a study of the electric circuit of a vibration energy...

A study of the electric circuit for a vibration energyharvesting absorber

F. Infante1, S. Perfetto1, S. Herold1, D. Mayer1

1 Fraunhofer Institute for Structural Durability and System Reliability LBF,Bartningstr. 47, 64289, Darmstadt, Germanye-mail: [email protected]

AbstractIn the last decade the demand of wireless sensors and low-power electronic devices for condition moni-toring in vibrating structures has been strongly increased. For this purpose piezoelectric transducers for harvesting the vibration energy are an eligible solution for powering these devices. In order to optimize the electromechanically coupled system and predict the highest power produced a complex model, including mechanical structure, piezoelectric element and electric circuit is required. When a practical electric circuit and a complex mechanical system are considered in the system design, the accuracy of the model becomes a challenging task. Simulating a two degree of freedom system, the aim of the present paper is to provide a comprehensive strategy to estimate the power generated by a piezoelectric layers. With the aim of har-vesting power a standard rectifier circuit is connected to the transducers. Afterwards in the experiments the numerical results of the energy harvesting vibration absorber (EHVA) were validated.

1 Introduction

Nowadays, most of the devices used in wireless sensor networks are still battery-driven. The intensification of low-power wireless sensors has led to increased studies in the conversion of different forms of energy into electrical energy. Various energy production techniques have been developed in order to power such electronic devices using the energy available in the working environment. While the mechanical vibrations are a potential power source to supply wireless sensors, they affect the ordinary operation of mechanical systems. The interest in using mechanical vibrations results in a conflict with the high number of works previously done in order to absorb the vibrations.

In this sense, vibration absorbers are usually installed to improve the mechanical performances. Such device is a single degree of freedom (SDoF) system attached to the main structure to control its motion. The relative motion between absorber and main structure is kept within admissible bounds, while the motion of the host structure has been reduced.

With integration of an energy harvesting device into a vibration absorber, mechanical vibrations can be converted in electric energy. Moreover, that converted energy can be used directly or can be stored.

An important step to design a practical configuration of an energy harvesting device is to model correctly the dynamic behavior of the mechanical system when the electrical load is integrated. The nature of metaphysics system has caused some modeling issues. The feedback from the electrical circuit to the mechanical behavior is very often neglected in the simulation model. Furthermore, several models present in literature were focused on simplifying the energy harvesting circuit by a simple resistor [1]. In this sense, the attention in most of the papers about piezoelectric energy harvesting models as [2] is to study the maximum power that can be dissipated by the simple resistor.

The consideration of only linear elements in the electromechanical system, as mainly resistor, does not

1469

represent correctly the real harvesting system when the energy required must be direct current. For practicaluse of the produced electric energy, the conversion of the Alternative Current (AC) to Direct Current (DC) isrequired. This conversion needs a more complex model than a simple resistance.

In the work of [3] a strategy to estimate the power provided by a cantilever beam with piezoelectric transduc-ers integrated and connected to a rectified circuit is proposed. Clementino [4] some years later consideredthe same system and obtained in his study the maximum power harvested by numerical optimization of thebeam and piezoelectric geometry, parameters of resistive load, capacitive filter and diodes.

The aim of this paper is to obtain and evaluate both the vibration reduction of a single degree of freedom sys-tem and the power generation using piezoelectric transducers. Using an absorber to damp the vibration at theresonance, the relative velocity between the bodies is used to cause transverse vibration of the harvester. Themechanical multi degree of freedom (MDoF) system is developed by Perfetto in [5]. Her work investigatesthe behavior of the structure in a range of absorber damping from original values to over-critical damping. Avoltage driven voice coil actuator is introduced in order to modify the damping.

For the purpose of the present paper, the original damping of the absorber is considered and the work of [3]is expanded for the multi body case. By the theoretical model of a full-wave diode bridge (rectifier) directlyconnected to the transducer, the power generated can be evaluated. In order to evaluate the highest amount ofenergy harvested a description for choosing the capacitance and resistance loads is provided. Considerationsregarding the working frequency are presented, and the frequency generating the greatest value of power isdefined by comparison of the experimental results at the two resonances.

