Peng Lv
email: peng.lv@isae.fr

Fazila Mohd-Zawawi
email: fazila.mohd-zawawi@isae.fr

Emmanuel Benard

Sebastien Prothin

Jean-Marc Moschetta

Joseph Morlier

Adaptive proprotors as applied to convertible MAVs

A passive twist control is considered as an adaptive way to maximize the overall efficiency of a proprotor developed for convertible Micro Air Vehicles (MAV). Incorporated into a database of airfoil characteristics, Blade Element Momentum Theory (BEMT) is implemented to predict the performance of proprotors at low Reynolds numbers. Using this model, it is found that low twist allows for efficient hovering while high twist helps to forward flight. The Centrifugal Force Induced Twist (CFIT) concept is proposed to realize the required torsion of proprotor between hover and forward flight. Tip mass is used to provide the nose-down twisting moment by centrifugal force and stabilize the flexible blade. Classical Lamination Theory (CLT) is employed to estimate the torsion behavior of glass/epoxy laminate blade and to study the feasibility of CFIT concept. The results indicate that the predicted torsion of CFIT blade is of the same level with required deformation. The laminate blades were tested in hover and forward flight modes, with deformations measured by Laser Displacement Sensor (LDS). In rotor mode, the laminate blade can generate approximately -9 • torsion at blade tip rotating at 1,300 RPM. By contrast, at 800 RPM and inflow velocity 8m/s, it is capable of providing around -5 • torsion at blade tip in propeller mode.

Introduction

Convertible rotor aircraft has been developed for versatility services for several years, as it combines the merits of a helicopter and and airplane. It has the capacity of Vertical/Short TakeOff and Landing (VSTOL) like a helicopter, through tilting rotor, then converts to forward flight at relatively high speed, as an airplane. The three main convertible rotor configurations are the tilt-rotor, tilt-wing and tilt-body. Tilt-rotor aircraft was developed in early 1950s, exemplified by the Bell XV-3 operating the first transition from hover to forward flight. In 1970s, XV-15 demonstrated the feasibility of tilt-rotor concept. The success of XV-15 led to the V-22 project, leading to the first production tiltrotor aircraft in the world. Recently, the tilt concept has attracted the attention of MAV research community. In 2008, Shkarayev and Moschetta introduced the concept of tilt-body MAV, which has a tilt-body configuration and is capable of flying in hover and forward flight [START_REF] Shkarayev | Aerodynamic Design of Micro Air Vehicles for Vertical Flight[END_REF]. This configuration of tilt-body MAV which was successfully tested in flight.

Designing a proprotor to operate efficiently in hover and forward flight presents a challenge since the inflow velocity and thrust requirement for each flight condition are quite distinct. In hover, the inflow velocity is small and the proprotor must provide high thrust to support the aircraft weight. By contrast, in forward flight, the inflow velocity is relatively large and the low thrust must only overcome the drag. The difference in the inflow and thrust requirements between the two flight modes suggests different blade twist and chord distributions. In terms of twist effect on efficiency, high blade twist on the proprotor allows the aircraft to fly faster and more efficiently, whereas low blade twist increases the efficiency in hover. In 1983, McVeigh obtained the twist of XV-15 proprotor through linear interpolation of twist between ideal rotor and propeller by a compromise analysis [START_REF] Mcveigh | Aerodynamic Design of the XV-15 Advanced Composite Tilt Rotor Blade[END_REF]. Although this trade-off solution provided an acceptable performance on XV-15, the stiff proprotor with certain twist cannot maximize the efficiency for both flights. In 1988, Nixon proposed a passive blade twist control for the proprotor on XV-15 [START_REF] Nixon | Improvements to Tilt Rotor Performance through Passive Blade Twist Control[END_REF]. The study demonstrated successfully the feasibility of the passive blade control on conventional tilt-rotor aircraft. The small proprotors also suffer the problem caused by different twist between hover and forward flight. However, due to the small size of MAV, the complex tailored cross section of blade for passive twist control based on conventional tiltrotor aircraft is not available any more. Therefore, based on CFIT concept, composite laminate is proposed to be a more practical method for proprotor blade of MAV.

A key issue to study flexible blade is to use validated predictive simulations and therefore, in the domain of aeroelasticity, to measure accurately deformations. Optical measurement techniques have been developing for some years in aerodynamics, materials and structure, such as Holographic Interferometry (HI), Electronic Speckle Pattern Interferometry (ESPI), Projection Moiré Interferometry (PMI) and Digital Image Correlation (DIC) [START_REF]Optical Methods of Measurement: Whole-field Techniques[END_REF]. In 1998, Fleming obtained the 3-D deformation of rotor blade using PMI technique [START_REF] Fleming | Measurement of Rotorcraft Blade Deformation Using Projection Moiré Interferometry[END_REF]. However, it has low sensitivity for in-plane deformation and moderate for out-of-plane deformation. By contrast, DIC has a relatively high sensitivity that can reach 1/30,000 of the test field [START_REF] Schmidt | Full-Field Dynamic Displacement and Strain Measurement Using Advanced 3D Image Correlation Photogrammetry: Part 1[END_REF]. In 2011, Lawson demonstrated the deformation of a rotating blade using DIC [START_REF] Lawson | Measurement of Deformation of Rotating Blades Using Digital Image Correlation[END_REF]. The technique was found to have many advantages including high resolution results, non-intrusive measurement, and good accuracy over a range of scales. However, DIC needs a preprocessing which is to apply a stochastic speckle pattern to the surface by spraying it with a high-contrast and non-reflective paint. This complex painting will probably affect the stiffness of small MAV blades. Hence, in this study, LDS based method was developed to measure blade deformation in both of hover and forward flight.

Optimum twist of MAVion proprotor

MAVion, a tilt-body MAV developed by ISAE, is designed to fly in both hover and forward flight, as shown in Fig. 1. The typical wing Reynolds number of its operation conditions is below 100,000. In hover mode, the nominal thrust coefficient is 0.1 while it becomes 0.03 in forward flight. The detailed operation conditions are shown in Tab. 1.

To obtain the optimum twist distributions of proprotor in hover and forward flight, the specifications of MAVion proprotor are presented in Tab .2 as arbitrary constraints. Flat plate cross section was used as airfoil of flexible blades since it is relatively practical for CFIT concept study in terms of fabrication. In addition, thin plates, cambered or flat, with extremely thin leading edge, exhibit characteristics less sensitive to variations in Reynolds number and turbulence [START_REF] Hein | Hover Performance of a Micro Air Vehicle: Rotors at Low Reynolds Number (International Specialists Meeting Unmanned Rotorcraft: Design, Control ans Testing[END_REF]. These airfoils achieved better lift-to-drag ratios than conventional airfoils at low Reynolds numbers. On one hand, to analyze the efficiencies in rotor and propeller modes. It has been implemented and validated in a previous study [START_REF] Lv | Study of A Flexible Blade for Optimized Proprotor[END_REF]. The optimum twist distributions for hover and forward flight is found when the efficiencies of rotor and propeller can be maximized, respectively. In rotor mode, after the inflow ratio λ is determined, the induced power coefficient C Pi , the profile power coefficient C P0 and the hovering efficiency FM can also be calculated using standard approach [START_REF] Leishman | Principles of Helicopter Aerodynamics[END_REF]:

C Pi = r=1 r=0 4λ(r) 3 rdr, (1)
C P0 = σ 2 r=1 r=0 C d (r)r 3 dr, (2)
FM = C P ideal C Pmeas = C 3/2 T / √ 2 C Pi + C P0 . ( 3
)
Where r is the non-dimensional radius, dr is the non-dimensional length of each element, σ is the local solidity, C d is the local drag coefficient and C T is the thrust coefficient.

