Control and Stability of Helicopters Maria Tomas Rodriguez E E

Control and Stability of Helicopters Maria Tomas–Rodriguez. E&E. engineering department. Control and Power Group. Imperial College. United Kingdom. e-mail: maria. tomas@imperial. ac. uk

System description. OVERVIEW Helicopter dynamics description. Accident statistics. Main Causes of accidents. Causes under study. LTE: Loss of tail rotor effectiveness Description of the problem. Contributing factors. VRS: Vortex Ring State. Rotor wake and tip vortices. Description of the problem. VTM as a research tool. AUTOSIM™ as modelling tool. Proposed research line. Auto. Sim Blades Dynamic Description. Code validation: Flapping and Lagging-AUTOSIM™. Flap-Feather Coupling-AUTOSIM™. Auto. Sim Fuselage and Tail Rotor Description. Code validation: Fuselage and Tail Rotor-AUTOSIM™. Conclusion and further work summary.

System description. Helicopter dynamics description. Accident statistics. Main Causes of accidents. Causes under study. LTE: Loss of tail rotor effectiveness Description of the problem. Contributing factors. VRS: Vortex Ring State. Rotor wake and tip vortices. Description of the problem. VTM as a research tool. AUTOSIM™ as modelling tool. Proposed research line. Auto. Sim Blades Dynamic Description. Code validation: Flapping and Lagging-AUTOSIM™. Flap-Feather Coupling-AUTOSIM™. Auto. Sim Fuselage and Tail Rotor Description. Code validation: Fuselage and Tail Rotor-AUTOSIM™. Conclusion and further work summary.

System description HH-60 H Seahawk helicopter from Helicopter Anti-Submarine Squadron Five (HS-5) flies over the Mediterranean Sea U. S. Navy's Digital Image site.

Main rotor Helicopter rotor, Aeronautics Department Lab. , Imperial college, 17/02/06.

Main rotor Main Rotor: Provides the lift for the helicopter to fly and the control that allows the helicopter to move laterally, make turns and change altitude. To handle all of these tasks: -The rotor must be strong. -It must also be able to adjust the angle of the rotor blades with each revolution of the hub. The adjustability is provided by a device called the swash plate.

Tail rotor: The tail rotor of a helicopter is mounted on the tail of a single-rotor helicopter, perpendicular to the main rotor. It is used in order to counteract the yaw motion and the torque that a rapidly turning disk naturally produces. Yaw control pedals counteract torque effect by providing a means of changing pitch (angle of attack) of the tail rotor blades).

Blades: To climb, the angle of pitch of the blades is increased. To descend, the pitch of the blades is decreased. Because all blades are acting simultaneously, or collectively, this is known as collective pitch. For forward, backward and sideways flight an additional change of pitch is provided. The pitch of each blade increases at the same selected point in its circular pathway. This is the cyclic pitch. This adjustability is provided by the swash plate.

Blades D. O. F. Flapping: Is the motion of the blade of the disk plane. Positive for upward motion of the blade. Blade flapping compensates the dissymmetry of lift. Retreating side: flap down - angle of attack becomes larger - lift increases. Advancing side: flap up - angle of attack becomes smaller - lift decreases.

Blades Dynamics Lagging: Is the motion of the blade in the disk plane. Positive when opposite the direction of rotation of the rotor. Modelled by using spring and damper. Constants are provided in an input file. VTM considers both linear and nonlinear dampers. Feathering: Blade pitch. Produced by rotation of the blade about a hinge or bearing at the root with its axis parallel to the blade spar. Positive for nose-up rotation of the blade. Provided in input file with the form: θ = θ 0+ θ 1 s sin(wt)+ θ 1 c cos(wt)

System description. Helicopter dynamics description. Accident statistics. Main Causes of accidents. Causes under study. LTE: Loss of tail rotor effectiveness Description of the problem. Contributing factors. VRS: Vortex Ring State. Rotor wake and tip vortices. Description of the problem. VTM as a research tool. AUTOSIM™ as modelling tool. Proposed research line. Auto. Sim Blades Dynamic Description. Code validation: Flapping and Lagging-AUTOSIM™. Flap-Feather Coupling-AUTOSIM™. Auto. Sim Fuselage and Tail Rotor Description. Code validation: Fuselage and Tail rotor-AUTOSIM™. Conclusion and further work summary.

