A study on the piezoelectric energy conversion system using motor vibration

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 4, pp. 573-579 APRIL 2012 / 573

DOI: 10.1007/s12541-012-0073-8

NOMENCLATURE

m = mass

c = damping coefficient

k = spring coefficient

w = excitation frequency

F0 = amplitude of force

x(t) = displacement of beam’s tip

Y = base displacement

wn = natural frequency

wb = excitation frequency

ζ = damping ratio

cp = elastic constant of the piezoelectric material

k31 = piezoelectric coupling coefficient

tc = thickness of one layer of the piezoelectric material

k2= geometric constant that relates average piezoelectric

material strain to the tip deflection

ε = dielectric constant of piezoelectric material

R = load resistance

V = voltage across the load resistance

Cb = capacitance of the piezoelectric birmorph

1. Introduction

In the last decade, energy harvesting technology has attracted

engineers and researchers of civil, electric and mechanical fields

with its potential for implementing a structural health monitoring

system of infra structures such as bridges, buildings, etc. Notably,

the wireless sensor applied in the monitoring system needs

electrical power without limit of life. Therefore, it is necessary to

develop an autonomous power system that operates sensors without

batteries or wired power. Energy harvesting technology is one of

the solutions to this power source problem. This technology that

convert wasted energy into electrical energy is one of the solutions

to overcome the disadvantages of a wireless sensor system. By

recycling wasted vibration energy from structures or environment,

energy harvesting technology is able to change typical vibration

energy into electrical energy.

Many studies and industrial approaches focus on the

piezoelectric elements to change vibration to electrical energy.

Many papers have been published by lots of university laboratories

and research centers. Methods of energy conversion of vibration to

electrical energy are piezoelectric, electromagnetic and

electrostatic.1-4 Researches on piezoelectric effect focus on

analytical modeling of piezoelectric material,5 efficiency of

piezoelectric material properties6,7 and proposition of new

structures for widening resonant frequency8,9 and increasing

efficiency of energy conversion.10-12 The study of multimodal

energy harvesting is improvement of efficiency to combine

A Study on the Piezoelectric Energy ConversionSystem using Motor Vibration

Jaeyun Lee1 and Bumkyoo Choi1,#

1 Department of Mechanical Engineering, Sogang University, 1 Sinsu-dong, Mapo-gu, Seoul, Republic of Korea, 121-742# Corresponding Author / E-mail: [email protected], TEL: +82-2-705-8639, FAX: +82-2-712-0799

KEYWORDS: Piezoelectric, Vibration, Energy conversion, Harvesting, Motor health monitoring

This study is focused on the piezoelectric system to use a fixed frequency range from the real motion of motor for

implementing wireless sensor network. The energy conversion system is made up of a cantilever beam including a

piezoelectric mechanism. The natural frequency of the system is designed near the frequency range of external source. The

design parameters are determined by FEM simulation of stress and strain distribution for various types of the beam

configurations. The simulation and experimental results show that the generating power from the trapezoidal configuration

is more efficient than that from the rectangular configuration. From the motor vibration (0.3g at 205Hz), the trapezoid

energy harvesting module extracts power of 56uW with the load resistance of 800k. Then, a test applicable to the motor

demonstrates that the conversed energy can be charged/discharged in a capacitor (22uF). Therefore, it is possible to power

motor health monitoring with energy harvesting using motor vibration.

Manuscript received: January 17, 2011 / Accepted: November 10, 2011

© KSPE and Springer 2012

574 / APRIL 2012 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 4

piezoelectric and electromagnetic types applied to a low frequency

region.13,14

This study focuses on motor health monitoring. Motors are

common parts of industry, construction and home appliance. An

energy conversion system for monitoring adopts a piezoelectric

resonant cantilever with PMN-PT. To determine an efficient

structure of cantilever, simulation is performed to understand stress

distribution on the beam. Simulated model is verified by

experiments.

2. Modeling of piezoelectric energy conversion system

2.1 Source of Energy Harvesting

When designing a resonant cantilever beam, it is important to

measure and analyze the external vibration source. First, the

motor’s vibration amplitude and frequency are measured using an

accelerometer. According to the motor’s size and operation rpm, the

vibration spectrum from the motor has various frequencies and

amplitudes. Fig. 1 shows the acceleration in the time domain and

frequency domain. At 218 rpm, maximum amplitude is 0.36g (g =

9.8m/s2) and frequency of maximum amplitude is 205Hz. Based on

data, the natural frequency of energy harvesting module is fixed at

about 205Hz. Energy harvesting systems with a resonant type

employ a cantilever. The natural frequency of the cantilever is

easily controlled by a mass of tip. In this study, two PMN-PT sheets

are attached to a beam and mass is located on the end of the beam.

