Design, Construction and Testing of a Smart Actuated Helicopter Blade
J. Monreal*, G. Giannopoulos*, F. Santafe*, J. Vantomme*, F. Buysschaert†, P. Hendrick†
*Royal Military Academy, Civil and Materials Engineering Department, Av. de la Renaissance 30, B-1000, Brussels
†ULB, Service of Fluid Mechanics, Av. F.D. Roosevelt, 50, B-1050 Brussels
[email protected], [email protected]
ABSTRACT
The paper deals with the conceptual design, the analysis as well as the experimental validation of a 0.8 m radius adaptive
helicopter blade. The innovative aspects are the high radius, giving it the possibility to carry high (pay)loads and most
importantly, its full control (cyclic and collective pitch control) through a smart actuation system. The design of the actuators is
presented from the early stages taking into account finite element analyses that were performed using Ansys, as well as other
types of solvers incorporating coupled mechanics. These analyses were used as guidelines for the displacement performance
of the actuators and to evaluate their capability to perform the necessary actuation at the rotational velocity of the blade. The
construction of the bimorph actuator is presented as well. Finally the structure was tested in both static conditions and in the
aerodynamic tunnel in order to simulate as much as possible the conditions that the blade will have to face during operation.
The testing data showed the applicability of the concept and proved that phenomena like resonance can be beneficial for
certain applications.
Introduction
Helicopters constitute one of the aeronautical domains that could benefit a lot from the use of smart materials. Hereby, rotor
and blade design can profit most of this technology since the application of smart materials can improve aerodynamic
performance as well as reduce noise and vibration. Most of the research done on using piezoelectrics in helicopter blades is
focused on the IBC (Independent Blade Control) technique. An example of this work is the one of Butter et al. [1]. In this work
the blade tip is equipped with an internal piezoelectric actuator that actuates in twisting mode the blade tip due to the tension
torsion coupling of this part of the blade. The aim of this design is to reduce vibration and noise problems. Analogous works
have been performed by Bernhard et al. [2], [3] and Chen et al. [4]. The same problems are addressed, using similar
techniques as long as the actuation of the edge of the helicopter blade (active part) is concerned. It is very important to
mention here that all these approaches could not produce adequate blade twisting, which could be used to obtain collective
and cyclic control of the helicopter, and eventually get rid of the heavy blade control mechanism that is part of the rotor. It’s
clear that piezoelectrics might reduce the overall weight of the aircraft. Especially small helicopters would benefit from this gain
in weight.
In this direction the work of Barrett et al. [5] offered some innovative aspects. Based on existing technology developed by
Barrett [6], [7], high blade twist angles were achieved. This type of piezoelectric actuator was used for the cyclic control of a
small helicopter blade, while the collective control was performed using another mechanism. The approach showed clearly that
piezoelectric actuators can be used for displacements that exceed those needed for vibration and noise suppression. This
study proved also that it is possible to reduce the amount of moving parts that a helicopter rotor needs in order to be
functional, by the intelligent use of piezoelectric actuators.
The work done in the RMA departs from piezoelectric actuators, developed on existing technology, which are used for cyclic
and collective pitch control of a helicopter blade, planned to be used on a small UAV helicopter. The aim is to fully substitute
the traditional actuation mechanism (swash plate) with piezoelectric actuators. With respect to the existing work, the innovative
aspect of the approach presented here is the size of the helicopter blade to be actuated (radius 0.9-1.0 m, chord length 60-70
mm) and the payload of a two-bladed UAV helicopter. The value set as target for the payload was the one of 100 N.
The aerodynamic optimization of the blade exceeds the scope of the present work, which is focused entirely on the actuation
mechanism. However, the airfoil selection is of critical importance. In order to reduce as much as possible the aerodynamic
loads exerted on the piezoelectric actuators, a symmetric airfoil seems to be a good choice. A good compromise between high
lift, low pitching moment and high drag divergence Mach number performance is found to be the NACA 0012 airfoil. One can
still improve performances using camber and with the use of an evolutive profile, though, this would complicate blade
construction. Moreover, such a profile should be selected carefully in order not to increase piezoelectric actuator load.
