Journal of Intelligent Material Systems
ÓThe Author(s) 2018
Article reuse guidelines:
Development, manufacturing, and
validation of a dielectric elastomer
membrane actuator–driven contactor
, Filomena Simone
, Gianluca Rizzello
and Stefan Seelecke
Dielectric elastomers represent a relatively new technology with high potentials for actuators’ applications. Thanks to
their lightweight, fast operations, energy efficiency, low power consumption, large deformations, and high scalability,
dielectric elastomers permit to develop novel mechatronic systems capable of overperforming standard actuation tech-
nologies, such as solenoid valves, in several applications. This article presents a novel design for a dielectric elastomer–
driven actuator system which enables closing and opening of a contactor. The design is based on a combination between
circular out-of-plane dielectric elastomer membranes and a bi-stable biasing system which allows to increase the out-of-
plane stroke. Characterization of the contactor is initially performed in order to establish the actuator requirements in
terms of force and stroke. Then, systematic design and manufacturing are carried out for both dielectric elastomer
membranes and biasing mechanism. Finally, the effectiveness of the actuator in closing and opening the contactor is vali-
dated experimentally. The results show comparable dynamic performance to a conventional electromagnetic drive, with
the additional advantage of a significantly lower energy consumption.
actuator design, actuators, circular out-of-plane dielectric elastomer actuator, contactor, dielectric elastomer, dielectric
electroactive polymer, membrane actuator, negative-rate bias spring, smart materials
One of the most recent technologies enabling light-
weight, compact, and energy-efficient mechatronic sys-
tems is represented by dielectric elastomer (DE)
transducers (York and Seelecke, 2010). Unique features
of DEs include high speed (Brochu and Pei, 2010) and
noiseless operations (Anderson et al., 2012), as well as
large deformations, low energy consumption, high
energy efficiency, high flexibility, and low cost. A DE
consists of a dielectric film surrounded by compliant
electrodes on each side, as shown in Figure 1(a).
Materials commonly used as elastomers are natural
rubber, different VHB acrylics (Berselli et al., 2013;
Kofod et al., 2003), polyurethane, or silicone (Koh
et al., 2011; Shankar et al., 2007). The overall system
obtained by combining the dielectric film and the com-
pliant electrodes results into a flexible capacitor, whose
capacitance is given as follows
is the vacuum permittivity, e
mittivity of the material, and Aand zrepresent electrode
surface and membrane thickness, respectively. When the
membrane is stretched in-plane, Aincreases while z
decreases. In addition, the volume V=Az remains con-
stant due to the material incompressibility, so that
From equation (2), it is clear that the capacitance can
be uniquely related to the material state of deformation
Departments of Systems Engineering and Materials Science and
Engineering, Saarland University, Saarbru¨cken, Germany
Center for Mechatronics and Automation Technology (ZeMA) GmbH,
Saarbru¨ cken, Germany
Philipp Linnebach, Departments of Systems Engineering and Materials
Science and Engineering, Saarland University, Campus A5 1, 66123
Saarbru¨ cken, Germany.
(described in terms of either zor A). This principle can
be properly exploited to develop DE-based sensors
(Pelrine et al., 2004; York et al., 2013) and energy har-
vesters (Graf et al., 2014; Koh et al., 2011; Moretti
et al., 2015; Pelrine et al., 2001). In addition, it is also
possible to use DEs as actuators (Plante et al., 2007).
The operating principle of DE actuators (DEAs) is
reported in the following. If a high voltage (HV) is
applied to the electrodes, they are attracted toward
each other due to electrostatic forces. The resulting
compressive stress, known as Maxwell stress, leads to a
reduction in the thickness of the elastomer membrane
and to an increase in area due to the incompressibility.
This effect is shown in Figure 1.
The Maxwell stress s
can be quantified as follows
where Uis the applied voltage. Some promising proto-
types based on DEAs have been presented in literature.
Relevant examples include loudspeaker (Heydt et al.,
2006), Braille displays (Choi et al., 2004), optical
switches (O’Halloran et al., 2008), medical robots
(Carpi et al., 2009; Kovacs et al., 2007), pumps (Carpi
et al., 2010; Kobayashi and Smoukov, 2015; Pelrine
et al., 2008), valves (Hill et al., 2017), micro-positioners
(Hau et al., 2017), and grippers (Araromi et al., 2015;
Mccoul et al., 2017). As an additional feature, sensing
and actuation modes can be combined and performed
simultaneously, leading to a so-called self-sensing
device. By means of self-sensing, DE technology allows
to design highly compact mechatronic systems which
can operate in closed loop without requiring external
sensors (Rizzello et al., 2017).