Duties performed during accident ocurrence

Accident statistics.

System description. Helicopter dynamics description. Accident statistics. Main Causes of accidents. Causes under study. LTE: Loss of tail rotor effectiveness Description of the problem. Contributing factors. VRS: Vortex Ring State. Rotor wake and tip vortices. Description of the problem. VTM as a research tool. AUTOSIM™ as modelling tool. Proposed research line. Auto. Sim Blades Dynamic Description. Code validation: Flapping and Lagging-AUTOSIM™. Flap-Feather Coupling-AUTOSIM™. Auto. Sim Fuselage and Tail Rotor Description. Code validation: Fuselage and Tail rotor-AUTOSIM™. Conclusion and further work summary.

LTE: Loss of Tail Rotor Effectiveness PROBLEM DESCRIPTION: Critical low speed aerodynamic flight condition that occurs when the flow of air through a conventional tail rotor is altered in some way either by, altering the angle or speed at which the air passes through the rotating blades of the tail rotor system. Characteristics of flight under LTE: - Pitch / angle of attack of tail rotor is changed abruptly. - Large change of power at low airspeed. - Uncontrolled right turns at low speed.

LTE: Loss of Tail Rotor Effectiveness Main contributing factors to LTE (Hypothesis): 1. Airflow / downdraft generated by the main rotor blades interfere with airflow entering the tail rotor assembly. 2. Turbulence and other natural phenomena (tail wind) as the generated vortices can be blown into the tail rotor.

LTE: Loss of Tail Rotor Effectiveness Parts of the tip vortices from the main rotor blades pass through the plane of the tail rotor. The resulting blade-vortex interactions could yield high levels of vibration or noise at this flight condition. Computational visualization of the wake generated by a representative attack Helicopter configuration in high speed forward flight.

LTE: Loss of Tail Rotor Effectiveness Possible solutions to LTE: - Nose down to gain forward airspeed altitude and space required. - Maintenance of max. power on rotor r. p. m. as if r. p. m. decrease, the antitorque thrust available is decreased proportionally not providing enough torque control. - If no correction is done, then RAPID YAW will take place.

System description. Helicopter dynamics description. Accident statistics. Main Causes of accidents. Causes under study. LTE: Loss of tail rotor effectiveness Description of the problem. Contributing factors. VRS: Vortex Ring State. Rotor wake and tip vortices. Description of the problem. VTM as a research tool. AUTOSIM™ as modelling tool. Proposed research line. Auto. Sim Blades Dynamic Description. Code validation: Flapping and Lagging-AUTOSIM™. Flap-Feather Coupling-AUTOSIM™. Auto. Sim Fuselage and Tail Rotor Description. Code validation: Fuselage and Tail rotor-AUTOSIM™. Conclusion and further work summary.

Rotor wake and tip vortices. - The 3 -D nature of the rotor wake is a difficult topic to study experimentally and to compute by means of mathematical models. . Picture taken from U. S. Navy's Digital Image site

Rotor wake and tip vortices. Helicopter wake is dominated by strong vortices trailed from the tips of each blade. Sketch of a helicopter rotor wake for a single blade. From Gray (1956).

Rotor wake and tip vortices. The rotors of an SH-60 Seahawk helicopter from the "Red Lions" of Helicopter Anti-Submarine Squadron One Five (HS-15) are illuminated by sparks as the downwash strikes the sands Picture taken from U. S. Navy's Digital Image site. Kuwait City, Kuwait, Aug. 10, 2000.