In propeller mode, the propulsive efficiency η is defined by conventional trust and power coefficients:

C T = (π 3 /4)σC y r 3 F 2 /[(F + σK ′ )cos(φ)] 2 , (4)
C P = C T πrC x /C y . (5)
η = C T J/C P , (6)
where J is the advance ratio, C x and C y are the propeller force coefficients, F is Prandtl's tip-loss factor, K ′ is equivalent interference factor and φ is the inflow angle. Propeller performance is typically described by plots of C T , C P and η vs J. CFIT concept aims at realizing a deformable, durable and stable blade for MAV proprotor, which are characterized by the deformation, failure performance and dynamics behavior. The initial step of the procedure is to select suitable reinforcing fiber for the laminate blade. The significant factor to select a reinforcing fiber for small-scale proprotor is linked to its tailoring capacity. Glass/epoxy was determined for the MAV flexible proprotor in current study. In order to improve the aerodynamic performance of flat plate at low Reynolds number, the thickness of laminate blade should be thin enough to provide a low thickness-to-chord ratio. Thus, two typical laminate configurations are considered here, a symmetric laminate [θ θ] T , and a antisymmetric laminate [θθ] T . A critical issue in the design of a laminate blade is failure analysis. The comparison of strength of UD and angleply laminates was described based on a typical carbon/epoxy composite (AS4/3501-6) using first ply failure analysis [START_REF] Daniel | Engineering Mechanics of Composite Materials[END_REF]. All of the uniaxial tensile strength, uniaxial compressive strength and in-plane shear strength of the angle-ply laminate are evidently higher than those of the off-axis UD material. Thus, in current study, antisymmetric laminates [θθ] T are employed as balanced laminates. The layup of specimen in the current study is selected as [45 -45] T . The Classical Lamination Theory (CLT) demonstrates that, for a general composite laminate, the forces and moments on it are related to the strains and curvatures at reference surface. The 6×6 matrix consisting of the components A ij , B ij , and D ij (i, j = 1, 2, 6) is the laminate stiffness matrix, is also called ABD matrix. In order to be able to obtain the strains and curvatures at the reference surface in terms of the force and moment resultants, the ABD matrix is inversed and then becomes the laminate compliance matrix consisting of the components a ij , b ij , and b ij . The torsion can be directly given by the curvature: The adaptive proprotor should not only be flexible to produce the required deformation, but also stable to maintain the required twist in each of flight mode. For a stable blade, the blade CG must be ahead of the aerodynamic center [START_REF] Sicard | Investigation of an Extremely Flexible Stowable Rotor for Micro-helicopters[END_REF]. Hence, in CFIT flexible concept, tip mass is designed to adjust the global CG of laminate blade. In addition, tip mass is beneficial for improving the nose-down twisting moment and increasing the torsion of laminate blades. On one hand, tip mass is required to be heavy enough to be able to adjust the global CG. On the other hand, it should be light enough to provide weight efficiency for the application on MAVs. Tab. 4 shows the basic parameters on the blade with tip mass. In order to estimate the twist of laminate blades, the tensile force and twisting moment of a spinning blade are introduced to CLT model. At any local section of blade, the total centrifugal force and total nose-down moment are defined by [START_REF] Sicard | Investigation of an Extremely Flexible Stowable Rotor for Micro-helicopters[END_REF]:

κ 0 xy = b 16 N x + b 26 N y + b 66 N xy + d 16 M x + d 26 M y + d 66 M xy (7)
N x (y) = F cf (y) = R y Ω 2 m y ydy + m T Ω 2 R, (8)
Where x is the chordwise coordinate, y is the spanwise coordinate, R is the proprotor radius, Ω is the rotation speed, m y is the local mass of laminate blade and m T is the tip mass. In addition, θ is the local twist angle and θ T represents the twist angle at the blade tip. The torsional moment of inertia of the blade I θ is small compared to the torsional moment of inertia of the tip rod I T , thus the nose-down moment acting on the blade airfoil is negligible compared to the nose-down moment acting on the tip mass. Similarly, the centrifugal force on the blade airfoil is negligible compared to the one on the tip mass. Hence,

F cf (y) = m T Ω 2 R, (10)
M nd (y) = I T Ω 2 sin(θ T ). (11)
The moment of inertia of the tip rod I T is defined as:

I T = (1-k)L -kL ρx 2 sdx. ( 12
)
Where L is the length of tip rod and k is the rotating axis factor. k is used to define the distance from one side of tip rod to the twisting axis, as shown in Fig. 3. For example, k=0.5 means that the twisting axis is on the midpoint of tip rod. If k is between 0 and 1, the twisting axis is on the tip rod. Else, the tip rod rotates about the off-body axis. Changing density ρ with mass m, section area s and rod length L, it becomes: Here, the twist behavior of laminate blades with low and high collective pitches based on 1,500 RPM. As discussed above, low collective pitch requires low twist for rotor mode while high twist is needed at high collective pitch for propeller mode. As it can be seen in Fig. 4, at both low and high collective pitches, the tip torsion shows the symmetrical behavior with respect to k=0.5 since the torsional moment of inertia of tip rod I T at k=0.5 is minimum. Through sliding the tip rod, the CFIT concept blade can achieve the beneficial torsion at the required level.

I T = (1-k)L -kL m sL x 2 sdx = m 3L [((1 -k)L) 3 -((-k)L) 3 ]. (13)
The final laminate blades with tip masses are shown in Fig. 5. The bending and torsion distributions during rotation are considered as the blade deformation, since beneficial torsion can increase the overall performance while bending tends to decrease the thrust.

Testing and discussion

In order to measure the deformation of rotating laminate blade, a LDS system was developed, as shown in Fig. 6. To avoid any disturbance on flow field, the two LDSs were fixed at an incidence angle to measure the blade deformation. The LDS used in this experiment is a KEYENCE LK-G502. The sampling frequency was set to 10,000Hz. Diffuse reflection mode of LDS was used for measurements. The distance of reference was 500mm, and the range of measuring was between -250mm to 500mm. For a long range measurement, the measuring accuracy is typically ±0.1% of Full Scale (FS). In The results on shape reconstruction are shown in Fig. 7. In both hover and forward flight, the obvious deformation occurred during rotation. The detailed bending and torsion were extracted according to surface function. From Figs. 8 and9, it was found that the CFIT blade is capable of generating -8.96 • torsion at RPM 1,300 in hover mode. In propeller mode, with high collective pitch, it generated around -5 • torsion at RPM 800, inflow 8m/s. Meanwhile, the maximum values of bending at blade tip are less that 5mm for both modes. In propeller mode, the blade can afford inflow and keep away from large bending.

Conclusion

The BEMT results showed high twist of blade is suitable for propulsive efficiency while low twist is beneficial for hovering efficiency. The CFIT concept of adaptive proprotor was verified first by CLT model. Glass/epoxy was used for the adaptive proprotor with the antisymmetric stacking sequence. A post-processing methodology was proposed to reconstruct deformed blade based on LDS technique, including uncertainty analysis based on Kline-McClintock method. In both of hover and forward flight, the adaptive proprotor produced evident torsion. However, the torsion generated in propeller mode was not capable of reaching the required twist. In coming tests, the motor of high torque capacity is expected to be used for high RPM and torsion. The adaptive proprotor based on CFIT concept showed the application on MAVion. The developed models and LDS technique are reliable tools for designing and analyzing the proprotor made of composite material.

Figure 1 :

 1 Figure 1: Wind tunnel model of MAVion. Hover Forward flight RPM 1500 1200 Velocity (m/s) 0 10 Advance ratio, J / 1.25 Thrust (N) 2 0.3 Thrust coefficient 0.01 0.003

Fig. 2 (

 2 a) shows the twist effect on hovering efficiency -Figure of Merit (FM) -with the variation to thrust coefficient. Thrust coefficient is adjusted by collective pitch for the five blades with built-in twist -10 • , -15 • , -20 • , -25 • and -30 • , respectively. The blade with built-in twist -10 • has the maximum efficiency at C T =0.01. In Fig. 2(b), the propulsive efficiencies of the five blades are all analyzed for a fixed value C T =0.003. They vary with the advance ratios in forward flight. The blade with twist -30 • exhibits the highest efficiency of all, at advance ratio J=1.25. Overall, high twist of blade is beneficial for forward flight while low twist can improve hovering efficiency. According to the mission requirement of MAVion, the solution of proprotor for MAVion is given in Tab. 3. Twist effect on propeller efficiency

Figure 2 :

 2 Figure 2: Twist effect to small-scaled proprotor

  Where the N x , N y and N xy are the tensile forces in the directions of x, y and xy. Besides, M x , M y and M xy represent the moments in varied directions. Terms b 16 , b 26 , b 66 , d 16 , d 26 and d 66 are the corresponding compliance factors.