DEAs represent the main focus of this article. For
such systems, a distinction is commonly made between
stack actuators (Bochmann et al., 2016; Kovacs et al.,
2009; Lotz et al., 2011; Reitelsho
¨fer et al., 2016), which
exploit the thickness change, and membrane actuators
(Hau et al., 2017, 2018b; Hill et al., 2017; Plante et al.,
2007; York et al., 2013), which generate a motion by
means of the surface expansion. In order to generate a
stroke, membrane DEAs must be combined with a pre-
stress mechanism, such as a mass or a spring. For these
actuators, the design of the biasing system turns out to
be of extreme importance for determining the overall
system performance (Hodgins et al., 2011).
The main objective of this article is to present design,
manufacturing, and experimental validation of a novel
membrane DEA used to drive a switch contactor.
Similarly to a relay, the switch contactor needs to be
opened and closed via an electrically driven system
which, in most of the cases, consists of a solenoid actua-
tor. A drawback of such a solenoid is represented by
the high-amount direct current (DC) required to keep
the switch closed, which results in large energetic losses
due to Joule heating. We have previously pointed out
that DE technology enables fast and low-power con-
suming actuation. These two features open up the pos-
sibility of using DEAs as a more energy-efficient means
to drive the contactor. Clearly, the strongly nonlinear
and rate-dependent response of DEs, as well as the
complexity introduced by the pre-stress mechanism,
makes the design of such systems a challenging task. In
this article, a design procedure is presented in order to
systematically address the design of both DEA mem-
branes and pre-stress mechanism. Afterwards, the
developed system is assembled and validated experi-
mentally. Finally, a performance comparison between
solenoid and DEA is presented.
The remainder of this article is organized as follows.
Experimental characterization of the commercially
available switch is presented in section ‘‘Switch contac-
tor analysis and characterization.’’ In section ‘‘DEA
concept,’’ the new actuator concept is illustrated, and
the design methodology is discussed. The resulting
designed parts are then manufactured and character-
ized in section ‘‘Manufacturing and characterization.’’
Subsequently, the computer-aided design (CAD) design
of the entire actuator is described in section
‘‘Actuator,’’ and the experimental validation of the
overall system is presented in section ‘‘Results.’’
Concluding remarks and future developments are
reported in section ‘‘Conclusion and outlook.’’
Switch contactor analysis and
In order to design an actuator for the switch contactor,
a prior experimental investigation is required. Such an
investigation is divided into two phases. The first step,
that is, the functional analysis, allows a comprehension
of the system behavior. Based on this knowledge, the
second step, namely, experimental measurements, can
be defined and carried out.
Overall system description
The contactor (model BC6 produced by ABB), shown
in Figure 2(a), can be divided into two different parts.
The lower part consists of the driving solenoid, which
Figure 1. Principle of the dielectric elastomer: (a) elastomer
with the electrodes and (b) effect of applied high voltage.
2Journal of Intelligent Material Systems and Structures 00(0)
has to be replaced by a DEA. The upper part includes
the principal system which has to be actuated.
A schematic view of the contactor is shown in
Figure 2(b). It consists of four connections (2) with
fixed contacts (1) on each side. A guided carriage is
located in the center part, on which the contact bridges
(3) are applied. In the state portrayed in Figure 2(b),
the solenoid is off and the switch is open. If a voltage is
applied to the solenoid, the lever arm rotates counter-
clockwise with respect to its pivot point, causing a
motion of the carriage to the left. While moving, the
carriage pushes the restoring springs (5) (depicted in
red) to a quasi-static intermediate configuration, as
shown in Figure 2(c). In this state, all the contacts close
almost simultaneously. When the system reaches this
state, the solenoid works against the four contact
springs (4) (depicted in yellow) and the two restoring
springs (5) (depicted in red) at the same time. The fully
closed contactor is shown in Figure 2(d).
When the voltage on the solenoid is switched off, the
compressed restoring springs push the carriage back to
its original position, thus opening the contacts and
restoring the initial configuration in Figure 2(b). The
most critical phase of the switch activation is the second
step (Figure 2(c)), that is, when the contacts are being
opened or closed. In fact, at this moment, the dielectric
strength of the air between the contact bridges and the
contacts itself cause an electric arc. According to data-
sheet, the contactor can manage voltages up to 690 V
(ABB, 2018), while the dielectric strength of the air with
flat electrodes is 3 kV/mm (Vedensky and Vul, 1965).