Rotor wake and tip vortices. In hover: The tip vortices follow helical trajectories below the rotor. Computational visualization of the wake structure generated by a four-bladed hovering rotor shortly after start up. In forward flight: The rotor wake is skewed back behind the rotor by the oncoming flow. Computational visualization of the wake of a four-bladed rotor in forward flight at about 70 knots.

Rotor wake at Hover

Rotor wake in forward flight

VRS: Vortex Ring State. PROBLEM DESCRIPTION: The vortices normally generated at the rotor blades are entrapped around the rotor in a turbulent, chaotic air mass that disturbs the production of rotor thrust. SOLUTION: Lower the nose and increase forward air speed. Main contributing factors to VRS [1]: HRD: High Rate of Descent [2]. Vertical descent of at least 300 feet p. m. SFF: Slow Forward Flight. Horizontal velocity slower than the effective translational lift velocity. [1]: FAA Rotorcraft Flying Handbook [2]: with respect to the down-wash velocity of airflow generated by the rotor.

System description. Helicopter dynamics description. Accident statistics. Main Causes of accidents. Causes under study. LTE: Loss of tail rotor effectiveness Description of the problem. Contributing factors. VRS: Vortex Ring State. Rotor wake and tip vortices. Description of the problem. VTM as a research tool. AUTOSIM™ as modelling tool. Proposed research line. Auto. Sim Blades Dynamic Description. Code validation: Flapping and Lagging-AUTOSIM™. Flap-Feather Coupling-AUTOSIM™. Auto. Sim Fuselage and Tail Rotor Description. Code validation: Fuselage and Tail rotor-AUTOSIM™. Conclusion and further work summary.

VTM as a research tool VTM: Vorticity Transport Model. Computational tool to analyse aerodynamic and dynamic performance of multiple-rotor helicopter configurations under both steady and manoeuvring flight conditions. Advantages versus classical CFD: - Vorticity Conservation: Preserves the integrity of the vortical structure of the wake over significant periods of time. Standard CFD methods that rely on a primitive variable formulation of the Navier– Stokes equations, in terms of velocity and pressure, are susceptible to numerical dissipation of vorticity [3]. - CFD intensive use of computational resources. [3]: Caradonna, F. X. , “Developments and Challenges in Rotorcraft Aerodynamics, ” AIAA Paper 2000 -0109, Jan. 2000.

VTM as a research tool Example Results: Predicted wake structure for rotor at advance ratio μ=0. 12. a) Resolved across 25 cells. b) Resolved across 62 cells.

Proposed Research Line AERODYNAMICS (VTM) VALIDATION STRUCTURAL DYNAMICS (VTM) MULTIBODY DYNAMICS (AUTOSIM) LTE, VRS Analysis. CONTROL STRATEGIES PREVENTIVE Geometric modifications to basic design rotorcraft. ON-LINE Control Techniques

Example of Structural Change: YAH-64 T-Tail Stabilizer. Phase 1 of design, the tail rotor mounted mid-way on the vertical stabilizer.

Example of Structural Change: YAH-64 In forward flight the main rotor wake interacts with tail rotor wake producing a disturbing effect that would remain under the T-Tail structure.

Example of Structural Change: YAH-64 Low Stabilizer. The tail was redesigned during the Phase 2 development process into the low-set, fully movable horizontal stabilizer and high mounted tail rotor.

System description. Helicopter dynamics description. Accident statistics. Main Causes of accidents. Causes under study. LTE: Loss of tail rotor effectiveness Description of the problem. Contributing factors. VRS: Vortex Ring State. Rotor wake and tip vortices. Description of the problem. VTM as a research tool. AUTOSIM™ as modelling tool. Proposed research line. Auto. Sim Blades Dynamic Description. Code validation: Flapping and Lagging-AUTOSIM™. Flap-Feather Coupling-AUTOSIM™. Auto. Sim Fuselage and Tail Rotor Description. Code validation: Fuselage and Tail rotor-AUTOSIM™. Conclusion and further work summary.