Therefore, the selection of the NACA 0012 airfoil for the rotor blades seems to be the most interesting at this time.
The actuators have been analyzed using coupled mechanics finite element solvers developed especially for this purpose. Two
different solvers were developed: A CLPT solver and a layerwise solver using thermal-electrical-mechanical coupled
constitutive formulation. In the work of Giannopoulos et al. [8] the formulation is presented, however, the most important
parameters will be presented here as well. Finite element analyses are verified through experiments on actual actuators.
Design of the Swash-Plate Free Rotor
The design of the actuation system was conceptualized and optimized under certain criteria. The mechanism to host the smart
actuator was designed taking into account that all its potential should be exploited in the actuation of the blade. It was decided
then that the actuator should not be an integral part of the structure since in that case it would carry structural loads that would
reduce the amount of available actuation. In order to achieve this, three bearings were used in the construction of the hosting
structure. The whole mechanism incorporates 2 radial bearings for the bending moments produced by the lift and drag of the
blade and one thrust bearing for the centrifugal forces. Although the blades used for UAVs are light (around 0.15-0.2 kg),
centrifugal forces can reach high values that can exceed 500 N. The design of the swash-plate free rotor hub and a detail of
the bearings are shown in figure 1.
a)
b)
Figure 1: a) Swash plate free rotor hub; b) Detail of the bearings: design (b, up) and actual construction (b, down).
Even though the aerodynamic optimization of the system goes beyond the aim of this work, the blade election is of crucial
importance because the actuation requirements depend directly on its dimensions. Firstly, the blades to be used should be
perfectly balanced, so that the aerodynamic centre coincides with the centre of gravity and the axis of rotation. This is
considered to avoid the creation of aerodynamic moments that the actuator will have to overcome in order to provide the
necessary actuation to the blade. Therefore, NACA 0012 is considered as the optimum choice. At any angle of attack (under
steady aerodynamic conditions, i.e. no stall), no aerodynamic moments are created around the aerodynamic centre, which
lays at one quarter of the chord length (c/4) from the leading edge.
The dimensions of the blade as well as the rotational speed are determined by two parameters. On the one hand, a blade has
to be selected that minimizes the actuation energy that has to be provided by the smart actuator. Cyclic control is the most
difficult task for pitch angle control due to its dynamic nature, requiring considerable amount of mechanical work from the
actuator; therefore, the dimensions of the blade and the rotational speed have to be selected so that they minimize the torque
for its cyclic control. Equation 1 links the required actuation torque with the rotational speed.
T ( t ) = Iα ( t ) = − I ω 2θ cy0 ( t ) cos ( ωt )
(1)
where T is torque, I the mass moment of inertia, α is the angular acceleration, ω is the angular velocity of the blades and θcy0
defines the amplitude of the cyclic blade pitch angle, which is assumed to be sinusoidal. A CAD model was developed to
estimate the moment of inertia I for different blade dimensions.
On the other hand, the blades have to create the necessary lift to carry a payload equal to the weight of the structure plus an
extra output that ensures perfect manoeuvrability. The payload chosen is 100 N (50 N on each blade), which guarantees a
regular UAV submission. The lift depends on the chord length, rotational velocity and length of the blade, and it is related with
all these variables through the lift coefficient (CL). For a small segment of the blade it is given by equation 2.
dL =
CL ρ cU 2
2
dr
(2)
where ρ is the air density, c is the chord length and U is the relative velocity of the free stream at the blade, which is assumed
to be only due to the rotational velocity of the blade, i.e. U = ω ⋅r.
An additional constraint is required in order to obtain a relatively stiff blade that does not deflect excessively in the vertical
direction. This deflection depends on the pressure distribution throughout the blade, which depends directly on the lift and drag
forces. For the NACA 0012 profile the drag force will be neglected since it will only weight around a 5% of the total lift force,
and CL is considered to depend only on the angle of attack and to remain constant with respect to the airspeed, due to the fact
that the maximum airspeed of the blade is bellow Mach number M = 0.3 (see reference [9]).
