Modeling, Design and Optimization of Hybrid ... - Semantic Scholar
IEEE 2008 Custom Intergrated Circuits Conference (CICC)
Modeling, Design and Optimization of Hybrid Electromagnetic and Piezoelectric MEMS Energy Scavengers Xiaochun Wu, Alireza Khaligh, Yang Xu Electrical and Computer Engineering Department, Illinois Institute of Technology 3301 South Dearborn Street Chicago, IL 60616 Abstract-A hybrid energy scavenging technique is introduced to harness ambient energy through electromagnetic and piezoelectric mechanisms to achieve higher power density and higher energy conversion efficiency in a high mechanical damping MEMS structure. By inspecting the second-order mechanical dynamic system for electromagnetic and piezoelectric energy conversions, a unified model is proposed to capture the relation of the recoverable hybrid energy and the input vibration frequency as well as the amplitude. Design trade-offs are considered for the hybrid scavenger size and power maximization. A hybrid MEMS energy scavenger design with optimization results for implementation is shown as an example. Keywords: energy scavenging, harvesting, piezoelectric, MEMS, hybrid energy conversion
battery. The battery supplies the power for the sensor, DSP, and low-power RF transceiver circuits. This paper presents a hybrid MEMS energy scavenging technique that coverts ambient kinetic energy to electricity both electromagnetically and piezoelectrically. The technique makes use of the commonality of ambient kinetic energy sources and has the advantage of improving the energy conversion efficiency, when the mechanical damping coefficient is high and the amounts of the two kinds of converted energy are comparable.
electromagnetic,
VDD
I. INTRODUCTION Energy scavenging from ambient energy sources is emerging as a potential solution to limited battery capacity. More and more electronics using batteries can be powered by energy from solar, electromagnetic fields, human motions, and mechanical vibrations. However, many applications are still limited by the recovered power and conversion efficiency. While low-power circuit design techniques are explored [1] to reduce the power requirements of electronics applications, it is of tremendous interest to develop new energy conversion devices to increase the power density and conversion efficiency [2-9]. Compared to the meso-scale counterparts, MEMS energy scavengers provide low power due to the small size. However, in ultra-low power applications such as wireless sensor nodes and implantable medical devices, MEMS energy scavenging becomes a plausible solution due to its small form factor and low cost in mass production. Since kinetic energy is a common source in the ambient environment, MEMS energy scavengers can be used in applications where other sources such as solar and chemical power are not available. Further, MEMS energy scavengers have the advantage of compatibility with integrated circuits. Fig. 1 shows the system diagram of an integrated selfpowered wireless sensor node. The voltage from the MEMS energy scavenger is regulated and then charges a storage
978-1-4244-2018-6/08/$25.00 ©2008 IEEE
Battery Vibration Energy Scavenger
Sensor
Power Regulation Circuit
DSP
TX RX
Fig. 1. Block diagram of an integrated self-powered wireless sensor node
II. BACKGROUND Human motions such as arm swing, horizontal foot motion, and center-of-mass motion are energy sources that have been attracting research on energy extraction for powering wearable electronic devices [11]. Energy extraction from human motion is especially useful for long-term monitoring of human body implantable devices. In [12], researchers have demonstrated a PZT unimorph piezoelectric power generator embedded in shoes with an RMS power of 1.8 mW and used it to power a digital RFID tag successfully. The authors in [13] introduced a meso-scale electro-magnetic energy scavenger for energy extraction from center-of-mass motion of human body. The scavenger has achieved a power density of 0.44 mW/cm3. But due to the large amplitude (a typical value of 4 cm – 7 cm) and low frequency (typically 2 Hz) for center-of-mass motion of human body, the power density will drop if the scavenger scales down to millimetre-
