-
a Engineering Laboratory for Detection, Control and Integrated
Systems, Chongqing Technology and Business University,
Department of Mechanical Engineering, University o
a r t i c l e i n f o
Article history:Received 24 November 2013Received in revised
form1 March 2014Accepted 8 April 2014Handling Editor: D.J.
WaggAvailable online 3 May 2014
cks and to dampin automobiles,ructural material
[3], dry friction [4], fluid friction [5] and magnetic effects
[6] has been used by the absorbers for damping shock impulses.
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/jsvi
Journal of Sound and Vibration
Journal of Sound and Vibration 333 (2014)
390439160022-460X/& 2014 Published by Elsevier Ltd.
http://dx.doi.org/10.1016/j.jsv.2014.04.020
n Corresponding author. Tel.: 1 613 562 5800x6269; fax: 1 613
562 5177.E-mail address: [email protected] (M. Liang).Hydraulic
shock absorbers are capable of yielding greater damping force
mainly by means of fluid friction, and are reliable to1.
Introduction
Shock absorbers, sometimes also known as dampers, are mechanical
devices designed to smooth out shovibrations [1]. As one of the
basic mechanical components, the shock absorber has been widely
usedmotorcycles, wheeled or tracked vehicles, aircrafts, as well as
some industrial machines [2]. Hysteresis of stis tuned to 7.5
.& 2014 Published by Elsevier Ltd.performance has been
characterized based on the experimental results from three testf
Ottawa, Ottawa K1N 6N5, Canada
a b s t r a c t
Hydraulic shock absorbers have been widely used to dissipate
kinetic energy of the shocksinto surrounding environment. By
employing oscillatory motion to drive power generator,the shock
energy can be converted into electricity for harvesting. However,
the frequentbidirectional oscillation of the generator can cause a
large impact force. This further leadsto deteriorated energy
harvesting performance, moving parts fatigue, and even
systemfailure. As such, this study introduces four check values to
form a hydraulic rectifier tointegrate the shock absorption and
energy harvesting functionalities. The bidirectionaloscillation of
the shock and the vibration is converted into unidirectional
rotation to drivethe generator. Following the proposed concept, a
prototype energy-harvesting shockabsorber has been designed and
fabricated. An electromechanical model has also beendeveloped to
examine the response behavior of the prototype device. The
prototype
setups. Both mechanical and electrical parameters of the
electromechanical model havebeen identified based on our cyclic
loading experiments. The results have shown that thedeveloped
energy-harvesting shock absorber is capable of harvesting the
energy andabsorbing the shock simultaneously. In our experiments, a
maximum of 248.8 Winstantaneous power (a maximum of 114.1 W on
average) has been captured and amaximum of 38.81% energy harvesting
efficiency has been achieved via harmonicexcitation with an
amplitude of 8 mm and a frequency of 2 Hz, when the load
resistanceChongqing 400067, ChinabIntegration of shock absorption
and energy harvestingusing a hydraulic rectifier
Chuan Li a,b, Rongrong Zhu a, Ming Liang b,n, Shuai Yang b
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C. Li et al. / Journal of Sound and Vibration 333 (2014)
39043916 3905work under harsh impulses. For these reasons, the
hydraulic absorbers enjoy one of the largest shares in the
currentabsorber market.
The hydraulic shock absorber works by converting kinetic energy
into acoustic or thermal energy, which is then releasedinto the oil
in the absorber and the surrounding environment. Essentially, the
shock absorbers, passive or active, are energy-wasting components
[7]. At the mWatt level or Watt level, vibration energy harvesting
has been well investigated usingpiezoelectric [8], electromagnetic
[9] or electrostatic [10] transducers. The Watt-level energy
consumed by shock absorbersalso has a great potential for
engineering applications if harvested. For example, for a passenger
car traversing on poor roadsurface at 30 mph (13.4 m/s), the wasted
energy of four shock absorbers is approximately 200 W [11,12].
Moreover, thedissipated energy may generate noises and heats that
are harmful to vehicle components and environment. Therefore,energy
harvesting from the shock absorption is a win-win strategy.
Different approaches have been suggested for integrating the
energy harvesting with the shock absorption. Theseapproaches can
fall into either direct-driven or indirect-driven categories. In
the direct-driven category, linear generators orsimilar transducers
have generally been used to harvest the energy of the vibratory
excitation directly. Suda et al. [13]developed a hybrid suspension
system by employing a linear DC generator to harvest vibration
energy for active vibrationcontrol. Choi et al. [14] suggested
integrating an electromagnetic-induction device into a
magnetorheological damper forharvesting energy from shocks and
vibrations. Chen and Liao [15] introduced a self-sensing
magnetorheological damperthat integrated energy harvesting, dynamic
sensing and damping into one device. A linear multi-pole
electromagneticgenerator was used to collect the energy at around
0.1 W. Choi and Wereley [16] proposed a self-powered
magnetorheo-logical damper integrating a spring-mass with an
electromagnetic induction device. Bogdan [17] introduced an
electro-magnetic power generator for a linear magnetorheological
damper. The advantage of the devices that follow a
direct-drivenapproach to the integration of energy harvesting and
the shock absorption is their structural simplicity. However,
thedownside is their limited energy harvesting capacity restricted
by the limited travel of the shock.
