Study On The Gyroscopic Coupled Vibration Of Rotating Blades In 3D Space

The vibration fault of rotating machinery is a significant factor to restrict the reliability and durability of rotating structures.The development of rotating blades' fault is very fast and it has tremendous destructiveness.The dynamic performance of the blade has a decisive effect for the safety of life as well as performance of the rotating machinery,and the fault of blades often leads to disastrous consequences.Therefore,it is necessary to study the dynamic modeling and dynamic characteristics.It is of great significance for the design of new type blades and the elimination of vibration faults.In this paper,the rotating blade was simplified as an Euler-Bernoulli beam model.Firstly,the transverse vibration of the cantilever beam was analyzed,and the vibration frequency and modes were studied by using the differential transformation method.Next,stretching-bending coupling vibration equations of the rotating Euler-Bernoulli beam model in 2D space has been established.The Galerkin truncation method was used for solving the vibration frequency and modal analysis.The vibration frequency and modal characteristics of different slenderness ratio,wheel radius and rotational speed were compared,and respectively explored the impacts on the vibration characteristics of gyro term,static centrifugal term,and the dynamic stiffness term.The centrifugal force is refined into the static centrifugal force generated by rotation and the dynamic centrifugal force generated by vibration.We obtained that during the modal motions,the longitudinal deformation reaches its maximum value,and the transverse motion goes through its equilibrium point with maximum velocity,and vice versa.The software was used to simulate the vibration of rotating blades,and the change of the vibration frequency as well as the modal are calculated.Then,considering the Euler angles of the beam cross section in 3D space,the partial differential equations of axial-bending-bending-torsional vibration of the cantilever beam were obtained by utilizing the principle of curvature and the Hamilton principle.The new mathematical model is more sophisticated than the previous models as a result of containing the centrifugal forces,Coriolis forces,rotary inertia,curvature items and other available terms.The static centrifugal terms cause the stiffening effect,making increasing frequencies.The dynamic centrifugal terms will decrease the frequencies.The vibration frequency and modal change of beam were analyzed in detail.