Impact of Rotor Blade Aeroelasticity on Rotorcraft Flight ... - AIAA ARC

Impact of Rotor Blade Aeroelasticity on Rotorcraft Flight Dynamics Simone Weber∗† Airbus Helicopters UK, Kidlington, OX5 1QZ, United Kingdom

Laura Ramos Valle‡, Xavier Barral§, David Hayes¶, Alastair Cooke∥, and Mudassir Lone∗∗ Cranfield University, Cranfield, MK43 0AL, United Kingdom

This paper presents a study of how variations in blade flexibility can affect flight dynamics and therefore, handling qualities. An in-house flight simulation model has been developed using a reduced-order beam model together with a dynamic inflow model to take into account aeroelasticity effects. A pilot’s control map has been implemented to effectively predict aerodynamic loading and dynamic movement of the blade for any flight condition. For this work only hover case is considered. Using a short pulse input, time histories predict the dynamic response of the helicopter in roll and yaw direction, as well as manoeuvre quickness for a range of blade stiffnesses. Results linking roll and yaw quickness to blade stiffness and damping are presented together with a comparison with data available in literature.

I.

Introduction

Helicopters are designed to operate over a wide range of flight regimes, due to which designers and engineers are faced with a large and challenging design space. However, many civil operators only exercise the aircraft over a small inner region of the flight envelope and rarely push the aircraft to its operational limits (see Figure 1). The emphasis on safety in the rotorcraft community has led to today’s operational practices to actively adopt state-of-the-art technology but also maintain highly conservative practices. Some areas where this conservatism is evident are operations, maintenance and servicing of rotor blades. The inability to explicitly monitor the operational loading environment and resulting blade deformations has led to pragmatic solutions that rely on human qualitative judgement that may not be economical from a customer perspective. Laying focus on the overall aircraft behaviour, often a compromise has to be met between comfort and high agility of the aircraft to satisfy customers requirements. These effects are experienced due to the flapping hinge offset and the global stiffness of the blade. Higher structural flexibility impacts the steady sate response of the rotor to control inputs and body motion.1 This results in a change of forces and moments transmitted to the hub. This aspect is important as the fuselage which is dynamically treated as a rigid body with six degrees of freedom is assumed to have different aeroelastic frequency range than the rotor blade system. Moreover, the frequency and amplitude of the structural blade motion are different to the frequency of the rigid body, where its dynamic mode is described through rigid body modes such as short-period pitch oscillation and phugoid. The difference in blade flexibility affects handling and ride quality of the aircraft. Several studies have been done examining the effects of aircraft design on flight dynamic response, such as the blade flexibility study of articulated rotors1 or the optimization of handling qualities (HQ) through the ∗ Technology

Integration Manager, Airbus Helicopters UK, [email protected] Student, Centre for Aeronautics, School of Aerospace, Transport & Manufacturing, [email protected] ‡ MSc Student, Centre for Aeronautics, School of Aerospace, Transport & Manufacturing, [email protected] § MSc Student, Centre for Aeronautics, School of Aerospace, Transport & Manufacturing, [email protected] ¶ Research Student, Centre for Aeronautics, School of Aerospace, Transport & Manufacturing, [email protected] ∥ Lecturer, Centre for Aeronautics, School of Aerospace, Transport & Manufacturing, [email protected] ∗∗ Lecturer, Centre for Aeronautics, School of Aerospace, Transport & Manufacturing, [email protected] † Research

