Robot Dynamics Rotary Wing UAS: Introduction, Mechanical Design and Aerodynamics

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1 Robot Dynamics Rotary Wing UAS: Introduction, Mechanical Design and Aerodynamics V Marco Hutter, Michael Blösch, Roland Siegwart, Konrad Rudin and Thomas Stastny Robot Dynamics: Rotary Wing UAS

2 Rotary Wing UAS: Introduction, Mechanical Design and Aerodynamics Introduction Robot Dynamics: Rotary Wing UAS

efficiency during hover Disadvantage High maintenance costs Poor efficiency in forward flight If you are in trouble anywhere, an

3 Rotorcraft: Definition Rotorcraft: Aircraft which produces lift from a rotary wing turning in a plane close to horizontal A helicopter is a collection of vibrations held together by differential equations John Watkinson Advantage Ability to hover Power efficiency during hover Disadvantage High maintenance costs 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 Robot Dynamics: Rotary Wing UAS

4 Types of Rotorcraft Helicopter Autogyro Gyrodyne Power driven main rotor The air flows from TOP to BOTTOM Tilts its main rotor to fly forward Un-driven main rotor, tilted away The air flows from BOTTOM to TOP Forward propeller for propulsion No tail rotor required Not capable of hovering Power driven main propeller The air flows from TOP to BOTTOM Main propeller cannot tilt Additional propeller for propulsion Robot Dynamics: Rotary Wing UAS

Rotor Configuration Single rotor Multi rotor Most efficient Mass constraint Need to balance counter-torque Reduced efficiency due to multiple

5 Rotor Configuration Single rotor Multi rotor Most efficient Mass constraint Need to balance counter-torque Reduced efficiency due to multiple rotors and downwash interference Able to lift more payload Even numbered rotors can balance countertorque Robot Dynamics: Rotary Wing UAS 5

Rotor Configuration 2 Tandem rotor (front-rear) Tandem rotor (side by side) Contra-rotating, no need for tail rotor Total disk-area < 2x disk-area The CoG position is not critical Less sensitive to

6 Rotor Configuration 2 Tandem rotor (front-rear) Tandem rotor (side by side) Contra-rotating, no need for tail rotor Total disk-area < 2x disk-area The CoG position is not critical Less sensitive to wind during hovering, less directional stability in forward flight Contra-rotating, no need for tail rotor Higher rotor efficiency in forward flight High structural drag Rarely used Robot Dynamics: Rotary Wing UAS

plane Contra-rotating, no need for tail rotor Losses due to upper-rotor

7 Rotor Configuration 3 Synchropter Coaxial helicopter Intermeshed contra-rotating rotors Torques do not cancel perfectly in the horizontal plane Contra-rotating, no need for tail rotor Losses due to upper-rotor downwash Compact size Complex mechanics ( hollow shaft ) Robot Dynamics: Rotary Wing UAS 7

gearbox) Very good torque compensation High maneuverability Very

8 Rotorcraft at UAS-MAV Size Quadrotor Std. helicopter Four propellers in cross configuration Direct drive (no gearbox) Very good torque compensation High maneuverability Very agile Most efficient design Complex to control Robot Dynamics: Rotary Wing UAS 8

Compact Complex mechanics Passively stable Compact

9 Rotorcraft at UAS-MAV Size 2 Ducted fan Coaxial Fix propeller Torques produced by control surfaces Heavy Compact Complex mechanics Passively stable Compact Suitable for miniaturization Robot Dynamics: Rotary Wing UAS 9

10 Rotary Wing UAS: Introduction, Mechanical Design and Aerodynamics Mechanical Design Robot Dynamics: Rotary Wing UAS

No blade flapping Fixed blade pitch angle or collective changes only Used to produce lift, thrust and

11 Rotor vs. Propeller Propeller Rotor Used to produce thrust Propeller plane perpendicular to shaft Rigid blade. No blade flapping Fixed blade pitch angle or collective changes only Used to produce lift, thrust and directional control Elastic element between blade and shaft Blade flapping used to change tip path plane Blade pitch angle controlled by swashplate Robot Dynamics: Rotary Wing UAS 11