In order to obtain the displacement in the blade due to bending moment, the later has to be calculated. Departing from the
differential bending moment on the blade, which can be expressed as dM = r⋅ dL, the bending moment along the blade takes
the following form:
M ( x ) = ∫ dM = ∫
R
x
R
x
C L ρ cω 2 ( x + r )
2
2
1
1
4
3
2
1
( R − x ) + x ( R − x ) + x 2 ( R − x ) 
8
3
4


rdr = C L ρ cω 2 
(3)
In figure 2 the variables of equation 3 are depicted. Hence, A < x < R.
Figure 2: Variables involved in the bending moment calculation.
Finally the displacement at the tip of the blade is calculated using the basic differential equation of the deflection curve:
v ( x) =
M ( x ) CL ρ cω 2  1
1  R 3 x 3 R 2 x 4 3Rx5 x 6  1  R 2 x 4 Rx 5 x 6  
6
=
R
−
x
+
−
−
− + 
−
+   + ax + b
(
)


∫∫ EI
3 6
4
20 30  4  12
10 30  
EI  240
(4)
The boundary conditions for a cantilevered beam are applied in order to determine the unknown constants a, b. After considering a
maximum radius of R = 1.1 m (A = 0,2 m, span = 0.9 m), a maximum chord length of 0.15 m, and a maximum deformation
(displacement at the tip/R) of 5%, the blade that minimizes the actuation at the smart actuator and carries a payload of 5 kg defines
as optimum, for 10º of cyclic pitch variation, a 0.9 m span blade with a 0.05 m chord length; the rotational velocity should be 650 rpm.
The closest commercial approximation to this optimal blade was found to be a carbon/epoxy blade with 0.06 m chord length and 0.81
m span. Thus, the rotational speed of the rotor should be increased to 750 rpm to achieve the same payload.
Design of Piezoelectric Actuators
The class of actuators used in the present work is based on the existing technology of bimorph actuators. In a simple bimorph
configuration two layers of piezoelectric material are attached on each side of an aluminium substrate ([5]), as shown in figure
3.a. By driving one element to expand while contracting the other one, the actuator is forced to bend, creating an out-of-plane
motion. The piezoelectric actuator has to perform two different actuation modes. By bending the actuator up and down by an
electric voltage (refer to figure 1) we will have a total control of the pitch. An oscillating bending will take care of cyclic control,
and the middle point in this oscillation will determine the collective pitch.
The design of the piezoelectric actuator is based on the mechanical work output that can be obtained, so that it can be high
enough to drive the pitch angle of the blade. The collective pitch control has quasi static characteristics since the pitch angle
that has to be provided is constant throughout the azimuthal movement of the blade. Thus the only force requirement from the
actuator is to overcome static friction that eventually exists in the system (aerodynamic loads are considered ideally zero for
the moment) and thus the mechanical output that the actuator has to provide is relatively small. On the other hand, the pitch
angle of the blade has to change dynamically with respect to its azimuthal position for the cyclic mode. As a consequence high
displacement and force actuation is demanded from the actuator and the work output requirements are highly increased. Using
equation 1 the maximum torque that has to be provided by the actuator to the blade is about 0.04 Nm for a peak-to-peak pitch
variation of 10º at 13 Hz actuation frequency.
a)
b)
Figure 3: a) Electrical connectivity for a parallel bimorph; b) Stacking sequence of the multilayered actuator.
Two parameters are of high importance to characterize a piezoelectric actuator: the maximum free displacement, which is
obtained when no force is applied on it, and the blocking force, which is attained when no displacement is permitted. If these
two limits are known, it is possible to know the actuator’s performance in all possible intermediate states since it is a linear
force/displacement relationship. The influence of the number of layers of piezoelectric material in the actuator’s performance
was studied with the methods that are presented in the following paragraphs. A simple bimorph structure was considered to be
too flexible with low resonance frequency and blocking force. Adding layers leads to the construction of much stiffer actuators.