1 of 14 American Institute of Aeronautics and Astronautics

Figure 1. Typical flight envelope for helicopter operations

maximization of damping ratio of lag progressive modes of rotor blades.2 Within the past years Lawrence et al3 and Antonioli et al4 proposed a methodology which shows the importance of including HQ assessment in the first stage of helicopter design and feedback control tuning. With the use of simplified simulation models it is possible to predict and estimate the impact on the complexity of flight control laws together with potential improvements in flying and handling qualities. In recent years, sophisticated models have been developed to accurately predict rotor blade behaviour. To account for structural mechanics linear and non-linear beam theories are used. Past studies extend small angle and small displacement approximations to be used to model moderate and large deflection type beams5 .6 This is achieved through variational formulation based on intrinsic equations, exact geometrical formulation, and multi-body formulation7 .8 To account for aerodynamic effects of flexible rotor blades considerable work has been done in this field by Peters et al, such as the development of three-dimensional induced flow model accounting for unsteady aerodynamics and finite-state wake models910 .11 Referring to the work of Lee et al,12 Eun et al,13 and Chun et al14 the main rotor is considered on its own and is coupled with an appropriate inflow model for hover and forward flight to precisely analyse the rotor blade’s behaviour119 .15 However, aerodynamic effects of fuselage, tail rotor, fin and other elements are ignored. Nevertheless, commercially available programmes with comprehensive codes are used to simulate the flight dynamic behaviour of rotorcrafts, such as CAMRAD, UMARC, RDYNE and more. Even though extensive work has been done in the area of main rotor modelling, there is a need for in-house fast simulation capability that captures the aeroelastic behaviour of rotor blades and simultaneously allows the investigation of the impact of blade flexibility on flight dynamics. For the purpose of this work a generic helicopter model is used. The main objectives are 1) the assessment of how blade flexibility changes the structural response of rotor blades and 2) the study of how manoeuvre quickness is influenced by using various stiffness factors for the blade. This will be assessed using ADS-33 requirements. The paper is structured so that Section I provides an overview of the main rotor model including aeroelastic coupling and implementation into the full six degree of freedom (6DoF) flight dynamic model. A rotor blade stiffness variation study is presented in Section II followed by conclusions and outlook.

II.

Model Development

A flight dynamic model of a generic helicopter simulation model (GHM) with a bearingless main rotor configuration has been developed in a MATLAB/Simulink environment which takes into account the flexibil-


ity of rotor blades. Its design structure is described as a feedback loop to precisely manage the interactions between aerodynamics on the blades, flight dynamics and structural mechanics. Several axis systems are introduced to transfer the forces and moments from the main rotor to the global aircraft system (see Figure 2). The structural model uses a reduced-order beam element model with its material properties concentrated on the nodes. Ω

STRUCTURAL MODELLING

ψs zs

xs

θs

φs ys

xa θa φa AERODYNAMIC MODELLING

ψa

ya

za

yf

φf

θf

FLIGHT DYNAMICS MODELLING ψf

xf

zf

Figure 2. Combination of different model components

A dynamic inflow model, developed by Peters and HaQuang,16 is introduced which is coupled with blade element analysis to calculate the angle of attack of the blade at each moment of time. To map the movement of the pilot’s controls to the blade pitch angles, a look-up table is produced using kinematic relationships of the rotor control system. As shown in Figure 3 collective input changes the blade pitch on all blades equally. If the cyclic longitudinal input is used by the pilot, then the blades which are perpendicular to the longitudinal axis will experience a blade pitch change. The same principle is valid for the cyclic lateral input. Assuming a linear link between pilot stick/lever position and feathering angle, a relationship for longitudinal and lateral rotor disk as a function of stick position is formed. This methodology is based on the work of Price17 and is adopted for the GHM used in this work. To calculate the overall forces and moments of the helicopter fuselage, tail rotor, tail plane, and fin are calculated in addition to the main rotor forces and moments. These are modelled using the equations and guidelines provided by Padfield.18 Standard aerofoils are used for the fin and tail plane, which take into account the influence of the main rotor wake. Using a first approximation, only lift is produced by the fin, which results in a lateral force that supports the tail rotor to overcome the yawing moment produced by the main rotor.19 To estimate the forces and moments of the fuselage wind tunnel data is used.18 The tail rotor is a simplification which only uses the collective control and the dynamics of the tail rotor. All forces and moments are summed up and transferred to the body axis coordinate system through a rotation transformation matrix. The properties of the GHM are given in Table 1.

Table 1. Properties of GHM

Properties

Values

Number of rotor blades Mass (MTOW) Rotor radius Rotor speed

4 2950 kg 5.2 m 41.36 rad/s


Figure 3. Principle of upper control system and its kinematic relationships

A.

