直升机飞行力学 Helicopter dynamics chapter 1

Helicopter Flight DynamicsHelicopter Flight Dynamics

Chapter 1: Introduction

Instructor

• Dr. Renliang Chen

• A18-204

• Phone: (025)84892141

• E-mail: crlae@nuaa.edu.cn

Time and Place

• Time: Tuesday 6:30-9:30 PM

• Classroom: A18-112

Prerequisites

• Theoretical Mechanics:

• Helicopter Aerodynamics

• Structure of Helicopter

• Automatic Control Theory

• Dynamics

Syllabus

• Introduction• Helicopter Control • Rotor Blade flapping motion• Helicopter Trim in Level Flight• Helicopter Stability• Helicopter Response to Pilot Controls• Introduction to Flying Qualities

Requirements

• Stressing on the physical meanings and basic concepts

• Understanding and gripping the analysis methods

• Being able to conduct the basic Calculation

Grade

• 50% Routine time

• 50% Final Exam

Textbook

• Bramwell, “Helicopter Dynamics”, Arnold, 2000.

Useful References

• Gao Zheng and Chen Renliang “Helicopter Flight Dynamics”, Science Press, 2003.

• Padfield, “helicopter Flight Dynamics: The Theory and Application of Flying Qualities and Simulation Modeling”, AIAA Education Series, 1995.

• R. Prouty, “Helicopter Performance, Stability and control”, PWS Publishers, 1986.

• Johnson, “Helicopter Theory”, Princeton University Press, 1980.

Introduction

• Definition of helicopter flight dynamics• Characteristics of helicopter flight• Scopes of helicopter flight dynamics• Methodologies• Objectives of helicopter flight dynamics

Definition of Helicopter Flight Dynamics

The subject of studying external forces applied on helicopter as well as motions and controls

External Forces: Only those changing flight path such as aerodynamic, inertial and gravity forces.

Motions: Accelerations(angular acceleration), velocities and position

Controls: Pilot controls from cockpit, augment stability and control

Flight qualities: Specification and flight quality assessment

Characteristics of Helicopter Flight

Example: from hover to forward flight

Pilot

Push forwardApply Long. cyclic pitch

Rotor disc tilt forward

H

zM

X

X

h

Adjustment

Apply Collective pitch control 7

T

kM

h

Paddle control Tail rotor T TT

Z

Z

Apply lateral Cyclic control

Rotor disc tilt sideS

xM

Characteristics of Helicopter Flight

1. There are 6 freedoms of motion in space, But there are only 4 controls. Therefore the control for each freedom of motion is not independent.

2. The response of helicopter to controls is coupled. The cross-coupling between axes is serious and needs to be removed by pilot controls or SCAS.

3. The controls for heaving, pitch and roll motions are implemented by blade flapping motion. Thus the delay of helicopter response to pilot controls is greater than that of fixed-wing aircraft.

4. The flight qualities of helicopter is poorer than that of fixed-wing aircraft

5. The flight dynamics of helicopter is more complicated than fixed-

wing aircraft

Scope of Helicopter Flight Dynamics

PilotCockpit controls

Aerodynamic surfaces(rotor, tail rotor)

Change aerodynamicForces and moments

Gust disturbance

External forcedisturbance

SCAS

Helicoptermotions

Flight qualityspecification

Flight qualityassessment

Methodologies

• Theoretical analysis• Computer simulation• Wind tunnel test with experimental model• Flight test

Objectives

• Study and improve helicopter trim, stability and control.

• Guide helicopter design– Aerodynamic and inertial distributions

– Primary design parameter determination (rotor, tail rotor, controls and empennage)

– Design of SACS and control laws

Rotor Hinge System

• Introduction of hinges to rotor system– Flap hinge– Lag or drag hinge– feathering

Teetering or See-Saw RotorTeetering or See-Saw Rotor

Underslung Teetering RotorUnderslung Teetering Rotor

Articulated RotorArticulated Rotor

Hingeless RotorHingeless Rotor

Coordinate System

XZ

Y

VX

VZ

VY

SX

SY

SZ

飞行方向DX

DY

DZ

DO

O

SO

XZ

Y

VX

VZ

VY

SX

SY

SZ

飞行方向DX

DY

DZ

DO

O

SO

V

1. Gravity axes

2. Body axes

3. Wind axes

4. Hub axes

Gravity Axes

XZ

Y

VX

VZ

VY

SX

SY

SZ

飞行方向DX

DY

DZ

DO

O

SO

XZ

Y

VX

VZ

VY

SX

SY

SZ

飞行方向DX

DY

DZ

DO

O

SO

V

1. The gravity axis system ODXDYDZD is used to determine the flight path of helicopter in space.

2. The origin of axes can be arbitrary point in space.

3. The axis YD always points in the direction of the vertical, regardless of the orientation of the helicopter.

4. The orientation of XD and ZD axes is less important, and to some extent arbitrary. A typical choice for XD axis to point North, and the ZD axis to point East.

