Helicopter dynamic stability in the ground spin-up mode with allowance for blades flexibility

Аuthors

Nikolaev E. I.^*, Pantyukhin K. N.^**

Kazan National Research Technical University named after A.N. Tupolev, 10, Karl Marks str., Kazan, 420111, Russia

*e-mail: nikolaev_ei@kazanhelicopters.com
**e-mail: Kostyapanty@gmail.com

Abstract

The study of helicopter dynamic stability is associated in most cases with such a phenomenon as ground resonance, which presents helicopter self-oscillations with increasing amplitude. The origin of this swaying consists in interaction of blades oscillations relative to the hinges, vertical in particular, with helicopter body on chassis oscillations.

Since helicopter presents a complex mechanism, assumptions and simplifications allowing saving computing resources and with sufficient accuracy easily correlated with the experiment were introduced while mathematical models building. At present, a researcher possesses considerable computing resources. Thus, one can afford building much more complicated models, allowing solving the problem of «ground» resonance computation in more detail.

The paper presents helicopter mathematical model, which body has six degrees of freedom, and flexible blades with three degrees of freedom in the attachment point to the hub. Helicopter alighting gear (chassis) is presented in the model by flexibility matrix. Helicopter equations of motion were obtained using second order Lagrange equation, and blades flexural oscillations equations were obtained with widely known Galerkins method. Flexible blade mathematical model considers only the first three forms of hinges flexure-flexure-torsion oscillations.

Following the above-described mathematical model the complex of programs was developed using Maple and MATLAB. Within the range from zero to main rotor operating speed computation of helicopter dynamic instability zones on the ground was made. Comparison of the results obtained by R. Coleman method and mathematical model with rigid blades for ANSAT helicopter revealed sufficient convergence. Mathematical models with rigid and flexible blades developed by the authors allow determine additional instability zones.

The model with flexible blades allows revealing a number of additional instability zones, which may have great significance.

Keywords:

ground resonance, flexible blade, natural frequencies and forms

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