Blade Model

The structural model is derived using a linear Timoshenko beam together with the classical beam theory.20 The static beam bending equation is defined as: ∂4w EI ∂ 2 p(x) = p(x) − (1) ∂x4 κAG ∂x4 where E is the Young’s modulus, I the second moment of area, κ is the shear coefficient, A is the area, G is the shear modulus, p(x) is the applied load dependent on x-direction, and w is the deformation in z-direction. The equation of motion for the dynamic system is defined using the Lagrangian as follows: EI

L=T −V

(2)

where T is the kinetic energy and V the potential energy. The following Rayleigh damping model is assumed: C = ηM + λK

(3)

where C is the damping matrix, K is the stiffness matrix, η and λ are the damping coefficients. The damping ratio ζ is defined as: ζ=

C C = √ 2M ωn 2 MK

(4)

where ωn is defined as the natural frequency. Substituting Eq.(4) in Eq.(3) and ωn : 2ζωn = η + ωn2 λ

(5)

the damping coefficients η and λ can be written in terms of ζ: ζ=

1 ωn η+ λ 2ωn 2

(6)

To be able to identify the structural system states the following equation of motion is used: M q¨ + C q˙ + Kq = F (t)


(7)

The full equations of motion in state space form can then be written in the following form: [ ] [ ][ ] [ ] q˙ 0 1 q 0 = + F (t) C K 1 |{z} q¨ −M −M q˙ M | {z } | {z } | {z } | {z } u x˙

x

A

(8)

B

The beam is divided in 13 nodal points with six degrees of freedom at each node as presented in Figure 4. The first node is constrained in translational and rotational direction to represent the root of a cantilever beam. The effects of shear deformations and rotary inertia are also included in the model.

Figure 4. Timoshenko beam model layout

Material and geometrical properties are concentrated and assigned to each node. The element connecting a pair of nodes effects twelve degrees of freedom in the system (six from each node). Therefore, the element mass matrix Me and element stiffness matrix Ke can be discretised into the interdependency of each nodal degree of freedom, M11 , M22 , K11 , K22 and the interconnection between the two nodal degrees of freedom, M12 , M21 , K12 , K21 as follows: [ ] M11 M12 Me = (9) M21 M22 [ ] K11 K12 Ke = (10) K21 K22 The coupled global mass and stiffness matrices (M , K) are built so that each node is interlinked to two elements, except the first node, n1 , and the last node, nN +1 (Figure 4). After obtaining the complete set of equations of motion, Eq.(7), in state space form, Eq.(8), the number of states in the system can be reduced by normalising the mass M and stiffness matrix K with a reduced ˜ and normalised stiffness matrix K ˜ is defined: modal matrix U such that the normalised mass matrix M ˜ = UT MU M

(11)

˜ = U T KU K

(12)

The force F is transformed into normal coordinates: F′ = UT F

(13)

By applying this method, a model covering the frequency range of interest can be derived. This method also ensures a reduction in computational time. It should be noted that the current beam model is only valid for small deflections. 5 of 14 American Institute of Aeronautics and Astronautics

B.

Aerodynamics

To provide forces and moments to the structural model for each blade element an advanced inflow and aerodynamic model has been developed. The process is shown in Figure 5. Control input, rotor and blade dynamics are used as direct input to calculate the element velocity and angle of attack. Lift, drag and pitching moments are estimated using a 2D aerofoil section. A look-up table for the coefficient of lift, drag and moment is created using commercially available programmes.

Figure 5. Flow chart of the aerodynamic analysis process

To determine parameters such as the effective angle of attack, pitching angle, inflow angle, and velocities geometrical relationships are used alongside a linear model21 based on blade element theory. The induced inflow velocity is computed using the dynamic model in combination with momentum theory which was developed by Peters and HaQuang16 and corrected by Basset22 to take into account tip loss and wake effects. In the dynamic inflow theory, the induced inflow λi is expressed in the wind axis system: ¯ = ν0 + r νs sin(ψ) ¯ + r νc cos(ψ) ¯ λi (r, ψ) R R

(14)

where ψ¯ is the rotor blade azimuth angle, ν0 , νs , and νc are the uniform, lateral, and longitudinal variations respectively. With the resultant flow VT through the rotor given by: √ VT = λ2 + µ21 + µ22 (15) where λ is the total inflow through the rotor, and µ1 , µ2 represent the nondimensionalised forward and sideward velocities respectively. The mass-flow parameter V due to cyclic disturbances is calculated as follows: V =

µ2 + (2λm − µ3 )(λm − µ3 ) VT

(16)

where µ is the resultant forward velocity, λm is the normal induced inflow, µ3 is a velocity component defined perpendicular to the rotor disk, and VT is the resultant flow through the rotor disk.16 The mass-flow parameter matrix V can be constructed as:




VT  V = 0 0

0 V 0

 0  0  V

(17)