12 Rotor Definitions 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 β Fl (ξ) Tilt angle of the blade Blade flapping video Blade azimuth angle ξ Azimuth position of the blade Blade pitch angle θ R (ξ) Tilt angle of chord line Used to control TPP motion θ R (ξ) T ξ TPP β Fl (ξ) Robot Dynamics: Rotary Wing UAS

Rotorhead Add DoF to rotor blade to allow for blade flapping Different types of

feathering axis Blades are rigidly connected Blade flapping through teetering hinge

rotorhead Controlled feathering axis Flap + lead-lag hinge replaced by elastic

13 Rotorhead Add DoF to rotor blade to allow for blade flapping Different types of rotorhead possible Teetering rotorhead Fully articulated rotorhead Controlled feathering axis Blades are rigidly connected Blade flapping through teetering hinge 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! Robot Dynamics: Rotary Wing UAS

Rotorhead: Fully Articulated 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

14 Rotorhead: Fully Articulated 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 Coriolisforce Blade flapping changes distance of blade to rotation shaft Speed due to rotation varies β Fl θr Robot Dynamics: Rotary Wing UAS

Steering a Helicopter 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

15 Steering a Helicopter 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! Robot Dynamics: Rotary Wing UAS

Swashplate TPP controlled by local change of blade pitch

pitch angle θ R, which leads to blade flapping β Fl

Can be tilted or moved along shaft Upper rotates with

16 Swashplate TPP controlled by local change of blade pitch angle Swashplate converts commands from pilot into blade pitch angle θ R, which leads to blade flapping β Fl 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 Robot Dynamics: Rotary Wing UAS

Collective pitch Cyclic pitch R ( ) 1 c cos( ) 2 sin( 0 s ) Θ 0 : Constant pitch

17 Swashplate DoF Blade pitch actuation 2 DoF for longitudinal motion with cyclic pitch 1 DoF for vertical motion Blade pitch angle changes within one revolution Collective pitch Cyclic pitch R ( ) 1 c cos( ) 2 sin( 0 s ) Θ 0 : Constant pitch angle Θ 1c and Θ 1s : Cyclic pitch changes Robot Dynamics: Rotary Wing UAS

18 Changing the Blade Flapping Angles Control input: Blade pitch angle θ R (ξ) Expected output: Blade flapping angle β Fl (ξ) Relation between flapping angle and blade pitch angle General dynamic equation Fl ( ) 1 c cos( ) 1 sin( 0 s ) dl fl ( R, R) L( R, ω, v, R, fl, fl ) Gyroscopic Lift β Fl Second order system Flapping dynamics behaves like a damped oscillator! Robot Dynamics: Rotary Wing UAS

Changing the Blade Flapping Angles: Coning Angle Blade flapping angle has a constant and cyclic term Consider constant blade pitch angle θ 0 in hover Constant lift force within full rotation Blades

19 Changing the Blade Flapping Angles: Coning Angle Blade flapping angle has a constant and cyclic term Consider constant blade pitch angle θ 0 in hover Constant lift force within full rotation Blades move to constant flapping angle β 0 (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 Robot Dynamics: Rotary Wing UAS

linear damped oscillator Phase lag between blade flapping angle and blade pitch angle Phase lag depends on the

20 Changing the Blade Flapping Angles: Flapping Angle Blade flapping due to cyclic changes in θ R (ξ) Behaves like damped oscillator excited by harmonic lift force with frequency ω R (rotor speed) Bode plot of a generic linear damped oscillator Phase lag between blade flapping angle and blade pitch angle Phase lag depends on the rotor structure and ω R Phase lag <90 (for teetering rotorhead = 90 ) Robot Dynamics: Rotary Wing UAS

21 Angles Changing the Blade Flapping Angles: Example 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 ξ β Fl θ R Blade azimuth angle Robot Dynamics: Rotary Wing UAS

Stability Augmentation: The Flybar (Bell System) The Bell bar system Masses on a bar Hinge supported on the shaft Damper at hinge Flybar plane slowly follows rotor shaft with

22 Stability Augmentation: The Flybar (Bell System) 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 Robot Dynamics: Rotary Wing UAS

