An Introduction to Rotorcraft Dynamics Dr. Wenbin Yu School of Aerospace Engineering Georgia Institute of Technology Email: wenbin.yu@ae.gatech.edu URL: www.ae.gatech.edu/~wyu

Outline of the Course Introductions Theory of resonance Introduction to DYMORE Blade dynamics The rotor as a filter, airframe dynamic response and coupled blade-fuselage response Vibration control devices Typical instabilities Ground resonance Pitch-lag instability Pitch-flap instability Flap-lag instability

Introduction Rotorcraft are dynamic machinery. The dynamic problem are very important Some dynamic problem are detrimental to the vehicle performance. If not dealt properly, they could cause catastrophic tragedies Three categories of rotorcraft vibration Vibrations due to rotor excitation. The frequencies are integral multiples of the rotor rotation speed Vibrations due to random aerodynamic excitation. The frequencies are the natural frequencies of the structure Self-excited vibrations, such as flutter and ground resonances. Negative damping could cause divergent oscillations

Theory of Resonance A single DOF dynamic system Natural frequency Forced vibration of the system without damping The importance of natural frequency for design Vibration with damping Mathematica example Flapping blade Lagging blade

Finite Element Based Formulation for Nonlinear Multibody Systems Model configurations of arbitrary topology: Assemble basic components chosen from an extensive library of structural and constraint elements Avoids modal expansion This approach is that of the finite element method which has enjoyed, for this very reason, an explosive growth This analysis concept leads to simulation software tools that are modular and expandable Elements of the library can be validated independently

Rotor as a Nonlinear Multibody System

Transmission as a Nonlinear Multibody System

Simulation of Rotor on Ship Board The complete model involves: 17 beam elements, 5 prescribed displacements, 1 prismatic joint, 1 relative displacement, 21 rigid bodies, 12 revolute joints, 12 relative rotation, 3 spherical joints, 1 universal joints, For a total of 950 degrees of freedom.

Element Library: Structural Elements Rigid bodies Flexible joints: linear and torsional springs and damper Cable element Beam elements: geometrically exact, shear deformable. Capable of modeling all the elastic coupling effects arising from the use of advanced laminated composite materials Shell elements: geometrically exact, shear deformable, modeling of composite material effects The finite element formulation is used for all elements, no modal reduction is performed

Element Library: Beam Elements Geometrically exact beam elements. Six degrees of freedom (three displacements, three rotations) per node Accounts for Shearing deformation effects Offsets of the center of mass, shear center, and centroid All elastic couplings that can arise from the use of laminated composite materials (Fully coupled 6x6 stiffness matrix) Material viscous dissipation

Element Library: Shell Elements Geometrically exact shell elements. Five degrees of freedom (three displacements, two rotations) per node. Locking free element is achieved using the mixed interpolations of strains tensorial components Accounts for Shearing deformation effects Offsets of the center of mass All elastic couplings that can arise from the use of laminated composite materials (Fully coupled 8x8 stiffness matrix) Material viscous dissipation

The Six Lower Pairs

Blade Dynamics Blade dynamics is important because High blade vibratory response results in high stresses High blade vibratory response leads to high fuselage vibration levels Blade resonances and mode shapes are important in stability analysis of rotor systems DYMORE example for a single blade DYMORE example for a complete rotor (ITU LCH) FAN plot for ITU LCH Changing frequencies by playing with weight

DYMORE Rotor Model The DYMORE model for the ITU LCH Rotor

Fan Plot of Frequencies for the Rotor Fan plot in Vacuum for the ITU LCH Rotor (Verifying the Auto-Trim concept)

Dynamic Responses - Displacements Time history of blade tip displacement red: axial displacement; green: in-plane displacement; blue: out-of-plane displacement

Dynamic Responses - Rotations Time history of blade tip rotations red: pitching; green: flapwise direction; blue: chordwise direction

Dynamic Responses - Forces Time history of forces at different locations red: at flex root; green: at flex tip

Dynamic Responses - Moments Time history of moments at different locations red: at flex root; green: at flex tip

Pitch-lag Instability

Pitch-flap Instability

Flap-lag Instability Ground resonance

Conclusions Dynamic problem are very important for rotorcraft. A good design must come from a good understanding to dynamic behavior of the vehicle Locating the natural frequencies of the system is the key to avoid resonance DYMORE is a handy tool to deal with rotorcraft dynamics Either passive (damping) or active devices (vibration absorbers) can be used to reduce the resonance or shift the natural frequencies Dynamic instabilities should and can be avoided by design tradeoffs