Proceedings of E240, Winter 2015 H Nguyen, R Ozer, and J Sanches

POWER FROM THE PEOPLE: HARVESTING ENERGY FROM HUMAN ACTIVITY

Huu Nguyen, Rachel Ozer, and Jordan Sanches,

Department of Mechanical Engineering, Stanford University

Stanford, California

Abstract. Our team designed a MEMS-based piezoelectric device that can harvest energy from human movement, based on the

design of a frequency up-conversion stopper. The piezoelectric device consists of two cantilever beams with PZT-4 deposited on top

of them and iron proof-masses on top of each cantilever beam. The entire fabrication of the cantilever beams involves bulk silicon

micromachining and patterning of functional film layers. After each cantilever beams are fabricated, they are then stacked and

bonded together. A MATLAB simulation shows that our device can produce a peak power density of 519.5 μW/cm3 with a 52.6 Ω

resistance, and that the device’s operational frequency is about 5.74HZ.

Background. The purpose of this project is to develop a

MEMS-based piezoelectric device that can convert vibrations

from human movements into usable power. The device must be

small and compact enough for people to carry without hindering

movement, yet capable of generating enough energy to power a

small device. Many designs in the past have also tried to convert

vibrations into power by using MEMS-based piezoelectric

devices [1, 2]; however, those designs are not suitable for

harvest energy from human movements. The reason is that

piezoelectric devices generate their maximum power when the

operational frequency and resonance frequencies are same.

Because the power generated from piezoelectric devices is

proportional to the cube of the operational frequency, previous

designs have targeted sources with high frequencies.

Unfortunately, the frequency of human movement is low

(<10Hz); thus, very little power could be generated with past

designs [3].

Recently, there is a new technology called frequency-up-

conversion (FUC) stopper that converts low input frequency

into high output frequency [3]. We will use this technology to

convert the frequency of human movement to a higher

frequency so that the piezoelectric device can generate a usable

amount of power.

Design. The overall design of the FUC stopper is shown in Fig.1

[3], but we will rescale this design such that it can harvest

energy from human movements. The FUC stopper involves two

cantilever beams with two proof-masses mounted to each beam.

One of the cantilever beam has low resonance frequency around

frequency of the human movement (<10Hz) while the other

beam has much higher resonance frequency. In Fig. 1, the high

frequency cantilever beam is a straight beam with rectangular

cross-section area while the low frequency cantilever also has

rectangular cross-section area but it is longer and bends in S

form. When human moves, the low frequency cantilever

vibrates and hits the high frequency cantilever. This collision

causes the high frequency cantilever to vibrate at its own

resonance frequency. On top of the high frequency cantilever

beam, there are piezoelectric materials so that as the high

frequency cantilever beam vibrates, the piezoelectric material

will generate power. As for materials, we selected iron to make

up the proof-masses since it is cheap compare to other metals.

We used PZT-4 since its couple factor is high compare to other

piezoelectric materials.

Figure 1: (Left) Side view of the FUC stopper. (Right)

Isometric view of lower frequency cantilever.

Fabrication. The FUC stopper is fabricated as two separate

cantilevers that are stacked and adhered together. The top

cantilever is constructed primarily through the use of bulk

silicon micromachining and patterning of functional film layers;

and the beam is aligned along <110> direction. This process is

detailed in the paper “Fabrication and performance of MEMS-

based piezoelectric power generator for vibration energy

harvesting,” by Fang et. al. and displayed in Fig. 2[1]: 1. Functional films preparation: SiO2/Ti/Pt/PZT/Ti/Pt

2. Functional films pattern

3. Silicon slot etching by RIE

4. Back silicon deep etching by KOH solution

5. Cantilever release by RIE

6. Metal mass micro fabrication and assemblage.

The bottom cantilever is constructed without the functional

layers (as it doesn’t vibrate at a high enough frequency to

produce much power), following steps 3-6 outlined above; and

the beam is aligned along <100> direction. Once each of the two

cantilevers are fabricated, our team proposes that they be

stacked on top of each other (shown in Fig. 3) and eutectically

bonded, using a low-temperature Au alloy.

Proceedings of E240, Winter 2015 H Nguyen, R Ozer, and J Sanches

Figure 2: Top cantilever fabrication steps.

Figure 3: Final assembly of top and bottom cantilevers.

Analysis of Performance. The movement of the cantilever

beams is treated as mass-spring-damper system. The equations

that govern the interaction between high frequency cantilever

and low frequency cantilever are:

(𝑚0 + 𝑚1)�̈� + (𝑏0 + 𝑏1)�̇� + (𝑘0 + 𝑘1)𝑧 − 𝑘1𝑥0

= −(𝑚0 + 𝑚1)𝑎 𝑖𝑓 𝑧 ≥ 𝑥0

𝑚0�̈� + 𝑏0�̇� + 𝑘0𝑧 = −𝑚0𝑎 𝑖𝑓 𝑧 < 𝑥0 (1)

where x0 is the distance between two cantilevers, k is the spring

constant, b is the damping coefficient, m is the mass of the proof

mass, z is the displacement of the cantilever with lower

resonance frequency, a is the input acceleration, and subscripts 0

and 1 denote the low and high frequency cantilever beams,

respectively [3]. The damping coefficient is calculated from

Christian’s damp coefficient and scaled by a factor of 3;

therefore, the damp coefficient is calculated as [4]