This means that when the contacts are open and the
space between them and the bridges is between 0 and
0.23 mm, a flashover occurs. To mitigate such electric
arc as much as possible, and to minimize its effects on
the contacts, the carriage must overcome this step at a
certain minimum speed.
To properly evaluate the system performance, the
three most critical parameters are represented by the
carriage stroke, the force required to close the switch,
and the velocity of the carriage while crossing the criti-
cal point. In addition, it is important to evaluate the
power consumption of the system in order to compare
its energetic performance with the ones obtained with
To determine all critical parameters established in sec-
tion ‘‘Overall system description,’’ two characterization
experiments are performed. The first test permits to
obtain the velocity and the system stroke and is con-
ducted by measuring the displacement of the carriage
by means of a laser sensor Keyence LK-G37. To inter-
face the laser with a personal computer (PC) and
acquire measurement data, a controller LK G300 1P
and a DAQ module NI 9205 are used. Voltage is
applied to the solenoid by means of a switch NI 9472
and a power supply HMC8042. The two NI modules
are connected to a PC by a NI cRio 9074. The data
acquisition is done with the integrated field-
programmable gate array (FPGA), while the user inter-
face is programmed and controlled via NI LabView
2014. The required post processing is performed with
MATLAB 2015. Figure 3(a) shows the displacement of
the carriage over the time. Two experiments are shown,
obtained by using a rated control circuit voltage (V
of U= 24 V (depicted in red, dashed line) and of
U= 14 V (depicted in blue, solid line), respectively.
Starting from these plots, the exact position of the
critical point (x
= 1.9 mm) and the entire system
= 2.7 mm) can be determined. In addition,
the velocity at the critical points can be calculated.
These results are shown in Figure 3(b) and (c). The
operation limit of the solenoid DC supply ranges
between 20 V (83% of V
) and 26 V (108% of V
according to the datasheet of the device. Under these
conditions, the velocity for the closing phase ranges
between 384 and 583.3 mm/s depending on the voltage
value. The speed to open the contacts mainly depends
on the restoring springs, which push the system back
when the solenoid is no longer activated. However, the
residual magnetization phenomena, occurring when
removing the voltage from the solenoid, results in a
Figure 2. (a) Picture of the contactor, (b) contactor completely open, (c) contactor in a quasi-static position in the middle, and (d)
switch completely closed.
Linnebach et al. 3
small variation in opening speed between 348.4 and
362.1 mm/s. This happens because the magnetizing cur-
rent follows the voltage with a delay, resulting from the
dynamics of the corresponding RL circuit. The higher
the voltage, the smaller the time necessary to reach the
current value which produces a sufficiently large mag-
netic field. This is in agreement with the obtained
results (Figure 3(c) and (d)).
The instantaneous power consumption P, based on
the current measurements shown in Figure 3(d), is then
calculated for each voltage value. The energy E
sary to hold the switch in closed position for 1 min is
calculated as follows
where iis the current. The resulting energy is
= 190.2 J.
For the second test, which aims at measuring the
force, the experimental bench is supplemented by a lin-
ear actuator Aerotech ANT-25LA and a load cell
FUTEK LSB200-5lb, as shown in Figure 3(f). The lin-
ear actuator permits to move the carriage and measure
the blocking force at the same time. The results are
shown in Figure 3(e), in which x
reported. Different regions can be observed in this
characteristic, namely, a first linear part (corresponding
to restoring springs), a second steep part, (during which
the contacts are closing), and a second linear part
which comprises both restoring and contact springs
(therefore, it is stiffer than the first linear part). Note
that the second part of the curve is significantly steeper
than the other two ones. This is due to the fact that
when the bridge is closed, the pre-compression of the
Figure 3. (a) Displacement versus time for a step voltage applied on the solenoid. (b) Velocity at critical point versus voltage in %
of Vcc, closing phase. (c) Velocity at critical point versus voltage in % of Vcc, opening phase. (d) Current versus voltage in % of Vcc.
(e) Force needed to close the contactor, as a function of the carriage position. (f) Sketch and photo of the test stand to measure the
Figure 4. Sketch of COP-DEA: (a) flat DEA, (b) deflected DEA, (c) COP-DEA with a pre-stress mechanism, and (d) the application
of a voltage to the pre-deflected mechanism produces a controllable stroke.