Figure 3 :

 3 Figure 3: Definition of rotating axis factor k

4 :

 4 Predicted torsion of adaptive blade

Figure 5 :

 5 Figure 5: Adaptive proprotor

Figure 6 :

 6 Figure 6: LDS rig model

  Propeller mode: RPM 800 and inflow 8m/s

Figure 7 :

 7 Figure 7: Shape reconstructions of adaptive proprotor

Figure 8

 8 Figure 8: Rotor mode

Figure 9 :

 9 Figure 9: Propeller mode

Table 1 :

 1

	Number of blades	2
	Stacking axis of airfoils 0.25 on the chord
	Pitch axis	0.25 on the chord
	Airfoils	Flat plate
	Chord	0.03m
	Radius	0.2m
	Hub radius	0.03m

Operation conditions of MAVion

the thickness of flat plate should be thin enough for aerodynamic performance. On the other hand, it is necessary to consider the stacking thickness of potential adaptive proprotor based on composite materials. Hence, flat plate with thickness 2.5% was selected as the airfoil for proprotor. Five linear built-in twists of proprotor are defined first, i.e. -10 • , -15 • , -20 • , -25 • and -30 • blade tip twist relative to root. Based on airfoil characteristics from XFOIL

[START_REF] Drela | XFOIL 6.9 User Guide[END_REF]

, BEMT was used to compute airloads and

Table 2 :

 2 MAVion proprotor specifications

Table 4

 4

	: Basic parameters of blade
	Weight of blade	7.0g
	Weight of tip mass	6.5g
	Chord	30mm
	Length	185mm
	Radius	200mm
	Thickness of blade 0.75mm
	Length of tip rod	35.0mm
	Diameter of tip rod 5.0mm
	Diameter of tube	7.0mm
			Tip rod
			L
		Feathering axis	kL


Peng Lv

Fazila Mohd-Zawawi

Emmanuel Benard

Sebastien Prothin

Jean-Marc Moschetta

Joseph Morlier

An Application of Adaptive Blades on Convertible MAVs

A passive twist control is considered as an adaptive way to maximize the overall efficiency of a proprotor developed for convertible Micro Air Vehicles. The varied operation conditions suggest different twist distributions for hover and forward flight with the constraint of identical planform. In this work, adaption of the proprotor geometry is achieved by centrifugal force induced twist. Classical Lamination Theory is used to predict structural loads, while Blade Element Momentum Theory is employed to understand the aerodynamic benefits of adaptive proprotor as applied on Micro Air Vehicles. Tip mass is proposed to increase the stability and generate negative torsion for rotating blade. Validation of the procedure is based on measurements of blade deformation, performed by laser displacement sensors. While negative torsion is found in both rotor and propeller modes, level of deformation is still below what is required for optimum dual operation.

INTRODUCTION

Convertible rotor aircraft has been developed for versatility services for several years, as it combines the merits of a helicopter and airplane. It has the capacity of Vertical/Short TakeOff and Landing (VSTOL) like a helicopter, through tilting rotor, then converts to forward flight at relatively high speed, as an airplane. The three main convertible rotor configurations are the tilt-rotor, tilt-wing and tilt-body. Tilt-rotor aircraft was developed in early 1950s, exemplified by the Bell XV-3 operating the first transition from hover to forward flight. In 1970s, XV-15 demonstrated the feasibility of tilt-rotor concept. The success of XV-15 led to the V-22 project, leading to the first production tilt-rotor aircraft in the world. Recently, the tilt concept has attracted the attention of MAV research community. In 2008, Shkarayev and Moschetta introduced the concept of tilt-body MAV, which has a tilt-body configuration and is capable of flying in hover and forward flight [START_REF] Shkarayev | Aerodynamic Design of Micro Air Vehicles for Vertical Flight[END_REF]. This configuration of tilt-body MAV was successfully tested in flight.

Designing a proprotor to operate efficiently in hover and forward flight presents a challenge since the inflow velocity and thrust requirement for each flight condition are quite distinct. In hover, the inflow velocity is small and the proprotor must provide high thrust to support the aircraft weight. By contrast, in forward flight, the inflow velocity is relatively large and the low thrust must only overcome the drag. The difference in the inflow and thrust requirements between the two flight modes suggests different blade twist and chord distributions. In terms of twist effect on efficiency, high blade twist on the proprotor allows the aircraft to fly faster and more efficiently, whereas low blade twist increases the efficiency in hover. In 1983, McVeigh obtained the twist of XV-15 proprotor through linear interpolation of twist between ideal rotor and propeller by a compromise analysis [START_REF] Mcveigh | Aerodynamic Design of the XV-15 Advanced Composite Tilt Rotor Blade[END_REF]. Although this trade-off solution provided an acceptable performance on XV-15, the stiff proprotor with certain twist cannot maximize the efficiency for both flights. In 1988, Nixon proposed a passive blade twist control for the proprotor on XV-15 [START_REF] Nixon | Improvements to Tilt Rotor Performance through Passive Blade Twist Control[END_REF]. The study demonstrated successfully the feasibility of the passive blade control on conventional tilt-rotor aircraft. The small proprotors also suffer the problem caused by different twist between hover and forward flight. However, due to the small size of MAV, the complex tailored cross section of blade for passive twist control based on conventional tiltrotor aircraft is not available any more.

In this paper, a numerical method is employed to obtain the optimal twist distributions of proprotor. In order to achieve the varied twist, the concept of centrifugal force induced twist will be introduced as a more practical method for proprotor of MAV. Then, the deformation of rotating laminate blade is measured using laser displacement sensors. Finally, this concept is assumed to be applied on a MAV and the potential benefits are evaluated using Blade Element Momentum Theory model.

OPTIMAL BALDE TWIST OF MAVION 2.1 Mission of MAVion

MAVion, a tilt-body MAV developed by ISAE, is designed to fly in both hover and forward flight, as shown in Fig. 1. The typical wing Reynolds number of its operation conditions is below 100,000. In hover mode, the nominal thrust 2N to support the weight while it becomes 0.3N to balance the drag in forward flight.

Optimum twist distributions in hover and forward flight

For a blade rotating in a free-stream with the rotational plane perpendicular to the flow direction, the optimum performance is realized when the blade twist distribution is such that the Betz condition is satisfied [START_REF] Nixon | Improvements to Tilt Rotor Performance through Passive Blade Twist Control[END_REF][START_REF]Optical Methods of Measurement: Whole-field Techniques[END_REF]. The Betz condition describes that the trailing vortex sheet moves aft as a rigid helical sheet, which means the wake displacement velocity is radically constant. Using Blade Element Momentum Theory (BEMT) to satisfy the Betz condition, the displacement velocity of the vortex sheet

Where ω is rotational velocity, R is the blade radius, µ is tip speed ratio which is defined by inflow velocity V, rotational velocity ω and blade radius R, µ = ωR V , C T is the thrust coefficient. Furthermore, the optimum blade twist distribution is:

(

) 2
Where r is the local radius, α opt is the optimum angle of attack in terms of lift-drag ratio.For a radically constant chord and airfoil section, α opt can be ignored since it is always the same for each of blade element. It cannot influence the built-in twist of blade. According to Tab. 2, the optimum twist distributions of MAVion were calculated using Eqs. 1 and 2, which are shown in Fig. 2.

In order to distinguish the twist distributions, they were plotted by the translations in Y axis direction so that the twist in each mode at 0.75R is 0. With respect to the built-in twist, it shows nonlinear with around -35˚ twist from blade root to tip. By contrast, the twist distribution in hover is shown to be highly nonlinear with -15˚ twist from blade root to tip. Hence, different flight modes suggest varied built-in twist distributions of blade. The solution is to find an adaptive proprotor which can deform in twist and adapt different flight conditions.

EXLORATION OF PASSIVE TWIST CONTROL 3.1 Concept of centrifugal force induced twist

A deformable, durable and stable blade for MAV proprotor is characterized by the deformation, failure performance and dynamics behavior. To be specific, with respect to the adaptive proprotor of convertible MAV, there are five requirements. Firstly, it should be capable of deforming in terms of twist to adapt different flight conditions. Meanwhile, the deformation should be stable during the rotation. Besides, the design should be practical to be applied on MAV without size problem. Moreover, it can take the airloads without large blade bending. Finally, this adaptive proprotor should have an acceptable fatigue performance.

The initial step of the procedure is to select suitable reinforcing fiber for the laminate blade. The significant factor to select a reinforcing fiber for small-scale proprotor is linked to its tailoring capacity. Glass/epoxy was determined for the MAV flexible proprotor in current study. In order to improve the aerodynamic performance of flat plate at low Reynolds number, the thickness of laminate blade should be thin enough to provide a low thickness-to-chord ratio [START_REF] Drela | XFOIL 6.9 User Guide[END_REF]. Thus, two typical laminate configurations are considered here, a symmetric laminate [θ, -θ] T , and an antisymmetric laminate [θ, θ] T . A critical issue in the design of a laminate blade is failure analysis. The comparison of strength of UD and angleply laminates was described based on a typical carbon/epoxy composite (AS4/3501-6) using first ply failure analysis [START_REF] Daniel | Engineering Mechanics of Composite Materials[END_REF]. All of the uniaxial tensile strength, uniaxial compressive strength and in-plane shear strength of the angle-ply laminate are evidently higher than those of the off-axis UD material. Thus, in current study, antisymmetric laminates [θ, -θ] T are employed as balanced laminates. The layup of specimen was selected as [45˚, -45˚] T .