However, testing of multilayered actuators showed that the increased actuation capacity due to the higher quantity of
piezoelectric material was cancelled out by the larger stiffness of the multilayered structure. Thus the optimum actuator was
found to be the one with 4 piezoelectric layers, 2 on each side of the aluminium substrate. The stacking sequence of the
actuator is depicted in figure 3.b.
For such a kind of actuator displacement and acceleration are in phase, which means that the maximum force output coincides
with the maximum displacement that the actuator must provide, and both determine the torque that can be applied by the
actuator. Due to construction restrictions, the maximum size of the actuator is limited to 0.07 x 0.05 m; nevertheless, the required
values of force and displacement output, which are calculated with the analysis methods explained next, cannot be achieved with
this actuator. The evident solution, which is to consider bigger actuators, was dropped and it was decided instead to investigate
the possibility of using the resonance characteristics of the system in order to increase the actuation capacity.
Analysis and Construction of Piezoelectric Actuators
The piezoelectric actuator is a thin plate structure (length/thickness > 50) and it is possible to use CLPT theory for its analysis.
A finite element CLPT model was developed for this purpose, as well as a coupled mechanics layerwise finite element solver.
The analysis results are compared with ANSYS and experimental results.
A full thermal-electrical-mechanical coupled formulation is used for the finite element CLPT and for the finite element layerwise
solvers. As it is shown in the work of [8] and [10] coupled formulation provides higher accuracy and must be considered
instead of equivalent strain approaches in order to model active materials. The formulation is shown in equations 5, 6 and 7.
σ i = Cij S j − eik Ek − λiθ
(5)
Dl = elj S j + ε lk Ek + piθ
(6)
ς = λi Si + pl El + αθ
(7)
where σi is the stress tensor, Cij is the elasticity tensor, Sj is the strain tensor, eik is the electromechanical coupling tensor, Ek is the
electrical field vector, λi is the thermal expansion tensor, θ is the temperature change, Dl is the electric displacement vector, εlk is
the electric permittivity tensor, pi is the pyroelectric tensor, ς is the entropy and finally α is the thermal dilatation tensor.
Based on this formulation, a linear 4-node plate element based on CLPT assumptions was developed and the corresponding
solver was implemented in Matlab. This solver was used to calculate both the maximum free displacement of the actuator as
well as the maximum blocking force. The layerwise solver was also explicitly developed for the analysis of smart structures.
The main difference with respect to the CLPT solver is that in a multilayer structure each layer is treated separately. In fact it is
a hybrid 3D theory where the integration in order to derive the stiffness matrix takes place in 2 stages and the in-plane and
through the thickness terms are decoupled. A finite element model was also created in Ansys using the Solid 5 coupled field
element for the representation of the active materials and the Solid 45 for the representation of the aluminium layer. It has to
be stressed out that in this case 3D mechanics are applied and thus in thin plates it is possible to have artificial stiffening. The
results for the different models are shown in table 1 and the force/displacement combinations depicted in figure 4.
Free Disp. (mm)
Bl. Force (N)
Res. Feq. (Hz)
Ansys
1.938
3.588
99.54
Layerwise
1.982
4.106
97.56
CLPT
2.143
2.793
83.14
Actual
2.327
3.198
97.96
Table 1: Free displacement, blocking force and first
resonance frequency for the studied actuator.
Figure 4: Force/displacements combinations for 240 V
actuation.
One can see clearly that all models are close to the predictions and agree with the experimental values as far as
displacements are concerned. However, this is not the case for the blocking force and this is due to the fact that the later
depends on the elastic properties of the material that are different for the 3D analyses and the CLPT analysis. The
experimental results and the first resonance frequency for the actuator show clearly that 3D theories are applicable and give
quite accurate results. Although the difference between experiment and 3D theories seems to be high for the blocking force,
finally this is not the case. In the FE analysis all the nodes of the free edge of the actuator are restricted and thus the blocking
force incorporates also the effect of the piezoelectric actuation in the transverse direction. The experimental procedure took
place using a load cell that pointed in the middle of the free edge of the actuator and as a consequence the effect in the
transverse direction is not measured. Additionally, the adhesive film was not included in the numerical analysis models due to
the fact that no reliable data for its properties were available, introducing one more possible reason for the discrepancy in the
blocking force.