4Journal of Intelligent Material Systems and Structures 00(0)
contact springs produces an abrupt change in force.
Since four contact springs exist, the total force is given
by the sum of each spring. We point out that for an
ideal system, all the spring would close at the same
time, resulting in a step jump in the force–displacement
characteristics. However, due to construction toler-
ances, the four contact bridges do not close exactly at
the same time and with the same pre-compression. This
has the effect of producing a large finite slope, rather
than an infinite one, in correspondence to the bridge
The actuator system used to replace the solenoid valve
is based on a circular out-of-plane dielectric elastomer
actuator (COP-DEA). In literature, these actuators are
commonly referred to as cone (Plante et al., 2007) or
diaphragm (Dastoor and Cutkosky, 2012) DEAs. A
sketch of the COP-DEA is shown in Figure 4(a). It con-
sists of a circular DE silicone membrane encapsulated
within a rigid frame (depicted in orange). External
frame and internal disk are made of a rigid passive
material. The ring-shaped electrodes (depicted in black)
are applied on the silicone foil via screen printing.
When an external force is applied perpendicularly to
the central disk, the membrane deflects out-of-plane as
shown in Figure 4(b). In order to generate a stroke with
the COP-DEA, a pre-stress mechanism has to be used
to produce an out-of-plane preloading force. The com-
bination between biasing system and COP-DEA defines
the overall actuator system. Figure 4(c) and (d) shows
the operating principle of such an actuator system.
When an HV is applied, the out-of-plane stiffness of
the DE decreases as a result of the Maxwell stress.
Consequently, the force of the biasing mechanism
pushes the membrane upward to a new equilibrium
position, generating a controllable motion. Typically,
the pre-stress mechanism used for COP-DEAs consists
of a linear biasing spring (LBS). In the work presented
in this article, however, a negative-rate biasing spring
(NBS) is also included in the overall design. Thanks to
the LBS-NBS combination, both stroke and velocity of
the actuator can be significantly improved (see Berselli
et al., 2011; Hodgins et al., 2011; Wingert et al., 2006;
York et al., 2010 for further details).
By exploiting the actuation principle described
above, it is possible to replace the solenoid drive of the
switch contactor with a DEA. The resulting system is
shown in Figure 5(a). The DEA element consists of a
stack of COP-DEAs mechanically connected in paral-
lel, which allows to amplify the actuation force. Note
that differently from the original design in Figure 2, no
lever mechanism is used for the DEA. In the upper
configuration in Figure 5(a), no voltage is applied and
the COP-DEA holds the contactor in the open
position. In this state, the pre-stress mechanism is in
tension. If HV is applied, as shown in the lower part of
Figure 5(a), the DEA becomes softer and the springs
push the DEA, closing the contactor. When the HV is
Figure 5. (a) Driving principle of the overall system for LV
(upper part) and HV (lower part). It consists of the contactor
on the left-hand side, and on the COP-DEA, the NBS and the
LBS on the right-hand side. Tunable parameters are also shown.
(b) Forces acting on different components. (c) Graphical
criterion for force equilibrium.
Linnebach et al. 5
removed, the stiffness of the membrane increases again,
allowing the restoring forces of the springs to open
again the contactor.
To design the actuator, a force analysis of the whole
system is required. Free-body diagrams of rigid parts
of the system are shown in Figure 5(b). Force F
the measured force of the contactor, which is a given
design curve. The other three forces, namely, F0
, and F
, are internal forces of the actuator itself
and describe DEA stack, LBS, and NBS, respectively.
By considering equilibrium among these forces, it is
possible to perform a proper design of DEA, LBS, and
NBS in order to successfully operate against the con-
tactor. In particular, at equilibrium we have
Fcon =FLBS +FNBS FDEA ð5Þ
DEA cos að6Þ
is the component of the elastomers’ stack force on the
direction of motion. Note that F
depends on the
applied voltage; therefore, the system equilibrium posi-
tion can be modified upon the activation of the DEA.
To let the system correctly operate against the switch,
, and F
in equation (5) have to be
designed in such a way the equilibrium states for low
voltage (LV) and HV occur at positions corresponding
to open and closed state of the switch, respectively.
