folienmaster eth zürich · pdf fileadvantage disadvantage ability to hover high...

||Autonomous Systems Lab

151-0851-00 V

Marco Hutter, Michael Blösch, Roland Siegwart, Konrad Rudin and Thomas

Stastny

20.10.2015Robot Dynamics: Rotary Wing UAS 1

Robot DynamicsRotary Wing UAS: Introduction, Mechanical Design and

Aerodynamics


Rotary Wing UAS: Introduction, Mechanical Design

and AerodynamicsIntroduction



Rotorcraft: Aircraft which produces lift from a rotary wing turning in a

plane close to horizontal


Rotorcraft:

Definition

“A helicopter is a collection of vibrations held together by differential equations” John Watkinson

Advantage Disadvantage

Ability to hover High maintenance costs

Power efficiency during hover Poor efficiency in forward flight

“If you are in trouble anywhere, an airplane can fly over and drop flowers,

but a helicopter can land and save your life” Igor Sikorsky


Helicopter Autogyro Gyrodyne

Power driven main rotor Un-driven main rotor, tilted

away

Power driven main propeller

The air flows from TOP to

BOTTOM

The air flows from BOTTOM

to TOP

The air flows from TOP to

BOTTOM

Tilts its main rotor to fly

forward

Forward propeller for

propulsion

Main propeller cannot tilt

No tail rotor required Additional propeller for

propulsion

Not capable of hovering


Types of Rotorcraft

||Autonomous Systems Lab 20.10.2015Robot Dynamics: Rotary Wing UAS 5

Rotor Configuration

Single rotor Multi rotor

Most efficient Reduced efficiency due to multiple rotors and

downwash interference

Mass constraint Able to lift more payload

Need to balance counter-torque Even numbered rotors can balance counter-

torque


Tandem rotor (front-rear) Tandem rotor (side by side)

Contra-rotating, no need for tail rotor Contra-rotating, no need for tail rotor

Total disk-area < 2x disk-area Higher rotor efficiency in forward flight

The CoG position is not critical High structural drag

Less sensitive to wind during hovering, less

directional stability in forward flight

Rarely used


Rotor Configuration 2


Rotor Configuration 3

Synchropter Coaxial helicopter

Intermeshed contra-rotating rotors Contra-rotating, no need for tail rotor

Torques do not cancel perfectly in the

horizontal plane

Losses due to upper-rotor downwash

Compact size

Complex mechanics (“hollow shaft”)


Rotorcraft at UAS-MAV Size

Quadrotor Std. helicopter

Four propellers in cross configuration Very agile

Direct drive (no gearbox) Most efficient design

Very good torque compensation Complex to control

High maneuverability


Rotorcraft at UAS-MAV Size 2

Ducted fan Coaxial

Fix propeller Complex mechanics

Torques produced by control surfaces Passively stable

Heavy Compact

Compact Suitable for miniaturization



and AerodynamicsMechanical Design



Rotor vs. Propeller

Propeller Rotor

Used to produce thrust Used to produce lift, thrust and directional

control

Propeller plane perpendicular to shaft Elastic element between blade and shaft

Rigid blade. No blade flapping Blade flapping used to change tip path plane

Fixed blade pitch angle or collective changes

only

Blade pitch angle controlled by swashplate


Tip path plane (TPP)

Plane spanned by blade tip

within one full rotation

Thrust perpendicular to TPP

Control UAS by controlling TPP

Blade flapping angle βFl(ξ)

Tilt angle of the blade

Blade flapping video

Blade azimuth angle ξ

Azimuth position of the blade

Blade pitch angle θR(ξ)

Tilt angle of chord line

Used to control TPP motion


Rotor Definitions

TPP

βFl(ξ)

θR(ξ)

T

ξ

https://www.youtube.com/watch?v=Ug6W7_tafnc


Add DoF to rotor blade to allow for blade flapping

Different types of rotorhead possible


Rotorhead

Teetering

rotorhead

Controlled feathering axis

Blades are rigidly connected

Blade flapping through teetering

hinge

Fully articulated

rotorhead


Blade attached to series of hinges

for 3 DoF

Hingeless

rotorhead


Flap + lead-lag hinge replaced by

elastic element

Rotor torques can be transmitted to

fuselage!