Piezoelectric material causes simultaneously electric and

mechanical behavior and its applications are various; Sensor

applications include force sensors and displacement sensors using

piezoelectric effect. Actuator applications include linear motors and

precision stages with inverse piezoelectric effect. With dipole

moments, piezoelectric element generates proportionally electric

energy when mechanical energy is applied to it and vice versa. The

piezoelectric constitutive equation represents the relation of stress

and voltage.

ES s T dE= + (1)

TD dT Eε= + (2)

where S is strain, s compliance, E electric field, T stress, D

electric displacement, d piezoelectric coefficient, and ε dielectric

constant. From Eqs. (1) and (2), energy conversion relation is

expressed in piezoelectric coupling factors. The piezoelectric

coefficient, d, represents the amount of charge generated by the

relationship between stress and dipole moment. The piezoelectric

coefficient is a constant value in static loading, but variable in

dynamic loading such as resonant frequency. Equation (3) shows

the piezoelectric relation in both cases,

j ij i

D d T= (3)

where the indices are able to express 1 to 6 in Eq. (3). The

piezoelectric resonant beam based on vibration usually takes 31-

mode. Bending motion from vibration induces stress on beam

surface, and then stress is applied on the piezoelectric material. The

piezoelectric material transfers mechanical energy into electrical

energy.

The base excitation causes the beam with the piezoelectric

material attached to it to generate power. The equation (4) that

describes this generated power is a second order differential

equation.

0cosmx cx kx F wt+ + = (4)

The response due to the beam’s vibration caused by the

excitation of the base is as follows.

1/ 22 2

1 22 2 2 2

1

1 2 2

1

2

(2 )( ) cos( )

( ) (2 )

2tan

tan2

n b

n b

n b n b

n b

n b

n

b

w wx t w Y w t

w w w w

w w

w w

w

w

ζθ θ

ζ

ζθ

θζ

−

−

+= − −

− +

=−

=

(5)

The base excitation causes mechanical vibration. The beam’s

stress distribution to this vibration can be calculated from a

simulation. The piezoelectric material produces electrical energy

from the stress on the beam. In energy harvesting, the maximum

generated power of the electrical energy can depend on the material

properties, configuration and the load’s impedance.

(a)

(b)

Fig. 1 Motor’s Acceleration (a) and FFT Result (b) at 218rpm

(revolution per minute)

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 4 APRIL 2012 / 575

2

2

231

2

2 22

2 2 2

31

1

2 2

2

1 22 (1 )

pcin

n nn n

b b b

VP

R R

ck tA

k

w ww w w k w

wRC RC RC

ε

ζζ

= =

×

− + + + + −

(6)

When the excitation frequency and the system’s resonant

frequency are equal, the greatest amount of energy is transferred.

Therefore, the generated power can be expressed as the following:15

2

2 231

2

2

2 4 2 2 2

31 31

2

2 (4 )( ) 4 4

pcb in

b b

ck tRC A

kmP

k k RC k k RC km m

ε

ζ ζ ζ

= ×

+ + + (7)

Unfortunately, it is difficult to predict the generated power for a

complicated shape using the equation above. For analysis of shapes

more complicated than the basic model, the generated voltage from

the piezoelectric material should be analyzed using a commercial

FEM tool in order to obtain more efficient results. For this reason,

ANSYS was used to analyze basic parameters in the experiments.

2.2 Simulation of cantilever beam with PMN-PT

Prior to determining the design parameters of the energy

harvesting module, simulation with ANSYS is performed to

understand stress distribution according to the shapes of the

cantilever beam under loading same displacement at the end of

beam. Boundary conditions of simulation are that the end of the

beam is fixed and that the other end is applied 1mm displacement.

According to the analysis results displayed in Fig. 2, stress is

concentrated on the corners in the case with them in the middle of

beam. The brittle PMN-PT attached to the beam could be cracked at

that position. Deciding on two shapes (rectangular and trapezoid

without corners) based on the simulation, specific analysis is

conducted to ascertain the region occupying 50% of maximum

strain. The trapezoid design has 40% more strained area than the

rectangular design. The results of simulation are below. When a

beam with PMN-PT is loaded, trapezoid model generates power

more efficiently than the rectangular model because of the

additional strained region.

