The MBS modelling of structural blade offsets and its impact on the eigenbehaviour of elastic helicopter rotors

Kurzfassung

Since Multi Body System codes (MBS) have been proved to be potentially powerful simulation tools in the whole range of helicopter rotor dynamics, in this study the question of modelling the structural blade cross-section offsets in the MBS models is highlighted. The relative positions of the characteristic points of the cross-sections of helicopter blades like the shear center, the neutral axis and the cross-sectional center of gravity are formative for the dynamic behaviour of the rotating structure. Even the location of the reference point of the cross-section — which is defined by the radial connection between the hub and the cross- section, standing normal on the respective plane — plays an important role concerning the equilibrium of a rotating blade differential mass element. Although in helicopter blade design generally efforts are made to keep the offsets of these characteristic structural points small they can reach non-negligible extents and thus, together with the gyroscopic effects, contribute significantly to the coupling mechanisms between the motion components of the vibrating elastic blade structure like the flapping, lagging and torsional deformation. Also in terms of aeroelastic stability the cross-sectional offsets may have a dominant influence. Here the scope of modelling blade offsets in MBS is to capture the complete variety of offsets resulting in the full range of mechanical coupling mechanisms like the bending-torsion coupling, the bending-longitudinal coupling and the bending-bending coupling (with “bending” meaning the flapping or lagging motion respec- tively). It is shown how special joint modelling techniques and the usage of “pseudo” bodies with additional DOF are introduced into the “pure” MBS model to reach this aim. The two basic approaches for incorpo- rating elastic properties into a MBS model are addressed. The way of mapping the continuously distributed elastic properties of the blade beam structure on dynamic equivalent discrete spring stiffnesses of a “pure” MBS model is compared with FEM models which can be used as basis in the strategy of importing separately built upp elastic Finite Element models with modal substructure techniques (FEMBS), thus resulting in a hybrid MBS model. While modelling of structural offsets within the pure MBS model refers to the genuine characteristics of the MBS modelling approach, the hybrid FEMBS model inherits all the advantageous (or deficient) properties of the incorporated Finite Element substructure. Since for the rotating blade the equilibrium state is now not only defined by the longitudinal normal forces but is three-dimensional, it is important for the geometric stiffness matix Sg of the FEM formulation to contain the whole set of second order terms, while the cutting forces depend linear on the cross-sectional offsets and contribute linear to the geometric stiffness. Because the completeness of the FEM model constitutes the quality of the FEMBS solution by providing in particular the geometric stiffness matrix of the rotating blade, a separate FEM model has been analysed. On the MBS side the commecial tool SIMPACK has been tested while on the FEM side the inhouse tool GYRBLAD is used. As fully elastic single blade examples generic test beam cases with considerable offsets are used. The validation of the models is done by comparing the eigenvalue results produced with the two independent elasto-mechanical methods MBS and FEM.