Feathering (pitch) hinge

Actively controlled bearing to

change local blade pitch angle

Flapping hinge

Allows for blade flapping to

change tip path plane

Reduces stresses in the blade

from non-uniform lift distribution

Lagging hinge

Reduce stresses due to Coriolis-

force

Blade flapping changes distance

of blade to rotation shaft

Speed due to rotation varies


Rotorhead:

Fully Articulated

βFl

θR


Helicopter has six DoF (position

and attitude)

Pilot has four control input

Vertical, with collective pitch (up

and down)

Directional, with tail rotor pitch

(yaw)

Longitudinal and lateral, with

cyclic pitch (forward/pitch or

sideward/roll)

Tilts TPP to desired direction

Controls are coupled!

Different for other configuration!


Steering a Helicopter

https://www.youtube.com/watch?v=Mx7vLB3KP1w


TPP controlled by local change

of blade pitch angle

Swashplate converts

commands from pilot into blade

pitch angle θR, which leads to

blade flapping βFl

Consists of two disks

Lower fixed wrt to fuselage. Can

be tilted or moved along shaft

Upper rotates with blades.

Connected to the feathering axis


Swashplate


Blade pitch actuation

2 DoF for longitudinal motion

with cyclic pitch

1 DoF for vertical motion

Blade pitch angle changes

within one revolution

Θ0: Constant pitch angle

Θ1c and Θ1s: Cyclic pitch

changes


Swashplate DoF

Collective pitch

Cyclic pitch

)sin()cos()( 210 scR


Control input: Blade pitch angle θR(ξ)

Expected output: Blade flapping angle βFl(ξ)

Relation between flapping angle and blade pitch angle General dynamic equation

Second order system

Flapping dynamics behaves like a damped oscillator!


Changing the Blade Flapping Angles

)sin()cos()( 110 scFl

Lift

flflRRL

Gyroscopic

RRfl ),,,,,(),( vωβFl

dL


Blade flapping angle has a constant and cyclic term

Consider constant blade pitch angle θ0 in hover

Constant lift force within full rotation

Blades move to constant flapping angle β0 (coning angle)

Coning angle at equilibrium point of forces

Lift force

Gravity force

Force of the hinge

Centrifugal force

Typical coning angle between 8°-10° for helicopter


Changing the Blade Flapping Angles:

Coning Angle


Bode plot of a generic linear damped oscillator

Blade flapping due to cyclic changes in θR(ξ)

Behaves like damped oscillator excited by harmonic lift force with

frequency ωR (rotor speed)

Phase lag between blade flapping angle and blade pitch angle

Phase lag depends on the rotor structure and ωR

Phase lag <90° (for teetering rotorhead = 90°)



Flapping Angle


How do you need to control the blade pitch angle if you

want to tilt the rotor forward?

Flapping angle minimum at ξ = 0° and maximum at ξ = 180°

Due to phase lag, the maximum blade pitch must be applied earlier



Example

An

gle

s

Blade azimuth angle

ξ θR

βFl


The Bell bar system

Masses on a bar

Hinge supported on the shaft

Damper at hinge

Flybar plane slowly follows rotor

shaft with given dynamic

Acts like a gyroscope

Rotates with the shaft

Changes cyclic blade pitch angle

Controls the TPP back to the

flybar plane


Stability Augmentation:

The Flybar (Bell System)


The Hiller system

Small but heavy paddles on a

bar

Acts like a small rotor

Only small changes due to

disturbances

Swashplate controls the attitude

of the flybar

The flybar controls the blade pitch

angle such that the TPP converge

to flybar plane

Obsolete for full scale systems

Active control used instead


Stability Augmentation:

The Flybar (Hiller System)


Main rotor driven by engine

Actio-reactio principle: Counter-

torque on the fuselage

The tail rotor provides torque to

balance the main rotor counter-

torque

Variable blade pitch enables yaw

control (collective pitch only)


