Motion And Deformation Coupling Modeling And Analysis For Rotating Blades

For research the coupling effects of motion and deformation the rotating bladestructures, a simple motion and deformation coupling model, which a concentrated massfixed on flexible beam in the rotating rigid body, is established in this paper. The rationfrequency and response of the model are researched. And the influence of rotating speedand eccentricity on the dynamic characteristics of the system are also analyzed. Basedon this study, simplifying the rotating blade with cantilever beam model, using thekinematics description research presented by Liu Zhanfang, dynamic equations ofrotating blades are built by using the Hamilton principle. The equations are discretizedwith the finite element method. Dynamic characteristics and dynamic response of therotating blade structure are studied. And the impact of the inertia force caused by thecoupling rotation motion and deformation on the frequency and response are alsoanalyzed. The main research contents and conclusions are as follows:①The system of a mass attached to a rotating flexible beam which the mass ofthe beam isn’t considered is research in chapter two. It assumes that the flexible beamhas the small deformation. And the displacement of the lumped mass along the rotatingshaft direction is ignored; meaning the motion of the mass is just in the rotating plane.With using the Hamilton principle, the dynamics equations of the system are established.In the rotation with constant speed, two order dynamic frequencies of the flexible beamlinear change with the angular velocity; the first order frequency decreased from thenatural frequency without rotating to the zero, while the second frequencies rise fromthe natural frequency. When the elastic limit of the deflection is given, the critical speedof the system is determined by the relationship between deflection and angular velocity.While in the condition of rotation with variable angular velocity, which the rotatingspeed of the system increases from zero to a constant value, then rotating at the constantspeed for a period of time, after that the rotating speed decreasing to zero again. Thedynamic response and trajectory of four stages are analyzed. The influence of the inertiaforce caused by coupling of the rotation and deformation are also researched.②Based on the Mindlin elastic couple stress theory, the rotational deformation ofelastomers is considered, modified the constitutive relation between the couple stressand the curvature tensor by the application of principle of virtual work and isotropictensor function the linear representation theorem, A generalized linear elastic model which the elastic body contains three material parameters is built. The rotating bladesare simplified with the rotating cantilever beam model. The rigid rotation is describedby a fixed coordinate system, while the translational and rotational deformations aredescribed with the floating coordinate system attached in the cantilever beam. By usingHamilton’s principle, dynamic equations of rotating blades are obtained.③The dynamic equation is solved with the finite element method: which theangle as an independent variable is added and the constraint conditions are introducedwith using the penalty function method. The rotating blades are discretized with thehexahedron element which has8nodes and48degree of freedom. The finite elementcontrol equations are obtained. The dynamic characteristics and dynamic response ofthe cantilever are analyzed. The equivalent stress and couple stress response areresearched at the same time.