Depolarization, together with the apparition of cracks due to fatigue problems, is the most severe problem that has to be
addressed in a piezoelectric actuator. The construction process helps to avoid it. The piezoelectric bimorph actuators are
constructed using continuous layers of PZT 5H material with dimensions 73 x 73 x 0.171 mm, which are cut to the desired
shape. The layers are attached using the Hysol 9689 adhesive film as well as conductive glue in order to have electrical
continuity. The middle aluminium foil acts as ground electrode. The curing of the adhesive film takes place at the temperature
of 177 ºC for one hour. Higher temperatures would lead to depolarization of the piezoelectric layers. Vacuum techniques are
used and a depression of 0.3 bar is applied throughout the whole procedure in order to reduce the amount of adhesive
material between the layers. For a width higher than 50 mm the material is not squeezed out homogenously, resulting in
actuators with thicker cross sections in the middle of their width. Due to the thermal expansion coefficient mismatch between
the PZT layers and the aluminium substrate, high compressive stresses are developed in the piezoelectric layers that
counteract the tensile stresses developed during actuation and reduce the risk of depolarization.
System Identification
The dynamic response of the actuators is essential considering possible resonance phenomena. The piezoelectric actuator
performing in resonance maximizes the amount of electrical energy that can be transformed to mechanical energy providing
the additional mechanical work that is necessary for the cyclic actuation. It can be seen in table 1 that its first natural frequency
is very high with respect to the operational frequency (12-13 Hz). However, when the actuator is coupled with the blade, this
frequency is dramatically altered. It is of particular interest to tune the connection between the actuator and the blade in order
to achieve the resonance in the desired frequency bandwidth. This is obtained by changing the free length of the actuator and
the point of attachment with respect to the axis of rotation of the blade (refer to figure 1.b).
A testing setup in order to perform the dynamic analysis of the system was elaborated. Using a PCMCIA input/output card
from National Instruments, a linear sinesweep signal that was generated in Matlab was transmitted to a high voltage amplifier
and finally to the piezoelectric actuator. The angle of attack of the blade was measured using a non conductive laser sensor
with a dynamic bandwidth up to 22 kHz. However, due to the fact that a rotational movement is measured using a linear
displacement device (a non contact LVDT), there is a small error that is introduced in the measurements. Taking into account
that the angle of the blade will never exceed 20º from peak to peak, the error remains small.
The system identification is necessary in order to consider in a later step a closed loop controller for the angle of attack of the
blade. It will be thus possible to eliminate any hysteresis imposed by the piezoelectric actuators or by the friction of the whole
mechanism, especially in collective actuation. At this stage the rotor is not put in rotation and thus the effect of centrifugal
forces could not be evaluated. However, the centrifugal stiffening imposed on the blades will be beneficial because it reduces
the undesired vibrations due to aerodynamic loading. As it will be shown later on, a flexible blade is susceptible to high
vibration amplitude even for low airspeed.
The linear sinesweep signal that was generated using Matlab Signal Processing Toolbox was then amplified by a gain of
30V/V and finally transmitted to the actuator. Different amplitudes were examined and the frequency sweeping was performed
in a time period of 10 seconds from 0 to 50 Hz. The sampling rate was set to 1 kHz. In figure 5 the signal sent to the high
voltage amplifier represented in the frequency domain is depicted.
Figure 5: Auto spectrum for the input signal.
The actuators used can safely handle signal amplitude of 240 V before depolarization occurs. Various amplitudes were
used for the sinesweep excitation starting from 30 V in order to avoid unexpected phenomena during resonance. In figure 6
the response of the blade-actuator system is presented for 60 V and 75 V of amplitude, showing clearly the resonance
around 13 Hz. In figure 7 the corresponding transfer functions of the system are presented, and in figure 8 the
corresponding phase shifting is depicted.
a)
b)
Figure 6: Sinesweep response of the system for a) 60 V and b) 75 V of amplitude.
a)
b)
Figure 7: Transfer functions for a) 60 V and b) 75 V of amplitude.
a)
b)
Figure 8: Phase shifting for a) 60 V and b) 75 V of amplitude.