The remainder of article is organized as followed: first an energetic evaluation of piezoelectric systems for abetter understanding of the different functions of the harvester. Next a description of the experimental setupthat is used to validate the simulation. After the numerical model of a bimorph piezoelectric energy harvestersystem, the description of the diode bridge circuit is illustrated. The non linear behavior of the rectifier withcapacitor filter are reviewed, considering their coupling with the electromechanical converter. After that, theoptimization method in the interesting frequency range is performed. To illustrate the model suitability, twoexperiments are validated by simulation in Matlab/Simulink. A practical example is experimentally executedin order to show the applicability of the idea. Finally, the results are discussed and suggestions are proposed.

2 Energy transfer paths in piezoelectric systems

Mechanical absorbers are usually introduced in systems in order to reduce the vibration amplitudes in acertain range of frequency, or to completely suppress them at a particular frequency (e.g. neutralizer). Thedissipation of energy in the system is obtained by the damping. Usually a dissipative process is consideredto an irreversible conversion of the energy from some initial form into heat. For instance, regarding wavesand vibrations, the lost energy raises the temperature of the system by friction.

Considering a more complex system, including piezoelectric energy harvesting, the idea of irreversible dis-sipative process needs to be amplified.

For a 2DoF system defined by a host structure and an absorber, the mechanical vibrations are dissipateddirectly into thermal energy. Figure 1 shows a schematic representation of the mechanical 2DoF system withthe piezoelectric device. The absorber is connected by a spring damper system to the base mass. In parallelit is introduced the piezoelectric material connected to an electric circuit.

Considering this mechanical system, in Figure 2 is shown the different forms of energy involved: mechanical,electrical and thermal. Mechanical or electrical energy can be directly dissipated into heat using elementssuch as mechanical dampers or electrical resistors. This kind of conversions are irreversible and the energy“lost” will not be recovered in the devices.

Through the piezoelectric device, part of the mechanical energy is converted into electrical energy. Someof the electrical energy is transformed into heat, while another part of it is converted into energy storage.

1470 PROCEEDINGS OF ISMA2016 INCLUDING USD2016

Since the piezoelectric device has a bi-directional effect, the amount of energy that is stored will affects themechanical energy.

Figure 1: Schematic representation of EHVA. Figure 2: Energy transfer paths.

These different paths represent different methods which can remove energy from the mechanical structure.Various applications can emphasize one or another effect. For example, with a pure resistive shunt damping,a maximization of the irreversible dissipated energy is considered. However, standard energy harvestingsystem is treated when the study focus is on the utilization of the harvested energy.

Using the definition of Liang in [6] the fractions of energy dissipated and harvested can be defined by twofactors: µd and µh respectively. For energy harvesting, the term harvesting factor is defined to evaluate theharvesting capability as :

µh =Eh

2πEmax(1)

where Eh and Emax are the harvested energy in one cycle and the energy associated with vibration respec-tively.

For the energy dissipation, the term dissipation factor is used to evaluate the dissipation capability as:

µd =Ed

2πEmax(2)

where Ed is the dissipated energy in one cycle.

In order to define the overall damping effect, the loss factor is used. It is defined as the ratio between theenergy removed per cycle and the energy associated with vibration. Using the eqs. 1 and 2, the loss factorparameter is defined as:

µL =∆E

2πEmax= µh + µd (3)

A comparison between resistive shunt damping (RSD) and standard energy harvesting (SEH) is made byLiang. It is demonstrated that in the two applications the flows of the extracted energy are different. InSEH the harvesting factor is also the loss factor without dissipation of energy. On the other side, in RSDapplications, the dissipation factor corresponds to the loss factor without energy being harvested.

In order to extract the higher amount of power, in the present work, the SEH application is considered andthe optimization of the rectified circuit is evaluated.

FP7 EMVEM: ENERGY EFFICIENCY MANAGEMENT FOR VEHICLES AND MACHINES 1471

3 Experimental setup

The test rig for the experimental validation is a 2DoF system defined in [5] and it is shown is Figure 3.

The original SDoF system is an aluminum host mass of 5.5 kg connected to a fixed support by two stealbeams characterized by a stiffness and damping value. Such system presents a resonance frequency at 41.3Hz as shown in black dashed line in Figure 4.

In order to absorb the vibrations, a stainless steal cantilever piezoelectric beam with a tip mass is usedas a vibration absorber. The mechanical parameters of the absorber are defined using the Den Hartog’soptimization. The new system presents two resonances at f1 = 32.25 Hz and f2 = 46.30 Hz (see red andblue line Figure 4).