Auto. Sim Dynamic Validation n The multibody dynamics analysis software, AUTOSIM™, is used to develop automated linear and nonlinear models of mechanical systems composed of multiple rigid bodies. n The equations derived by AUTOSIM™ are automatically written for each model in the form of a computer program. Parameters are represented by symbols in the equations, so that the same equations can be applied many times, using different numerical values of the parameters. n Produces a FORTRAN or C program which solves the nonlinear equations of motion and generates time histories, another version can generate linearized equations of motion as a MATLAB file that contains the state-space model in symbolic form.

Auto. Sim Dynamic Validation n n Parent-child structure. Helicopter implementation in AUTOSIM: N Parameters are given at each run of the program: Simulation time Size step Fuselage Initial conditions for D. O. F. Main rotor Blades Tail rotor Blades Constant parameters values.

Auto. Sim Dynamic Validation n Blade structure in AUTOSIM™: Blade Structure Parameters for the blade are given before running the program: Flapping hinge Blade Inertia moments. Blade Mass. Lagging hinge Feathering hinge Blade CM. Rotational Degrees of freedom for each hinge. Hinge offset. BLADE

(add-point rtp 11 : body rt : coordinates p 11) (add-body fj 1 : parent rt : name "the First Flapping Joint" : joint-coordinates rtp 11 : body-rotation-axes x : parent-rotation-axis x : reference-axis y : inertia-matrix 0 : mass 0 ) (add-point ljp 12 : body fj 1 : coordinates p 12) (add-body lj 1 ; massless for lagging hinge : parent fj 1 : name "First Lagging Joint" : joint-coordinates ljp 12 : body-rotation-axes z : parent-rotation-axis z : reference-axis x : inertia-matrix 0 : mass 0 ) (add-point pjp 13 : body lj 1 : coordinates p 13) (add-body pj 1 : parent lj 1 : name "Pitching joint" : joint-coordinates pjp 13 : body-rotation-axes y : parent-rotation-axis y : reference-axis z : inertia-matrix 0 : mass 0 ) (add-position-constraint "rq(pj 1)(f 0+(f 0 s*cos(omega*t))+(f 0 c*sin(omega*t))(rq(fj 1)*tan(delta 3)))" : q "rq(pj 1)") (add-speed-constraint "ru(pj 1)-((f 0 s*omega*sin(omega*t))+(f 0 c*omega*cos(omega*t) -(ru(fj 1)*tan(delta 3)))))" : u "ru(pj 1)") (add-point pjp 14 : body pj 1 : coordinates p 14) (add-body bl 1 ; blade : parent pj 1 : name "First Blade" : joint-coordinates pjp 14 : inertia-matrix (Iblx Ibly Iblz) ; moments of inertia for blade : mass mbl : cm-coordinates (xbl ybl zbl) : no-rotation t )

; ; ; ; ; ; ; MOMENTS, SPRINGS and DAMPER ; ; ; ; ; (add-moment flapspring : name "Spring Torque Flapping" ; Spring Flapping Torque : body 1 fj 1 : body 2 rt : magnitude "-kfj*rq(fj 1)" : direction [rtx] ) (add-moment Laggdamper : name "Damping Torque" : body 1 lj 1 : body 2 fj 1 : magnitude "-dfj*ru(lj 1)" : direction [rtz] ) ; Lagging Torque (add-moment lagspring : name "Spring Torque Lagging" ; Spring Lagging Torque : body 1 lj 1 : body 2 fj 1 : magnitude "-klj*rq(lj 1)" : direction [rtz] )

VTM In VTM the dynamics of the rotor blades are modelled by numerical reconstruction of the nonlinear Lagrangian of the system so that the coupled flap–lag–feather dynamics of a set of rigid blades are fully represented. Fully flexible blades are still to be included in the model. VTM simulations for a forward flight, 1 blade only rotor.