Piezoelectric material for energy harvesting is adopted as PMN-

PT which has excellent coupling factors among piezoelectric

materials, especially k31. PMN-PT’s properties are listed in Table 1.

With two beam shapes, modal analysis is performed because of the

natural frequencies of the cantilever beams at each mode. To

simulate modal analysis by ANSYS, the beam’s dimensions are in

Table 1. Beams are consisted of 2 PMN-PT layers and 1 stainless

steel layer as tri-morph (PMN-PT, Stainless steel, PMN-PT). Modal

Analysis results are in Table 2. Based on the beam’s natural

Fig. 2 Stress distribution for various shapes with same areas

Table 1 Material properties and dimensions of PMN-PT, elastic

compliance constants, Sij(10-12m2/N), piezoelectric coefficients,

dij(pC/N), eij(C/m2), electromechanical coupling factor, kij

(material properties offered by courtesy of Ceracomp Co. which

manufactures PMN-PT)

Material Properties

S11

ES12

E S13

E S33

E S44

E S66

E

52.2 -24.8 -25.5 57.5 16.3 33.2

d33 d31 d15 e33 e31 e15

1500 -679 169 22.1 -4.4 10.4

k33 k31 k15 kt k31 (45oC)

0.90 0.43 0.35 0.60 0.80

Dimension

(mm)

TrapezoidLength Width (narrow) Width (wide) Thickness

16.9 4.4 14 0.3

RectangularLength Width Thickness

20 8 0.3

Table 2 Modal analysis of rectangular and trapezoid beam with

PMN-PT

ModeThickness

(mm)

Beam

Shape

Freq.

(Hz)

Beam

Shape

Freq.

(Hz)

1

0.3 Rectangular

444.1

Trapezoid

808

2 6752.9 11187

3 8234.5 11670

440 441 442 443 444 445 446 447 448 449 4500

20

40

60

80

100

120

Freqeuncy(Hz)

Generated Voltage

Damping 0.01

Damping 0.05

Damping 0.1

24.29

12.74

110.9

(a) Rectangular (444Hz)

790 795 800 805 810 815 820 825 8300

10

20

30

40

50

60

70

80

90

100

Frequency(Hz)

Generated Voltage(V)

Damping 0.01

Damping 0.05

Damping 0.1

9.80

19.18

95.07

(b) Trapezoid (808Hz)

Fig. 3 Generated voltage according to damping ratio in the case of 1g

external vibration source with each natural frequency (444Hz,

808Hz)


frequency, harmonic simulation is conducted to predict the

generated voltage by external vibration source. Simulation results

are shown in Fig. 3 that shows generated voltage near resonant

frequency as function of damping ration in the case of 1g external

vibration source. Figure 4 represents that generated voltage near

natural frequency of acceleration with damping ratio 0.06.

According to the simulation results, generated voltage is

proportional to external source amplitude. With same area, the

trapezoid model which has a large clamping length has higher

resonant frequency and generates small voltage. However, trapezoid

model can produce high voltage when the frequency is adjusted to

match that of the external source (205Hz).

3. Experiments of piezoelectric energy conversion system

3.1 Experiment of piezoelectric beam

Compared with FEM analysis results, the energy harvesting

module is manufactured with the same dimensions as that of the

trapezoid modeling. Dimensions of the module are in Fig. 5.

Devices are manufactured with the same conditions of simulation.

Equipments of test consist of a shaker for sine vibration (Labworks

product), a controller (m+p controller) for signal generation and

feedback from an accelerometer (PCB product (50g)) on the shaker

and an oscilloscope (HP MSO 6104A) for measuring the generated

voltage from PMN-PT. Figure 6 is pictures of the test equipments

and the energy harvesting module on the shaker.