𝑏 = 𝐴 ∗4

3𝑃√

2𝑚𝑚

𝜋𝑘𝑏𝑇 (2)

where T is temperature, P is pressure, mm=48.1*10-27

kg for air,

kb=1.380658*10-23

J/K, and A is the cross section area of the

proof-mass assuming each proof-mass has 1mm thickness. The

output power of the piezoelectric device is calculated as

𝑃 =𝑉2

2𝑅=

1

2𝑅

∗ (

2𝑘31𝑡𝑐𝑐2

)2𝑐𝑝

𝜀�̈�2

[𝑤𝑛2

𝑤𝑅𝐶𝑏−𝑤(

1

𝑅𝐶𝑏+2𝜁𝑤𝑛)]2+[𝑤𝑛

2(1+𝑘312)+

2𝜁𝑤𝑛𝑅𝐶𝑏

−𝑤2]2 (3)

where w is vibrating frequency, wn is resonance frequency, cp is

the elastic constant of the piezoelectric material, k31 is the

piezoelectric couple coefficient, tc is the thickness of the

piezoelectric, c2 is a geometric constant that relates average

piezoelectric material strain to tip deflection, ε is the dielectric

constant of piezoelectric material, Cb is the capacitance of

piezoelectric, ζ is the damping ratio due to air, R is the load

resistance, V is the load voltage, and �̈� is the magnitude of

acceleration from eq. (1) when z ≥ x0 [5]. We used MATLAB to

simulate the output power and the operational frequency

(frequency of human movement) from the dimensions of

cantilever beams, proof-masses, and properties of PZT-4 [6].

Table 1 lists all input parameters and output parameters.

Parameter Values

m0 10-7

(kg)

l0 10-3

(m)

h0 10-6

(m)

t0 10-6

(m)

m1 5*10-8

(kg)

l1 3*10-6

(m)

h1 4*10-5

(m)

t1 10-5

(m)

tc 10-4

(m)

a 0.5 (m/s2)

x0 10-4

(m)

k31 0.6

cp 135 (GPa)

𝜀 1475 (F/m)

Cb 7.08*10-18

(F)

Operational frequency 5.74 (Hz)

Optimize R 52.61 (Ω)

Peak power 0.01 (μW)

Estimated volume 1.92*10-5

(cm3)

Peak power density 519.5 (μW/cm3)

Table 1: Dimensions of cantilever beams, properties of PZT-4,

and output result

In Table 1, l is the length of the cantilever beam, h is the width, t

is thickness, and estimated volume is the volume that the proof-

masses occupy. Fig. 4 summarizes our device’s power density

output compared to those prototyped in other studies.

Figure 4: Power density vs. excitation frequency of MEMS

devices

Conclusions. From the MATLAB simulation, we expect that

our device has a power density of about 519.5 μW/cm3 with

operational frequency about 5.74Hz and load resistance of 52.6

Ω. Compared to other works, our device is more suitable to

harvest energy from human movement which has a low

Proceedings of E240, Winter 2015 H Nguyen, R Ozer, and J Sanches

frequency; and the power density is good compare to Lui et al.’s

work. However, we have not simulated whether the cantilever

beams would break when they vibrate and hit each other. At the

same time, in the simulation, we used the maximum acceleration

to calculate peak power even though the acceleration has

sinusoid behavior due to the spring-mass-damper system.

Therefore, the actual peak power might change as the

acceleration changes.

References.

[1] H Fang, J Liu, Z Xu, L Dong, L Wang, D Chen, B Cai, and Y Liu,

"Fabrication and Performance of MEMS-based Piezoelectric

Power Generator for Vibration Energy Harvesting", in

Microelectronics Journal, vol. 37, 2006, pp. 1280-284. [2] G. Tang, B. Yang, J. Liu, B. Xu, H. Zhu, C. Yang, “Development

of high performance piezoelectric d33 mode MEMS vibration

energy harvester based on PMN-PT single crystal thick film”, in

Sensors and Actuators A, vol. 205, 2014, pp. 150-155. [3] H. Liu, C. Lee, T. Kobayashi, C. Tay, C. Quan, “Piezoelectric

MEMS-based wideband energy harvesting systems using a

frequency-up-conversion cantilever stopper”, in Sensors and

Actuators A, vol.186, 2012, pp. 242-248. [4] H. Sumali, T. Carne, “Air-Drag Damping on Micro-Cantilever

Beams,” Sandia National Laboratories. [5] S. Roundy, E. Leland, J. Baker, E. Carleton, E. Reilly, E. Lai, B.

Otis, J. Rabaey, V. Sundararajan, P.Wright, "Improving Power

Output for Vibration-Based Energy Scavengers", in IEEE

Pervasive Computing, vol.4, no. 1, 2005, pp. 28-36. [6] C. Liu, “Piezoelectric Sensing and Actuation,” in Foundation of

MEMS, 2nd ed. Upper Saddle River, NJ: Pearson, 2012, ch.7, sec.

2, pp. 276-285.