The adaptive proprotor should not only be flexible to produce the required deformation, but also stable to maintain the required twist in each of flight mode. For a stable blade, the blade Center of Gravity (CG) must be ahead of the aerodynamic center [START_REF] Sicard | Investigation of an Extremely Flexible Stowable Rotor for Micro-helicopters[END_REF]. Hence, a concept of centrifugal force induced twist was proposed for adaptive proprotor of convertible MAV. In this concept, tip mass is designed to adjust the global CG of laminate blade. In addition, tip mass is beneficial for improving the nose-down twisting moment and increasing the torsion of laminate blades. On one hand, tip mass is required to be heavy enough to be able to adjust the global CG. On the other hand, it should be light enough to provide weight efficiency for the application on MAVs. Fig. 3 demonstrates the tip mass which can slide in the chordwise direction at blade tip. The concept of CFIT for adaptive proprotor is described in Fig. 4. The blade is rotating in the anticlockwise direction in a rotation speed Ω. Factor k is used to define the position of tip rod in the chordwise direction. For example, k=0.5 means that the twisting axis is on the midpoint of tip rod. If k is between 0 and 1, the twisting axis is on the tip rod. Else, the tip rod rotates about the off-body axis. The length of tip rod is represented by L. There is a mass element dm on the rotating blade which can generate a certain centrifugal force F C . It has a component in the chordwise direction of blade. The component tends to flat the blade cross section with an initial pitch angleθ. This is the method of centrifugal force induced twist blade to generate torsion.

At any local section of blade, the total centrifugal force and total nose-down moment are defined by [START_REF] Lv | Study of A Flexible Blade for Optimized Proprotor[END_REF]:

(3) (4)
Where y is the spanwise coordinates, x represents the chordwise coordinates, R is the proprotor radius, Ω is the rotation speed, m y is the local mass of laminate blade and m T is the tip mass. In addition, θ is the local twist angle and θ T represents the twist angle at the blade tip. The torsional moment of inertia of the blade Ι θ is small compared to the torsional moment of inertia of the tip rod I T , thus the nose-down moment acting on the blade airfoil is negligible compared to the nose-down moment acting on the tip mass. Similarly, the centrifugal force on the blade airfoil is negligible compared to the one on the tip mass. Hence, (

The moment of inertia of the tip rod I T is defined as: [START_REF] Sicard | Investigation of an Extremely Flexible Stowable Rotor for Micro-helicopters[END_REF] Changing density ρ with mass m, section area s and rod length L, it becomes: [START_REF]Optical Methods of Measurement: Whole-field Techniques[END_REF] Finally, for a given blade with a tip mass rotating at certain RPM, the nose-down pitching moment can be obtained by Eq. 6. The nose-down pitching moment is expected to help rotating blade to achieve stable deformation and generate the required torsion.

Global Center of Gravity of laminate blade

In order to achieve the stable deformation of rotating laminate blade, the tip mass was designed to ensure global CG of laminate blade ahead of aerodynamic center. Tab. 3 shows the basic parameters of the blade with tip mass. According to the equilibrium of moment, the global CG of laminate blade can be expressed as a function of position factor k. As it can be seen in Fig. 5, with sliding the tip mass forward in the chordwise direction (decreasing factor k), the global CG of blade approach the aerodynamic center. After k=0.3, the global CG position is ahead of aerodynamic center 0.25, which is

Torsion of rotating laminate blade

The Classical Lamination Theory (CLT) demonstrates that, for a general composite laminate, the forces and moments on it are related to the strains and curvatures at reference surface. The 6 × 6 matrix consisting of the components A ij , B ij and D ij (i, j = 1, 2, 6)is the laminate stiffness matrix, is also called ABD matrix. In order to be able to obtain the strains and curvatures at the reference surface in terms of the force and moment resultants, the ABD matrix is inversed and then becomes the laminate compliance matrix consisting of the components ij , and d ij (i, j = 1, 2, 6). The torsion can be directly given by the curvature: Since the nose-down pitching moment is obtained, the torsion of rotating laminate blade can be calculated directly using Eq. 9. Fig. 6 gives the blade tip twist of rotating laminate blade with the variation of tip mass position at 1,500RPM. The torsion of adaptive proprotor is generated at the reasonable level which is between 0 and -30˚.

Measurement of blade deformation

A key issue to study flexible blade is to use validated predictive simulations and therefore, in the domain of aeroelasticity, to measure accurately deformations. Optical measurement techniques have been developing for some years in aerodynamics, materials and structure, such as Holographic Interferometry (HI), Electronic Speckle Pattern Interferometry (ESPI), Projection Moiré Interferometry (PMI) and Digital Image Correlation (DIC) [START_REF]Optical Methods of Measurement: Whole-field Techniques[END_REF]. In 1998, Fleming obtained the 3-D deformation of rotor blade using PMI technique [START_REF] Fleming | Measurement of Rotorcraft Blade Deformation Using Projection Moiré Interferometry[END_REF]. However, it has low sensitivity for in-plane deformation and moderate for out-of-plane deformation. By contrast, DIC has a relatively high sensitivity that can reach 1/30,000 of the test field [START_REF] Schmidt | Full-Field Dynamic Displacement and Strain Measurement Using Advanced 3D Image Correlation Photogrammetry: Part 1[END_REF]. In 2011, Lawson demonstrated the deformation of a rotating blade using DIC [START_REF] Lawson | Measurement of Deformation of Rotating Blades Using Digital Image Correlation[END_REF]. The technique was found to have many advantages including high resolution results, non-intrusive measurement, and good accuracy over a range of scales. However, DIC needs a preprocessing which is to apply a stochastic speckle pattern to the surface by spraying it with a high-contrast and nonreflective paint. This complex painting will probably affect the stiffness of small MAV blades. Hence, in this study, LDS based method was developed to measure blade deformation in both of hover and forward flight.

The final laminate blades with tip masses are shown in Fig. 7. The bending and torsion distributions during rotation are considered as the blade deformation, since beneficial torsion can increase the overall performance while bending tends to decrease the thrust. In order to measure the deformation of rotating laminate blade, a laser displacement sensor system was developed, as shown in Fig. 8. To avoid any disturbance on flow field, the two laser displacement sensors were fixed at an incidence angle to measure the blade deformation. The laser displacement sensor used in this experiment is a KEYENCE LK-G502. The sampling frequency was set to 10,000Hz. Diffuse reflection mode of laser displacement sensor was used for measurements. The distance of reference was 500mm, and the range of measuring was between -250mm to 500mm. For a long range measurement, the measuring accuracy is typically ±0.1% of Full Scale (FS). In order to reconstruct the deformed blade and to extract the bending and torsion, the post-processing methodology based on polynomial surface fitting was developed for LDS technology. The adaptive proprotor were respectively tested in rotor mode, 1,100RPM, 1,300RPM and propeller mode, inflow velocity 8m/s, 800RPM (limited by current motor). The position factor k of tip mass on adaptive proprotor was set to 0.25. The results were compared with the predictions from a Fluid Structure Model (FSI) which was based on the combination of BEMT and beam model. inflow airloads acting on the blade. The torsion is also low since there was no adequate nose-down pitching moment in this case (Fig. 10(c)). It was found that the centrifugal force induced twist blade is capable of generating negative torsions in two modes. Besides, in propeller mode, the laminate blade can take airloads without large negative bending.

