![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.](https://image.slidesharecdn.com/d5912b93-f480-465c-a92a-5911c40fc68c-150413205255-conversion-gate01/85/E240-project-report-2-1-320.jpg)
![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)𝑧̈ + (𝑏0 + 𝑏1)𝑧̇ + (𝑘0 + 𝑘1)𝑧 − 𝑘1 𝑥0
= −(𝑚0 + 𝑚1)𝑎 𝑖𝑓 𝑧 ≥ 𝑥0
𝑚0 𝑧̈ + 𝑏0 𝑧̇ + 𝑘0 𝑧 = −𝑚0 𝑎 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
3
𝑃√
2𝑚 𝑚
𝜋𝑘 𝑏 𝑇
(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
∗
(
2𝑘31 𝑡 𝑐
𝑐2
)2 𝑐 𝑝
𝜀
𝑧̈2
[
𝑤 𝑛
2
𝑤𝑅𝐶 𝑏
−𝑤(
1
𝑅𝐶 𝑏
+2𝜁𝑤 𝑛)]2+[𝑤 𝑛
2(1+𝑘31
2
)+
2𝜁𝑤 𝑛
𝑅𝐶 𝑏
−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 𝑧̈ 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](https://image.slidesharecdn.com/d5912b93-f480-465c-a92a-5911c40fc68c-150413205255-conversion-gate01/85/E240-project-report-2-2-320.jpg)
![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.](https://image.slidesharecdn.com/d5912b93-f480-465c-a92a-5911c40fc68c-150413205255-conversion-gate01/85/E240-project-report-2-3-320.jpg)
E240. project report (2)
- 1. 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.
- 2. 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)𝑧̈ + (𝑏0 + 𝑏1)𝑧̇ + (𝑘0 + 𝑘1)𝑧 − 𝑘1 𝑥0 = −(𝑚0 + 𝑚1)𝑎 𝑖𝑓 𝑧 ≥ 𝑥0 𝑚0 𝑧̈ + 𝑏0 𝑧̇ + 𝑘0 𝑧 = −𝑚0 𝑎 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 3 𝑃√ 2𝑚 𝑚 𝜋𝑘 𝑏 𝑇 (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 ∗ ( 2𝑘31 𝑡 𝑐 𝑐2 )2 𝑐 𝑝 𝜀 𝑧̈2 [ 𝑤 𝑛 2 𝑤𝑅𝐶 𝑏 −𝑤( 1 𝑅𝐶 𝑏 +2𝜁𝑤 𝑛)]2+[𝑤 𝑛 2(1+𝑘31 2 )+ 2𝜁𝑤 𝑛 𝑅𝐶 𝑏 −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 𝑧̈ 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
- 3. 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.