Comparing Explicit and Implicit Modeling of Rotor Flapping Dynamics for the EC 135

Abstract

In order to be valid up to higher frequencies, state space models derived by system identification methods have to include rotor states describing the dynamics of flapping and sometimes even downwash and regressive lag motion. In the case of flapping, the rigid-body equations are usually augmented by the explicit differential equations for the longitudinal and lateral flapping angles which are then coupled to the rigid-body equations through the corresponding force and moment terms. Alternatively, an implicit formulation can be used that includes the pitch and roll acceleration as model states. The paper compares the two modeling approaches for the EC 135 helicopter. It can be shown that for this helicopter the formulation with flapping angles in its classical hybrid form yields a poor match in the longitudinal and lateral accelerations. A comparison with results obtained from the equivalent formulation allows augmenting the model to better match the two linear accelerations. Numerical results from the two modeling approaches are compared to each other and to theoretical predictions.