Computational aspects of helicopter trim analysis and damping levels from Floquet theory

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated

Use of Multiblade Coordinates for Helicopter Flap-Lag Stability with Dynamic Inflow

Rotor flap-lag stability in forward flight is studied with and without dynamic inflow feedback via a multiblade coordinate transformation (MCT). The algebra of MCT is found to be so involved that it requires checking the final equations by independent means. Accordingly, an assessment of three derivation methods is given. Numerical results are presented for three- and four-bladed rotors up to an advance ratio of 0.5. While the constant-coefficient approximation under trimmed conditions is satisfactory for low-frequency modes, it is not satisfactory for high-frequency modes or for untrimmed conditions. The advantages of multiblade coordinates are pronounced when the blades are coupled by dynamic inflow

Prediction of inplane damping from deterministic and stochastic models

This paper reviews computational reliability, computer algebra, stochastic stability and rotating frame turbulence (RFT) in the context of predicting the blade inplane mode stability, a mode which is at best weakly damped. Computational reliability can be built into routine Floquet analysis involving trim analysis and eigenanalysis, and a highly portable special purpose processor restricted to rotorcraft dynamics analysis is found to be more economical than a multipurpose processor. While the RFT effects are dominant in turbulence modeling, the finding that turbulence stabilizes the inplane mode is based on the assumption that turbulence is white noise