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scale or micro-scale, since the scavenger size will limit the amplitude of the proof mass vibration. Mechanical vibration is a common kinetic energy source in the environment, including vibrations of buildings, machine tools, and car engines. Typical ambient mechanical vibrations have a higher frequency and smaller amplitude than human motions. Researchers in [15] fabricated early prototypes of piezoelectric cantilevers (9 to 25 millimeters in length) with a relatively heavy mass on the free end, capable of generating 2 375 μW / cm 3 from a vibration source of 2.5 m/s at 120 Hz. The smaller vibration amplitude makes MEMS energy scavengers more applicable. Authors in [16] showed a conceptual design of a 5 × 5 × 1 mm 3 electromagnetic microgenerator and predicted power generation of 1 µW at 70 Hz and 0.1 mW at 330 Hz, assuming a deflection of 50 µm. To improve the power density of MEMS scavengers, hybrid energy scavenging is proposed, which has the advantage of extracting energy from multiple energy sources so that even if one energy source is not available in the environment, alternative energy sources may still supply power and the probability of “power outage” is smaller, increasing the reliability of the systems and enabling the energy diversification. Therefore, hybrid energy scavenging is a promising energy scavenger design trend. III. ANALYSIS AND MODELING A. Mass-Damper-Spring Model for Vibration Energy Scavengers Electromagnetic and piezoelectric energy scavengers based on proof mass vibration can be modelled as a second-order mass-damper-spring dynamic system. Fig. 2 demonstrates the schematic of a second-order energy scavenger model proposed by Williams and Yates [16]. The system consists a proof mass, m, a spring, k, a mechanical damping coefficient, bm, and an electrical damping coefficient, be. x and y represent the spring deflection and the input displacement, respectively. The differential equation that describes the system is given as Eqn. (1). (1) m&x& + (b m + b e )x& + kx = m&y&
The extracted output power is maximized, if the resonant frequency of a mass-damper-spring system, described in Eqn. (1), is equal to the input vibration frequency [16]. In this particular case and under the assumption that the power scavenging doesn’t hamper the source vibration, the extracted power is given in Eqn. (2), or equivalently, (3) [6]. mζ e ω3 Y 2 (2) PEM = 4ζ T2 PEM =
mζ e A 2 4ωζ T2
(3)
where PEM is the magnitude of the electromagnetically generated power, Y is the magnitude of the input displacement, and ζ e is the electrical damping ratio ( b e = 2mζ e ω ), which can be controlled for output power maximization [16]. ζ T is the total damping ratio ( ζ T = ζ m + ζ e ), ω is the input frequency, ζ m is the mechanical damping ratio, and A is the input acceleration magnitude. Eqn. (2) and (3) represent the maximum recoverable power for a scavenger. And the maximum extraction power is achieved when the electrical damping ratio matches the mechanical damping ratio. C. Piezoelectric Energy Conversion Eqn. (2) and (3) also set an upper bound for piezoelectric energy conversion, where ζ e represents the effective electrical damping ratio resulting from piezoelectric energy conversion. Referred to Eqn. (15) in [6], the effective damping ratio is limited by the coupling coefficient, k31, of the piezoelectric material. When the effective electrical damping ratio is much lower than the mechanical damping ratio in MEMS structures, the piezoelectric power generation can be calculated as follows. Fig. 3 shows a piezoelectric energy scavenging structure. A piezoelectric beam with a length L, thickness t, and width of W is clamped on both ends with a seismic mass in the center. When the system resonant frequency is equal to the input vibration frequency, the power generation in the bending mode can be derived from Eqn. (47) in [14] as Eqn. (4) here. 2
PPZ
⎛ t ⎞ YPZT 2 ⎟⎟ C b ⎜⎜ A ε ⎝ 2k 2 ⎠ = 2 ⎡ ⎛ ⎤ ζ ⎞ 2ω 3 ζ m ⎢ ⎜⎜ 2m ⎟⎟ + 1 + 1⎥ ⎢ ⎝ k 31 ⎠ ⎥ ⎣ ⎦
(4)
where Ppz is the magnitude of the piezoelectric power generation, C b = 2εWL / t is the equivalent piezoelectric
Fig. 2. Schematic of a vibration energy scavenger
B. Electromagnetic Energy Conversion
capacitance, k 2 = L2 / 3t is the geometric constant relating strain to deflection for a clamped-clamped beam, ε is the dielectric constant of the piezoelectric material, Ypz is the Young’s modulus of the material. D. Hybrid MEMS Energy Conversion
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A multi-turn Cu coil and a pair of Neodymium Iron Boron (NdFeB) magnets can be mounted on the scavenger.