5. The orientation of XD and ZD axes becomes very important in the analysis of flight test data, in piloted simulations and

navigation problems

Body Axes

XZ

Y

VX

VZ

VY

SX

SY

SZ

飞行方向DX

DY

DZ

DO

O

SO

XZ

Y

VX

VZ

VY

SX

SY

SZ

飞行方向DX

DY

DZ

DO

O

SO

V

1. The body axis system OXYZ is used to determine the attitude of helicopter in space.

2. The origin of axes is at the center of mass of helicopter.

3. The axis X points toward the nose of helicopter, the Z axis points to the right side (starboard), and the Y axis points upward .

4. Body axes play an especially important role in flight dynamics.

Wind Axes

XZ

Y

VX

VZ

VY

SX

SY

SZ

飞行方向DX

DY

DZ

DO

O

SO

XZ

Y

VX

VZ

VY

SX

SY

SZ

飞行方向DX

DY

DZ

DO

O

SO

V

1. The wind axis system OXVYVZV is used to determine aerodynamic loads, rotor wake and rotor flap due to wind.

2. The origin of axes is at the center of mass of helicopter.

3. The axis XV points toward the velocity vector of helicopter, the YV axis lies in the plane of symmetry of the vehicle. The orientation ZV of points toward right side.

Hub Axes

XZ

Y

VX

VZ

VY

SX

SY

SZ

飞行方向DX

DY

DZ

DO

O

SO

XZ

Y

VX

VZ

VY

SX

SY

SZ

飞行方向DX

DY

DZ

DO

O

SO

V

1. The hub axis system OXSYSZS is used to determine the rotor aerodynamic loads and rotor flap due to controls and body angular rates.

2. The origin of axes is at the center of rotor hub.

3. The axis YS points upwards and aligns with the rotor shaft.

4. The axis XS points toward the nose of helicopter and perpendicular to axis YS . the ZS axis points to the right side..

Definition of Angles

The Euler angles:

The orientation of any axes relative to another can be given by three angles, which are the consecutive rotations about three axes in that order to carry one frame along with the other. This is a particular case of Euler angles. In helicopter flight dynamics, only one sets is

commonly used, that for the body axes.

1. A rotation ψ about OYD, carrying the axes to OX1YZ1, is the azimuth angle.

2. A rotation υ about OZ1, carrying the axes to OXY2Z1, is the pitch angle.

3. A rotation γ about OX, carrying the axes to OXYZ, is the bank angle.

Z1

X1

Y2

Quatemions

Definition of Angles

The Aerodynamic angles:

The linear motion V of the vehicle relative to the atmosphere can be given either by its three orthogonal components (vx,vy,vz) in the body axes system, or alternatively by the magnitude V and two suitable angles. These angles, which are of fundamental importance in determining the aerodynamic forces that act on the vehicle, are defined as:

Angle of attack:

Sideslip angle:

It will be observed that, in the sense of Euler angles, the aerodynamic angles related the bode axes and wind axes by the rotation sequence (,,0) which carrying the former into the latter

X1

x

y

v

vtg 1

V

vy1sin

Transformation from Gravity Axes to Body Axes

A rotation of ψ:

A rotation of :

A rotation of γ:

The complete coordinate transformation from gravity axes to body axes is:

cos0sin

010

sin0cos

1T

100

0cossin

0sincos

2

T

cossin0

sincos0

001

3T

coscossinsinsincossinsincoscossinsin

cossinsinsincoscoscossinsincossincos

sincossincoscos

cos0sin

010

sin0cos

100

0cossin

0sincos

cossin0

sincos0

001123 TTTTDB

Z1

X1

Y2

Transformation from Body Axes to Wind Axes

A rotation of :

A rotation of : X1

cos0sin

010

sin0cos

1T

100

0cossin

0sincos

2

T

The complete coordinate transformation from body axes to wind axes is:

cos0sin

sinsincoscossin

sincossincoscos

12 TTTBV

Transformationfrom Body Axes to Hub Axes

Y Y S

X

X S

Z, ZS

o

100

0cossin

0sincos

BST

In order to improve the flight performance and pilot Vision in cruse flight, the rotor shaft always tilts Forward as an angle . Thus:In the sense of Euler angles, the rotor shaft tilt angle related the bode axes and hub axes by the rotation sequence (0,,0) which carrying the former into the latter

Comparison of Coordinate System in Different Country

XZ

O

Y

X

Z

O

Y

China and Russia West Country

Comparison of Definition of Parameters in Different Country

OO

NM y ry

B

ZY

XX

YZ

wVy

LM x

px

B

uVx

MM z

qz

B vVz

Comparison of Definition of Parameters in Different Country

Meanings

Hide force coeff.

Side force coeff.

Anti torque coeff.

Lock Number

China and Russia West country

Thrust coeff.