Figure 3: Set up of the electromechanical system [5].

The entire system is considered almost undamped, reason of the quite high amplitude of in-phase and out-of-phase resonances. The piezoelectric patch PI 151 is introduced on the base of the cantilever beam. Therelative velocity between host structure and absorber can be exploited to mechanically deform the piezo-electric material. The transducer bonded on the beam is connected on the shunt circuit. Measurement andsimulation of the acceleration are performed in open circuit in order to avoid influence from the electriccircuit.

Once the mechanical model is validate by comparison of the host mass acceleration, it is possible to performthe simulation of the relative velocity between host structure and absorber (see Figure 5). It is important toobserve, as it will be defined in the following chapter, that the amount of power generated by piezoelectricmaterial is proportional to the deformation velocity of the transducer.

The excitation force has been generated by a TIRA shaker TV 50018 directly on the host structure.

Obviously, the highest amplitude at the resonance will generate the highest voltage. The aim of the author isto define the electric storage circuit connected to the transducer in order to have an optimal power generation


101 32.25 46.30 102

Mag

nitu

de [

-]

10-2

100

Single Degree of FreedomSimulationMeasurement

Frequency [Hz]101 102

Phas

e [°

]

-180

-90

0

90

180

Figure 4: FRF acceleration host structureagainst excitation force.

(Hz)

Frequency [Hz]101 102-180

-90

0

90

180

Phas

e [°

]

101 32.25 46.30 10210-4

10-2

Mag

nitu

de [

-]

Figure 5: FRF relative velocity against excita-tion force.

in the frequency range between the two resonances. The electrical parameters are defined by a inclusivestudy for choosing the capacitance and resistance loads. The combination between the dissipation effect ofthe absorber and the power generation of the harvester for the same frequency range is performed.

4 Piezoelectric device modeling

The system considered for the purpose of energy harvesting is based on an electromechanical model neces-sary to describe the dynamic behavior. The absorbed system defined in the previous chapter is implementedwith a piezoelectric material attached to the beam. The piezoelectric is considered to be perfectly bonded tothe beam and the electrodes are assumed perfectly conductive.

The relative velocity between base mass and absorber generates the transverse displacement of the beamgenerating the alternative current at the electrode attached to the piezo-material.

Thus, the governing equation of the electromechanical structure, can be written as:

Mx(t) + Cx(t) + Kx(t) + αv(t) = F (t) (4)

−αT xrel(t) + Cpv(t) = −q(t) (5)

where M is the total mass matrix, C is the damping matrix, K is the stiffness matrix, Cp is the piezoelectriccapacitance, F (t) is the external force applied and α is the electromechanical coupling matrix. The temporalvariables q(t), v(t) and x(t) are the charge, the voltage generated and the displacement vector respectively.The dot over this variables represents the time derivative. Finally xrel represents the relative displacementbetween base mass and absorber. The equation defined above can represent a real power harvesting systemonly if the piezoelectric transducer is connected to a rectifier circuit.

For the piezoelectric element, it is supposed to be bonded on a vibrating beam and is working under 3-1 mode(see Figure 6). Under some assumptions, as motion wavelength is much larger than the length (l) and lengthand width (w) of the element much larger than the thickness (t), it is possible to define four dimensionalrelations:

F = twT1, x = lS1, V = −tE3, Q = wlD3. (6)


Figure 6: Scheme of piezoelectric patch

where F, x indicate force and displacement in the direction 1st; while V and Q denote respectively voltageand charge in the 3rd.

For the dynamic behavior, more relations are needed. In particular, the definition of short circuit stiffnessKE , clamped capacitance Cp and electromechanical coupling coefficient of the harvester element. Theinternal clamped capacitance of the piezoelectric transducer without external load is given by Eq. 7 [3]. It isa function of the size and the permittivity constant of the harvester εS33.

Cp =wl

tεS33 (7)

For the dimensionless coupling coefficient (kd), it can be calculated by the knowledge of the open circuitnatural frequency ωD and the short circuit natural frequency ωE :

k2d =

(ωD)2 − (ωE)2

(ωD)2(8)

A clear physical interpretation of the dimensionless electromechanical coupling is defined by Premountin [7].