APPLICATIONS ON MAVION

Since the adaptive proprotor showed the potential negative torsion generated respectively in rotor and propeller mode, hence, this concept was applied on MAVion. Based on the geometry of widely used APC86 commercial propeller with a diameter 0.2m (Fig. 11), a rigid blade, a rigid blade with collective pitch control and an adaptive blade with collective pitch control were compared using BEMT [START_REF] Leishman | Principles of Helicopter Aerodynamics[END_REF][START_REF] Lv | Study of A Flexible Blade for Optimized Proprotor[END_REF]. The detailed chord and twist distributions of APC86 are given by Figs. 12 and 13.The twist distribution of APC86 exhibits the bi-linear behavior. The root twist of rigid APC86 is around 45˚ and the tip twist is 20˚. In order to compare the adaptive concept with current propeller on MAVion, two additional linear twist distributions are defined, based on -10˚ and -30˚ of global twist. was inputted to BEMT model to find a RPM which can provide 2N for hover and 0.3N for forward flight.APC86 rigid blade with collective pitch control (∆β ≠ 0) means the APC86 rigid blade was mounted with different collective pitches. A number of RPMs were obtained by BEMT model to achieve the given thrusts for each collective pitch. On the adaptive blade with collective pitch control (∆β ≠ 0), the blades with two potential twist distributions -10˚ and -30˚ were analyzed with a series of collective pitches through BEMT model respectively. With the required thrusts, the corresponding RPMs were obtained. Finally, FM and propulsive efficiency can be calculated and compared in both rotor and propeller modes (Fig. 14).

The marker ᭹ corresponds to the APC86 rigid blade without collective pitch control. The curve with marker ᭺ shows the required RPMs of APC86 rigid blade for different collective pitches in each mode. Fig. 15 demonstrates the required RPM for the cases discussed above to achieve 2N for rotor mode. As can be seen, 6,500RPM is required to reach the thrust target (∆β = 0).In Fig. 16, the APC86 rigid blade without collective pitch control needs around 6,000RPM to obtain the thrust 0.3N at inflow velocity Fig. 17 gives the FM comparison among three cases in rotor mode. For APC86 rigid blade, the FM is approximately 0.57 when 2N thrust is provided. With additional collective pitch control, the maximum value of FM is 0.65 where is variation of collective pitch ∆β = -7˚. The FM peak of blade with adaptive twist -30˚ is lower than APC86 rigid blade with collective pitch control. However, the blade with adaptive twist -10˚ has the maximum value of FM 0.68. This indicates, using adaptive blade with collective pitch control which can generate -10˚ torsion can improve the FM more than using rigid blade with collective pitch control. The propulsive efficiencies are compared in Fig. 18 for propeller For the APC86 rigid blade without collective pitch control, the propulsive efficiency is 0.6. When the APC86 rigid blade is with collective pitch control, the peak of propulsive efficiency becomes 0.7 at ∆β = 15˚.

The adaptive blade with collective pitch control which can generate torsion -30˚ has the same efficiency peak with APC86 rigid blade with collective pitch control, since the original twist of APC8X6 is relatively high with a bi-linear -45˚. generate negative torsion by increasing nose-down pitching moment. LDS rig and corresponding postprocessing method were implemented to measure the deformation of rotating blade. The feasibility of adaptive blade was verified since the negative torsion was observed respectively in rotor and propeller mode. The potential adaptive proprotor which can generate -10˚ torsion has the peak of FM in rotor mode. In propeller mode, the blade with -30˚ has the same maximum value of efficiency with APC86 rigid propeller of bi-linear twist. The application of adaptive blade is not only in aerodynamic efficiency but also in dynamic performance. In the next study, an optical derotator, a sophisticated tool for performing non-contact vibration measurements on rotating parts with laser vibrometers, will be employed to study the dynamic response of rotating adaptive proprotor for MAVion. In addition, the aerodynamic performance is also going to be tested in each mode.

Figure 1 :

 1 Figure 1: The MAVion, a convertible MAV developed in ISAE

Figure 2 :

 2 Figure 2: Optimum twist distributions

Figure 3 :Figure 4 :

 34 Figure 3: Tip mass model

0 Table 3 :

 03 Diameter of tip rod (mm) 5.0 Diameter of tube (mm) 7.The basic parameters on tip mass normalized by the chord of blade. This indicates the tip mass can help to improve the stability of rotating blade.

Figure 5 :

 5 Figure 5: Global CG

( 9 )

 9 Where N x , N y and N xy are the tensile forces in the directions of x, y and xy. Besides, M x , M y and M xy represent the moments in varied directions. Terms b 16 , b 26 , b 66 , d 16 , d 26 and d 66 are the corresponding compliance factors.

Figure 7 :Figure 9 :

 79 Figure 7: Adaptive proprotor

Figure 9 :Figure 10 :

 910 Figure 9: Bending distribution

Figure 11 :Figure 12 Figure 13 :

 111213 Figure 11: Top and side views of APC86

Figure 14 :

 14 Figure 14: Program of evaluating potential benefits of adaptive twist

  in propeller mode (∆β = 0).In both modes, with reducing collective pitch, RPM is needed to increase for the given thrust. The two blades with adaptive twist distributions -10˚ and -30˚ also suggest the same trend.

Figure 15 :

 15 Figure 15: The required RPMs for given thrust 2N in rotor mode

Figure 17 :

 17 Figure 17: FM comparison in rotor mode

Figure 18 :

 18 Figure 18: Propulsive efficiency comparison in propeller mode

°

Table

Table 2 :

 2 Mission of MAVion

ACKNOWLEDGEMENTS

This work is supported by the China Scholarship Council(CSC) and Malaysian Ministry of Higher Education (MOHE). The authors thank Rémy CHANTON and Xavier FOULQUIER for their support in conducting the experiments.


Fazila Mohd-Zawawi

Sebastien Prothin

Peng Lv

Emmanuel Benard

Joseph Morlier

Jean-Marc Moschetta

Numerical and experimental study on exible blade for tilt-body drones

Keywords: Tilt-body drones, Pale exible, Scanner tridimensionnel, Intéraction Fluides-structure

Cet article introduit une évaluation des techniques de designes, à la fois pour les performances propulsives et pour le comportement structural d'un proprotor souple en composite pour les drones. Un modèle numérique a été développé en utilisant une combinaison du modèle aérodynamique basé sur Blade Element Momentum Theory (BEMT), et le modèle d'élément ni dune poutre anisotrope, an d'évaluer le couplage entre et les caractéristiques aérodynamiques et structurals d'une pale de proprotors souples. Le modèle numérique a ensuite été validé par des mesures de la performance statique et la reconstruction de la forme par Laser Distance Sensor (LDS). Les résultats de la validation du modèle couplé aérodynamique et structure permettent de conclure que l'approche numérique développée par les auteurs est valide comme un outil able pour designer et analyser le proprotor de drones en matériaux composites. La technique expérimentale est également capable de fourir des données ables de la géométrie et de la performance des pales.

Introduction

Tilt-body drones has been developed to be multifunctional in order to oer a wide range of services. It can y in both of hover and forward ight. In 2008, Shkarayev and Moschetta introduced the eorts on the aerodynamic design of a tilt-body drones named mini-Vertigo, which had a tilt-body conguration [START_REF] Shkarayev | Aerodynamic design of micro air vehicles for vertical ight[END_REF]. The results were realized in the design of a tilt-body drone prototype which was successfully tested in ight. A key issue to solve for optimal operation is the problem that a sti proprotor cannot operate eciently for both hover and forward ights. Nixon proposed a passive blade twist control method for conventional proprotor of tilt-rotor aircraft using extension twist coupling [START_REF] Nixon | Improvements to tilt-rotor performance through passive balde twist control[END_REF].

Unfortunately most of large scale adaptation techniques are not transferrable to small scale rotor based drones. In the present study a passive twist control is considered as a potential way to improve the overall ight eciency of drone proprotor. The proprotor blade made of composite material is preferred to be used. It is due to their potential benets such as aeroelastic tailoring, ability to manufacture, more rened aerodynamic designs, signicant enhancements in fatigue performance and damage tolerance of the blade. The blade is expected to be deformed in torsions under dierent airloads and structural load. This paper is aimed at developing an evaluation of design techniques of a composite exible proprotor. The aerodynamic model based on BEMT is used as a tool to compute the aerodynamic loadings. In forward ight modelling, the BEMT proposed by Adkins is adapted, meanwhile ; a classical BEMT is used for hover case. The detailed equations used for both are described in [START_REF] Leishman | Helicopter aerodynamics[END_REF] and [START_REF] Adkins | Design of optimum propellers[END_REF], respectively. In this model, the ow angle is iteratively computed until the convergence criteria are reached. In the classical approach of low order proprotor analysis, lift polar is a linear function. Hence, in order to consider non-linear airfoil characteristics prevalent in low Reynolds number regime (Re < 70, 000), XFOIL, an airfoil design and analysis code developed by Drela [START_REF] Drela | An analysis and design system for low Reynolds number airfoil, low Reynolds number aerodynamic[END_REF] was integrated into the design iterative process. The turbulence eect was eliminated by using at plate [START_REF] Hein | Hover performance of a micro air vehicle : rotor at low Reynolds number[END_REF]. In this respect, the Ncrit parameter, used to dene the turbulence level in XFOIL, can be set as 0.1 for both ight modes. A 2-bladed rotor with rectangular planform (R = 0.1m, c = 0.02m), at plate blade prole with thickness t/c = 2.5% and blade pitch of 25 was used for validation(hover case), in Fig. 1(a). Meanwhile, the propeller APC 8x6 was used to validate the FPROP for forward ight case. The inow velocity was 16m/s. From the validation result as shown in Fig. 1(b), it is found that the developed BEMT method with the integration of XFOIL shows better agreement with the experimental measurement compared to the linear model QPROP. A slight increase in torque observed in the experimental result can be due to the heavy material (aluminium) used in the blade.

