Comparing explicit and implicit modeling of rotor flapping dynamics for the EC 135

Abstract

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. For this helicopter, the formulation with flapping angles in its classical hybrid form shows some higher order deficiency in the match of the longitudinal and lateral accelerations, which are not apparent in the implicit model. After ruling out other effects, the discrepancies can be attributed to a vertical offset of the center of gravity from its assumed position. Once this offset is accounted for in the data, results from the two modeling approaches can be compared to each other and to theoretical predictions.