ˆ is expressed as: The non-linear version of the inflow gains matrix L ˆ = V L−1 L

(18)

with L :    L= 

1 √ 2 1−sin χ 15π 64 √ 1+sin χ 1−sin χ 15π 64 1+sin χ

− 15π 64

sin ∆ cos ∆

√

1−sin χ 1+sin χ sin ∆ 4 sin χ 2 4 2 1+sin χ cos ∆ + 1+sin χ sin χ 4 1−sin 1+sin χ cos ∆ sin ∆

− 15π 64

∆

√

1−sin χ 1+sin χ cos ∆ 1−sin χ 4 1+sin χ sin ∆ cos ∆ 4 sin χ 2 4 2 1+sin χ sin ∆ + 1+sin χ cos

and the wake angle with respect to the rotor disk16 is given by: [ ] −1 | λm − µ3 χ = tan µ

    

(19)

∆

(20)

The normal induced inflow λm due to the effect of rotor thrust CT is defined as:16 T   1 λ0 1    =  0  L−1  λs  2 0 λc 

λm

(21)

where λ0 , λs , and λc are the uniform, lateral, and longitudinal variations in rotor inflow respectively. To calculate the non-linear dynamic inflow with respect to the rotor disk plane a first order differential equation is presented:16       λ˙ 0 λ0 CT  ˙    −1 ˆ −1  −1  (22)  λs  = −[M ] [L]  λs  + [M ]  C1  ˙λc λc −C2 where CT , C1 and C2 are the instantaneous rotor thrust and roll and pitching moments coefficients, respectively, to the wind hub system. As explained by Peters and HaQuang,16 M is “the matrix of the apparent mass terms, which is a time delay effect due to the unsteady wake”. It should be noted that the ˆ is completely non-linear in CT and λ0 , but linear in C1 and non-linear version of the inflow gains matrix L 16 C2 . Only aerodynamic contributions are considered in CT ,C1 and C2 .16 With the knowledge of the induced inflow velocity at each element, the element inflow angle and the element angle of attack is calculated. Figures 6 and Figure 7 show the model predicted effective angle of attack over one revolution of the blade for hover and forward flight. The angle of attack αef f in hover is distributed uniformly over the rotor disk, whereas for forward flight αef f is concentrated at the aft of the rotor disk. The pilot required input is displayed on the figures, where 100% collective input means pull, 100% cyclic longitudinal input means push, and 100% cyclic lateral input means right in terms of pilot’s lever and stick deflection. Elementary lift, drag and pitching moment at each node is determined using aerodynamic coefficients, such as CL (α), CD (α) and CM (α), which are calculated relative to the effective angle of attack as follows: CL (α) = CLα α + CL0

(23)

CD (α) = CDα2 α2 + CDα α + CD0

(24)

CM (α) = CMα3 α3 + CMα2 α2 + CMα1 α + CM0

(25)


Figure 6. Variation of angle of attack α at each aerofoil section over one revolution at hover

Figure 7. Variation of angle of attack α at each aerofoil section over one revolution at forward flight


The aerodynamic coefficients are dependent on Mach and Reynolds number and change with density, velocity, and viscosity of the fluid. Look up tables were created for the aerodynamic coefficients and to make sure that a wide range of data points are covered, the look up tables interpolate linearly to yield values of polynomial coefficients for each flow condition. Finally, the elementary lift, drag and pitching moment are defined,

dL =

1 2 ρV lcCL (α) 2 tot

(26)

dD =

1 2 ρV lcCD (α) 2 tot

(27)

1 2 2 ρV lc CM (α) (28) 2 tot is the magnitude of the airspeed experienced by the aerofoil and l is the spanwise length of dM =

where Vtot an element.

C.

Structural and Aerodynamic Coupling

In order to analyse the rotor blade motion, the structural, inertial, and aerodynamic analysis of the rotor blade must be coupled. This is done by means of a time-domain approach of the inflow model, evaluated at the appropriate number of nodal points in the beam model to validate its aeroelasticity in virtue of experimental evidence. Aerodynamic loads, and therefore the angle of attack is dependent on the flow field, rotor and body dynamics and blade controls, which in fact change the pitch angle of the blade. The flow chart in Figure 8 shows that the aeroelastic problem is treated as a feedback system, where the blade displacement, angles and velocities are provided from the structural to the aerodynamic model.

