Efficient Trim In Helicopter Aeroelastic Analysis

Abstract

Helicopter aeroelastic analysis is highly complex and multidisciplinary in nature; the flexibility of main rotor blades is coupled with aerodynamics, dynamics and control systems. A key component of an aeroelastic analysis is the vehicle trim procedure. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which cause the six steady forces and moments about the helicopter center of gravity to be zero. Trim simulates steady level flight of the helicopter. The trim equations are six nonlinear equations which depend on blade response and aerodynamic forcing through finite element analysis. Simulating the behavior of the helicopter in flight requires the solution of this system of nonlinear algebraic equations with unknowns being pilot controls and vehicle attitude angles. The nonlinear solution procedure is prone to slow convergence and occasional divergence causing problems in optimization and stochastic simulation studies. In this thesis, an attempt is made to efficiently solve the nonlinear equations involved in helicopter trim. Typically, nonlinear equations in mathematical physics and engineering are solved by linearizing the equations and forming various iterative procedures, then executing the numerical simulation. Helicopter aeroelasticity involves the solution of systems of nonlinear equations in a computationally expensive environment. The Newton method is typically used for the solution of these equations. Due to the expensive nature of each aeroelastic analysis iteration, Jacobian calculation at each iteration for the Newton method is not feasible for the trim problems. Thus, the Jacobian is calculated only once about the initial trim estimate and held constant thereafter. However, Jacobian modifications and updates can improve the performance of the Newton method. A comparative study is done in this thesis by incorporating different Jacobian update methods and selecting appropriate damping schemes for solving the nonlinear equations in helicopter trim. A modified Newton method with varying damping factor, Broyden rank-1 update and BFGS rank-2 update are explored using the Jacobian calculated at the initial guess. An efficient and robust approach for solving the strongly coupled nonlinear equations in helicopter trim based on the modified Newton method is developed. An appropriate initial estimate of the trim state is needed for successful helicopter trim. Typically, a guess from a simpler physical model such as a rigid blade analysis is used. However, it is interesting to study the impact of other starting points on the helicopter trim problem. In this work, an attempt is made to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of trim solution in the aeroelastic analysis of helicopter are proposed.