Considering a piezoelectric transducer subjected to the following mechanical cycle: first, it is loaded witha force F with short-circuited electrodes. The resulting energy stored (W1) in the system is proportional tothe stiffness of short circuit and the load force. At this point, the electrodes are open and the transducer isunloaded according to the new electrical boundary conditions. The energy recovered (W2) leaves an amountof energy stored in the transducer. The ratio between the remaining stored energy and the initial energy is:

k2d =

W1 −W2

W1(9)

Such relation persists in case of the transducer is subjected to an electrical cycle. From that, the dimensionalelectromechanical coupling can be obtained by Eq. 10:

α2 = k2dK

ECp (10)

5 Energy storage circuit modeling

5.1 Energy storage circuit

The standard energy harvesting is the basic circuit to storage energy from the environmental vibrations. Inthis application only the harvesting function contributes to the effect of structural damping. In Figure 7 isdepicted the interface circuit applied in linear processing of harvested power. The electromechanical beam issimulated through an equivalent source voltage with a piezoelectric capacitance CP . In the real applications,


a rectifier circuit is necessary to convert the AC voltage generated from the piezoelectric transducer in DCthat it is able to feed directly an electronic device. The non linear circuit is composed of a full wave rectifier,a filter capacitor (CL) and a load resistance in parallel (RL).

Figure 7: Schematic circuit for SEH

The filter capacitor is assumed to be large enough in order to that the voltage across the resistance (Vrect)is relatively constant. The capacitor yields also a reduced ripple parameter. It is a small unwanted residualperiodical variation of the DC output which has been derived from a AC source. It is due to the incompletesuppression of the alternating waveform. A high value of the ripple parameter is inappropriate for poweringdevices with DC voltage.

The goal of the optimization of the electric circuit is principally to maximize the power generated (Pavg)by the piezoelectric harvester. Moreover, since the capacitor is required to collect the energy produced,the energy stored in the capacitor (EC) needs to be considered. This energy is directly proportional to thecapacitance value. It must be considered that higher is the capacitance, more time is needed to power theresistance load. In the same time, the combination between CL and RL has to be taken into account sincethis affects the time of charge and discharge (τ ) by:

τ = RLCL (11)

For small value of RL, the discharging of the circuit takes a short time. To conclude, τ has to be maximizedin order to obtain a good quality of the rectified signal and a better ripple value.

The set of relations that needs to be used for the optimization of the electric circuit are defined in Eqs. 12,13 and 14:

Pavg =v2avg

RL; (12)

EC =1

2CLv

2L(t); (13)

ripple[%] =vrmsAC

vavg× 100; (14)

where vrmsAC is the root mean square of the component AC of the signal and vavg the average DC voltage.The ripple calculation is possible only for stationary voltage signals. In this case the root mean square caneasily be calculated.


For the study, in order to reduce the ripple value, a LC filter is implemented in the circuit (see Figure 8).The inductor is placed at the input to the filter and it is in series with the output of the rectifier circuit. Theaction of the inductor is to keep a constant current flowing to the load throughout the complete cycle of theinput voltage. Consequently, the output voltage instead to reaches the peak value of the applied voltage,it approximates the average value of the input at the filter. As a result, the amplitude of ripple voltage isreduced without reducing the DC output voltage.

It is possible in this way to consider a lower value of resistance load -and a consequently higher powergenerated- than without LC filter.

Figure 8: Schematic circuit for SEH with LC filter

Using the study of Motter [3], the optimization of the electric circuit is developed. Once the piezoelectric material and the diodes have been selected, the optimal capacitance CL and the optimal resistance RL can be defined. The selection of electrical parameters is performed in order to have, in the range between the first and second resonance, the best compromise of power generated.

After checking several kind of diode, the Schottky BAT48 is selected for its good electric characteristic. The interest is focused on the low forward voltage drop, in order to have a voltage amplitude reduction as lowest as possible. To identify correctly the relationship between current and voltage of the diode, a small simple test was performed using a DC power supply, and a small resistance. By measuring the voltage across the resistance, the electrical parameters of the diode can be determined and the behavior defined by a representative curve.

For the piezo-element, the set-up defined in [5] is used. The transducer material introduced in the test rig is the PI 151. The patches attached on the cantilever beam have the dimension of 70mm x 25mm x 2mm. Finally all the main electrical parameters used in the simulation are listed in Table 1.

