Mathematical Model of the Blades and Main Rotor Hub Conjoint Aeroelastic Oscillations on the Elastically Damping Base at the Helicopter Spatial Motion

Aeronautical and Space-Rocket Engineering


Аuthors

Kargaev M. V.1, 2

1. National Helicopter Center Mil & Kamov, 26/1, Garshina str., Tomilino, Moscow region, 140070, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: kargaev_mv@mail.ru

Abstract

Relatively high demands are being placed on the newly developed helicopters in terms of the fatigue life levels of their aggregates and passenger comfort, due to the magnitude of loads and vibrations in flight. Meeting these requirements is impossible without availability of the appropriate mathematical models and methods for computing the loads and stress-strain state of the main rotor blades (MRB). Throughout the history of the helicopter industry, many relevant models and methods, characterized by the complexity and completeness of the equations, as well as the obtained results accuracy, have been created. 
The development of the abve mentioned mathematical models proceeded in several directions:
- from the equations of oscillations of MRB in one plane to the equations of conjoint oscillations of MRB in the planes of thrust, rotation and torsion;
- from the “geometrically” linear equations to the “geometrically” nonlinear equations of spatially deformable rods with large displacements;
- from considering the blade as a rod with a rectilinear axis prior to deformation to considering the blade as a spatially curved rod with an initial curvature;
- by the method for the aerodynamic loads computing from linear dependences of aerodynamic coefficients to the “circular” purges and accounting for the unsteadiness of the flow around the blade cross sections;
- according to the method for the inductive velocities computing from traditional disk models to the blade nonlinear vortex models and CFD-methods;
- from considering blade oscillations in steady-state flight modes to considering oscillations in unsteady flight modes at the helicopter arbitrary spatial movement;
- from consideration the isolated blades oscillations on a “rigid” support to the of conjoint oscillations consideration of the blades and main rotor hub on an elastic-damping support. The latter is especially important for the helicopter vibrations computing.
The presented article proposes a generalized mathematical model of conjoint aeroelastic oscillations of the blades and main rotor hub on an elastic-damping support during the helicopter spatial movement. The proposed mathematical model may be recommended for application in the tasks of the stress-strain state determining of the main rotor system aggregates and helicopter vibrations inflight.

Keywords:

blades and hub of the main rotor, elastically damping base, helicopter flight dynamics, conjoint aeroelastic oscillations

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