FLIGHT DYNAMIC MODELING OF MINI HELICOPTERS

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FLIGHT DYNAMIC MODELING OF MINI HELICOPTERS FOR
TRIM AND STABILITY
K. R. Prashanth and C.Venkatesan
Rotary Wing R D Centre, HAL, Bangalore.
Department of Aerospace Engineering, IIT,
Kanpur.
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Outline

• Mini Helicopters and its Features
• Idealisation
• Coordinate Systems
• Blade Inertia /Aerodynamic Loads
• Flight Dynamic Equations
• Pitch Mechanism of Stabiliser Bar and Main
  Rotor Blades
• Trim and Stability Equations
• Results
• Conclusion / Future work

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Mini Helicopters and its Features
Conventional Helicopter
Model Helicopter

• Variable rpm
• Stabiliser bar for passive control
• system
• Rigid blade

• Fixed rpm
• No Stabilizer bar
• Flap-lag-torsion dynamics
• of blade

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Forces and Moments on Fuselage
HORIZONTAL STABILIZER
VERTICAL FIN
HELICOPTER DYNAMICS
STABILIZER
MAIN ROTOR
FUSELAGE LOADS
Hub Loads Due to All Blades
TAIL ROTOR
Blade Root Loads
Sectional Inertia Aerodynamic Loads on Blade
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Idealisation of the Model Helicopter

• The blades are assumed to have symmetric cross
  section.
• Vertical fin and a horizontal tail plate have
  symmetric
• airfoil cross sections
• Fuselage, rotor shaft, rotor blades are assumed
  to be rigid
• The feathering axis coincides with elastic axis
  of the blade
• CG of the helicopter lies on x-z plane

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Ordering Scheme

• The basis of the ordering scheme is a small
  dimensionless
• parameter which represents typical slopes due to
  elastic
• deflections. It is known that for helicopter
  blades
• it is in the range of

The ordering scheme is based on the assumption
that
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Coordinate Systems
lK - Non-inertial hub fixed non
rotating system
R - Hub fixed inertial system
1K and 2K Rotating systems
4K and systems
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Coordinate Systems

• 2K and 3K Rotating systems

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Coordinate Systems

• 1K and s1 coordinate systems

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Blade Inertia Loads
Distributed inertia forces
Inertia forces at blade root
Inertia moments at blade root
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Blade Aerodynamic Loads

• Classical Unsteady Aerodynamic Theories
• Theodorson
• Greenberg
• Loewy

- Quasi steady aerodynamics based on
Greenberg theory is assumed
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Blade Aerodynamic Loads
Expression for Circulatory and Non-circulatory
Lifts and Moment
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Blade Aerodynamic Loads
Distributed aerodynamic load in y direction
Distributed aerodynamic load in z direction
Distributed torsional moment
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Blade Aerodynamic Loads
Aerodynamic forces at blade root
Aerodynamic moments at blade root
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Main Rotor Hub Loads
Main rotor hub forces due to all blades
Main rotor hub moments due to blades
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Forces and Moments on Fuselage

• Forces and Moments are transformed to CG of the
  Fuselage

Forces
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Forces and Moments on Fuselage
Moments
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Flight Dynamic Equations

• Number of degrees of freedom are six
• Kinematic relations developed relating
• Instantaneous angular velocities of the
  helicopter
• Rate of change of orientation of the helicopter
  to
• the earth based coordinate system.

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Flight Dynamic Equations
Helicopter in manoeuvre
PITCH
ROLL
YAW
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Flight Dynamic Equations
Force Equations
Moment Equations
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Pitch Mechanism of Stabiliser and Main Rotor
Blades
BLADE PITCH
STABILISER FLAP RESPONSE
COLLECTIVE
CYCLIC
Swash Plate Mechanism
Hub Motion
Collective Input
Cyclic Input
From Servo Actuator
From Servo Actuator
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Pitch Mechanisms of Stabiliser and Main Rotor
Blades
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Pitch Mechanisms of Stabiliser and Main Rotor
Blades
Blade Pitch due to Collective Input
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Pitch Mechanisms of Stabiliser and Main Rotor
Blades
Blade Pitch due to Cyclic Input
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Pitch Mechanisms of Stabiliser and Main Rotor
Blades
Pitch Angle of Stabiliser Bar
Pitch of stabilizer
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Pitch Mechanisms of Stabiliser and Main Rotor
Blades
Blade Pitch due to Stabiliser Flap
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Flap Equation of Motion for Stabilizer Bar
Flap Equation of Motion
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Flap Equation of Motion for Stabilizer Bar
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Trim Equations
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Stability Equations
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Results
Baseline Data
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Influence of Mass on Control Angles
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Influence of Density on Control Angles
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Influence of Mass on Power Requirement
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Influence of CG Shift(X-Axis) on Control Angles
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Influence of CG Shift(Z-Axis) on Control Angles
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Influence of Altitude on Power Requirement
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Influence of Density on Power Requirement
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Stability of the Baseline Vehicle
Eigen Values and Eigen Vectors Baseline Helicopter
Eigen values
Eigen vectors
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Blade Root Loads
Axial Load Px2k 1307.3 N Shear Load (Y)
Py2k -2.98 N Shear Load (Z) Pz2k 30.4
N Torsional Moment Qx2k 0 Flapping Moment
Qy2k -16.37 Nm Lead-lag Moment Qz2k -1.37
Nm
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Conclusion

• Flight dynamic equations for a mini helicopter
  developed
• including all the essential features
• Sample results indicate instability of the
  vehicle in hover.

Future Work

• Trim and stability of the helicopter in forward
  flight
• Parametric estimation using test data
• Design of a feedback controller for stability
  augmentation
• Development of a simulator model for autonomous
  flight

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THANK YOU