Parameter Simbol ValueForward voltage drop diode VD 0.24 VInternal resistance diode RD 100 Ω

Piezoelectric capacitance Cp 36 nFElectromechanical adimensional coupling k2 0.035

5.2 Capacitance and resistive load definition

The main idea is to expand the optimization method of a SDoF defined in [3] for a MDoF system. Theoptimization is performed in the range of frequency between the two resonances of the mechanical system.

Table 1: Electrical parameters utilized in the simulation.


Assuming that the electric circuit is in open circuit by setting for the load resistor RL an infinity value, asinusoidal excitation signal of 5V is applied to the source voltage. Considering the time charging, level ofvoltage provided on the load and the stored energy, the capacitance load CL is performed.

For the analysis the frequency f = 32.25 Hz is used. At this frequency the greatest intensity of vibration inthe mechanical system is obtained (see Figure 4). The results slightly differ in case one of the frequencies ofthe interest range has been used for the analysis.

Figure 9 shows the estimation of the voltage in output from the full-wave rectifier circuit.

Time [s]0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Vol

tage

[V

]

-1

0

1

2

3

4

5

CL

=1mF

CL

=1007F

CL

=107F

CL

=17F

CL

=100nF

CL

=10nF

Figure 9: Evaluation of capacitive load.

The simulation is performed for different values of capacitance. Low value of CL yields long time to reachthe steady state. Thus the value of 1 mF is unacceptable. For the other values, the steady state is reached ina quite short time (with CL = 10 µF in t = 0.07 s the voltage reaches the 80% of steady state value).

Using Eq.13, the energy stored is defined and can be utilized for the determination of the right choice. For thefirst resonance frequency, when CL = 100 µF the steady voltage amplitude vL is 4.45 V and the EL = 990µJ. For CL = 10 µF, vL = 4.51 V and EL = 103 µ J, when CL = 1 µF, the simulation yields vL = 4.52 Vand EL = 10 µ J. Finally either with CL = 100 nF and CL = 10 nF the steady voltage amplitude reached isvL = 4.53 V but the energy stored dropped to EL = 1 µJ and EL = 102 pJ respectively.

Thus the right choice results CL = 100 µ F for all the interesting frequency range (32.25 Hz ÷ 46.30 Hz).With this solution the charging time is a bit higher than in the other cases but the level of energy resulted isconsiderable bigger compared to the other values.

Once the capacitance value is defined, an appropriate resistive load RL to absorb the active power needs tobe selected. Any kind of electronic device can be, in the simplest approximation, defined as such passiveelement. As in the analysis above, the simulation is performed in all the frequency range of interest andwith an input voltage amplitude of 1V . In Table 2 are listed the average results in all the range for differentvalues of resistance. In particular, average voltage values vavg, rms amplitude of AC voltage vrms and theaverage of power consumed Pavg. The filter LC is employed in the circuit to maintain a certain amount ofripple and voltage level measured at the resistance terminals (see Figure8). In addition, the Table 2, the rippleparameters without (Ripple) and with (RippleLC) filter are shown.

For an arbitrarily chosen frequency of 42 Hz, is shown in Figure 10 the different of the DC current when theLC filter is employed or not.


Table 2: Evaluation for the optimal resistive load.

RL vavg [V ] vrms [V ] Ripple [%] RippleLC [%] Pavg [µW ]

1kΩ 0.3245 0.1225 71.91 37.77 105.2810kΩ 0.4943 0.0250 10.07 5.05 24.43100kΩ 0.5449 0.0033 1.19 0.60 2.971MΩ 0.5564 0.0004 0.15 0.08 0.3110GΩ 0.5592 0.0001 0.02 0.01 0.001TΩ 0.5592 0.0001 0.02 0.01 0.00

time [s]0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5

Vol

tage

[V]

1.05

1.06

1.07

1.08

1.09

1.1

1.11

DC Voltage No FilterDC Voltage Filter

Figure 10: Steady state output voltage without and with LC filter.

Analyzing the results it is detected that a higher resistance yields a lower ripple parameter. It is due to thecharging time τ . When this parameter grows, the discharging signal became smoother. The filter allowsto keep the ripple parameter even lower than without. Increasing the parallel CL and RL (while CP is thesame), also a higher voltage on the load is obtained.

As can be seen numerically in Eq.12 the power generated decreases significantly when the resistance in-crease. With RL higher then 1 MΩ the output voltage is not changing anymore, and the residual periodicalvariation is almost completely canceled. Consequently the power generated is approximately zero.