To increase the travel of the vibratory excitations, some
researchers have employed the indirect-driven methods tocapture
more energy for the energy-harvesting shock absorber. Choi et al.
[18] applied a rackpinion mechanism to amplifythe vibration
response for providing more power to control an electrorheological
damper. Li and Tse [19] fabricated anenergy-harvesting hydraulic
damper using a hydraulic motor to transmit the vibration into the
bidirectional rotation of anelectromagnetic generator. The maximum
power harvested by such a structure was 435.1 W(ms1)1 in the
experiments.Nevertheless, the energy harvesting efficiency was
dropped at higher frequencies due to the frequent
bidirectionaloscillation of the generator. Fang et al. [20]
developed a hydraulic electromagnetic shock absorber using
separatedcomponents. The energy recovery efficiency is only 16.6%
in 10 Hz 3 mm excitation. Li et al. [21] introduced a
mechanicalmotion rectifier to commutate the oscillatory motion for
an energy-harvesting shock absorber. The mechanical motionrectifier
is composed of a pair of rack and pinion, one shaft, three bevel
gears and two roller clutches. An experiment on asmooth paved road
shows that more than 15 W of electricity can be harvested at 15 mph
speed. Aly et al. [22] used a levermechanism incorporating a smart
damper to improve flexural response of a very slender building. Li
et al. [23,24] applied aninverse screw transmission for a
two-terminal flywheel to convert the oscillatory vibration into the
reciprocating rotation ofthe flywheel. By adjusting the
transmission ratio between the rectilinear vibration and the
bidirectional rotation, an electro-hydraulic approach was developed
to realize a variable inertial mass [25].
In this research, we propose an energy-harvesting shock absorber
that employs a hydraulic rectifier to integrate theenergy
harvesting with the shock absorption. The hydraulic rectifier
consists of four check valves to commutate theoscillatory shock to
a unidirectional rotation for an electromagnetic generator. As the
hydraulic nature is preserved inthe integration, the reliability
and durability inherent in the hydraulic shock absorber can be
sustained.
The rest of the paper is structured as follows. The conceptual
design of the integrated shock absorber and the energyharvester is
proposed in Section 2. The fabrication of the prototype device is
also described in this section. Section 3 presentsan
electromechanical model to describe the mechanical and the
electrical behaviors of the energy-harvesting shockabsorber.
Section 4 reports the experimental results and discussion.
Conclusions are drawn in Section 5.
2. Design and prototyping
In this section, our design idea of the energy-harvesting shock
absorber based on a hydraulic rectifier is first illustrated.Based
on this idea, the fabrication details of the prototype device are
then elaborated.
2.1. Conceptual design of the energy-harvesting shock
absorber
Energy-harvesting absorbers with motion transmissions are
capable of converting the rectilinear vibration into abidirectional
rotation, yielding the electricity via the power generator. The
frequent reversing of the generator,unfortunately, causes a large
impact force, which further leads to deteriorated energy harvesting
performance, movingparts fatigue and even system failure. For this
reason, we rectify the bidirectional oscillation to a
unidirectional rotation ofthe generator. Employing the hydraulic
circuit rather than the mechanical transmission leads to smoother
response toirregular shocks. For real applications, a hydraulic
system is more durable due to the reduced wear and tear resulting
fromthe rigid, frequent contacts between the mechanical components
as compared with a non-hydraulic system.
-
through a 3-phase electrical rectifier. The proposed conceptual
design makes it possible for the rectilinear vibration between
Three-phaseA C22
C. Li et al. / Journal of Sound and Vibration 333 (2014)
390439163906the two terminals of the absorber to be used to drive
the unidirectional rotation of the hydraulic motor in a smooth
manner,and generate the electricity on the load at the same time.
The shock energy is absorbed as a result of: (1) energy
harvestingby the load, and (2) energy dissipation through the oil
flow and the motion transmission. Apparently, shock absorption
andenergy harvesting can be achieved simultaneously using the
proposed design.