To adjust the force characteristics of DEA stack and
springs, two possibilities are given. On the one hand, it
is possible to manipulate geometrical parameters D1,
D2, and D3 shown in Figure 5(a), to change relative
positions (and thus pre-compressions) of the different
elements. On the other hand, one can also adjust the
intrinsic characteristics of each individual part of the
system. More specifically, the parameters for F
the stiffness and the pre-stress, while the parameters for
are the pre-compression of the beam springs, the
thickness, the beam width, and the material (for more
details on the NBS manufacturing, one can refer to
Hau et al., 2018b). For the COP-DEA, the design para-
meters are the inner diameter and the outer diameter,
as well as the number of layers in the stack. In fact, by
adjusting the above-mentioned parameters, the force
profile of the contactor can be fitted into the actuator
characteristics (Hau et al., 2015). Using measured
force–displacement characteristics of the springs, and
an available material model which permits to estimate
given the membrane geometry, the applied vol-
tage, and the number of layers (Rizzello et al., 2015), a
preliminary model-based design is performed (details
on the model are omitted for conciseness). The results
are shown in Figure 5(c), in which the intersections
between contactor and additional forces occur in corre-
spondence to the closed and open positions. According
to this design, 26 COP-DEA layers are required, whose
inner and outer diameter are fixed at d= 13.1 mm and
D= 21 mm. We also point out that the calculations
do not take into account the rate-dependent hysteresis
; therefore, it is expected that such performance
holds at steady state only.
Manufacturing and characterization
Manufacturing and characterization of each individual
part of the actuator system, namely, DEA membrane
and springs, are presented in this section.
The COP-DEA used in this work consists of a 50 mm
silicone film (ELASTOSIL
FILM 2030), two flexible
electrodes, and the frame material which handles it (see
Figure 6(a)). The electrodes are made of a carbon–
silicone mixture, while the frame is made of epoxy.
Manufacturing is performed via screen printing (Fasolt
et al., 2017). To optimize overall size, the COP-DEAs
are designed in modules, each one containing a double-
layer (DL) DE membrane (see Figure 6(a); Hau et al.,
2018b). To obtain these modules, the actuator is manu-
factured with two distinct outer electrodes and a unique
inner electrode, which is shared by both layers (Figure
6(a)). This process allows to reduce thickness of the
COP-DEA stack, since less frame material has to be
used (note that the frame represents the thickest part of
a DL module). Design of DL DEAs, however, poses
some practical challenges concerning reliability of elec-
trical connection of each membrane in the stack, in
particular for the inner electrode. On one hand, the
Figure 6. COP-DEA design, processing, and manufacturing: (a)
screen-printed parts, (b) electrical connection, (c) picture of the
final COP-DEA, and (d) CAD model of the final COP-DEA.
6Journal of Intelligent Material Systems and Structures 00(0)
connections should not increase the overall thickness
significantly. On the other hand, reliability of connec-
tions has to be ensured.
To meet these requirements, two recesses are carried
out at one side of the frame in Figure 6(a). Through
this hole, the outer electrode can be set in contact with
a copper strip. To ensure contact for the inner electrode
as well, a further copper strip is attached directly to the
inner side on the electrode. When folding as shown in
Figure 6(b), the inner connection fits into the other
recess in the frame. Both strips are fixed with a custom-
developed conductive glue, based on epoxy. The corre-
sponding CAD design of the resulting DL COP-DEA
system is shown in Figure 6(d), while a picture of the
device is reported in Figure 6(c).
Unavoidable inaccuracies in the manufacturing pro-
cess described so far, combined with material inhomo-
geneities, could cause a malfunctioning of the COP-
DEAs. Therefore, preliminary evaluation tests are con-
ducted after manufacturing in order to assess the correct
operation of the devices. The main failure mechanism of
the membranes is represented by the electrical break-
down induced by the high electrical field. Thus, the
easiest test to evaluate system functioning consists of
applying to the undeformed DEAs the maximum elec-
tric field they will undergo under standard operations.
The electric field can be calculated according to the fol-
lowing equation (Rizzello et al., 2015)
In equation (7), Eis the electric field, Uis the applied
voltage, xis the out-of-plane deflection of the mem-
is the difference between outer and inner radii
of the membrane, while zand z
are the thickness of the
undeformed and deformed membrane, respectively.
