The Bell 427, 8 seat helicopter, executive, commuter or cargo transport is a proof ofexcellence in the modem aviation. The Bell 427 is assembled at Bell Helicopter Canada, a division ofTextron Canada Ltd. It received the basic certification by Transport Canada in December 1999. It presents new challenges due to its advanced technology of the four-blade composite main rotor system. To overcome the increased number of failure analyses required by certification agencies worldwide, Bell Helicopter Textron chose to utilize a model-centered design methodology. Simulation models would thereby be utilized in all phases of the design process and would be deployed from desktop anal y sis to hardware in the loop test rigs. Furthermore, a single model would be used in as many different applications as possible, minimizing model maintenance and maximizing efficiency.To use a single model for many different applications, such as flight dynamics analysis, training, control law design, functional hazard analysis and hardware in the loop test rigs, the model had to be matched beyond standard requirements and the complexity extended beyond the norm. In the present aviation era, most flight dynamics simulation models are built with the focus on the need for training simulators. The level D requirement (simulator certification level) is the target of model matching. The flight-control team needs fairly sophisticated controls and aerodynamics models to design the control law. The handling qualities team needs the same kind of models to guarantee design objectives. The engine team needs a complete engine model to evaluate integration issues. The systems team needs to analyze all possible combinations of failure cases, and so on. The demands on the simulation model have grown substantially.

Equations of motions for a rotorcraft

   In order to develop a mathematical model for a rotorcraft simulator we need to recall the basic laws of physics. The purpose of this mathematical model is the validation of a real flight simulator which is done by the implementation of a programming code to calculate real time motion of the helicopter. Several assumptions are made to simplify the model and should give close results to the reality in order not to compromise the real motion described by the model. Although a rotorcraft is a vehicle which flies in the au and obeys the laws of aerodynamics, its motion is different from an airplane due to its different design. Its particularities are given by the rotor which is the main sustentation deviee. A vehicle flying in the air, such as a helicopter or an airplane, develops forces to counterbalance the gravitational attraction force. Airplanes develop aerodynamic forces by the relative motion of the air around stationary wings, while helicopters create aerodynamic forces by the rotational motions of a deviee named rotor-wing, or shortly rotor.

Newton’s laws of motion

   The first assumption is that the helicopter is a rigid body, in which the relative motions of the rotor with respect to the helicopter’ s structure, and the vibrations dues to engine, gearbox, pumps, or shafts are not considered. In this section, Newton’s laws of motion which are known from various references are described [1], [2]. According to Newton’s laws of motion for a rigid body, the sum of all forces acting on the body has to be calculated. A set of rectangular axes ( 0, x, y, z) called body fixed axes is attached to the helicopter in the manner . The centre of body axes is located in the centre of gravity (CG= 0 ), the Ox axis is oriented in the longitudinal direction of the fuselage pointing to the helicopter’s front, the Oy axis is oriented to the right direction of the pilot, perpendicular on the xOz plane formed by the longitudinal and vertical axes, and the Oz axis is oriented downwards perpendicular to the xOy plane formed by the longitudinal and lateral axes.

The attitude and the position of the helicopter

  The helicopter’ s translational and rotational motions during the flight described by the Newton’s equations, the moments, velocities and attitudes coordinates are expressed in the body axes system b. To simulate the flight of the helicopter between two fixed points on the earth it is needed to express the velocities and attitudes in Earth coordinates system e. The Earth reference system has the Ze axis perpendicular on the Earth and its positive direction is oriented to the center of the Earth and the altitude of the aircraft His oriented in the opposite (negative) direction of the Ze axis. The Xe axis is oriented arbitrarily to the East and the Ye axis is oriented to the South, perpendicular to the Xe axis. The transformation from body reference to Earth reference is calculated by use of three successive rotations of the Euler angles