Fig. 3. Schematic of piezoelectric energy scavenger
PPZ =
9 ⎡ 128ζ m ⎢ ⎢ ⎣
⎛ ζm ⎞ ⎜ 2 ⎟ ⎜k ⎟ ⎝ 31 ⎠
2
⎤ + 1 + 1⎥ ⎥ ⎦
mω3 Y 2
(5)
As we can see from Eqn. (2) and (5), both the electromagnetic and piezoelectric power generations are proportional to the mass, the cube of the input frequency and the square of the vibration amplitude. Adding the two parts of energy, we have, PHB = (
ζ EM + 4ζ T2
9 ⎡ 128ζ m ⎢ ⎢ ⎣
2 ⎤ ⎛ ζm ⎞ ⎜ 2 ⎟ + 1 + 1⎥ ⎜k ⎟ ⎥ ⎝ 31 ⎠ ⎦
)mω 3 Y 2
(6)
where ζ EM is the damping ratio resulting from the electromagnetic conversion, and ζ T is the effective total damping ratio. IV. STRUCTURE DESIGN EXAMPLE
Fig. 4. Schematic of a hybrid energy scavenger
V. DESIGN CONSIDERATIONS As the energy scavenger size scales down to millimeters and microns that are the typical scales of MEMS structures, the proof mass vibration amplitude is limited if the ambient vibration amplitude is too large. So for constant acceleration vibration, meso-scale energy scavenging structures are suitable for low-frequency large-amplitude vibration applications while MEMS energy scavengers are more desirable for high-frequency small-amplitude applications, as shown in Fig. 5 (the acceleration is 12 m/s2 in this example). 3
Meso-scale Scavengers
2 Log(amplitude) [Log(mm)]
For a hybrid electromagnetic and piezoelectric MEMS energy scavenger, when the total effective damping coefficient of the system is less than the mechanical damping coefficient, the two separate energy scavengers can be modelled as a single simple system using a unified expression as follows. Substituting the expressions of the spring constant 192 t 3 W k=2 YPZT and the resonant frequency ω = k / m 12L3 into Eqn. (4), we have,
ω2Y=12 m/s2 Vibration Amplitude = 1 mm
1
MEMS Scavengers
0 -1 -2 -3
Fig. 4 shows a hybrid electromagnetic and piezoelectric energy scavenger designed for vibration energy harvesting. In the center, a movable vibration proof mass is connected to the sides of the stator frame by four piezoelectric serpentine springs. High magnetic flux density permanent magnets are placed on the mass. A copper coil is fixed relative to the stator frame in the middle of the mass. When the mass vibrates up and down, the coil generates an AC voltage, and the piezoelectric springs, electrically connected through the stator frame, convert the strain in the springs into another AC voltage. For millimetre-scale hybrid structures, silicon, tungsten or PZT can be selected as the material of the vibration mass, stator frame and serpentine springs. A silicon, tungsten or PZT wafer can be patterned to the desired shape using deep reactive ion etching (DRIE). If silicon is used, PZT needs to be deposited on the top and bottom of the serpentine springs.
