Donald L. Kunz

Introduction to GRASP - General Rotorcraft Aeromechanical Stability Program - A Modern Approach to Rotorcraft Modeling,

Abstract : The General Rotorcraft Aeromechanical Stability Program (GRASP) is described in terms of its capabilities and development philosophy. The program is capable of treating the nonlinear static and linearized dynamic behavior of structures represented by arbitrary collections of rigid-body and beam elements that may be connected in an arbitrary fashion and are permitted to have large relative motions. The main limitation is that periodic coefficient effects are not treated, restricting the solutions to rotorcraft in axial flight and ground contact conditions. Rather than following in the footsteps of other rotorcraft programs, GRASP is more of a hybrid between finite element programs and spacecraft-oriented multibody programs. GRASP differs from standard finite-element programs by allowing multiple levels of substructures in which the substructures can move and/or rotate relative to others with no small-angle approximations. This capability facilitates the modeling of rotorcraft structures, including the rotating/nonrotating interface and details of the blade/root kinematics for various rotor types.

Influence of elastomeric damper modeling on the dynamic response of helicopter rotors

Several modeling approaches that describe the behavior of elastomeric materials used in helicopter rotor lag dampers are examined and evaluated, using laboratory test data. Two of the models are then used in a simulation of a helicopter rotor startup, and the simulation results are compared to one another and to flight test data. The models created using laboratory test results show that the simple, complex modulus model will yield good predictions of damper energy dissipation, but the simulation results indicate that this model is inadequate for predicting forced response. Although some of the models evaluated performed better than the others, none were free from limitations that would make them unsuitable for some applications. It is recommended that more effort be put into acquiring and analyzing damper test data to facilitate the development of more robust modeling approaches.

A comparison of main rotor smoothing adjustments using linear and neural network algorithms

Helicopter main rotor smoothing is a maintenance procedure that is routinely performed to minimize destructive airframe vibrations induced by non-uniform mass and/or aerodynamic distributions in the main rotor system. This important task is both time consuming and expensive, so improvements to the process have long been sought. Traditionally, vibrations have been minimized by calculating adjustments based on an assumed linear relationship between adjustments and vibration response. In recent years, artificial neural networks have been trained to recognize non-parametric mappings between adjustments and vibration response. This study was conducted in order characterize the adjustment mapping of the Vibration Management Enhancement Programs PC-ground base system (PC-GBS), and compare it to the linear adjustment mapping used in the aviation vibration analyzer (AVA). Results show that, in a majority of situations, the neural network algorithms in PC-GBS produce adjustments that are identical to those produced by a linear algorithm similar to that used by AVA. Therefore, the use of neural networks for creating the mapping between adjustments and vibration response, provides no significant improvement over a linear mapping.

Numerical simulations of cantilever beam response with saturation control and full modal coupling

Numerical simulations of the response of a uniform, cantilever beam subjected to a base excitation are performed. A saturation absorber is implemented to control the beam response. In previous investigations of similar configurations, the inertial and structural properties of the piezoelectric actuators have been neglected, resulting in an analytical model of a uniform beam. This investigation includes the nonuniformities in the beam properties that are introduced when piezoelectric actuators are bonded to the uniform beam. The resulting coupling between uniform, cantilever beam modes is fully included in the analytical model. It is shown that this modal coupling has a significant effect on the beam response, which is not present when modal coupling is neglected.

Analysis of structures with rotating, flexible substructures applied to rotorcraft aeroelasticity

Abstract : The initial version of the General Rotorcraft Aeromechanical Stability Program (GRASP) was developed for analysis of rotorcraft in steady, axial flight and ground contact conditions. In these flight regimes, the material continua of the rotorcraft may experience deformations which are independent of time. GRASP can obtain this steady-state solution and can solve the eigenproblem associated with perturbations about such a steady-state solution. GRASP is the first program implementing a new method for dynamic analysis of structures, parts of which may be experiencing discrete motion relative to other parts. Application of this new method to GRASP, including substructuring, frames of reference, nodes, finite elements and constraints, is described in the paper. The library of finite elements includes a powerful nonlinear beam element that incorporates aeroelastic effects based on a simple nonlinear, aerodynamic theory with unsteady induced inflow.

Dynamic Coupling of the KC-135 Tanker and Boom for Modeling and Simulation

Current Automated Aerial Refueling (AAR) research requires precision modeling and simulation of the refueling process between a KC-135 tanker aircraft and an unmanned aircraft. In order to meet this requirement, both steady-state and dynamic interactions between the tanker aircraft, the refueling boom, and the receiver aircraft must be accurately represented. Boom orientation and motion is known to change the trim of the tanker aircraft, which in turn influences the formation flying and station keeping tasks involved in current Air Force AAR concepts of operation. This paper describes the development of the coupled equations of motion for the refueling boom, which model its motion and its dynamic interactions with the tanker. For the purposes of this investigation, and to validate the boom model dynamics, the coupled boom model is first implemented as a boom-only simulation. The coupled model is compared to two existing boom-only models: one of which has been used for aerial refueling improvement studies, and the other is currently being used for boom operator training. Steady-state and dynamic responses to control inputs to the boom are calculated by the coupled boom model, then compared to those calculated using the existing models.

AN OBJECT-ORIENTED APPROACH TO MULTIBODY SYSTEMS ANALYSIS

This paper describes the design of a multibody systems analysis program that implements the principles of object-oriented programming to simplify the architecture of the code. A minimum coordinate set approach is used to generate the equations of motion. The principal features of the program include a unified treatment of rigid, flexible, and generic bodies, and the use of a single algorithm for both open-loop and closed-loop systems.

The effect of varying freestream velocity on dynamic stall characteristics

A low speed wind tunnel equipped with an axial gust generator to simulate the aerodynamic environment of a helicopter rotor was used to study the dynamic stall of a pitching blade. The objective of this investigation was to find out to what extent harmonic velocity perturbations in the freestream affect dynamic stall. The study involved making measurements of the aerodynamic moment on a two-dimensional, pitching blade model in both constant and pulsating airstreams. Using an operational analog computer to perform on-line data reduction, plots of moment versus angle of attack and work done by the moment were obtained. The data taken in the varying freestream were then compared to constant freestream data, and to the results of two analytical methods. These comparisons showed that the velocity perturbations had a significant effect on the pitching moment which could not be consistently predicted by the analytical methods, but had no drastic effect on the blade stability.

Analysis of Proprotor Whirl Flutter: Review and Update

Whirl flutter instabilities have been a matter of concern for propeller-driven aircraft, aircraft having tilting proprotors, and helicopters ever since two Lockheed Electras crashed more than 40 years ago. A significant body of literature exists, which details the analyses used to predict whirl flutter and the experiments that have validated the analyses. The factors that contribute to whirl flutter are reviewed, and with use of simple analysis methods, their effect on stability are demonstrated. Whereas previous efforts in the literature have tended to concentrate exclusively on propellers, proprotors, or helicopter rotors, a unified treatment of all three configurations is presented.

Multibody System Analysis Based on Hamilton' s Weak Principle

The double pendulum, a simple system that exhibits complex dynamics, is used to demonstrate a method based on Hamilton’ s weak principle (HWP) for assembling and solving the maximum coordinate set equations for a multibody system. Results calculated using HWP are compared to a reference solution obtained by integrating the ordinary differential equations (ODE) in minimum coordinate set form. The HWP solution is shown to be comparable to the ODE solution in accuracy and computational efe ciency. These results suggest an alternative architecture for multibody system analysis, which implements the maximum coordinate set form of the system equations, and a simple, efe cient, and robust solution algorithm.