For the first two values of resistance (RL = 1 kΩ and RL = 10 kΩ) the power obtained is very high.Nevertheless the output average voltage and the high ripple parameter make both the choices unacceptablefor powering loads with voltage DC.

Therefore, the final electrical configuration chosen is a parallel of CL = 100 µF and RL = 100 kΩ for allthe frequency range. For the filter, the inductance LF selected is equal to 10 µH.

5.3 Validation electric circuit

The experimental validation of the electrical circuit model is performed setting two different frequencies,the first one between the two resonance frequencies (f = 41.3 Hz), and the second completely outside ofit (f = 300 Hz). In this subsection, the alternative voltage from the piezoelectric and the rectified outputvoltage are recorded with an oscilloscope. In order to detect the transitory conditions, the input is applied att = 0.25 s and both simulation and measurement are performed for a total of T = 0.50 s. For the amplitudeof the simulation, it is considered the maximum applied voltage in the measurement. By using the peak valueof the sinusoidal voltage source measured experimentally, a voltage of 1.52V is applied in both analysis.


In Figure 11 is shown the comparison between the measurement and the simulation when the working fre-quency is equal 41.30 Hz. As it is possible to see, the value of steady state DC voltage and the rising timematch quite well. Same conclusions can be extrapolated with different working frequencies. In Figure 12,the comparison is performed for a frequency of 300 Hz.

time [s]0 0.1 0.2 0.3 0.4 0.5

Vol

tage

[V

]

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

AC Voltage MeasuredDC Voltage Measured

time [s]0 0.1 0.2 0.3 0.4 0.5

Vol

tage

[V

]-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

AC Voltage SimulatedDC Voltage Simulated

Figure 11: Piezoelectric and load voltage measured (left) and simulated (right) at f = 41.30Hz.

time [s]0 0.1 0.2 0.3 0.4 0.5

Vol

tage

[V

]

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

AC Voltage MeasuredDC Voltage Measured

time [s]0 0.1 0.2 0.3 0.4 0.5

Vol

tage

[V

]

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

AC Voltage SimulatedDC Voltage Simulated

Figure 12: Piezoelectric and load voltage measured (left) and simulated (right) at f = 300Hz.

The simulation gives a satisfactory result, but shows a lower level of ripple. It is due to the linear behaviorassumed for the diodes. The dynamic of the ripple can not be completely evaluated by a linear model. In anycase, due to the relatively small value of this parameter in the experimental and simulated results, the modelcan be considered satisfactory for the simulation of the shunt circuit behavior.

As suggested in [3], the absorber power harvesting device can be tested as a indicator of the charging level ina battery. Introducing a Light Emitting Diode (LED), in parallel to a capacitor, it is possible to determinatethe time to charge completely the battery. The measurements are performed with an excitation at the basemass of amplitude equal to 1 N and at different frequencies. In particular the two resonance frequencies(f = 32.25 Hz and f = 46.30 Hz), the initial SDoF resonance (f = 41.30 Hz) and a frequency completelyoutside of the optimization range (f = 65.0 Hz) are used. In the circuit a big capacitor of C = 1000 µF isemployed. Considering the LED with a null internal impedance, the resistance used is equal to the optimalload determinate in the study above.


The results are compared and showed in Figure 13. The high relative displacement at the resonance frequen-cies implicates a short charging time for the battery and moreover a quite high level of voltage across theLED. In particular, as excepted from the FRF, the out-of-phase resonance generates the highest voltage level.It is interesting to denote that also at the frequency of 41.30 Hz, the voltage collected is enough to be em-ployable, even if it needs a longer time. Therefore, it is possible to have at the same frequency, the absorptionof the base mass and the production of electric energy for charging small sensors. Finally, analyzing the lastfrequency of 65.0 Hz, the voltage collected is still almost zero after almost three minutes. Those workingpoint results completely not suitable for powering monitoring devices.

time [s]0 50 100 150

Vol

tage

[V

]

0

0.5

1

1.5

2

2.5

3f=32.25 Hzf=41.30 Hzf=46.30 Hzf=65.00 Hz

Figure 13: Charging time of the battery for different working frequencies.

6 Application in real scenario

As a possible real application it was decided to use a precision centigrade temperature sensor LM35 of Na-tional Semiconductor. Those are device whose output voltage is linearly proportional to the environmentaltemperature. Usually it can be used with a power supply to guarantee the minimum voltage needed for thecorrect measurement.