Structural Model (FBEAM)

The structural analysis is based upon the use of anisotropic beam nite element model to determine the blade deections during operation. The FBEAM consists of an integrated set of programs, which perform a two-dimensional cross-sectional analysis of the blade, followed by a one-dimensional nite element of a proprotor blade. A global coordinate system is used for the description of the blade geometry and the calculation of the loads. BECAS [START_REF] Blasques | BECAS V2, A cross-section analysis tool for anisotropic and inhomogeneous beam sections of arbitrary geometry[END_REF], a cross-sectional analysis tool which is developed at Denmark Technical University (DTU) was incorporated in this structural analysis program. The motivation of employing BECAS is due to the fact that BECAS has ability to determine the cross section stiness properties while accounting for all the geometrical and material induced couplings.The linear relation between generalized forces F and the resulting strains and curvatures q is written in a matrix form as follows :

Kq = F (1)
where K is the sectional stiness matrix. The nal form of elastic energy and kinetic energy are written in Eq. 2.

K e = L 0 B T SBdz; M e = L 0 N T M s N dz (2)
where M s sectional mass matrix, B is the strain-displacement matrix and N is the polynomial matrix.

The details of equation used in these relationships are described in [START_REF] Kim | Developing anisotropic beam element for design composite wind turbine blades[END_REF]. Global stiness of the blade is obtained through spanwise integration. As for the one-dimensional nite element, the classical Timoshenko beam theory is used for considering nite element analysis. With the obtained shape function, the principle of virtual displacements is used to derive the elemental stiness. For structural model validation, a static analysis on a rectangular planform with dimension (190.5mmx12.7mmx3.175mm) was performed. Material properties of graphite-epoxy are : E11 = 129GP a; E22 = 9.4GP a; E33 = 9.4GP a; G12 = 5.16GP a; G13 = 4.3GP a; G23 = 2.54GP a; µ = 0.3 and ρ = 1550kg/m 3 . The ply angle with respect to pitch axis was 30 . The result obtained in FBEAM was validated by MSc. Nastran, in Fig. 3.

Coupled-aero-structure (FAE)

In order to compute the blade deformation, the coupled-aero-structure (CAS) model is developed. To begin with, the basic geometry (zero deections) is assumed. Then the FBEAM calculates the blade deformations. The deformed blade shape is used to update the aerodynamic model. The aerodynamic loads are transferred to the beam nodes as concentrated forces. A new structural analysis is performed to calculate the deformed shape of the blade under the inuence of aerodynamic and centrifugal loads. The aero-structural interaction is repeated until equilibrium between deformation and loadings is achieved. The approach described above was applied to the constant chord untwisted 2-bladed system for drones-sized proprotor made of laminate composite. The deection results in bending and torsion.

The eects of camber changes are not included in this study due to limitation in the modeling. Iteration 1 denotes the deection due to centrifugal loads only and the rest include the aerodynamic loads. The dierence between single-step (SS) simulation and coupled-aero-structure simulation was investigated and the result is illustrated in Fig. 4. The slight eect on deformation is observed.

3 Experimental Setup Optical measurement techniques have been developing for a couple of years in applications of aerodynamics, materials and structure, such as Holographic Interferometry (HI), Electronic Speckle Pattern Interferometry (ESPI), Projection Moiré Interferometry (PMI) and Digital Image Correlation (DIC) [START_REF] Williams | Optical Methods in Engineering Metrology[END_REF]. In 1998, Fleming obtained the 3-D deformation of rotor blade using PMI technique [START_REF] Fleming | Measurement of Rotorcraft Blade Deformation Using Projection Moire Interferometry[END_REF]. However, it has low sensitivity for in-plane deformation and moderate for out-of-plane deformation. By contrast, DIC has a relatively high sensitivity that can reach 1/30,000 of the test eld [START_REF] Schmidt | Full-Field Dynamic Displacement and Strain Measurement Using Advanced 3D Image Correlation Photogrammetry : Part 1[END_REF]. In 2011, Lawson demonstrated the deformation of a rotating blade using DIC [START_REF] Michael | Measurement of Deformation of Rotating Blades Using Digital Image Correlation[END_REF]. The technique was found to have many advantages including high resolution results, non-intrusive measurement, and good accuracy over a range of scales. However, DIC needs a preprocessing which is to apply a stochastic speckle pattern to the surface by spraying it with a high-contrast and non-reective paint. This complex painting will probably aect the stiness of blade. Hence, in this study, LDS was developed to measure blade deformation and validate the above numerical models. Two LDSs are driven by track systems to scan the blade from blade root to tip with an incremental distance 2mm. The LDS used in experiment is KEYENCE LK-G502. The distance of reference is 500mm, and the range of measuring can be between -250mm to 500mm. The sampling frequency of this laser was selected as 10,000Hz. In order to determine the overall uncertainty U laser of the experimental result, the bias and precision limits, B laser and P laser , must be combined. This is accomplished using the Root-Sum-Square (RSS) method, U laser = (B laser + P laser ) 1/2

(3)

A reference surface was measured rst to determine the precision limits, then the total uncertainty is obtained, ± 0.1%. LDS records the Z coordinates which is the distance from the position detected on blade surface to reference plane. Meanwhile, square wave in time domain is measured by RPM sensor.

Then, average RPM and angular speed at each blade section can be extracted from the square wave.

Furthermore, with the azimuth of feathering, polar coordinates is possible to be transferred to Cartesian coordinates X and Y. Combining coordinates X, Y and Z, a polynomial surface tting is performed to obtain the bending and torsion of rotating blade. To evaluate the exible blade performance, the thrust and torque were measured using two transducers.

Results Validation

The validation results in performance are shown in Fig. 5. As can be seen, the FPROP agrees well with experimental data of thrust. However, it over-predicts the torque. Fig. 6 shows the good agreement between the FAE simulation and the experimental data as obtained from LDS measurements. This is the result obtained for the blades clamped at collective pitch 35 . The uctuations that can be observed through scattered plot of deformations are the results by the preliminary post-processing method. In this method, the deformation was extracted through the data interpolation at each section. Since the vibration of rotating blade probably generated uncertainty to the LDS data in spanwise, hence, the deformation exhibits unsmoothness in the plots.

Conclusions

As conclusion, the evaluation of design techniques, both for the aerodynamic performance and for the structural behavior of a composite exible proprotor has been presented in rotor modes. The Additionally, the developed structural model which uses cross-sectional analysis enables a more complex blade with highly-twisted and/or arbitrarily-shaped blades to be eciently analyzed. As perspectives, an investigation of static aeroelasticity on the drone-sized exible proprotor will be carried out using the validated numerical model. In future, the study will focus on propeller modes and optimization to enhance the proprotor eciency. Likewise, based on inverse method, the loads on blade are expectedly able to be deducted from blade deformation.

  numerical model has capability of prediction in proprotor aerodynamics and structure. The model presents coupling between anisotropic beam nite element model and an aerodynamic model that takes into consideration of low Reynolds number. The numerical model has also been experimentally validated by LDS technique and transducers of thrust and torque. It can be concluded that the developed numerical model is a reliable tool for designing and analyzing the proprotor made of composite material.

