Research On Nonlinear Dynamic Characteristics Of A Rotating Blade With Dovetail Attachment Based On Dry Friction Theory

Rotating machinery such as aeroengine,turbine and steam turbines is important basic equipment in the national construction and economy development.It not only represents the national advanced level of science and technology,but also plays a decisive role in the development of industry and agriculture.In recent years,it has received great attention and development and widely been used in aerospace,energy power and many other fields.However,the requirements of it are getting higher and higher with the development of society and the progress of science and technology,for example,high speed,light weight,high thrust weight ratio and so on.The blade,as one of the most important and key parts of rotating machinery,has been in a high speed,heavy load,automation and complex work environment,resulting in a series of serious and complex problems.Because most fault of rotating machinery is caused by the blade and rotating machinery often plays an important or key role in large equipment,it will cause very serious harm once there is a fault or loss of stability.What’s more,it will also make a great loss of economic and sometimes even cause casualties or inestimable and irreplaceable damage to the society.Therefore,many scholars at home and abroad has made a detailed analysis on inherent characteristics and incidental faults of blade.This paper,the research of nonlinear inherent characteristics and rub impact response characteristics on blade with dovetail attachment is studied based on dry friction theory.The main contents of this paper include:(1)Firstly,based on the semi analytical method,Timoshenko bending theory,the material mechanics,elastic mechanics and mechanical vibration theory,the contact boundary of blade with dovetail attachment is simplified as an elastic support beam with an inclined angle,the dynamic model is established and the differential equation of vibration is derived by using the energy method and the Lagrange equation in this paper.What’s more,the correctness of the elastic support beam model is verified.Then,the effects of spring stiffness and torsional stiffness on the natural frequency and mode shape of the blade are studied respectively.Finally,assuming the contact boundary of the dovetail attachment into the nonlinear spring force and spring force,the influence of blade length,installation angle,dovetail angle,damping coefficients and excitation amplitude on the inherent nonlinear characteristics is studied.(2)Secondly,the force of the dovetail attachment is further studied and the new dry friction theory and approximate slip model are introduced,which is the nonlinear dry friction with piecewise linear,on the basis of what we have got.At the same time,in order to simplify the calculation,the nonlinear force and mode function are made a simplified processing.Then the vibration mode function and the differential equation of vibration of the blade are derived.What’s more,the research of blade is compared with the previous results.At last,the influence of blade length,installation angle,dovetail angle,damping coefficients,excitation amplitude,coefficient of sliding friction and rotation speed on the inherent nonlinear characteristics is studied under the nonlinear dry friction.(3)Finally,the impact of impact-rubbing between the blade and the casing in the actual working process is taken into consideration.The kinetic model of blade is still established by using the dry friction theory and the force of impact-rubbing is applied on the basis.What’s more,the vibration differential equation of the blade is obtained.Then the response of the blade is studied.The influence of different factors on the response of blade under the condition of no external excitation was studied at first and then the influence of different factors on the response of blade under the condition of external excitation was studied.At last a series of pretty meaningful conclusions are obtained.