It is evident that for any frequency between 11-15 Hz the actuation is maximized and this defines the rotational speed of the
rotor. The relatively low voltage actuation and the fact that piezoelectrics are excellent dampers reduce the risk of failure for
the actuators at resonance.
Although the transfer functions and the phase shifting diagrams look very similar for all levels of actuation, a closer look
reveals that above 30 Hz the output signal gets significantly distorted. The mechanism that transforms the bending actuation
into twisting of the blade is responsible for this response. Additionally the angle of attack reaches the maximum permitted
value by the support plate and this is shown in the truncation of the output signal of figure 6.b.
In figures 7 and 8 it is shown that for the frequency domain between 30 Hz and 50 Hz some unexpected amplitude and phaseshifting noise-like response occurs. This is attributed to tolerances in the assembly of the structure and not to electrical noise,
since a low pass filter has been applied during the signal acquisition.
It can be seen from these results that taking advantage of the resonance frequency, the actuation requirements for cyclic
control can be achieved at much lower voltages. This is an important parameter taking into account that the necessary
electronics to create high voltages are complicated, heavy and in many cases there is a fear of interference with other devices
when high voltages exist.
Aerodynamic Testing
The aerodynamic testing took place at the premises of Von Karman Institute. The structure was fixed in a wind tunnel with a
diameter of 4 m and maximum airspeed of 60 m/s. The setup is shown in figures 9.a and 9.b.
Figure 9: a) Aerodynamic setup; b) Detail of the encoder for the measurement of the angle of attack.
The only difference with respect to the static testing procedure is that the voltage and current that are sent to the actuator after
amplification are measured too. The airspeed just in front of the blade is also measured to investigate whether an eventual
oscillatory component of the airspeed would impinge on the blade and provoke fluttering or divergence phenomena. As it is
shown in figure 9.b, the angle of attack is measured directly using a rotational digital encoder and thus there is no linear to
rotation transformation error, as it would be the case with the laser LVDT.
The main issue of the testing course was the fact that the blade was fixed instead of rotating. In that case, the blade would benefit
from centrifugal stiffening, which would induce the shifting of its eigenfrequencies to higher values, avoiding resonance phenomena
that would initiate divergence. This is not the case in this testing setup. Already at 15 m/s of airspeed the blade bending vibration was
excessive and led to the initiation of an uncontrolled twisting moment that resulted to the destruction of a piezoelectric actuator. The
solution that was adopted was the attachment of very thin plastic threads at the free end of the blade and thus the bending of the
blade was dramatically reduced. These threads were put exactly at the aerodynamic centre. Eventually the divergence of the
structure was highly reduced and it became possible to continue with the testing procedure. However, as it will be shown in the next
paragraphs, this experimental setup imposed some restrictions on the performance of the blade.
First of all, the capability of the actuator to provide the necessary collective pitch angle was tested for several values of airspeed
and voltage amplitude. The sampling rate for both data acquisition and signal generation was set to 500 Hz. The duration of each
test was 30 seconds. The voltage profile sent to the actuator starts from zero, it goes up linearly to the desired value and it is kept
constant for 26 seconds, going back to zero linearly within a time frame of 2 seconds. This value was chosen to have a quasistatic loading condition and to monitor the hysteresis of the response of the piezoelectric actuator as well as its behaviour to the
friction of the system. The voltage profile for collective pitch angle control at -60 V is shown in figure 10.
Figure 10: Voltage profile for collective pitch angle control at -60 V.
At airspeed close to 20 m/s the structure was put in resonance due to the first bending mode that induces a twisting vibration
as well. The amplitude of this vibration depends mostly on the piezoelectric actuator; when it is not actuated with a certain
voltage, it is a passive element that works in open circuit conditions and thus it can provide a certain amount of damping.