1

 1 Comparison of BEMT simulation and corresponding measurements for hover (V=0)

2 4 5 6

 2456 Comparison of BEMT simulation and corresponding measurements with inow (V=16m/s) The eect of SS and CAS simulation on the blade deformations Thrust and torque of rigid and exible proprotor at dierent rotational speed (V=0) Comparison of FAE simulation with the corresponding measurements Références


Fazila Mohd-Zawawi
email: fazila.mohd-zawawi@isae.fr

Sebastien Prothin

L V Peng

Emmanuel Benard

Jean-Marc Moschetta

Joseph Morlier

Study of a Flexible UAV Proprotor 48 th APPLIED AERODYNAMICS SYMPOSIUM

This paper is concerned with the evaluation of design techniques, both for the propulsive performance and for the structural behavior of a composite flexible proprotor. A numerical model was developed using a combination of aerodynamic model based on Blade Element Momentum Theory (BEMT), and structural model based on anisotropic beam finite element, in order to evaluate the coupled structural and the aerodynamic characteristics of the deformable proprotor blade. The numerical model was then validated by means of static performance measurements and shape reconstruction from Laser Distance Sensor (LDS) outputs. From the validation results of both aerodynamic and structural model, it can be concluded that the numerical approach developed by the authors is valid as a reliable tool for designing and analyzing the UAV-sized proprotor made of composite material. The proposed experiment technique is also capable of providing a predictive and reliable data in blade geometry and performance for rotor modes.

INTRODUCTION

Tilt-body Micro Air Vehicle (MAV) has been developed to be multifunctional in order to offer a wide range of services. It can fly in both of hover and forward flight. In 2008, Shkarayev S. and Moschetta J.M. introduced the efforts on the aerodynamic design of a tilt-body MAV named mini-Vertigo, which had a tilt-body configuration [START_REF] Shkarayev | Aerodynamic Design of Micro Air Vehicles for Vertical Flight[END_REF]. The wind tunnel measurements were conducted for a motor, a wing, and an arrangement of a wing with a motor. The results were realized in the design of a Tilt-body MAV prototype which was successfully tested in flight. Tilt-body MAV attracts growing interest as they offer great versatility in the field of urban reconnaissance.

A key issue to solve for optimal operation is the problem that a stiff proprotor cannot operate efficiently for both hover and forward flights. Mark W. Nixon proposed a passive blade twist control method for conventional proprotor of tilt-rotor aircraft using extension twist coupling [START_REF] Nixon | Improvements to Tilt Rotor PerformanceThrough Passive Blade Twist Control[END_REF]. Unfortunately most of large scale adaptation techniques are not transferrable to small scale rotor based MAV. Finally, the combination of passive twist control and active pitch control enhanced the proprotor performance. In the present study a passive twist control is considered as a potential way to improve the overall flight efficiency of MAV proprotor. The proprotor blade made of composite material is preferred to be used. It is due to their potential benefits such as aeroelastic tailoring, ability to manufacture more refined aerodynamic designs for platform/airfoil geometries and significant enhancements in fatigue performance and damage tolerance of the blade. Additionally, the difference in rotor speeds in hover and forward flight modes may cause a change in the blade centrifugal forces so that extension-twist structural coupling can be optimized for a given proprotor blade for convertible air vehicles. Hence, this paper is aimed at developing an evaluation of design techniques of a composite flexible proprotor.

2.

NUMERICAL MODEL

Aerodynamic Model (FPROP)

The aerodynamic model based on BEMT is used as a tool to compute the aerodynamic loadings in terms of lift force, drag force and pitching moment around quarter of the chord distributed in spanwise. The quasi-steady aerodynamic loading is calculated using a twodimensional aerodynamic theory in a stripmanner. In the aerodynamic modeling for forward flight case, the BEMT proposed by Adkins is adapted, meanwhile; a classical BEMT is used for hover case. The detailed equations used for both are described in [START_REF] Leishman | Helicopter Aerodynamics[END_REF] and [START_REF] Adkins | Design of Optimum Propellers[END_REF], respectively. In this model, the flow angle is iteratively computed until the convergence criteria are reached. This iterative analysis procedure determines the characteristics of a given proprotor (C T , C P ) and its corresponding performance ( proprotor , FM). The radial and axial interference factors (a, a'), and Reynolds number (Re) depending on the operating condition are also iteratively computed in the analysis process. In the classical approach of low order proprotor analysis, different assumptions are used, i.e lift polar is a linear function, in order to obtain a closed loop solution or even to quickly converge the iterative process. Hence, in order to consider non-linear airfoil characteristics prevalent in low Reynolds number regime (Re<70,000), XFOIL, an airfoil design and analysis code developed by Drela [START_REF] Drela | XFOIL: An Analysis and Design System for Low Reynolds Number Airfoil[END_REF] was integrated into the design iterative process to eliminate this assumption as well as to precisely compute the aerodynamic coefficients. The airfoil sensitivity to the turbulence level and Reynolds number variation was eliminated by using flat plate [START_REF] Hein | Hover Performance of a Micro Air Vehicle: Rotor at Low Reynolds number[END_REF] as a blade profile for analysis in this study. Flat plate profile also promises better performance than other airfoils in MAVs Reynolds number regime [START_REF] Laitone | Wind tunnel tests of wings at Reynolds numbers below 70[END_REF]. In this respect, the n crit parameter, used to define the turbulence level in XFOIL, can be set as 0.1 for both flight modes. The developed iterative process of analysis procedures using BEMT method was validated with the QPROP and the experimental measurement [START_REF] Drela | Elements of Airfoil Design Methodology in Applied Computational Aerodynamics[END_REF]. The BEMT procedure of FPROP is shown as a block diagram in Fig. 1. The result validation of BEMT for hover and forward flight cases in terms of thrust and torque are shown in Fig. 2 and Fig. 3, respectively.

A 2-bladed rotor with rectangular planform (R=0.1m, c=0.02m), flat plate blade profile with thickness t/c=2.5% and blade pitch of 25° was used in the aerodynamic model validation for a case without inflow (hover case). Meanwhile, the propeller APC 8x6 was used to validate the FPROP for forward flight case. The inflow velocity was 16m/s. From the validation result, it is found that the developed BEMT method with the integration of XFOIL shows better agreement with the experimental measurement compared to QPROP. QPROP, a propeller analysis tool with simplification of linear lift polar, showed unacceptable results due to its incapability to predict aerodynamic coefficients at post-stall angle of attacks. A slight increase in torque observed in the experimental result is can be due to the heavy material (aluminium) used in the blade.

Structural Model (FBEAM)

The structural analysis is based upon the use of anisotropic beam finite element model to determine the blade deflections during operation. The FBEAM consists of an integrated set of programs, which perform a two-dimensional cross-sectional analysis of the blade, followed by a one-dimensional finite element of a proprotor blade. A global coordinate system, shown in Fig. 4 is used for the description of the blade geometry and the calculation of the loads. This is a right-handed Cartesian coordinates system where; the Yaxis is co-linear with the proprotor rotation axis and its positive in the direction of flight. The Zaxis is in the plane of rotation and points towards the blade tip. The X-axis is chordwise direction where the feathering axis is referred to. In this study, feathering axis was set at quarter-chord. where S ij is the sectional stiffness matrix.

Using the sectional stiffness matrix and mass matrix obtained in BECAS, the elemental stiffness matrix and mass matrix are evaluated. Elastic energy and kinetic energy of the beam element are considered in order to compute the elemental properties. The final form of elastic energy and kinetic energy are written in Eq. 2.1 and Eq 2.2, respectively.

(2.1)

(2.2)
where sectional mass matrix, is the strain-displacement matrix and is the polynomial matrix. The details equation used in these relationships are described in [START_REF] Kim | Developing Anisotropic Beam Element for Design Composite Wind Turbine Blades[END_REF]. Global stiffness of the blade is obtained through spanwise integration. As for the onedimensional finite element, the classical Timoshenko beam theory is used for considering finite element analysis. Static equilibrium equations are solved with the geometric boundary conditions in order to compute the shape function. With the obtained shape function, the principle of virtual displacements is used to derive the elemental stiffness. And for the purpose of integration, a Gauss quadrature is used where for this study, four-noded one-dimensional elements were chosen.

The load caused by the body forces generated by the central acceleration field, including centrifugal effects are included in the structural model. The stretching induced by the centrifugal inertia force due to the rotational motion causes the increment of the bending stiffness of the structure which naturally results in the variation of natural frequencies and mode shapes.

