rotorcraft introduction
TRANSCRIPT
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151-0851-00 V
Marco Hutter, Roland Siegwart and Thomas Stastny
27.10.2015Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling 1
Robot DynamicsRotary Wing UAS: Introduction Design and Aerodynamics
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Contents | Rotary Wing UAS
1. Introduction - Design and Propeller Aerodynamics
2. Propeller Analysis and Dynamic Modeling
3. Control of a Quadrotor
4. Rotor Craft Case Study
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IntroductionRotary Wing UAS: Introduction Design and Aerodynamics
27.10.2015Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling 3
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Rotorcraft: Aircraft which produces lift from a rotary wing turning in a plane close to horizontal
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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
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Rotorcraft | Overview on Types of Rotorcraft
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Rotorcraft | Rotor Configuration 1
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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Rotorcraft | at UAS-MAV Size 1
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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Mechanical DesignRotary Wing UAS: Introduction Design and Aerodynamics
27.10.2015Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling 9
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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
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Rotorcraft | Rotor Definitions
TPP
βFl(ξ)
θR(ξ)
T
ξ
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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!
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Rotorcraft | Steering a Helicopter
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AerodynamicsRotary Wing UAS: Introduction Design and Aerodynamics
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2D flow around an airfoil creates aerodynamic force due to change in momentum of fluid.
Lift force
Drag force
Moment
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Aerodynamics | 2D
22
2dyVcCdM m
2
2cdyVCdD d
2
2cdyVCdL l
with
: Density of fluid (air)c : Chord lengthV : Relative flight speedCl : Lift coefficientCd : Drag coefficientCm : 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
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Aerodynamics | 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 radius07.11.2016Robot Dynamics: Rotary Wing UAS 15
Aerodynamics | 2.5D Lift/Force Distribution along Blade
Lift
Induced velocityBlade 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
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Aerodynamics | Blade-tip Vortex at 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
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Aerodynamics | 2.5D Lift Distribution with Accounting for Blade Vortex
Lift
Induced velocityBlade radius r
dL/dvi
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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
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Aerodynamics | 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
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Aerodynamics | 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.
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Aerodynamics | References