From equation (7), it can be noted how the electric field
increases with both Uand x; therefore, the highest
value of Eoccurs, and then, the membrane is loaded at
maximum voltage and is deformed with maximum
deflection. By evaluating equation (7) for voltage
U= 2.5 kV and deflection x= 3.2 mm, correspond-
ing to maximum load conditions for the systems design
in Figure 5, one can obtain the maximum electric field
E= 92.6 V/mm, which will be applied during standard
operations. Then, by inverting equation (7), the voltage
corresponding to maximum electric field (by also
including an additional safety factor of 5%) and an
undeformed membrane configuration (i.e. x=0) is
calculated. The resulting voltage U= 3.38 kV is then
used to test the undeformed membranes to evaluate
their ability of sustaining the critical electric field with-
out actually deforming them. Since DEs behave as
capacitors, the voltage has to be applied with a con-
stantly increasing rate in order to avoid current spikes.
In the conducted experiments, the voltage increasing
rate is chosen in such a way the maximum value of
3.38 kV is reached in 1 s. In normal conditions, the cur-
rent should have a small positive peak during charging
and a negative peak during discharging. If the DEA is
damaged, the voltage collapses and the current rises to
the limit of the voltage source because of a short circuit.
These phenomena make it easy to detect defective mem-
branes and thus discard them. After completing DEA
manufacturing and evaluation, experimental characteri-
zation is performed. To measure the force–displacement
characteristics, a general test bench is assembled. A host
PC is connected and interfaced with a linear motor
(Stable Micro Systems) and an NI cRio9076, which
contains an NI9237 module, used to read data from a
load cell FUTEK LCM300-50lb, and a NI9205 mod-
ule, used to read data from voltage and the current
monitors of the power supply Ultravolt 4HVA24P1.
The linear actuator is built according to a gallows-
shaped design. It contains a test platform for fixing
the parts to be tested. Behind a vertical linear guide is
arranged, on which the gallows can move. At the top
of this moving part, the load cell is fixed via two
threads between the actuator and the adapter to the
DEA or the NBS. Displacement is recorded via a laser
sensor Keyence LK-G37. Finally, a NI9401 module is
used to enable the power supply and a NI9263 module
permits to supply the required voltage. Data acquisi-
tion is performed by the FPGA module in the cRio.
Programming is done in LabView 2014 and post pro-
cessing in MATLAB 2015. The test bench is shown in
Figure 7(a), for COP-DEA on the left-hand side and
NBS on the right-hand side, respectively.
For characterizing a COP-DEA, the frame is kept
fixed, while a linear motor is used to deflect out-of-
plane the rigid center inclusion of the membrane,
and the force is measured at the same time with the
load cell. Figure 7(b) shows the measured force–
displacement curve of one DL module, obtained at
constant speed of 1 mm/s for different constant vol-
tages. Figure 7(c) shows the maximum forces at the
maximum displacement as functions of the applied
voltage. A quadratic trend is observed and can be
explained by recalling the Maxwell stress in equation
(3). In fact, due to the incompressibility of the DE
material, the Maxwell stress which squeezes the mem-
brane along its thickness produces an equivalent
expansive stress along the in-plane direction. This
expansive stress has the effect of reducing the mechan-
ical in-plane force for the same radial strain, thus
leading to a reduction in the measured out-of-plane
force as well. Since the in-plane expansive stress is still
given by equation (3) (Rizzello et al., 2015), the result-
ing decrease in mechanical force is a quadratic func-
tion of the applied voltage, in agreement with the
observation in Figure 7(c). The HV is fixed at 2500 V,
and the LV is defined as 0 V. These measurements are
Linnebach et al. 7
repeated for stacks having a different number of DL
DE membranes, and the results are reported in Figure
7(d). The diagram nearby, in Figure 7(e), shows the
blocking force at a deflection of 3.5 mm for both LV
and HV. It is expected that the force increases linearly
with the number of DL DE membranes, since they are
mechanically connected in parallel. The small devia-
tion with the linear cases is mainly due to tolerances
in manufacturing and assembly.
The NBS is made out of stainless steel, manufactured
via laser cutting, having a thickness of 0.004 in and a
beam width of 2.5 mm. After cutting, the NBS is
buckled into a three-dimensional (3D)-printed frame
with 96% compression. In this assembly, the spring ele-
ment has two stable configurations which are separated
by an unstable one. Nearby unstable equilibrium, the
NBS exhibits a negative local stiffness.
To characterize the NBS, the same test bench
described for the COP-DEA is used. The linear motor
displaces the spring, while its force is measured. The
test is done multiple times with different number of
NBS in a stack, and the results are shown in Figure
7(f). The displacement of different stacks is nearly the
same, while the force increases linearly with the num-
ber of NBS. As a result, the negative stiffness in the
middle of the force characteristics increases linearly
In this work, a commercially available LBS is used.