For structural model validation, a static analysis on a rectangular planform with dimension (190.5mmx12.7mmx3.175mm) was performed. Graphite-epoxy with material properties E 11 =129GPa, E 22 =9.4GPa, E 33 =9.4GPa, G 12 =5.16GPa, G 13 =4.3GPa, G23=2.54GPa, vu=0.3 and ρ=1550kg/m 3 was used. The ply anglewith respect to pitch axis was 30°. The result obtained in FBEAM was validated by commercial structural analysis program namely MSc. Nastran and the validation result is illustrated in Fig. 7. Several simulations were carried out to observe the operating condition and fiber orientation effect on blade deformations which later will be used for prediction in the design process. Fig. 8 illustrates the effect of using anisotropic material on the bending and torsion deformations. Fig. 9 demonstrates the deformations at different RPM. From the result in Fig. 8, it is found that the load in flapwise direction not only produces flapwise defelction but also torsion.

Coupled-aero-structure (FAE)

In order to compute the blade deformation under aerodynamic loadings, the coupledaero-structure model is developed. The coupled aero-structure of the proprotor combines the aerodynamic and structural analysis models. To begin with, the basic geometry (zero deflections) is assumed. Then the FBEAM structural model calculates the blade deformations under centrifugal loads. The deformed blade shape is used to update the aerodynamic model. The quasi-steady aerodynamic loads are computed for the update geometry, using the 2D aerodynamic theory based on stripwise manner model as described in section 2.1. The aerodynamic loads are transferred to the beam FE nodes as concentrated forces. A new structural analysis is performed to calculate the deformed shape of the blade under the influence of aerodynamic and centrifugal loads. The variation of the blade twist angle along the blade is monitored for convergence. The aerostructural interaction is repeated until equilibrium between deformation and loadings is achieved. After convergence the proprotor performance characteristics are computed. The approach described above was applied to the constant chord untwisted 2-bladed system for UAV-sized proprotor made of laminate composite. The deflection results in two basic modes of deformation; spanwise bending and torsion. The effects of camber changes are not included in this study due to limitation in the modeling. Iteration 1 denotes the deflection due to centrifugal loads only and the rest include the aerodynamic loads. Fig. 10 shows the corresponding variation of the calculated thrust and power coefficients.

The effect of single-step (SS) simulation, where the simulation stops at first iteration, and coupled-aero-structure (CAS) simulation, where the iterative process is converged when equilibrium between deformation and loading is achieved, was investigated and the result is illustrated in Fig 11 . The slight effect on deformation is observed.

EXPERIMENTAL SETUP

Optical measurement techniques have been developing for a couple of years in applications of aerodynamics, materials and structure, such as Holographic Interferometry (HI), Electronic Speckle Pattern Interferometry (ESPI), Projection Moiré Interferometry (PMI) and Digital Image Correlation (DIC) [START_REF] Williams | Optical Methods in Engineering Metrology[END_REF].

In 1998, Fleming G. A. obtained the 3-D deformation of rotor blade using PMI technique [START_REF] Fleming | Measurement of Rotorcraft Blade Deformation Using Projection Moire Interferometry[END_REF]. However, it has low sensitivity for in-plane deformation and moderate for outof-plane deformation. By contrast, DIC has a relatively high sensitivity that can reach 1/30,000 of the test field [START_REF] Schmidt | Full-Field Dynamic Displacement and Strain Measurement Using Advanced 3D Image Correlation Photogrammetry: Part 1[END_REF].

In 2011, Lawson M. S. demonstrated the deformation of a rotating blade using DIC [START_REF] Michael | Measurement of Deformation of Rotating Blades Using Digital Image Correlation[END_REF]. The technique was found to have many advantages including high resolution results, non-intrusive measurement, and good accuracy over a range of scales. However, DIC needs a preprocessing which is to apply a stochastic speckle pattern to the surface by spraying it with a high-contrast and nonreflective paint. This complex painting will probably affect the stiffness of blade. Hence, in this study, LDS was developed to measure blade deformation and validate the above numerical models. As is shown in Fig. 12, the two LDSs are driven by track systems to scan the blade from blade root to tip with an incremental distance 2mm.

Figure 12. LDS rig

The LDS used in experiment is KEYENCE LK-G502. The distance of reference is 1000mm, and the range of measuring can be between -250mm to 500mm. The sampling frequency of this laser was selected as 10,000Hz. At each blade section, the laser scans for 2 seconds. Finally, 20,000 data points were obtained totally for each section. The post-processing of LDS measurement is shown in Fig. 13. Firstly, LDS records the Z coordinates which is the distance from the position detected on blade surface to reference plane. Meanwhile, square wave in time domain is measured by RPM sensor. Then, average RPM and angular speed at each blade section can be extracted from the square wave. Furthermore, with the azimuth of feathering, polar coordinates is possible to be transferred to Cartesian coordinates X and Y. Combining coordinates X, Y and Z, a polynomial surface fitting is performed to obtain the bending and torsion of rotating blade. Fig. 14 shows the surface fitting visualization of a deformed blade.

To evaluate the flexible blade performance, the thrust and torque were measured using two transducers. The close-up of mounted blade is shown in Fig 15. Then, in order to evaluate the convergence of experimental data to the variation of sampling step, the standard deviation and average value were analyzed for both of thrust and torque. As we can see from Fig. 16, the deviations fluctuate when the sampling step is lower than 20,000. With increasing of sampling step, the deviations decrease and become relatively stable. By a compromise between data quality and time efficiency, the sampling step was determined as 60,000. The data convergence of torque was shown in Fig. 17. Sampling step 60,000 is also enough to obtain acceptable data of torque. Tests were operated two times to ensure the measuring stability. Acquisition precision is determined by Eq. 3.1 with 95% confidence intervals (factor =1.96) [START_REF] Thipyopas | Experimental Analysis of a Fixed Wing VTOL[END_REF]. (3.1) where is the total sampling number 60,000 in this study, is the standard deviation, and is the precision of acquisition.

RESULT VALIDATIONS

The validation results in performance are shown in Fig. 18. As can be seen, the FPROP agrees well with experimental data of thrust. However, it over-predicts the torque. Fig. 19 shows the good agreement between the FAE simulation and the experimental data as obtained from LDS measurements. This is the result obtained for the blades clamped at collective pitch 35°. The fluctuations that can be observed through scattered plot of deformations are the results by the preliminary post-processing method. In this method, the deformation was extracted through the data interpolation at each section. Since the vibration of rotating blade probably generated uncertainty to the LDS data in spanwise, hence, the deformation exhibits unsmoothness in the plots.

CONCLUSIONS

As conclusion, the evaluation of design techniques, both for the aerodynamic performance and for the structural behavior of a composite flexible proprotor has been presented in rotor modes. The numerical model has capability of prediction in proprotor aerodynamics and structure. The model presents coupling between anisotropic beam finite element model and an aerodynamic model that takes into consideration the low Reynolds number aerodynamic. The influence of deformations is taken into account during the iteration procedure. The numerical model that utilizes the above-described approach has also been experimentally validated by LDS technique and transducers of thrust and torque. Through validation results of both aerodynamic and structural model, it can be concluded that the developed numerical model is valid as a reliable tool for designing and analyzing the proprotor made of composite material. Additionally, the developed structural model which uses cross-sectional analysis enables a more complex blade with highlytwisted and/or arbitrarily-shaped blades to be efficiently analyzed.

As perspectives, an investigation of static aeroelasticity on the UAV-sized flexible proprotor will be carried out using the validated numerical model. In future, the study will focus on propeller modes and optimization in composite laminates to enhance the proprotor efficiency. Likewise, based on inverse method, the loads on blade are expectedly able to be deducted from blade deformation.

Figure 1 .

 1 Figure 1. BEMT procedure in FPROP

Figure 2 .

 2 Figure 2. Comparison of BEMT simulation and the corresponding measurements for hover case (V=0)

Figure 3 .

 3 Figure 3. Comparison of BEMT simulation and the corresponding measurements with inflow (V=16m/s)

Figure 4 .Figure 5 .

 45 Figure 4. Global coordinate system of the blade

Figure 6 .

 6 Figure 6. Cross section coordinate system, forces and moments (a) and corresponding strains and curvatures (b)written in a stiffness form as follows:

Figure 7 .

 7 Figure 7. FBEAM validation by MSc. NASTRAN

Figure 8 .Figure 9 .

 89 Figure 8.Effect of fiber orientation on blade deformations (β=15°, RPM=1500)

Figure 10 .Figure 11 .

 1011 Figure 10. Variation of thrust coefficient during the iteration

Figure 13 .

 13 Figure 13. Post-processing procedure of LDS measuring

Figure 14 .

 14 Figure 14. Surface fitting of a deformed blade

Figure 16 .

 16 Figure 16. Convergence of thrust data

Figure 18 .

 18 Figure 18. Thrust and torque of rigid and flexible proprotor at different rotational speed (V=0)