As shown in Fig. 1, the hydraulic rectifier consists of four
check valves, namely, AD, in a bridge configuration. In responseto
the positive vibration (i.e., tension between the two terminals of
the absorber), the oil inside the left chamber flows intothe right
chamber via the path of port 11, valve A, port 21, port 22, valve D
and port 12. Supposing the rotation of thehydraulic motor in
response to the flow direction from the port 21 to the port 22 is
clockwise, the positive vibration resultsin the clockwise rotation
of the hydraulic motor. Under the negative vibratory excitation
(i.e., compression between the twoterminals), the oil flows through
port12, valve C, port 21, port 22, valve B and port 11
successively. In this case, the hydraulicmotor still rotates
clockwise. Consequently, the rotation of the hydraulic motor (or
the power generator) is alwaysunidirectional, though the vibratory
excitation is bidirectional.
Table 1 demonstrates the electromechanical transmission of the
system in response to the external shocks and vibrations. Forboth
the tensile (positive half-circle) and the compressive (negative
half-circle) excitations, the hydraulic motor and the
powergenerator rotate in the positive direction. The three phases
of the generated electricity are commutated by the 3-phase
electricalrectifier. According to the principle of the 3-phase
electrical rectifier, the waveform of the output voltage on the
load representsthe sum of the moduli of the three phases. As shown
in Table 1, in the mechanical domain, the rotations of the
hydraulic motorand the power generator are always unidirectional
thanks to the application of the hydraulic rectifier. In the
electrical domain,the waveform of the output voltage is also
unidirectional owing to the use of the 3-phase electrical
rectifier.
2.2. Fabrication of the prototype device
Based on the conceptual design as shown in Fig. 1, a prototype
device integrating both the energy-harvesting and the
shockabsorption was fabricated in the Engineering Laboratory for
Detection, Control and Integrated Systems at Chongqing
Technologyand Business University. As shown in Fig. 3, a steel
frame with the rod cap is fabricated to accommodate all the parts
shown inFig. 1. The oil cylinder with an internal diameter of 40 mm
and a maximum travel of 80 mmwas installed on the steel frame.
Thehydraulic rectifier and the hydraulic motor are fixed on the two
sides of the cylinder. The hydraulic rectifier is composed of
fourThe conceptual design of the proposed absorber is illustrated
in Fig. 1. Similar to conventional hydraulic absorbers, thecore of
our design is a hydraulic cylinder, which is divided into two
chambers by a piston. Two rods, across the twochambers, connect
with two sides of the piston respectively. The reason of using the
two-rod cylinder is to guaranteeidentical oil flow between the two
chambers. One of the rods is attached directly to one terminal of
the absorber, whileanother one is sheltered by a cap, to which
another terminal is connected. As shown in Fig. 1, the two ports
(11 and 12) ofthe cylinder are connected to the two ports (21 and
22) of a hydraulic motor via a hydraulic rectifier. The output
shaft of thehydraulic motor is connected to a 3-phase
electromagnetic generator, whose output electricity is used to
power a load
PistonRod
Cylinder
Hydraulicrectifier
electrical rectifierDB
2111
Fig. 1. Schematic diagram of the proposed energy-harvesting
shock absorber.Hydraulic motor
Electromagnetic generatorLoad21check valves, each of which has
nominal diameter of 10 mm and opening pressure of 0.2 MPa. The
displacement of the hydraulicmotor (BMM8-MAE) was 8.2 mL/rev. The
permanent-magnet generator was connected to the output shaft of the
hydraulic motorvia a coupling. The nominal rotational speed of the
generator was 500 rpm. The output of the power generator was
connected tothe electrical rectifier (30 A, 600 V), which was used
to power the load resistor directly.
To assemble the hydraulic circuit, four custom-made brass tubes
(8 mm in diameter) were used to connect ports 11, 12,21, 22 with
the hydraulic rectifier, respectively. For oil filling, exhausting
and refilling as necessary, a release valve 8 mm innominal diameter
was also connected to port 11.
3. Electromechanical modeling
The electrical response of the electromagnetic generator is
first modeled in Section 3.1. The shock force response in
themechanical domain is subsequently analyzed in Section 3.2.
Through combining the electrical and the mechanical domain
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C. Li et al. / Journal of Sound and Vibration 333 (2014)
39043916 3907Table 1Electromechanical transmission of the proposed
design.
Scene Tensile excitation Compressive excitation Full-circle
excitation
Shock waveformmodels together, an electromechanical model is
proposed in Section 3.3 to illustrate the system response to the
vibratoryexcitation.
3.1. Energy harvesting analysis
For the 3-phase electromagnetic generator (Fig. 2), the energy
harvesting circuit can be represented by the model shownin Fig. 3
[26].