Figure 8. Flow chart for the aeroelastic coupling of the main rotor


D.

Trimming

Before the main rotor and other helicopter elements are coupled with the equations of motion, an initial study is performed to be able to estimate values for initial condition of existing states within the model, such as inflow, alongside position and velocities of the blade nodes. The pilot input is chosen so that the forces and moments are zero. Finally, the states for both, inflow and structural model are saved and applied to the overall model coupled with the equations of motion block. Additionally a control feedback loop has been implemented to be able to stabilize the helicopter in hover condition, which was chosen to be the baseline for the following studies.

III.

Rotor Blade Stiffness Variation Study

Two different approaches will be taken within within this work to study the impact of blade flexibility on flight dynamics. One is to look at the effects of blade flexibility on the structural behaviour in time through the introduction of a stiffness factor. The second part focuses on handling qualities assessment of manoeuvre quickness for moderate amplitude attitude changes using ADS-3323 requirements. Results are assessed against roll and yaw response criteria. A.

Effects of Blade Flexibility

Modifying the structural blade system’s state space equation as: ˜ x˙ = HAx + Bu

(29)

with matrix A being the mass and stiffness matrix of the system, B the input matrix, u the input vector. ˜ is the flexural weighting matrix and is defined as follows: Matrix H ] [ 1 0 ˜ H= (30) C M (H − 1) H The factor H is introduced as the flexural weighting factor, where H = 1 represents the nominal case, H > 1 introduces a stiffer and H < 1 a more flexible rotor blade. Substituting Eq.(30) into Eq.(29) the modified state space representation of the structural beam model can be written as follows: [ ] [ ][ ] [ ] 0 1 0 q˙ q = + F (t) (31) K 1 C |{z} −H M q¨ q˙ −M M | {z } | {z } | {z } | {z } u x˙

x

˜ HA

B

The effect on the dynamic flapping response is shown in Figure 9. This compares the displacement and velocity of the blade tip as a result of change in weighting factor from H = 0.5 to H = 2. The red solid line in the displacement plot depicts the nominal stiffness case (H = 1) with a displacement in flapping direction of approximately 0.42 m. The velocity plot shows pronounced oscillation and damping for increased blade stiffness. Stable condition is reached after around 0.2 s whereas for decreased blade stiffness the velocity settles later in time. In this current study only the stiffness matrix K is affected by H. To ensure high versatility of the methodology, variation of the damping and mass matrix should be considered as well. B.

Handling Qualities Assessment via ADS-33 Requirements

The rotorcraft responses due to its softer or stiffer rotor characteristics are assessed against ADS-3323 requirements. The handling quality assessment is done against attitude quickness, which is a moderate amplitude response criterion. Here, pitch and yaw attitude changes are investigated. It requires the helicopter to undergo rapid attitude changes from one steady attitude to the other. To derive a value for attitude quickness the response to a short pulse input is considered. Maximum ratio of the peak rate response to attitude change can be identified for a discrete manoeuvre18 via:


Displacement in flapping direction (m)

0

-0.2

-0.4

-0.6

-0.8

-1 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time (s)

Velocity in flapping direction (m/s)

5

0

-5 H=0.5 H=0.75 H=1 H=1.5 H=2

-10

-15 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time (s)

Figure 9. Displacement and velocity of blade tip due to variation of weighting factor H

) ppk Lp ( ˆ 1 − e−t1 =− ∆ϕ tˆ1

(32)

where ppk is the ratio of peak change, ∆ϕ is the attitude change, LP the roll damping. The normalised time tˆ1 is defined as follows:18 tˆ1 = −Lp t1

(33)