Airspeed, angle of attack and angle of sideslip

   Due to the rotor’ s air wake, all the airspeed measurements of the instruments installed on the helicopter are not sufficiently accurate. The airspeed in the vicinity of the helicopter is influenced by the induced airspeed of the rotor wake, so that more precise measurements are done by use of a nose boom as far as possible from the wake of the measurements are done by use of a nose boom as far as possible from the wake of the rotor, in the front of aircraft. The nose boom contains a static and a Pitot probe, an alpha vane which is installed in the horizontal direction to measure the vertical incidence of the air with respect to the A/C longitudinal axis i.e. angle of attack a, and a beta vane whichis installed vertically with respect to the A/C longitudinal axis to measure the sideslip angle of the helicopter, fJ.  Alpha and Beta van es installations on the no se boom of the helicopter Nose boom’s alpha and beta vanes are used to record the True Air Speed orientation in the body axes system. The location where TAS measurements are taken (positions of alpha and beta van es) is different than the Pitot tube location where TAS value isrecorded; therefore we need to effectuate corrections to calculate the a and fJ values recorded in the nose boom location (NB) with respect to the Pitot tube location which is defined as the Instrumentation Center (IC).

Global model

  The global model is a composition of several distinct simulation models for various helicopter loadings and flight conditions. The flight conditions such as Hover, Vertical Climb, Level Flight, Climb or Descent are sorne particular zones in the flight envelope. From aerodynamical point of view, the Ho ver and Vertical Climb flight conditions are different from the Level Flight, Climb or Descent flight conditions; therefore there exist two distinct aerodynamic models defining these two sets of flight conditions: the Hover model and the Up And Away (UAA) model. There exist also other distinct models for One Engine Inoperative (OEI) flight condition and Autorotation flight condition. Hover model has two distinct models for defining the In Ground Effect (IGE) and Out of Ground Effect (OGE) aerodynamical interferences. Each model is divided in several sub-models for each point in the flight envel ope ( each combination airspeed and altitude) where the first set of flight tests were performed. The same helicopter in different configurations of loading and center of gravity positions acts differently from point of view of aerodynamics laws. Therefore there are three combinations of loading-position of center of gravity defined as: Light-Aft (LA) model which simulates the motion of the helicopter with no loading and the aft CG position due to the weight of the engines; Heavy-Aft (HA) model which simulates the motion of the helicopter with maximum loading allowed for the maximum aft CG position; and Heavy-Forward (HF) model which simulates the motion of the helicopter with the maximum loading allowed for the maximum CG forward position. For each flight conditions combination of loading, airspeed, altitude (such as: Level Flight, lAS 70 knots, Heavy/Fwd, altitude 6000 ft), there is a unique A* matrix which defines entirely the helicopter’ s motion at that specifie flight condition.

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Table des matières

1.1 Equations of motion for a rotorcraft
1.1.1 Newton’ s laws of motion
1.1.2 The attitude and the position of the helicopter
1.2 Stability and control theory
2.1 Methodology
2.1.1 Flight conditions
2.1.2 Flight parameters
2.2 C:orrections of the raw data
2.2.1 Airspeed, angle of attack and angle of sideslip
2.2.2 Corrections of accelerations
3.1 Modified mathematical model
3.2 Simulink model
3.3 Global model
4.1 flelicopter simulator qualification
4.2 Quality test guide (QTG)
4.3 Proof-of-Match (POM)
5.1 General considerations
5.2 Directional static stability- trimmed flight in cruise, climb or descent
5.3 Lateral control response
5.4 Directional control response
5.5 Dynamic lateral and directional stability- spiral stability
5.6 Dynamic lateral and directional stability -lateral and directional oscillations
6.1 General considerations
6.2 Hover performance In Ground Effect (IGE) validation
6.3 Hover performance Out of Ground Effect (OGE) validation
6.4 Control response in hover Out of Ground Effect (OGE) validation
7.1 General considerations
7.2 Autorotation entry validation
7.3 Steady descent autorotation validation
7.4 Autorotation landing

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