The rotational motion of the hydraulic motor can lead to a
3-phase electromotive force, i.e.,
Ve1t Em sin t; Ve2t Em sin t2=3; and Ve3t Em sin t4=3; (1)
Oil flow path 11-A-21- 22-D-12 12-C-21- 22-B-11 11-A-21-22-
D-12-C-21- 22-B-11Hydraulic motor
Power generator
3-phase electricity
Output voltage
Fig. 2. Prototype device.
-
C. Li et al. / Journal of Sound and Vibration 333 (2014)
390439163908where Ve1, Ve2 and Ve3 denote the electromotive
voltages at 3 phases, represents the angular velocity, t is the
time, and Emis the electromotive voltage that is given by
Em km; (2)where km stands for the electromotive voltage
constant. For the 3-phase electromagnetic generator, one has
L1 L2 L3; and R1 R2 R3; (3)where L1, L2 and L3 represent the
internal inductances of the three phases respectively, R1, R2 and
R3 denote the internalresistances of the three phases respectively.
The circuit equations of the three phases can be derived using
Kirchhoffsvoltage laws as
Ve1tL1di1tdt
i1tR1 i1tRd 0
Ve2tL2di2tdt
i2tR2 i2tRd 0
Ve3tL3di3tdt
i3tR3 i3tRd 0 (4)
For the 3-phase electrical rectifier as shown in Fig. 3, the
voltage on the load resistor Rd can be determined by
vt ji1tjji2tjji3tjRd 3
pmodi1tRd: (5)
where mod is the modulo function. The power Pd harvested by load
resistor Rd can be therefore calculated as
Pdt vt2=Rd: (6)
3.2. Mechanical force responses to the vibratory shocks
With a shock excitation x(t), the mechanical behavior of the
proposed absorber can be approximated by Fig. 4.As shown in Fig. 4,
the shock excitation x(t) can be divided as two constituents: the
backlash x1(t) caused by the hydraulic
transmission, and the effective excitation x2(t) to drive the
generator. Upon neglecting the elasticity of the system, there
arefive difference forces related to x1(t) and/ or x2(t),
respectively. Following the mechanical model of the shock absorber,
thefive forces can be introduced in detail as follows.(1)
(2)
(3)Fig. 3. Energy harvesting circuit of the proposed absorber.V
e3 L3 R3V e1 L1 R1
V e2 L2 R2RdOil damping force Fd(t). The flow of the oil inside
the absorber results in a viscous damping effect, which is given
by
Fdt cs _xt: (7)where cs denotes the equivalent viscous damping
coefficient of the hydraulic system.Friction force Ff(t). Supposing
the value of the piston friction is f0, the friction force is
formulated as
Ff t sgn_xtjf 0j: (8)where _xt is the first derivative of x(t)
with respect to t, and sgn(.) is the sign function.Inertial force
Fi(t). The inertial force is mainly caused by the rotation of the
rotor of the generator. Letting m denote theequivalent inertial
mass of the rotor, the inertial force is given by
Fit mx2t: (9)It should be noted that the equivalent inertial
mass m is neither the gravitational mass nor the moment of inertial
of therotor. Instead, the equivalent inertial mass is associated
with both the transmission ratio and the moment of inertia ofthe
rotor. For more details on the calculation of the equivalent
inertial mass m, one can refer to our previous work [25].
-
Ocon
3.3.
Hthe
C. Li et al. / Journal of Sound and Vibration 333 (2014)
39043916 3909TheBasbac
wheconfunFvt 2PcSc; x1t 0Fvt 0; jx1tj40
(: (15)
where Sc is the cross-sectional area of the cylinder.
ne may notice that there are two conditions for the mechanical
model as shown in Fig. 4: contact and backlashditions. If the
maximum backlash is and the bidirectional backlashes are identical,
one has
Z jx1tjZ0: (16)
Electromechanical model of the proposed design
aving analyzed the five force components and the contact/
backlash conditions, the mechanical governing equation ofabsorber
in response to the shock excitation x(t) can be therefore obtained
as
Ft FdtFf tFitFetFvt; x1t 0Ft FdtFf t; jx1tj40
(: (17)(5)where
ce 3 mod kmkjL1R1Rd
2Rd: (14)
Opening force Fv(t) of the hydraulic rectifier. Denoting the
opening pressure of a check valve by Pc, for the hydraulicrectifier
as shown in Fig. 1, one has(4) Energy-harvesting induced force
Fe(t). According to the law of conservation of energy, the
harvested energy by the loadresistor Rd is equal to the input power
of the generator, i.e.,
Fet_x2t it2Rd: (10)Combining Eqs. (1), (2) and (4) results
in
it 3
pmod
kmjL1R1Rd
: (11)
Supposing
t k _xt; (12)one can obtain the following equation from Eqs.