Time histories are produced to derive the attitude quickness for each stiffness case of the rotor blade. Also, to be able to compare the different responses, the amplitude for the chosen impulse input is kept constant. The obtained results of roll attitude quickness and yaw attitude quickness are shown Figure 10(a) ¯ ϕ are normalised with respect to the nominal case H = 1. Both and 10(b) respectively. Values p¯pk and ∆ Figures depict a trend due to the variation of H. The yielded data points for ratio of roll peak to roll attitude change is linear, with little change for very high stiffness factors. Increasing the factor of H → ∞, in this case H = 3, the maximum limits for attitude quickness for the GHM are shown. Using Eq.(32) the roll damping Lp is calculated for the GHM and compared with available aircraft roll damping values, which include inertia effects to convey more information about the overall aircraft dynamics24 (see Figure 11). Comparing the roll damping Lp of the current GHM for minimum (H = 0.7), nominal and maximum flexibility (H = 3) yields that Lp is 6.3 % smaller compared to the nominal case and 0.9 % higher for the maximum case. A similar trend for attitude quickness is described above. The results in this study clearly show that a flexible blade responds slower to a given pilot input than a stiff rotor blade. However, rotor blade stiffness is not the only factor which affects the response of the helicopter. Lawrence3 showed that a variation of rotor radius, chord, and main rotor hub stiffness influences the dynamic response and therefore, handling qualities parameters. Furthermore, other factors such as the ratio of in-plane damping252 or the gain of the feedback control4 influence attitude quickness. Also depending on the mission task of the helicopter, higher roll damping is required for agile aircraft such as the Bo-105. This


3.5

0.5 H = 0.7 H = 0.8 H = 0.9 H=1 H = 1.2 H = 1.4 H = 1.6 H = 1.8 H=2 H = 2.5 H=3

-0.5

-1

2.5

∆¯ rpk (%)

∆¯ ppk (%)

0

H = 0.7 H = 0.8 H = 0.9 H=1 H = 1.2 H = 1.4 H = 1.6 H = 1.8 H=2 H = 2.5 H=3

3

2 1.5 1

-1.5

0.5 -2 -2

-1

0

1

2

¯ φ (%) ∆

3

4

5

0 -1

6

(a) Impact on ratio of roll peak rate to roll attitude change Figure 10. factor H

0

1

¯ ψ (%) ∆

2

3

4

(b) Impact on ratio of yaw peak rate to yaw attitude change

Impact on ratio of roll and yaw peak rate to attitude change due to variation of blade flexural

-10 -9 -8 -7

Lp

-6 -5 -4 -3 -2 -1 0 OH-6A

BO-105C

AH-1G

UH-1H

CH-53D

GHM (H=1)

Figure 11. Comparison of roll damping Lp of GHM with various aircraft types

would question whether an aircraft which is used for two completely different missions, such as for EMS (emergency medical services) or for high precision tasks, can be optimised in its handling qualities criteria by exploiting aspects at the overall aircraft design stage.

IV.

Conclusion & Further Work

This paper presents a coupled aeroelastic and rotorcraft flight dynamic model that has been used to study the impact on roll and yaw response through the introduction of a structural stiffness factor to the global structural system matrix. The developed flight dynamic model uses a reduced-order beam element model with its material properties concentrated on the node. Coupled with a dynamic inflow model and combined with momentum theory, it allows the prediction of aerodynamic loading and therefore, blade movement. Several assumptions were made for the flight dynamic model, such that tip loss effect and wake interaction of the rotor blades are only introduced through a correction factor. Flow separation and dynamic stall have not been taken into account. However, this becomes important when the helicopter is simulated for forward flight condition and will be amended accordingly. The dynamic response due to a short pulse input is simulated for handling qualities assessment of manoeuvre quickness relevant to moderate amplitude attitude changes. The current study shows that varying


the stiffness of the rotor blade results in a linear relationship for the roll response and a slightly non-linear relationship for yaw. The differences in roll damping between the minimum and maximum investigated flexibility case compared to nominal case are 6.3% and 0.9% respectively. The small differences between nominal and maximum case show that the currently implemented rotor blade model is close to its limit of maximum roll attitude quickness. However, the results of a change of attitude quickness have to be observed critically as other aircraft design factors are important for the behaviour of the aircraft. One of the current limitations of the model is the use of a reduced order beam model for the rotor blade. It has not been investigated how this affects the dynamic response of the GHM in comparison to a full structural blade model. To increase the accuracy of blade aeroelastic model, it is intended to extract mass and stiffness matrices from a validated Nastran beam element model and couple with the flexible main rotor model in the flight dynamic model. This upgrade to the model not only allows independent tailoring of its stiffness, mass, and damping characteristics, it can also be used for further studies, such as extracting information of magnitude and location of critical deflections of the rotor blade. Additionally the development of novel flight control design methods that take into account blade flexibility effects is another potential exploitation route.

V.

Acknowledgements

The author would like to acknowledge the support of Airbus Helicopters UK, as well as ATI and Innovate UK. The work was carried out as part of the BLADESENSE project.

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