Dynamics Of Functionally Graded Rotor In Thermal Environment

Functionally graded materials have been widely used in various fields since the concept was proposed.Employing different material gradient indices,it can be used to optimize the dynamic characteristics of the structure and the thermodynamic behavior.Taking the aero-engine rotor as the research background and the rotating Timoshenko beam as the analysis mechanical model,the thermodynamic behavior of the static state of engine rotor under temperature gradient distribution and the dynamic characteristics of the rotor rotation under uniform temperature field are studied in the article.Firstly,utilizing the finite element software of the Abaqus,the thermal deformation,thermal stress and thermal mode of the aero-engine rotor are analyzed.The results show that the smaller the material gradient index,the smaller the thermal deformation of the rotor,the shorter the heat transfer time,and the smaller the natural frequency of the structure because of the thermal expansion coefficient of the Ti-6Al-4V material is smaller than that of the Zr O2 material however the thermal conductivity is higher.Then,based on Timoshenko beam theory,Gauss-Lobatto sampling and Chebyshev polynomials were used to discretize deformation fields of the beams,and the discrete governing equations are obtained by utilizing Chebyshev spectral method and Lagrange equation.After that employing projection matrices are incorporated in the governing equation,and the numerical solution of whirling frequency is obtained.The results show that there is an optimal material gradient value which maximizes the first third order whirling frequencies for the cantilever boundary.Finally,the dynamic equation of Timoshenko beam in the thermal environment is deduced first,and the numerical solution of the natural frequency is obtained in the thermal environment.The correctness of the method is verified by comparing with the results calculated in Abaqus.The rotating Timoshenko beam dynamics equation is established using the same method.The effects of various parameters,such as boundary conditions,temperature field,material gradient index,the rotation speed of the beam and the critical speed are analyzed.The results show that the natural frequency decreases as the temperature increases and the thermal stress cannot be ignored in the thermal buckling temperature.The whirling frequencies vary obviously when the stiffness of the elastic support is within the sensitive range.There is an optimal material gradient value which maximizes the first third order whirling frequencies and the critical speed of rotor can be increased by optimizing gradient index for the cantilever boundary.The forward whirling frequencies increase and the backward whirling frequencies decrease with the increase of rotating speed.A conclusion can be drawn from what is discussed above,with different material gradient indices employed,functionally graded materials can optimize the thermodynamic behavior of the structure and the dynamic characteristic of the rotor rotation.