(10), (11) and (12)
Fet ce _x2t; (13)
xx1 x2
d
Ff
Fe
Fi
Fv
F
Fig. 4. Mechanical model of the proposed shock absorber.proposed
design can be regarded as a system with one input x(t) and two
output variables F(t) and v(t) (or, i(t), Pd(t)).ed on the above
mechanical governing equation and letting y1(t)F(t)Ff(t), the
mechanical transfer function under theklash condition is given
by
TF1s css2y1txt : (18)
re s is Laplaces complex variable, TF1(s) is the mechanical
transfer function under the backlash condition. Under thetact
condition, moreover, letting y2(t)F(t)Ff(t)Fv(t) and omitting the
effect of the backlash, the mechanical transferction TF2(s) can be
expressed as
TF2s ms2cssces2y2txt (19)
-
On the other hand, the transfer function between x(t) and v(t)
is valid only under the contact condition. Combining Eqs. (6),(13)
and (14) yields the electrical transfer function
TF3s 3
pmod
kmkL1sR1Rd
s2
vtxt (20)
It is worth noting that the electromechanical model as
illustrated by Eqs. (1820) is a simplified expression as most
ofnonlinear parameters are omitted or linearized. Nevertheless, the
above electromechanical model can provide an intuitiveunderstanding
on the proposed energy-harvesting shock absorber. Hence we apply
the above electromechanical model toanalyze the experimental
results as illustrated in the following section.
4. Experimental results and discussion
C. Li et al. / Journal of Sound and Vibration 333 (2014)
390439163910In this section, three test rigs are introduced to
characterize the electrical parameters, mechanical parameters and
theperformance of the prototype device, respectively. The modeling
results are also compared with the experimental results.
4.1. Experiments for electrical parameter characterization
An experiment (namely, test setup #1) was designed to
characterize the electrical parameters of the power generator.
Asshown in Fig. 5, the power generator was removed from the
prototype device and was fixed on a platform. A 370Welectrical
motor was directly connected to the generator via a coupling, on
which an encoder (1000 pulses per revolution)was fixed to measure
the angular velocity of the generator. A frequency inverter (400 W,
1/3-phase) was used to drive themotor with adjustable speed. The
pulse output of the encoder was counted by a USB data acquisition
(DAQ) and was sent toa laptop computer. The acquired number of
pauses, along with the sampling time, are used to calculate the
instantaneousangular velocity ((t)) of the generator. An adjustable
resistor (150 W, 050 ) was connected to the electrical rectifier of
thegenerator as the electrical load (Rd). During the experiments,
the electrical load was variable achieved by adjusting
theresistance of the resistor. The voltage (v(t)) of the load was
measured by a multimeter and an oscillator. The multimeter ismore
intuitional, while the waveform of the voltage can be more clearly
observed by the oscillator.
As shown on the specification list of the generator, the static
resistance and inductance are respectively 7.5 and 0.02 H. Withthis
observation, the resistance values during the experiments were set
at 2.5 , 5 , 7.5 , 10 , 15 , 50 , respectively. At eachresistance
level, we manually adjusted the rotational speed ranging from 30
rpm to 300 rpm. The measured voltage values overthe load are
plotted in Fig. 6. Based on Eqs. (1)(6), km and R1 were tuned to
find the best fitted parameters
fkmopt;R1optg arg minkm ;R1
JucaumeJ22; (21)
where kmopt and R1opt denote the optimal km and R1 parameters to
be identified, uca() and ume() are respectively the
calculated(using Eqs. (4) and (6)) and the measured voltage values
for a given , and JJ2 stands for 2-norm operation. The right-hand
sideof the above equation represents the parameter fittings of km
and R1 under the condition of minimal error between the
calculatedand the measured values.
With the fitting algorithm, the optimal parameters are found to
be kmopt0.57 V s/rad and R1opt7.6 . The identifiedparameters are
then substituted into Eqs. (4) and (6). The calculated uca() values
with different loads and differentrotational speeds can thus be
obtained and plotted in the same figure. Comparing ume() with
uca(), one can see that thecalculated values are consistent with
the measured counterparts.
4.2. Experiments for mechanical parameter characterization
In this subsection, the prototype device excluding the power
generator was tested as shown in Fig. 7 (test setup #2).Since the
power generator was removed, the influence of the electrical
characteristics could be eliminated so as to facilitatethe
mechanical parameter characterization. As shown in Fig. 7, the
prototype (without the generator) was fixed on anelectro-hydraulic
servo fatigue testing machine (20 kN), which was controlled by a
desktop computer via a controller.
Laptop
Oscillator
DAQInverter
GeneratorEncoderMotor
Adjustable resistor
Multimeter
Fig. 5. Test setup #1 for the electrical parameter
characterization.
