Dynamic Analysis Of Wide-Range Rotating Beam

To investigate the motion of a rotating flexible beam, there are many different methods to deal with the effects of rigid-flexible coupling where Euler-Bernoulli beam model is adopted. Some research works applied the models that ignore inertia force of beam rotation and gyroscopy force of coupling of rotating and bending, in order to simplify the numerical calculations. The numerical results of these models lose their stability in high rotating speed. Other research works used the models that considered inertia and gyoscopy forces, but encountered many difficulties in numerical calculation due to effect of dynamic stiffening.This paper presents a new perturbation method to take inertia and gyoscopy forces into account, and expresses system dynamical equation in the form of matrix so as to simplify numerical calculations. The detailed numerical analyses in higher precise quantity for the effects of rigid-flexible coupling show the applicability of the present method for the uncoupling of rigid-flexible equations.According to the main characteristics of rotating manipulator, Euler-Bernoulli beam theory is applied to model the motion under driving torque, gravity, gyroscopy force. The beam motion is divided into two parts: rigid rotation and flexible vibration. And the root-rotating angle of beam is divided into two parts: rigid angle caused only by gravity and torque, and flexible angle caused merely by flexible vibration. The beam displacement is also divided into two parts: one is whole rigid rotating displacement, and another is the combination of rigid-flexible coupling rotating angle and rigid-flexible coupling terms.The displacement of rigid-flexible coupling rotating angle and rigid-flexible coupling vibration is a much smaller part. This results uncoupling of the motion partial differential equation. The rotating angle and vibration of the whole rigid rotating motion are solved by numerical method. The rotating angle and vibration of rigid-flexible coupling are solved by the perturbation method.The new method exposes the role of rigid-flexible coupling rotating motion on angle displacement and vibration displacements, and the coupling effect of rotating motion and small deformations. The dynamical simulation shows that the terms of rigid-flexible motion and rigid rotating angle motion have deep influence upon the beam vibration, especially, with initial deformation.