Stability Augmentation: The Flybar (Hiller 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

23 Stability Augmentation: The Flybar (Hiller 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 Robot Dynamics: Rotary Wing UAS

blade pitch enables yaw control (collective

24 Tail Rotor Main rotor driven by engine Actio-reactio principle: Countertorque on the fuselage The tail rotor provides torque to balance the main rotor countertorque Variable blade pitch enables yaw control (collective pitch only) Robot Dynamics: Rotary Wing UAS

25 Tail Rotor: Alternative Concepts (Fenestron) 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 Robot Dynamics: Rotary Wing UAS

to deflect the main rotor downwash Steering nozzle at the

26 Tail Rotor: Alternative Concepts (NOTAR) 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 Robot Dynamics: Rotary Wing UAS

27 Rotary Wing UAS: Introduction, Mechanical Design and Aerodynamics Aerodynamics Robot Dynamics: Rotary Wing UAS

28 2D Aerodynamics 2D flow around an airfoil creates aerodynamic force due to change in momentum of fluid. Lift force Drag force Moment dl C l dd C dm C d m 2 cdyv 2 cdyv c 2 2 dyv 2 with : Density of fluid (air) 2 2 c : Chord length V : Relative flight speed C l C d C m : Lift coefficient : Drag coefficient : Moment coefficient Robot Dynamics: Rotary Wing UAS

Rotor/Propeller Speeds across the Blades

29 Rotor/Propeller Speeds across the Blades Hover Speed increases linearly with radius Axisymmetric Forward flight Dissymmetric speed distribution Lower speed at retreating blade Reverse flow region V ω R ω R Robot Dynamics: Rotary Wing UAS

2.5D Lift Distribution: Force Distribution along Blade Example: Rectangular infinitely long blade in hover Lift and induced velocity distribution along radius (const. θ R ) Neglecting 3D boundaries!

30 2.5D Lift Distribution: Force Distribution along Blade Example: Rectangular infinitely long blade in hover Lift and induced velocity distribution along radius (const. θ R ) Neglecting 3D boundaries! dl/dv i Lift Blade radius r Induced velocity 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 Robot Dynamics: Rotary Wing UAS

Blade-tip Vortex: Hover and Axial Climb Change in momentum of fluid creates pressure difference High pressure below the blade Low pressure above the blade High pressure difference at outer blade

31 Blade-tip Vortex: Hover and Axial Climb 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 Robot Dynamics: Rotary Wing UAS

decreases over blade Effect decreases at inner radius Use blade twist and tapering to reduce tip vortex Twist: decrease θ

32 2.5D Lift Distribution: Accounting for Blade Vortex Lift distribution considering tip vortices Rectangular blade with constant θ R dl/dv i Lift Blade radius r 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 θ R with blade radius Taper: Decrease chord length with blade radius Induced velocity Robot Dynamics: Rotary Wing UAS

retreating blade Main rotor wake tail rotor interaction Simulated

33 Forward Flight 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 Simulated airflow of coaxial configuration Robot Dynamics: Rotary Wing UAS

flapping (rotor)/rolling moment (propeller) Drag torque Q is integration of dq distribution over blade In

34 Forces/Moments on a Rotor/Propeller 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 V ω R Robot Dynamics: Rotary Wing UAS

35 Autorotation 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 Driven region: Driving region: Stall region: Robot Dynamics: Rotary Wing UAS

36 References Books [1]Leishman J. Gordon: Principles of Helicopter Aerodynamics, 2nd Ed. Cambridge University Press, [2]Bramwell Anthony R.S. et al.: Bramwell s Helicopter Dynamics, 2nd Ed. Butterworth-Heinemann, [3]Padfield Fareth D.: Helicopter Flight Dynamics. Wiley, Robot Dynamics: Rotary Wing UAS

Die Lösungen müssen manuell überpüft werden. Die Buchstaben stimmen nicht mehr überein.

HELI Final Test 2015, Winterthur 17.06.2015 NAME: Mark the best answer. A B C D A B C D Die Lösungen müssen manuell überpüft werden. Die Buchstaben stimmen nicht mehr überein. 1 1 Principles of Flight