Tail Rotor

teaching/lecture/movies/Tail Rotor Failure.wmv

teaching/lecture/movies/Tail Rotor Failure.wmv


Fenestron

Ducted fan at the tail

Enclosed

Protection

Area smaller than for a

conventional tail rotor

Higher ground clearance

Large amount of blades

irregularly spaced

Avoids creating noise


Tail Rotor:

Alternative Concepts (Fenestron)


NOTAR (No tail rotor)

Airstream out of tail boom

Uses the Coanda effect to

deflect the main rotor downwash

Steering nozzle at the end for

yaw control


Tail Rotor:

Alternative Concepts (NOTAR)



and AerodynamicsAerodynamics



2D flow around an airfoil creates aerodynamic

force due to change in momentum of fluid.

Lift force

Drag force

Moment


2D Aerodynamics

22

2dyVcCdM m

2

2cdyVCdD d

2

2cdyVCdL l

with

: Density of fluid (air)

c : Chord length

V : Relative flight speed

Cl : Lift coefficient

Cd : Drag coefficient

Cm : Moment coefficient


Hover

Speed increases linearly with

radius

Axisymmetric

Forward flight

Dissymmetric speed distribution

Lower speed at retreating blade

Reverse flow region


Rotor/Propeller Speeds across the Blades

ωR ωR

V


Example: Rectangular infinitely long blade in hover

Lift and induced velocity distribution along radius (const. θR)

Neglecting 3D boundaries!

Lift proportional to relative speed squared

But angle of attack decreases at outer radius

Lift increases less than squared with respect to blade radius

Most of the lift is produced at outer blade radius


2.5D Lift Distribution:

Force Distribution along Blade

Lift

Induced velocity

Blade radius r

dL/dvi


Change in momentum of fluid

creates pressure difference

High pressure below the blade

Low pressure above the blade

High pressure difference at outer

blade

Boundary condition: No pressure

difference at blade tip

Generation of strong vortices

trail at blade tip

Trail downstream with induced

velocity

Aerodynamic interference when

moving vertically downwards


Blade-tip Vortex:

Hover and Axial Climb


Lift distribution considering tip vortices

Rectangular blade with constant θR

Loss of lift due to the vortices

Due to vortex induced velocity, angle of attack decreases over blade

Effect decreases at inner radius

Use blade twist and tapering to reduce tip vortex

Twist: decrease θR with blade radius

Taper: Decrease chord length with blade radius


2.5D Lift Distribution:

Accounting for Blade Vortex

Lift

Induced velocityBlade radius r

dL/dvi


Analysis even more complex in

forward flight

Blade-tip vortices interaction

Transonic flow over advancing

blade

Blade stall on retreating blade

Main rotor wake tail rotor

interaction


Forward Flight

Simulated airflow of coaxial configuration


Represent aerodynamic force in

tip path plane coordinates

Total thrust T is integration of

dT over blades

In forward flight asymmetric

distribution over blade

Additional blade flapping

(rotor)/Rolling moment (propeller)

Drag torque Q is integration of

dQ distribution over blade

In forward flight asymmetric

distribution over blade

Additional hub force


Forces/Moments on a Rotor/Propeller

ωR

V


Absorb energy from the air to

rotate the rotor blades

Principle of the Autogiro. Used

by helicopter in case of engine

failure

Consider pure vertical

autorotation

Relative airflow has

Horizontal component from

rotation

Upward component from descent

Resulting aerodynamics force

can have forwards or rearward

component


Autorotation

Driven region:

Driving region:

Stall region:


Books

[1]Leishman J. Gordon: Principles of Helicopter Aerodynamics, 2nd

Ed. Cambridge University Press, 2006.

[2]Bramwell Anthony R.S. et al.: Bramwell‘s Helicopter Dynamics,

2nd Ed. Butterworth-Heinemann, 2001.

[3]Padfield Fareth D.: Helicopter Flight Dynamics. Wiley, 2008.


References

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