-
C. Li et al. / Journal of Sound and Vibration 333 (2014)
39043916 39110 50 100 150 200 250 3000
5
10
15
20
25
30
Rotational speed(rpm)
Vol
tage
(V)
Fig. 6. Generated voltages vs loads and rotational speeds: The
marked points are associated with the measured ume() values, while
the lines denote thecalculated uca() values.
SpecimenEncoder
Controller
Laptop
DesktopThe testing machine was driven by a hydraulic unit (30
L/min, to be shown in Fig. 11). According to the vibration signal
(x(t))predefined by the desktop computer, the lower terminal of the
specimen moves up and down, yielding a unidirectionalrotation ((t))
of the hydraulic motor and a relative force (F(t)) between the two
terminals of the specimen. To measure therotational speed of the
output shaft of the hydraulic motor, the encoder (with a resolution
of 1000 pulses per revolution),the USB DAQ, and the laptop
introduced in the previous subsection were again used for test
setup #2. The oscilloscope asintroduced in Section 4.1 was used to
monitor the output waveform of the encoder. The actual vibration
displacement andthe mechanical force were acquired by the desktop
computer via the controller.
There are 7 parameters, namely, Fv(t), k, , cs, f0, m and ce for
the electromechanical description of the prototype deviceusing Eqs.
(17)(20). As the power generator was disabled in this subsection, m
and ce cannot be identified in thissubsection, while the other
parameters can be obtained from test setup #2 as follows.
(1) Calculate Fv(t). As introduced in Section 2, the opening
pressure of each check valve for the hydraulic rectifier is0.2 MPa,
and the cross-sectional area Sc of the cylinder is measured as
9.425104 m2. One can calculate that the openingforce Fv(t) is 377 N
when 0 (using Eq. (15)).
(2) Identify k and . Based on the above test setup, we applied
cyclic loading to carry out the mechanical
parametercharacterization experiments [27]. In the cyclic loading
experiments, the excitation displacements between the twoterminals
were defined as sinusoidal signals (x(t)X sin 2ft) with different
amplitudes (X) and frequencies (f). Throughassociating the measured
vibratory displacement (xme(t)) with the measured force response
(Fme(t)), one can estimatemechanical model parameters as shown in
Fig. 4. Fig. 8(a) displays the output of the encoder in response to
a vibratoryexcitation (excitation 1) x(t)0.015sin 0.2t (X15 mm and
f0.1 Hz). The encoder, unfortunately, can only count thenumber of
impulses. Hence we have to calculate the differentiation of the
smoothed encoder output. In this way, one canobtain the angular
velocity me(t) that is plotted in Fig. 8(b). From the figure one
can estimate two parameters: the backlashof the transmissionE3 mm,
and ca(t)6.8|sin 0.2t|. Substituting the ca(t) and x(t) into Eq.
(12) yields
k 765:96rad=m; xtZ0765:96rad=m; xto0
(: (22)
Testing machineUSB DAQ Oscilloscope
Fig. 7. Test setup #2 for mechanical parameter
identification.
-
C. Li et al. / Journal of Sound and Vibration 333 (2014)
390439163912-1000
-500
0
500
1000
1500
Forc
e(N
)
Excitation2Excitation3Excitation4
Backlash effect
0 5 10 15 20 25 300
0.5
1
1.5
2x104
Time(s)
Num
ber o
f im
puls
es
0 5 10 15 20 25 300
2
4
6
8
Time(s)
Ang
ular
vel
ocity
(rad
/s)
Difference due to backlash(t)(t)
Fig. 8. Rotational motion of the hydraulic motor in response to
x(t)0.015sin 0.2t (excitation 1): (a) number of impulses collected
by the encoder;and (b) angular velocity.It is worth noting that
both k and may vary with the change of the shock excitations. In
this research both parametersare regarded as constants to simplify
discussions.
(3) Identify cs and f0. In the cyclic loading method, a
sinusoidal signal with greater amplitude-frequency ratio can
beapproximated as a triangular one with slope |r|A2/(8f). After
disabling Fi(t) and Fe(t), among all the mechanical forces,only
Fd(t) and Ff(t) are sensitive to the triangular excitation.
