From FEM to MBS: Stability analysis of the elastic H/C-rotor

Abstract

As a consequence of the variety of effects the rotation has on the vibrating structure it is important to take into account the complete shares of the gyroscopic influence in the equation of motion. One prerequisite will be the formulation of the mass terms for all three axis of rotational movement of the vibrating rotor even if it deals with slender beam like structures. This is the case as well in the in-house Finite Element Method code GYRBLAD (FEM) as in the commercial Multi Body System code SIMPACK (MBS), which both have been applied in this investigation. The numerical calculations of the eigenmodes and the stability behaviour of the rotor will be conducted by using two different modelling concepts: the advantage of the FEM code lies in the capability of describing the deformation of a flexible structure in an already linearised manner (Euler-Bernoulli beam), whereas the potential of the MBS code comes from the complete nonlinear formulation of the arbitrarily large movements of elastically interacting (rigid) bodies in an equilibrium or accelerated state. In order to take into account the characteristics of the flexible continuum also in MBS the code offers the special feature FEMBS for combining the FEM with MBS modelling. Thus the potential of a sophisticated, hybrid MBS code like SIMPACK as a powerful simulation tool for helicopter dynamics will be demonstrated with respect to the dynamics of the elastic rotor.

For validation purpose the results of the FEM and the MBS code are quantitatively compared to the results of the analytical description of the dynamic behaviour of the rigid body rotor. Representing the case of fixed boundary conditions at a rigid hub the results of a single rotating blade are shown. The Princeton beam with its double symmetric cross section allows the focus on the DOF coupling as a result only from the rotation. For a single blade the pure gyroscopic coupling will be displayed for the flapping-torsion and the lagging-stretching movement. The investigation of the complete rotor (four and six blades) follows where all classes of rotor eigenmodes (collective, cyclic and reactionless) will be studied. As results for the eigenbehaviour the coupled complex eigenmodes and the variation of the eigenfrequencies with respect to the rotation speed will be shown (fan diagrams). Resonance phenomena in the eigenmodes occur at specific rotor speeds and frequencies where the pitch (torsion) amplitude rises over all measures. Although slim and slender bodies with a high aspect ratio are investigated not negligible coupling effects specially on the blade pitch movement have to be stated. For the aeroelastic stability analysis of the rotating elastic helicopter blade this can be highly hazardous.