440 441 442 443 444 445 446 447 448 449 4500

5

10

15

20

25

0.2g

0.5g

1g20.8

10.4

4.16

(a) Rectangular (444Hz)

790 795 800 805 810 815 820 825 8300

2

4

6

8

10

12

14

16

18

Frequency(Hz)

Generated Voltage(V)

0.2g

0.5g

1g

16.12

8.06

3.23

(b) Trapezoid (808Hz)

Fig. 4 Generated voltage according external vibration source with

each natural frequency (444Hz, 808Hz with damping ratio 0.06)

Experimental results are in Fig. 7. The tri-morph rectangular

beam generates 40.9V (pk to pk), but the trapezoid beam produces

30.19V (pk to pk) at 1g acceleration. Table 3 shows the comparison

between simulations and experiments. These results are almost the

same as simulation in the case of damping ratio 0.06. However, in

Dimesion: 16 x (14+4.4)/2 x 0.3mm

Area of PMN-PT: 147.2mm2

Dimesion: 20 x 8 x 0.3mm

Area of PMN-PT: 160mm2

(a) Trapezoid Beam (b) Rectangular Beam

Fig. 5 Dimensions of energy harvesting module

(a) (b)

Fig. 6 Test equipments (a) and energy harvesting module on the

shaker (b)

(a) Rectangular

(b) Trapezoid

Fig. 7 Generated voltage according external vibration source


the cases of low acceleration (0.5g, 0.2g), results are different. Also,

generated voltage increases according to acceleration in the

simulation, but not proportional in experiments. When decreasing

acceleration, natural frequency also shifts forward to increasing

direction. In underdamped motion, frequency of underdamped

vibration is not the same as the natural frequency. The relationship

is represented by Equation (8).

21

d nw w ξ= − (8)

Therefore, frequencies based on measured data are the

frequency of underdamped vibration which affects the damping

ratio. Measured data informs damping ratio changeable depending

on applied acceleration magnitude.

3.2 Experiment of energy conversion system

This paper proposes motor health monitoring. The motor as a

target application has a natural frequency of 205Hz, and a

maximum amplitude of 0.4g. Even though the system frequency is

changeable depending on the applied acceleration, experiments of

the energy conversion system are conducted on acceleration and

205Hz environment for evaluation. For adjusting natural frequency,

mass is attached on tip of beam. The mass of rectangular beam is

1.04g, trapezoid beam 2.06g. According to the acceleration of

driving, generated voltage are listed in Table 4.

Table 3 Comparison between simulations and experiments

Acceleration

Condition

Voltage(pk-pk)/Frequency

Simulation (damping ratio 0.06)

Experiment

Rectangular

1g 40.16/444 40.9/444

0.5g 20.8/444 24.79/445.5

0.2g 8.32/444 11.16/446.5

Trapezoid

1g 32.24/808 31.93/808

0.5g 16.12/808 18.17/811.5

0.2g 6.46/808 7.966/812.5

Table 4 Peak to peak voltage according to acceleration at the

individual cases

Rectangular

with mass (1.04g) Trapezoid

with mass (2.06g)

Resonant Frequency(@1g)

205Hz 205Hz

Peak to peak Voltage(@1g)

58.75V 70.31V

Peak to peak Voltage(@0.5g)

20.62V 45.31V

Peak to peak Voltage(@0.2g)

6.25V 22.93V

Table 5 Experimental results of Trapezoid PMN-PT under 1g

acceleration

Resonant Freq.(Hz) 205

Internal Capacitance(nF) 7.2

Electrical Potential(V) 35.1

Generated Charge(C)(Q=CV)17 253e-9

Analytical Power (mW) (Power =1/2(CV2ω))8 0.894

Stored Energy(mW) in 100uF Capacitor 0.147

Following the prediction that the trapezoid beam can generate

higher voltage than the rectangular beam, the trapezoid beam can

show 1.2 times to 3 times higher voltage at a fixed frequency

(205Hz). Higher electric potential can make more electric power.

For energy harvesting that recycles wasted small energy, it is a

critical issue to convert as much of the mechanical energy as

possible into electrical energy. Therefore, the trapezoid beam is

more attractive structure. Energy conversion system with trapezoid

beam changes mechanical energy to electrical energy. Then the

converted energy is stored in a 100uF capacitor. It can produce

0.147mW electrical power as listed in Table 5.

To evaluate the damping coefficient, logarithmic decrements are

calculated based on various peak voltages. Figure 8 shows

responses of PMN-PT on the trapezoidal beam caused by different

initial conditions. Table 6 shows the peak voltages measured in each

case. In addition, in Table 6 are the calculated values of the

damping coefficients according to the peak’s number. At a peak

voltage of about 11V, the damping coefficient was 0.0267 and at

35V, the damping coefficient was 0.088. This shows that the

difference between the simulation results and the experiment results

was caused by the change in the damping coefficient.