In the case presented, the power supply is replaced by the 2DoF with EHVA. It is supposed to have a cyclicstory of load on the base mass. A sinusoidal load with frequency of f1 = 65.0 Hz is active for t1 = 45 s onthe system. Afterwards, for t2 = 15 s another harmonic load at f2 = 41.30 Hz is exciting the multi body. Asexpected from the study above, the high frequency excitation is not able to power the sensor. For this reasonthe first semi-cycle is called “discharge time”. The vibration amplitude of the SDoF at the resonance (41.30Hz) is damped by the presence of the vibration absorber. Taking advantage of the relative velocity betweenhost structure and absorber, the deformation of piezoelectric material is performed. The energy produced atthis frequency is collected to power the temperature sensor when the working conditions do not allow a goodgeneration of energy. Thus this semi-cycle is considered the “charging time”.

With an amplitude excitation of 5 N, in Figure 14 is shown the dynamics of the system. In Figure14-a isdepicted the voltage generated in output from the rectifier related to the frequency working evolution. It isvisible that in the first part of the excitation cycle (t1) the produced voltage is very low, while it increases inthe second part (t2).

In Figure14-b the charge in the battery is illustrated in blue. It is compared with the signal used to activate thetemperature sensor in orange. The capacitance of the battery is 1000 µF, and when the sensor is disconnected,


the discharging time is quite slow. The activation time is 8% of the excitation total cycle, and it is performedtwo times per cycle. In this way it is guaranteed the minimum voltage across the battery needed for the user.

0 50 100 150 200

Vol

tage

[V

]

0

5

10

15

20Voltage rectifiedFrequency story

time [s]0 50 100 150 200

Vol

tage

[V

]

3

4

5

6

7Voltage batteryActivation sensor

a

b

f=41.3 Hz

f=65 Hz

Off

On

Figure 14: Time dynamics of rectified voltage during the excitationcycle (a). Time dynamic of the battery charge level and signal foractivation sensor (b).

Obviously it is a good idea avoid to activate the sensor during the charging time. In the case the sensor is on,in fact, the charging dynamic is slower than when it is off (compare in Figure 14-b at t = 50 s and t = 55 s).

Finally, in Figure 15 the aim of this application is shown. The sensor is intermittently activated, in order tohave eight measurements in a total range time of T = 220 s. In the picture are depicted also the referencetemperature and the activation signal of the sensor. In particular, the reference is measured by another equaltemperature sensor collocated in the same room and continuously externally powered.

Conclusively, a good result can be appreciate. The measured temperature completely match with the refer-ence. Keeping the capacitance voltage the minimum working voltage of the sensor it is possible to avoidthe presence of error in the measurement. The measurement is performed either during the charging anddischarging time.

It is proved how vibration power harvesting represents a huge potential for different applications simultane-ously. The resonance frequency of the SDoF is absorbed and the introduction of the new body is used todeform an harvesting material.

Surely, one of the two resonance frequencies of the multi body represents a better condition for the generationof power. However, in this case a high and probably unacceptable value of vibration is presented.

7 Outlook and conclusion

Mechanical vibrations represent a potential source for generating electric power. In particular, the amount ofpower is suitable for applications mainly in networks for structural health monitoring. Obviously mechanicalvibration affects the ordinary operation of the systems. For that reason several solutions are defined in order


time [s]0 20 40 60 80 100 120 140 160 180 200 220

Tem

pera

ture

[°C

]

-5

0

5

10

15

20

25

30Measured temperatureReference temperatureActivation signal

OnOff

Figure 15: Temperature measurement compared with the reference mea-surement.

to absorb the vibrations, avoiding their effects on the ordinary operations. In this sense, vibration absorbersare usually installed to improve the mechanical performance. The energy absorbed of the host structure isbalanced by the existing relative displacement between the two bodies. It is demonstrated in this article thatit is possible to convert the relative deformation into electrical energy by the introduction of an harvestertransducer.

In the paper it is illustrated how to achieve such aim with a simple and intuitive design process. The electricalparameters have to be optimized in order to obtain a low value of energy dissipation. In fact, the mainchallenge in harvesting ambient mechanical energy with micro scale energy harvesting device is conditioningand transferring energy without dissipating considerable power in the process. Nevertheless, a net continuouspower output of micro-watts is enough to charge a battery to supplement the energy for a sensor. Thepractical example performed in the paper is regarding the exploitation of a temperature sensor powered justby mechanical vibration.

