Dias nummer 1

1
Modelling of Helicopter
Next Presenter Ulrik
Topic Modelling of the Helicopter
Ulrik
2
Motion of Rigid Body
Purpose of Block

• To describe the motion of the helicopter (frame)
  generated by forces and torques

Output Motion-parameters

• V the translatory velocity-vector
• w the angular velocity-vector
• (Q) the Euler-angles (used as feedback to
  Forces and Torques Block)
• (P) the position of the helicopter (used as
  input to VR model)

Ulrik
3
Motion of Rigid Body
1st Objective

• Relate vector-description in BF to its
  description in SF

Direction Cosine by 3-2-1 Euler angle rotation
Thus, a vector x stated in BF is stated in SF as
Ulrik
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Motion of Rigid Body
2nd Objective

• Rotational motion of the helicopter

Angular Acceleration
External torque-vector
Angular momentum
Angular acceleration-vector
Ulrik
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Motion of Rigid Body
3rd Objective

• Translatory motion of the helicopter

Translatory Acceleration
Translatory acceleration originating from
rotation created by w
Translatory acceleration not originating from
rotation created by w
Ulrik
6
Generation of Forces and Torques
Purpose of Block

• To describe forces and torques leading to the
  motion of the helicopter

Output Parameters

• F the resultant force-vector acting on the
  helicopter
• t the resultant torque-vector acting on the
  helicopter

Ulrik
7
Generation of Forces and Torques
1st Objective

• The derivation of the forces acting on the
  helicopter

Origin of Forces

• bFMR Force generated by main rotor
• bFTR Force generated by tail rotor
• bFg The gravitational force

The Resultant Force-Vector
Ulrik
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Generation of Forces and Torques
Force Generated by Main Rotor
The resultant force-vector
Ulrik
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Generation of Forces and Torques
Force Generated by Tail Rotor
The resultant force-vector
Gravitational Force
Ulrik
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Generation of Forces and Torques
2nd Objective

• The derivation of the torques acting on the
  helicopter

Origin of Torques

• btMR Torque caused by main rotor
• btTR Torque caused by tail rotor
• btD Counter-torque caused by drag on main rotor
• (Torque caused by tail-rotor drag)

The Resultant Torque-Vector
Ulrik
11
Generation of Forces and Torques
Torque Caused by Main Rotor
Resultant torque-vector
Ulrik
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Generation of Forces and Torques
Torque Caused by Tail Rotor
Resultant torque-vector
Ulrik
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Generation of Forces and Torques
Counter-Torque Caused by Drag on the Main Rotor
Simple model Koo et al
Resultant torque-vector
Ulrik
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Generation of Flapping and Thrust
Purpose of Block

• To describe aerodynamic relations that yield
  thrust and flapping angles, when control inputs
  are applied.

Output Parameters

• TMR Thrust generated by main rotor
• TTR Thrust generated by tail rotor
• b1s Lateral flapping angle
• b1c Longitudinal flapping angle

Ulrik
15
Generation of Flapping and Thrust
1st Objective

• Describe the thrust-generation process.

Thrust Generated By Main Rotor
Ulrik
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Generation of Flapping and Thrust
Thrust Generated by Tail Rotor

• Purpose is to compensate for the resultant
  torque about bz (bN)
• This is assumed done by an onboard
  yaw-controller, so bN0

Thus
..becomes

• uped is inserted such that it is possible to
  perform a yaw movement

Ulrik
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Generation of Flapping and Thrust
2nd Objective

• Describe the flapping angles

Mixer System
Ulrik
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Generation of Flapping and Thrust
Control-Rotor Flapping equations Mustafic et al

• Cross-Coupling is present

Mixer System
Ulrik
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Generation of Flapping and Thrust
Main-Rotor Flapping equations Mustafic et al

• No cross-coupling because of teetering rotor (no
  hinge-offset)

Ulrik