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||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
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Rotary Wing UAS: Introduction, Mechanical Design
and AerodynamicsIntroduction
20.10.2015Robot Dynamics: Rotary Wing UAS 2
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Rotorcraft: Aircraft which produces lift from a rotary wing turning in a
plane close to horizontal
20.10.2015Robot Dynamics: Rotary Wing UAS 3
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
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 4
Types of Rotorcraft
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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
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 6
Rotor Configuration 2
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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”)
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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
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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
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Rotary Wing UAS: Introduction, Mechanical Design
and AerodynamicsMechanical Design
20.10.2015Robot Dynamics: Rotary Wing UAS 10
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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
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 12
Rotor Definitions
TPP
βFl(ξ)
θR(ξ)
T
ξ
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Add DoF to rotor blade to allow for blade flapping
Different types of rotorhead possible
20.10.2015Robot Dynamics: Rotary Wing UAS 13
Rotorhead
Teetering
rotorhead
Controlled feathering axis
Blades are rigidly connected
Blade flapping through teetering
hinge
Fully articulated
rotorhead
Controlled feathering axis
Blade attached to series of hinges
for 3 DoF
Hingeless
rotorhead
Controlled feathering axis
Flap + lead-lag hinge replaced by
elastic element
Rotor torques can be transmitted to
fuselage!
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 14
Rotorhead:
Fully Articulated
βFl
θR
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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!
20.10.2015Robot Dynamics: Rotary Wing UAS 15
Steering a Helicopter
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 16
Swashplate
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 17
Swashplate DoF
Collective pitch
Cyclic pitch
)sin()cos()( 210 scR
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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!
20.10.2015Robot Dynamics: Rotary Wing UAS 18
Changing the Blade Flapping Angles
)sin()cos()( 110 scFl
Lift
flflRRL
Gyroscopic
RRfl ),,,,,(),( vωβFl
dL
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 19
Changing the Blade Flapping Angles:
Coning Angle
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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°)
20.10.2015Robot Dynamics: Rotary Wing UAS 20
Changing the Blade Flapping Angles:
Flapping Angle
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 21
Changing the Blade Flapping Angles:
Example
An
gle
s
Blade azimuth angle
ξ θR
βFl
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 22
Stability Augmentation:
The Flybar (Bell System)
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 23
Stability Augmentation:
The Flybar (Hiller System)
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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)
20.10.2015Robot Dynamics: Rotary Wing UAS 24
Tail Rotor
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 25
Tail Rotor:
Alternative Concepts (Fenestron)
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 26
Tail Rotor:
Alternative Concepts (NOTAR)
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Rotary Wing UAS: Introduction, Mechanical Design
and AerodynamicsAerodynamics
20.10.2015Robot Dynamics: Rotary Wing UAS 27
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2D flow around an airfoil creates aerodynamic
force due to change in momentum of fluid.
Lift force
Drag force
Moment
20.10.2015Robot Dynamics: Rotary Wing UAS 28
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
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Hover
Speed increases linearly with
radius
Axisymmetric
Forward flight
Dissymmetric speed distribution
Lower speed at retreating blade
Reverse flow region
20.10.2015Robot Dynamics: Rotary Wing UAS 29
Rotor/Propeller Speeds across the Blades
ωR ωR
V
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 30
2.5D Lift Distribution:
Force Distribution along Blade
Lift
Induced velocity
Blade radius r
dL/dvi
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 31
Blade-tip Vortex:
Hover and Axial Climb
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 32
2.5D Lift Distribution:
Accounting for Blade Vortex
Lift
Induced velocityBlade radius r
dL/dvi
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 33
Forward Flight
Simulated airflow of coaxial configuration
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 34
Forces/Moments on a Rotor/Propeller
ωR
V
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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
20.10.2015Robot Dynamics: Rotary Wing UAS 35
Autorotation
Driven region:
Driving region:
Stall region:
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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.
20.10.2015Robot Dynamics: Rotary Wing UAS 36
References