4. Application of energy harvesting using a motor

vibration

The measured results using a shaker to harvest energy at a

vibration acceleration of 0.3g at 205Hz are shown in Fig. 9. The

acceleration of 0.3g at 205Hz was chosen according to the motor’s

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09-40

-30

-20

-10

0

10

20

30

40

Time(sec)

Voltage(V)

Case III

Case II

Case I

Fig. 8 PMN-PT responses depending on the various initial

conditions

Table 6 Peak voltages measured according to various initial

conditions

Voltage (V) Damping cofficient

Case I Case II Case III No. of

peak Case I Case II Case III

1 Peak -10.8 -25.5 35.2 2 0.0325 0.0653 0.1123

2 Peak -8.8 -16.9 17.3 3 0.0250 0.0529 0.0754

3 Peak -7.88 -13.1 13.6 4 0.0225 0.0408 0.0768

4 Peak -7.06 -11.8 8.23 Average 0.0267 0.0530 0.0882


driving frequency using a trapezoidal beam. According to the

results, the resonance of the energy harvesting module is 205Hz and

the generated voltage at this resonance is 18. The external

resistance enabling to extract the maximum electricity is 800kΩ and

the generated power at this resistance is 56uW. To show that power

can be extracted, a test of charging/discharging capacitor on the

circuit was conducted by applying the energy harvesting systems to

a motor. Figure 10 shows the energy harvesting systems applied to a

motor. The measured data are shown in Fig. 11. Left figure

represents generated voltage from the PMN-PT beam and right

graph shows charging/discharging a capacitor.

190 195 200 205 210 215 2200

2

4

6

8

10

12

14

16

18

20

Frequency(Hz)

Voltage(V)

Measurement of Voltage according to Freqeuncy at the 0.3g

(a)

101

102

103

0

5

10

Resistance(KOhm)

Voltage(V)

101

102

103

0

0.05

0.1Measured Voltage according to Resistance at the 0.3g, 205Hz

Power(mW)

(b)

Fig. 9 Measured peak voltages around resonant frequency (a) and

generated power according to external resistance (b)

Fig. 10 The energy harvesting systems applied to a motor

5. Conclusions

The vibration from the motor is the most attractive energy

source due to its abundance. Therefore, the aim of this paper is to

propose an energy conversion system that changes the vibration

into the electrical energy during motor’s operation. The target

frequency of the energy harvesting module is about 205Hz

occurring continuous vibration in 205Hz frequency region at fixed

condition. Inclinations of generated voltages in simulation and

experimental results are similar with each other. However,

underdamped system is affected by the damping ratio depending on

the amplitude of the applied acceleration. Generated voltage

according to acceleration is nonlinear because the damping factor is

not constant value. The main reason for the difference between

simulation and experiment results is the damping factor. Even

though the system frequency shifts, the trapezoid beam is more

suitable to the energy harvesting system at 205Hz driving frequency

because it converts mechanical energy into electrical energy more

efficiently. If the only purpose is to store high power, piezoelectric

material can produce higher voltage if the clamping boundary

lengthens. However, a long clamping area induces high stress and

fatigue of the bonding layer, which reduces system life. In future

work, it is necessary to optimize clamping length. To be stable,

energy conversion system must adopt a lower natural frequency

beam which has a light tuning mass light and a thinner PMN-PT

with high internal capacitance.

This system has improving points which are to optimize

structural design and impedance matching between the piezoelectric

material and the storage circuit. However, the experiments of the

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-20

-15

-10

-5

0

5

10

15

20

Time(sec)

Voltage(V)

(a)

0 2 4 6 8 10 12 14 16 18 202

2.2

2.4

2.6

2.8

3

3.2

3.4

Time(sec)

Voltage(V)

(b)

Fig. 11 The generated voltage from the PMN-PT beam (a) and

charging/discharging a capacitor (b)


energy conversion system demonstrate the feasibility of converting

ambient energy into electrical energy and then storing that energy.

The system is able to power wireless monitoring system to success

the long term usage by harvesting the required energy from the

ambient environment.

ACKNOWLEDGEMENT

This research was supported by the Converging Research

Center Program through the National Research Foundation of

Korea (NRF) funded by the Ministry of Education, Science and

Technology (No. 2010K000986).

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Documents

A study on the piezoelectric energy conversion system using motor vibration