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 blade0.5 1 1.5 2

2

4

6

8

10

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

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

FLAP1

L-L1

FEATHERING1

FLAP2

1P

2P

3P

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

Dynamic Responses - Displacements

0 0.5 1 1.5 2 2.5 3TimeSec-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

edalBpit

tnemecalpsidteeF

Time history of blade tip displacementred: axial displacement; green: in-plane displacement; blue: out-of-plane displacement

Dynamic Responses - Rotations

Time history of blade tip rotationsred: pitching; green: flapwise direction; blue: chordwise direction

0 0.5 1 1.5 2 2.5 3TimeSec

-0.02

0

0.02

0.04

0.06

0.08

edalBpit

noitator

snaidaR

Dynamic Responses - Forces

Time history of forces at different locations

red: at flex root; green: at flex tip

0 0.5 1 1.5 2 2.5 3TimeSec0

500

1000

1500

2000

2500

ecroFni

gnippalfnoitceridbL

Dynamic Responses - Moments

Time history of moments at different locationsred: at flex root; green: at flex tip

0 0.5 1 1.5 2 2.5 3TimeSec

-500

0

500

1000

gnippalFtnemom

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