However, the most important parameter was proved to be its free length from the support to the attachment point in the cams.
This parameter is responsible for the force/displacement trade off, the resonance frequency of the system and also for the
damping of the vibration of the blade. However, the control authority of the actuator was such that once actuated it managed to
cancel out the vibration and provide an additional (small) collective pitch angle. When this critical airspeed is surpassed, the
authority of the actuator is used for the twisting of the blade and not for its stabilization and thus higher values of collective
pitch angle are attained. The angles of attack are calculated using FFT techniques to filter out the measurement noise and
parasitic rotation due to aerodynamic phenomena. In figure 11.a the angle of attack profile for the whole procedure is depicted.
From similar graphs for various angles of attack, the values shown in figure 11.b were calculated.
a)
b)
Figure 11: a) Angle of attack profile for 150 V actuation and 38 m/s airspeed; b) Collective pitch angle for various airspeeds
and voltage actuation.
One can see in figure 11 that although the voltage at the end of the testing period goes back to zero, the angle or attack of the
blade does not follow precisely this input. The hysteretic behaviour of the PZT material, the friction of the system and the
aerodynamic loading (even though ideally it should be zero due to the symmetric profile) restrains the structure from reaching
the initial (zero) angle of attack. Future developments of this mechanism should be considered with a closed loop control
technology. The spikes shown in this figure are due to noise at the digital/analogue converter.
The cyclic pitch control capability of the actuator was examined as well under a variety or air stream velocities, frequency and
voltage actuation. The main issue for investigation was the way that resonance affects the cyclic pitch angle. The sampling
rate for data acquisition was set again to 500 Hz. The testing period was now shorter: 15 seconds were enough to evaluate
the dynamic characteristics of the structure. The airspeed ranged from 15-40 m/s and the voltage amplitude was in the range
of 30-240 V. The cyclic actuation frequency was between 5 and 12 Hz.
The majority of the tests were conducted for 60 V and 90 V of amplitude. Higher voltage amplitude, especially close to
resonance frequencies induced excessive twisting to the blade, resulting in stall and in divergence of the later. This
phenomenon was even more severe at higher airspeeds where the smallest imbalance could induce aerodynamic moments
around the axis of rotation. The voltage signal sent to the actuator is depicted in figure 12.a for a 2 seconds time interval.
a)
b)
Figure 12: a) Voltage sent to the actuator at 9 Hz, 90 V of amplitude and 31 m/s airspeed; b) Cyclic pitch angle for various
airspeeds and frequencies at 90 V.
From figure 12.b it is obvious that the airspeed has a significant impact on the cyclic pitch angle of the blade. The support at
the tip (thin threads) finally altered the dynamic characteristics of the blade. The difference in the resonance frequency as the
airspeed increases reveals exactly this influence. At 33 m/s airspeed the resonance frequency has dropped close to 6 Hz.
However, in realistic rotational conditions, the inverse trend is expected due to the centrifugal stiffening. Nevertheless, it is still
possible to see from this figure that the angle of attack that the actuator can provide is influenced by the airspeed; yet the
impact is not dramatic if we also consider the actuation losses due to the support at the tip of the blade.
What is of particular interest in the case of cyclic actuation is the energy consumption of the piezoelectric actuator. More
specifically the profile of the electrical current supplied to the piezoelectric actuator shown in figure 13 can be used for the
calculation of the energy consumption. The electrical current waveform reveals the electrical energy requirements of the
actuator in order to produce work and the way it reacts to external loads (aerodynamic, inertial, etc.). As a result, the current
does not follow the same waveform as the voltage input.
Figure 13: Current sent to the actuator at 9 Hz, 90 V of amplitude and 31 m/s airspeed.
From the FFT analysis of the current and voltage profiles and performing the necessary calculations, the energy consumption of the
actuator and the phase between the voltage and the current were calculated. This type of analysis revealed that indeed the
resonance and antiresonance frequencies of a piezoelectric actuator can be very close. This narrows the optimum area of actuation.