Capacitance of the load, resistance and filter LC must be carefully designed. The electrical parameters affectnot only the output power generated level, but also the ripple parameter. Another important point is tochoose an adequate value of excitation frequency. It is showed that, in this case, the out-of-phase resonancegenerated the higher amount of voltage.

Finally, the paper conclude with a basic example using a temperature sensor. Thanks to the converted energygenerated by an absorbed base mass, the monitoring of temperature of the room is performed.

In the paper the standard energy harvesting circuit is used. It represents the simplest real circuit that canbe implemented and it is characterized by low complexity, poor load independence, but presents also a lowpower generation. The low power is due to the present in the waveform of negative power in some intervals.It is indicating that the energy returns from the electrical system to the mechanical system. This behaviorinhibits the energy conversion efficiency [8].

In order to improve the conversion efficiency, new techniques called synchronized switch harvesting (SSH)is proposed by Richard et al [9]. The SSH technique involving an electrical switch (usually an active switchand a small inductor) increases the piezoelectric transducer output voltage. Thus results in a relevant increaseof the power generated. The switch allows the circuit to convert the energy only on the maxima and minimaof the displacement. With this appropriate control of the switch, this circuit can overcome the energy returnphenomenon. In particular, it make sure that the power always flows into the electrical part.


In the last years several kinds of SSH are developed in the literature. While the application of this tech-niques has significantly increased the power harvested using piezoelectric generators, the energy losses inthe switching elements cannot be neglected. As consequent, the losses reduce the voltage inversion effi-ciency. Moreover, those circuits represent an high implementation complexity, high effort for simulate thebehavior and therefore optimize the parameters.

More work is planned in order to implement the idea in the rotating systems. As shown in this article, avibration absorber is used to damper the torsional vibration in a drive-train. Moreover, the additional body isused to generate transverse displacement of piezoelectric transducer. The aim of the author for the next studyis to create an additional source of power, directly on the system. The issues in the energy transfer betweenstationary system and rotating part are partially exceed in this way.

Acknowledgements

The authors gratefully acknowledge the European Commission for its support of the Marie Sklodowska-Curie program through the ITN EMVeM project (GA 315967).

References

[1] F. Infante et al, Modelling of drive-train using a piezoelectric energy harvesting device integrated with a rotational vibration absorber, Proceedings NOVEM, Dubrovnik, Croatia (2015).

[2] H. A. Sodano, G. Park, D. J. Inman, Estimation of Electric Charge Output for Piezoelectric Energy Harvesting, Strain, Vol. 40, pp:49-58 (2004).

[3] D. Motter, J. V. Lavarda, S. da Silva, Vibration energy harvesting using piezoelectric transducer and non-controlled rectifiers circuits, J. of the Braz. Soc. of Mech. Sci. & Eng., Vol. 34, pp:378-385 (2012).

[4] M. A. Clementino, M. J. Brennan, S. Da Silva, Optimization of the electrical and mechanical parame-ters of a vibration energy harvesting, Blucher Mechanical Engineering Proceedings, Sao Paulo, Brasil (2014).

[5] S. Perfetto et al, Test rig with active damping control for the simultaneous evaluation of vibration control and energy harvesting via piezoelectric transducers, Proceedings MOVIC, Southampthon, UK (2016).

[6] J. R. Liang, W. H. Liao, Piezoelectric energy harvesting and disipation on structural damping, Journal of Intelligent Material Systems and structures, Vol. 00, (2008).

[7] A. Preumont, Mechatronics. Dynamics of Electromechanical and Piezoelectric Systems, ULB Active Structures Laboratory, Brussels,Belgium (2006).

[8] A. Nechibvute et al, Piezoelectric energy harvesting using synchronized switching techniques, Interna-tional Journal of Engineering and Technology, vol.2, no.6 pp. 936-946, (2012).

[9] C. Richard et al, Synchronized switch harvesting applied to self-powered smart systems: piezoactive microgenerators for autonomous wireless transmitters, Sensor. Actuat. A: Phys, vol.138, no.1 pp. 151-160, (2007).


a study of the electric circuit of a vibration energy...

Documents