Code validation: Flapping and Lagging- AUTOSIM™ Flapping for differerent Offsets of flapping hinge

Code validation: Flapping and Lagging- AUTOSIM™ Flapping and Lagging dynamical behaviour of 1 blade with 0 R% Offset.

Code validation: Flapping and Lagging- AUTOSIM™ Flapping and Lagging dynamical behaviour of 1 blade with 0. 2 R% Offset.

Code validation: Flapping and Lagging- AUTOSIM™

Code validation: Flap-Feather Coupling in AUTOSIM™ θ = θ 0+ θ 0 ccos(wt)+ θ 0 ssin(wt)- β tan(δ 3) θ 0 = Constant value. Rotor Collective pitch. w = Rotational velocity of rotor. θ 0 = Constant value. Rotor Cyclic pitch. β = Flap angle. tan(δ 3) = feedback gain. • The pitch-flap coupling is a kinematic feedback of the flapping displacement to the blade pitch motion. • Pitch- Flap coupling reduces the flapping magnitude relative to the rotor shaft. • A rotation about the hinge with a flap angle β must also produce a pitch change of -β tan(δ 3).

Code validation: Feathering - AUTOSIM™ FLAPPING Flapping Spring No Flapping Spring VTM Frequency (rd/s) Auto. Sim Frequency (rd/s) 46. 01 46. 0307 44. 4000 44. 4041 44. 5559 44. 53 44. 4222 44. 4041 FEATHER Flapping Spring No Flapping Spring

System description. Helicopter dynamics description. Accident statistics. Main Causes of accidents. Causes under study. LTE: Loss of tail rotor effectiveness Description of the problem. Contributing factors. VRS: Vortex Ring State. Rotor wake and tip vortices. Description of the problem. VTM as a research tool. AUTOSIM™ as modelling tool. Proposed research line. Auto. Sim Blades Dynamic Description. Code validation: Flapping and Lagging-AUTOSIM™. Flap-Feather Coupling-AUTOSIM™. Auto. Sim Fuselage and Tail Rotor Description. Code validation: Fuselage and Tail rotor-AUTOSIM™. Conclusion and further work summary.

Code validation: Fuselage - AUTOSIM™ N Parameters for the fuselage are given before running the program: Fuselage Inertia matrix. Fuselage Main rotor Blades Fuselage Mass. Fuselage CM. Degrees of freedom: Translational (X, Y, Z) and rotational (yaw, pitch and roll) (add-body fuselage : parent n : name "Fuselage" : mass @Mf : joint-coordinates (0 0 0) : translate (x y z) : body-rotation-axes (z y x) : parent-rotation-axis z : reference-axis x : inertia-matrix ((1433 0 0) (0 4973 0) (0 0 4099)) : cm-coordinates (cmfx cmfy cmfz) )

Code validation: Tail Rotor - AUTOSIM™ Tail rotor already implemented in AUTOSIM™ Validation with VTM still to be done in immediate future.

Conclusions and further work summary • A description of the system (helicopter) has been presented. • Two specific problems of rotorcraft have been described: - VRS and LTE. • Aim of this project: - To study dynamics of rotorcraft by developing AUTOSIM model. - Study the nature of VRS and LTE by combining dynamics from AUTOSIM and aerodynamics from VTM. - Define and implement a control strategy for these two cases. • Work to follow in forthcoming months: - Validate tail rotor with VTM. - Combine VTM aerodynamics of the system with AUTOSIM dynamical model. - Control of the system.

To be continued…

Thanks: Professors R. Brown, R. Sharp and D. Limebeer. Mr. Tim Fletcher Mr. Gary Ahlin Mr. Adam R Mr. Kim Hyowon Mr. Martin Gerber