of the dynamic model of turbine blades with under platform damper considering the bladed disc's rotation and the distribution of normal pressure between adjacent blades.It is necessary to deeply study the dynamic modeling and vibration reduction characteristics of the underplatform dry friction damper.To predict the response of the turbine blade with an under-platform damper more accurately,many studies in the calculations and analyses of under-platform dry friction damper have been carried out,which are mainly about the dynamic model,the dry friction contact model,and methods for solving the nonlinear system's response.Based on these studies,the vibration and vibration reduction characteristics of the underplatform dry friction damper are intensely studied in this paper.The specific research contents are as follows:(1)In this paper,a dynamic model considering the bladed disc's rotation has been developed with the theories of compositive motion.To analyze the vibration reduction characteristics of the steady-state response and the transient response of the blade,a method for determining the time when the system reaches steady-state vibration is proposed with the normalized cross-correlation function(NCCF)and the bisection method.In this dynamic model,the influences of the changes of the convective inertial force and Coriolis inertial force on the normal pressure and the friction between the contact surfaces are considered.The fourth-order Runge-Kutta method is applied to study the dynamic characteristics of the bladed disc from startup to steady-state.The effects of the mass of the damper,the stiffness of the damper,and the amplitude of the external excitation on the damping characteristics of the system are studied.(2)For the under-platform damper in the rotating state,the variation of the Coriolis inertial force changes the normal pressure,especially the distribution of normal pressure between the damper and adjacent blades changes with the relative displacement of the blades,which may have a significant influence on the damping effects.Based on the motion of the damper,a method for calculating the normal pressure distribution is presented in this section.Considering the bladed disc's rotation and the normal load distribution,the dynamic model of the blades with under platform damper is established.With different system parameters,the influences of the bladed disc's rotation,the normal pressure distribution,and their combined influences on the dynamic responses of the blades are respectively studied.The results will provide an effective reference for the design of the under-platform damper in engineering.(3)By introducing an oblique spring which considers the coupling of two orthogonal directions,a vibrator model for analyzing the friction coupling vibration in two dimensions is proposed.The concept of the friction direction angle is defined to determine the direction of the friction vector.Furthermore,the stick-slip transition boundaries of the two-dimensional coupled dry friction oscillator are given.On this basis,the dynamic characteristics of the system on the response are studied with the varying-step Runge-Kutta method.