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: liang@eng.uOttawa.ca (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

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

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

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C. Li et al. / Journal of Sound and Vibration 333 (2014) 390439163914-0.02 -0.01 0 0.01 0.02-5000

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Displacement(m)

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olta

ge(V

)

V (t)

V (t)Difference due to backlash

30

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olta

ge(V

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5000

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e(N

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F (t)

0

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e(N

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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

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V

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er(W

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Input powerHarvested power

0 0.2 0.4 0.6 0.8 10

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er(W

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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 CSTC (2012JJJQ70001), and the Project

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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