Since the stiffness is available from the datasheet of the
component, no characterization test is required.
After characterization of all forces in equation (5), the
actuator design is performed once again with the DEA
measured data, rather than using a model. To perform
the new design, we rewrite equation (5) as follows
Fcon +FDEA =FLBS +FNBS ð8Þ
Equation (8) has the advantage that forces on each side
of the equation have the same sign, making the graphi-
cal design more intuitive. The design of the actuator is
done in MATLAB 2015, and the result is seen in Figure
7(g). All for the manufacturing relevant parameters for
the actuator are reported in Table 1.
The number of needed COP-DEAs is designed with
the same procedure previously illustrated in Figure 5(c).
To describe F
, experimental force–displacement
curves are adopted instead of simulated ones. For this
design phase, outer and inner diameters are kept fixed,
while only the number of layers is varied. This is a con-
sequence of the fact that changing inner and outer dia-
meters requires a redesign of the COP-DEAs, while
Figure 7. Experimental characterization: (a) test bench for COP-DEA (right-hand side) and NBS on (left-hand side); (b) force–
displacement characteristics of one DL DEA for different applied voltages; (c) maximum force as a function of the voltage, for the
maximum displacement; (d) DEA force–displacement curves at different voltages, for different number of stacked DL; (f) maximum
stack force for low and high voltage as a function of the number of layers in the DEA stack, for a constant displacement of 3.5 mm;
(f) NBS force–displacement characteristics, for a different number of stacked elements; and (g) final design of the actuator.
8Journal of Intelligent Material Systems and Structures 00(0)
changing the number of layers is simply performed by
stacking different elements. In addition, it is expected
increases proportionally to the number of
layers, so this effect can be predicted and used as a
design parameter. The overall number of layers turns
out to be higher in comparison to the preliminary
design based on material model in Rizzello et al. (2015).
This is due to small model inaccuracies and additional
hysteresis due to the 3D printed material, as well as
errors resulting from the viscoelastic hysteresis of the
COP-DEA, which is not considered in the graphical
design method. For these reasons, after graphical
design is performed, an additional fine tuning of LBS
and NBS pre-compression has to be performed.
In Figure 7(g), it is also shown that the actuator does
not allow to perform the complete stroke, due to the
hysteresis of the COP-DEA. Theoretically, it is possible
to arbitrarily stack more DEs to increase the actuator
force. Nevertheless, this further design optimization
goes beyond the scope of this article, and therefore, it is
To investigate the actuator performance, the system
shown in Figure 8(a) is assembled. Pictures of the test
rig used to measure the actuator characteristics are
shown in Figure 8(b) and (c). Results of actuator char-
acterization are shown in Figure 8(d) and (e). In each
case, a different external load is considered. In particu-
lar, in Figure 8(d), the external load is the force of the
contactor, while in Figure 8(e) the system works with-
out any external load. In both configurations, hard
stops are placed on the left-hand side and also on the
right-hand side for the lower configuration only. The
left hard stop is a part of the actuator design itself
(Figure 8(a)), while the right one is an external
As it can be seen, a stroke of 1.8 mm is expected
from both systems. At first, the configuration without
external load is tested and is shown in Figure 9(a). The
hard stop can be clearly seen in Figure 9(b). The displa-
cement is measured via a laser sensor Keyence LK-
G37, and the voltage is applied by a Trek model 610E.
The current is measured by the monitor output of the
power supply. The signal consists of two steps from LV
to HV with the frequency of 0.5 Hz. The resulting cur-
rent is shown in Figure 9(d) and the displacement in
Figure 9(e). A stroke of 1.8 mm is measured, as
The system velocity, obtained by direct differentia-
tion of measured displacement, is shown in Figure 9(f).
The maximum speed reached by the actuator when HV
is applied amounts to 524.2 mm/s, while the velocity
during deactivation equals 147.2 mm/s only. By com-
paring velocity with measured current and voltage, it
can be observed that the speed depends on the time at
which the desired voltage is applied, that is, the dura-
tion of the ramp during voltage charging/discharging
phases. Thus, the actuator speed is strongly related to
the maximum current which can be provided by the
amplifier, since for a capacitive load it is directly related
to the voltage time derivative. In our case, the maxi-
mum current of the amplifier equals 2 mA.
