The Vibration Analysis Of Timoshenko Beam With High Rotating Speed

Rotating structure is one of the most important parts in power machinery.Under the condition of high pressure and high rotating speed,the vibration fault of Aeroengine Blades is more and more serious,which has become an important research subject of engine reliability,durability and life.The vibration problem of Aeroengine Blades,often occur in our country a large number of service advanced engine and key model engine,seriously restrict the development of aero engines in China,attracted the attention of people.Therefore,the in-depth study of the vibration of rotating blades has become an important issue to be solved in the development of China's aero-engine.In this paper,the aeroengine blade is simplified as a high-speed rotating Timoshenko beam model,and the complete dynamic equation of the high-speed rotating Timoshenko beam under the non-inertial system is established.The influence of different factors on the vibration characteristics of the blade is studied in detail.The main contents of the research include:(1)The Euler angle is used to describe the motion of a rotating Timoshenko beam,and the complete differential equation of three displacement and three angular vibration is obtained based on the exact geometric relation.In the model,not only the centrifugal force and gyroscopic force caused by rotation are considered,but also the static axial deformation and torsional deformation caused by rotation are considered.(2)The frequency and modal functions of the rotating beam are solved by the power series expansion method.The effects of centrifugal force,gyroscope force,setting angle,the radius of the hub,slenderness ratio and other factors on the dynamic frequency of rotating beam in the rotation process of Timoshenko beam are studied.The modal function of the system under different parameters is studied,and the influence of the rotational speed on the modal function of the rotating beam is analyzed.The gyro coupling relationship between the degrees of freedom of the rotating beam at different pre-installed angles is studied.The gyro coupling between the degrees of freedom is not the same at different pre-installed angles.It is found that due to the influence of the gyroscopic coupling,there will be a phase difference of ?/2 between the degrees of freedom.(3)In the model,the ratio of the pre twist angle and the taper ratio is added to make the model closer to the actual situation.The vibration differential equation of six degrees of freedom is derived by using Hamilton's principle.Due to the influence of the angle of rotation and the taper ratio,the vibration equation is changed into a complex system of variable coefficient partial differential equations.Using the power series expansion method,the dynamic frequencies and modal functions of a rotating Timoshenko beam are solved.(4)The effects of the pre-twist angle and the taper of the beam on the inherent characteristics of the rotating beam are studied in detail.In this paper,the modal functions of the rotating Timoshenko beam under different parameters are obtained,and the gyroscopic coupling relationship of six degrees of freedom is discussed.