The energy consumption shown in figure 14.a incorporates the reactive part as well. It is evident that the higher the actuation
frequency, the higher the consumption of the actuator, but through the phase shifting it is possible to see what is the amount of
energy transformed into mechanical work. Although figure 14.b shows a trend for the phase shifting, it is evident that more
points would help to identify better the performance of the actuator. However, we see that after the resonance frequency the
phase goes to negative values influencing the amount of mechanical work that the actuator can perform.
a)
b)
Figure 14: a) Energy consumption of the actuator; b) Phase shifting at 31 m/s airspeed and 90 V amplitude actuation.
Conclusions
The main target of the present work is to give an overview of the design, construction and testing of a complete system for the
cyclic and collective control of a UAV helicopter blade. Finite element methods were used in order to design the actuators in
terms of displacement and blocking forces. The design elaborated for the support of the actuators helped to reduce the loads
that pass to them, reducing at the same time friction and thus maximizing the performance of the actuator.
Static and aerodynamic testing have been performed, revealing some interesting characteristics of bimorph multilayered actuators.
The feasibility of the concept has been proved, although modifications are necessary in order to be flightworthy. Taking advantage of
the resonance of the system, it is feasible to obtain actuation amplification for cyclic control. Finally, some of the energy
transformation aspects of the piezoelectric actuators showed the significance of resonance frequencies for mechanical actuation.
Acknowledgments
The authors of the present work would like to thank Dr. Jean Marie Ndambi Mulambula as well as the manufacturing division of
the Mechanics Department of the Royal Military Academy. Finally the help of the personnel of Von Karman Institute and
especially the aid of Mr Vincent Van der Haegen is greatly acknowledged.
The present work is taking place in the framework of the MX-04 research project financed by the Belgian Ministry of Defence.
This support is greatly appreciated.
References
1.
Butter Andreas, Breitbach Elmar, Adaptive blade twist-calculations and experimental results, Aerospace Science
Technology, vol. 4, 2000, pp. 309-319
2. Bernhard Andreas, Chopra Inderjit, Development and hover testing of a smart trailing edge flap with a piezo-induced
bending-torsion coupled actuator, American Helicopter Society National Technical Specialist’s Meeting on Rotocraft
Structures, Williamsburg, Virginia, October 30-November 2, 1995, pp. 107-137
3. Bernhard Andreas, Chopra Inderjit, Development of a smart moving blade tip activated by a piezo-induced bending-torsion
coupled beam, SPIE proceedings, vol. 2717, pp. 63-79
4. Chen Peter, Chopra Inderjit, Induced strain actuation of composite beams and rotor blades with embedded piezoceramic
elements, Smart Materials and Structures, vol. 5, 1996, pp. 35-48
5. Barrett Ron, Frye Phillip and Schliesman Michael, Design, construction and characterization of a flightworthy piezoelectric
solid state adaptive rotor, Smart Materials and Structures, vol. 7, 1998, pp. 422-431
6. Barrett Ron, Aeroservoelastic dap missile fin development, Smart Materials and Structures, vol. 2, 1993, pp. 55-65
7. Barrett Ron, Active plate and wing research using EDAP elements, Smart Materials and Structures, vol. 1, 1992, pp. 214226
8. Giannopoulos Georgios, Vantomme John, A fully thermoelectromechanicaly coupled FE analysis for the dynamic behavior
of smart plates using discrete layer kinematics, Proceedings of the 12th SPIE International Symposium on Smart Materials
and Structures, 6-10 March 2005, San Diego, CA, USA
9. Carpenter P.J., Lift and profile-drag characteristics of a NACA 0012 airfoil section as derived from measured helicopterrotor hovering performance, National Advisory Committee for Aeronautics, Technical Note 4357, 1958
10. Saravanos D.A., Heylinger Paul R., Hopkins Dale A., Layerwise mechanics and finite element for the dynamic analysis of
piezoelectric composite plates, International Journal of Solids and Structures, vol. 34, no. 3, pp. 359-378