According to Eq. (19), the steady-state response of the system
isgiven by
y2tjt-1 A2f cs
2: (23)
As y2(t)F(t)Ff(t)Fv(t), the above equation can be rewritten
as
jFtj377jf 0jt-1 A2f cs
2: (24)
In this way, one can tune cs and f0 to find the best fit between
the measured and the calculated values:
fcsopt; f 0optg arg mincs ;f
JFcatFmetJ22; (25)
where csopt and f0opt respectively denote the optimal cs and f0
parameters to be estimated, Fca(t) and Fme(t) are the
calculated(using Eqs. (17) and (24)) and the measured force values
for the given excitation x(t). We then employ 0.015sin
0.4t(excitation 2), 0.01sin 0.4t (excitation 3) and 0.015sin 0.2t
(excitation 4) to drive the shock absorber, whoseresponses are
plotted in Fig. 9. It is noted that the measured vibratory
displacements are not completely identical to thepredefined signal
in the cyclic loading experiments. This is due to the difference
between the signal input and the actuationoutput of the testing
machine. Based on the experimental results, one can search for the
optimal parameters which arefound to be csopt10,697 N s/m and
f0opt452 N, using the fitting algorithm expressed by Eq. (25).
The estimated optimal parameters csopt and fopt are in turn
substituted into Eq. (24). The calculated damping loops inresponse
to the three excitations are also displayed in Fig. 9. Comparison
between the calculated and the measured dampingloops indicates that
there are differences occurred at the reversing time periods of the
terminal. This is mainly caused by theexistence of the backlash
.
-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02-1500
Displacement(m)
Fig. 9. Damping loops of vibration inputs of excitations 2, 3
and 4 for identifying cs and f0. The dotted lines are generated by
substituting csopt and f0opt intoEq. (24).
-
C. Li et al. / Journal of Sound and Vibration 333 (2014)
39043916 39134.3. Energy-harvesting and shock absorption
experiments
In this subsection, the test of the prototype device as shown in
Fig. 2 was carried out using test setup #3 (Fig. 10). As theencoder
was replaced by the power generator in this subsection, the laptop
computer and the USB DAQ were no longer usedin this test setup.
Moreover, the output voltage of the energy-harvesting shock
absorber was recorded by the oscilloscopethat was connected to the
desktop computer for data acquisition. The adjustable resistor as
shown in Fig. 5 was again usedas the load of the shock absorber. By
associating the load resistance (Rd) with the instantaneous voltage
(v(t)), one cancalculate the instantaneous power (Pd(t)) to be
harvested. In this test setup, the measurement methods of the
vibrationsignal (x(t)) and the relative force (F(t)) acting on the
shock absorber are the same as test setup #2 (acquired by the
desktopcomputer via the controller).
As of now, we have only 2 parameters, i.e., m and ce to be
identified from Eq. (17). Since the two parameters are
directlyrelated to the load, we take a 7.5- resistor as an example
for parameter identification. Again, to drive the shock absorber,we
define the vibratory displacement x(t) in the computer. The
experimental results can be used to find the optimalceopt|7.5 and
mopt|7.5 using the fitting approach
fceopt;moptgj7:5 arg mincs ;m JFcatFmetJ22: (26)
Letting excitation 5 denote the vibration signal 0.015sin t,
Fig. 11(a) and (c) displays the mechanical and the
electricalresponses of the energy-harvesting shock absorber,
respectively. We then use 0.008sin 4t (excitation 6) to excite
theshock absorber, whose mechanical and electrical responses are
displayed in Fig. 11(b) and (d), respectively. Using the
abovefitting equation, the optimal parameter can be estimated as
ceopt5.185104 N m/s and mopt180 kg. The parameters ceoptandmopt are
in turn substituted into Eq. (17) to yield the calculated Fca(t)
and Vca(t) which are also shown in the same figure.
One may notice thatm (the equivalent inertial mass as shown in
Eq. (9)) is very large comparing to the gravitational massof the
rotor of the generator. The reason is that such a design can
amplify the inertia of the rotor of the generator.
Similarobservations have been made in the literature [25].
For the proposed structure, the energy harvesting performance is
one of the main concerns. The harvested energy can becalculated
using Eq. (6), while the input power Pin(t) resulting from the
vibratory excitation can be obtained by
Pint Ft_xt: (27)
Testing machine
Hydraulic unit
Prototype
Resistor
ControllerDesktop
Oscilloscope
Fig. 10. The developed prototype device for energy-harvesting
and shock absorption experiments (test setup # 3).The energy
harvesting efficiency can therefore be calculated by combining Eqs.
(6) and (27) as
tb
t ta
PdtPint
: (28)
where [ta, tb] denotes the time interval of interest for the
efficiency calculation. To be meaningful, the range [ta, tb] should
beat least no shorter than one period of the vibratory excitation.
Fig. 11(e) and (f) display the comparisons between the inputpower
and the harvested power of the prototype device for excitation 5
and excitation 6, respectively. With excitation5, the peak value of
the harvested power is 43.2 W, with a mean value of 18.63 W. By
contrast, excitation 6 generatesmuch more power with a peak value
of 248.8 W and a mean of 114.1 W. Based on the above equation, the
energy harvestingefficiencies for the excitation 5 and excitation 6
inputs are 21.44% and 38.81%, respectively.