The second test is performed by letting the actuator
work against the contactor. This design is shown in
Figure 10(a) and (b). The voltage signal is the same as
in the previous case (Figure 10(c)). The measured dis-
placement in Figure 10(e) is as expected. By differen-
tiating the displacement measurements, velocity is
calculated and shown in Figure 10(f). The obtained
speed equals 410.2 mm/s and is above the minimum
required value of 384 mm/s. The velocity to open the
contacts, however, equals 149 mm/s and is the half of
the required one. Finally, energy consumption of the
system is reported in Figure 10(g). The actuator
= 0.06 J to load the DEAs, and after
Table 1. Construction parameters.
Symbol Quantity Value Unit
COP-DEA DOuter diameter 21.1 mm
dInner diameter 13.1 mm
Distance between DEA and NBS 5.2 mm
No. of DL 40 pcs.
LBS kStiffness 1.53 N/mm
Pre-strain 12.75 mm
NBS eEdge length 25.4 mm
bBeam width 2,5 mm
tThickness 0.004 in
cCompression 96 %
No. of NBS 7 pcs.
Material Stainless steel
LOAD D1Distance between load and NBS 66.5 mm
Relevant parameters for the construction and design of the overall system are presented.
Linnebach et al. 9
that, it requires only a power of P
= 0.015 W to
hold the contacts closed. Theoretically, the power
consumption at steady state should be zero for a capa-
citive load. However, the non-zero value reported in
our experiments is a consequence of the unavoidable
current leakage. Energetic performance of the DEA is
then calculated by testing the system in similar settings
with respect to the solenoid case, that is, the position is
closed for a time of 60 s. The resulting energy equals
= 0.96 J. Compared with the value obtained for
the solenoid, namely E
= 190.2 J, it can be deduced
that the DE enables to save about 99.5% of the energy
Figure 8. (a) CAD design of the whole system, (b and c) test
rig used to measure the actuator characteristics, (d) actuator
performance when operating against switch contactor, and (e)
actuator performance with operating with no external load.
Figure 9. Actuator performance without external load: (a and
b) pictures of the system, (c) applied voltage, (d) measured
current, (e) measured displacement, and (f) calculated velocity.
10 Journal of Intelligent Material Systems and Structures 00(0)
used for the solenoid. The energy saving can be eventu-
ally increased up to 99.9% if the dissipation occurring
during transients occurring in contactor opening/
closing phases is reduced, for example, by means of
optimal control strategies.
The results in terms of operating speed and energy
consumption are summarized in Table 2.
In order to increase the speed, a voltage source with
a higher maximum current has to be used. This is neces-
sary in order to charge the COP-DEA stack, which is a
capacitive load, as fast as possible. The faster the charg-
ing phase, the higher the speed that can be achieved.
Conclusion and outlook
This article has presented the development of a novel
actuator system based on DE technology, to replace a
solenoid-based valve for an electric contactor. Several
issues related to design, manufacturing, contacting dur-
ing stacking, quality testing, and characterization of
DEA have been discussed in detail. A systematic
method has also been proposed in order to design DE-
based system operating against external forces, based
on a graphical criterion.
Several experimental results have shown how the
developed actuator can produce high deformations at
high speed and, most importantly, permits to drive the
system with a very low power consumption. In particu-
lar, DEs permit to accomplish the same actuation task
of a solenoid by requiring only the 0.5% of the energy
needed for the latter. The developed system, however,
does not allow to achieve the same speed of the sole-
noid, especially during the closing phase. Nevertheless,
this issue can be potentially addressed by adopting more
efficient power supplies capable of charging the mem-
brane faster, that is, with a higher amount of current.
In future research, different design solutions for the
membrane actuators will be considered, for example,
the configuration presented in Hau et al. (2018a), in
order to increase stroke, force, and velocity without
increasing the size. To make the overall system faster
and more compact, the driving electronics needs to be
optimized in terms of output power and size, as well as
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of this
Figure 10. Actuator performance when operating against the
switch contactor: (a and b) Pictures of the system, (c) applied
voltage, (d) measured current, (e) measured displacement, (f)
calculated velocity, and (g) calculated energy consumption.
Table 2. Performance comparison between solenoid actuator
Solenoid COP-DEA Unit
Operating speed Closed 384 410.2 mm/s
Open 348.4 149 mm/s
Energy consumption to hold
the contactor closed for 60 s
190.2 0.96 J
Linnebach et al. 11
The author(s) disclosed receipt of the following financial sup-
port for the research, authorship, and/or publication of this
article: The authors would like to thank ABB AG Corporate
Research Center Germany for financial support of this work.
Philipp Linnebach https://orcid.org/0000-0002-5184-660X
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