In addition to the excitation signal, the load resistance also
plays an important role on energy harvesting efficiency.
Toillustrate this, we use a single vibratory signal, x(t)0.01sin 2t
(excitation 7), and adjust the load resistance in the range[2.5 ,
50 ]. Fig. 12 shows the change of the energy harvesting
efficiencies. When tuning resistance from 2.5 to 7.5 ,
theefficiency increases with the rise of the load resistance.
However, the efficiency drops if we further increase the
resistanceabove 7.5 , and the efficiency declines much faster when
the resistance is higher than 15 (about twice of the
internalresistance). As shown in Fig. 12, the maximum efficiency
(27.49%) occurs at 7.5 , which is almost identical to the
internal
-
-5000
C. Li et al. / Journal of Sound and Vibration 333 (2014)
390439163914-0.02 -0.01 0 0.01 0.02-5000
Displacement(m)-0.01 -0.005 0 0.005 0.01
Displacement(m)
10
15
20
25
olta
ge(V
)
V (t)
V (t)Difference due to backlash
30
40
50
60
olta
ge(V
)
V (t)
V (t)0
5000
Forc
e(N
)
F (t)
F (t)
0
5000
Forc
e(N
)
F (t)
F (t)resistance of the generator. This suggests that impedance
matching [28] is a feasible way towards optimal energy
harvestingwith maximum harvesting efficiency.
Considering the capability of simultaneous shock absorption and
energy harvesting, the proposed device has a promisingpotential for
real-world applications, e.g., as vehicle dampers. At this stage,
however, the developed prototype device cannotbe directly used for
such purposes yet. The reason is that the prototype device was
developed using separated componentswhich make it slightly too
bulky and heavy. A more compact design is required to reduce its
size and to improve itsreliability for real applications, in
particular for vehicles. In addition, the present structure is more
expensive compared withthe existing vehicle shock absorbers because
of the additional components including four check valves, a
hydraulic motor,and an electric. Therefore, a more compact yet
cost-efficient design is highly desirable. The next phase of our
research willhence focus on the design optimization based on the
size, weight and cost criteria.
5. Conclusions
In this paper, a hydraulic rectifier has been introduced in the
development of an integrated device for simultaneousshock
absorption and energy harvesting. The bidirectional shock acting on
the two terminals of a hydraulic absorber wastransformed into
unidirectional rotation by the four check values of the rectifier.
This unidirectional rotation wassubsequently employed to drive a
power generator to harvest the shock energy. This improves the
reliability and thedurability of the generator by eliminating the
frequent reversing of the shock. An electromechanical model was
alsodeveloped to analyze the behavior of the structure. A prototype
was fabricated and tested using three test setups and cyclic
0 0.5 1 1.5 2 2.5 3 3.5 40
5
Time(S)
V
0 0.2 0.4 0.6 0.8 10
10
20
Time(s)
V
0 0.5 1 1.5 2 2.5 3 3.5 40
50
100
150
200
250
Time(s)
Pow
er(W
)
Input powerHarvested power
0 0.2 0.4 0.6 0.8 10
200
400
600
800
Time(s)
Pow
er(W
)
Input powerHarvested power
Fig. 11. Responses of the prototype device under 0.015sin t
(excitation 5) and 0.008sin 4t (excitation 6), respectively. (a)
and (b) present themechanical responses; (c) and (d) show the
electrical responses; and (e) and (f) display the comparison
between the input power and the harvested powerassociated with the
two excitations.
-
of Chongqing Innovation Team in University (KJTD201313). The
authors would like to thank the reviewers for their valuable
C. Li et al. / Journal of Sound and Vibration 333 (2014)
39043916 3915comments and suggestions.
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Acknowledgments
This work is supported in part by the Natural Sciences and
Engineering Research Council of Canada (I2IPJ 387179 andRGPIN
121433), the Ontario Centre of Excellence for Child and Youth
Mental Health (OT-SE-E50622), the Natural ScienceFoundation Project
of China (51375517), the Natural Science Foundation Project of CQ
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C. Li et al. / Journal of Sound and Vibration 333 (2014)
390439163916
Integration of shock absorption and energy harvesting using a
hydraulic rectifierIntroductionDesign and prototypingConceptual
design of the energy-harvesting shock absorberFabrication of the
prototype device
Electromechanical modelingEnergy harvesting analysisMechanical
force responses to the vibratory shocksElectromechanical model of
the proposed design
Experimental results and discussionExperiments for electrical
parameter characterizationExperiments for mechanical parameter
characterizationEnergy-harvesting and shock absorption
experiments
ConclusionsAcknowledgmentsReferences