-4
0
0.5
1 1.5 2 Log(frequency) [Log(Hz)]
2.5
3
Fig. 5. Design regimes for meso-scale and MEMS energy scavengers
Maximizing the scavenging power also requires the total electrical damping ratio to match the mechanical damping ratio. At meso-scale, the mechanical damping coefficient of energy scavengers is small (e.g., less than 0.1). It is easy to design an electrical damping coefficient as large as the mechanical damping coefficient using either electromagnetic conversion [16] or piezoelectric conversion [6]. In MEMS scavengers, the mechanical damping coefficient is large (e.g., higher than 0.5), and it is difficult to design an electrical damping coefficient for electromagnetic or piezoelectric scavengers as large as the mechanical coefficient, since it is
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not practical to fabricate too many turns of coils on MEMS structures for electromagnetic conversion, or the electrical damping coefficient is limited by the piezoelectric coupling coefficient. Therefore, hybrid energy scavenging technologies are suitable for MEMS scavengers, where the electromagnetic and piezoelectric power generations are comparable. With a larger total electrical damping coefficient (not exceeding the mechanical damping coefficient), hybrid energy scavenging maximizes the overall output power density and improves the energy conversion efficiency. VI. OPTIMIZATION RESULTS FOR MEMS IMPLEMENTATION Most ambient mechanical vibrations have a small acceleration, e.g., 2.25 m/s2 at a peak frequency of 121 Hz for a small microwave oven [6]. But a car engine compartment has a typical vibration acceleration of 15 m/s2 at around 50 Hz. Since the corresponding vibration amplitude is about 150 μm , MEMS hybrid energy scavengers can be designed for powering low power electronics, such as wireless sensor nodes on cars. For a volume constraint of 20 mm3 for car engine vibration energy harvesting, the dimensions of the frame in Fig. 4 are chosen as 7 × 7 × 0.4 mm 3 . The proof mass is designed as large as possible [16], as long as the left volume is enough for the serpentine springs to meet the resonant frequency matching requirement. For compact non-vacuum packaging, a mechanical damping ratio of 0.5 is assumed. But the electrical damping ratio due to the electromagnetic or piezoelectric conversion cannot be higher than 0.5. Otherwise the total damping ratio would be higher than 1. PZT is used as the proof mass and serpentine spring materials, and the thicknesses are both 0.4 mm. The dimensions of the proof mass and each serpentine and spring are designed as 5 × 5 × 0.4 mm 3 3 40 × 0.1 × 0.4 mm , respectively. A tungsten mass with dimension of 5 × 5 × 0.6 mm 3 is mounted on the PZT mass to increase the total mass. Using Eqn. (6) in [16] to select the load resistor for electromagnetic output maximization, we get an output power of 16.3 μW , or a power density of 0.83 mW / cm 3 . Here, a resistive load as low as 10 Ω is selected (lower load resistances will result in higher dissipated power), and a 400 turn coil and a flux density of 0.5 T are used. The estimated electromagnetic damping ratio is about 0.2. Based on the above parameters and assumptions, we get an output power of 6.9 μW , or a power density of 0.35 mW / cm 3 as the piezoelectric contribution. So the total power density for this MEMS scavenger would be 1.18 mW / cm 3 .
VII. CONCLUSION Hybrid energy scavenging is proposed to maximize the MEMS energy density when the vibration amplitude is
limited and the MEMS scavenger has a much higher mechanical damping coefficient. A hybrid power expression is derived for modeling hybrid electromagnetic and piezoelectric energy conversion. The hybrid power is proportional to the cube of the input vibration frequency and the square of the amplitude. Practical design considerations are discussed that when the electromagnetic power generation is comparable with the piezoelectric power generation, hybrid MEMS energy scavenging improves the output power. A MEMS energy scavenger example with optimized dimensions for car vibration energy scavenging is presented with an output power density of 1.18 mW / cm 3 . REFERENCES [1] T. Sterken, K. Baert, C. Van Hoof, R. Puers, G. Borghs, and P. Fiorini, “Comparative modelling for vibration scavengers”, Sensors, Proceedings of IEEE, Oct. 2004, vol. 3, pp. 1249-1252. [2] N. S. Shenck and J. A. Paradiso, “Energy scavenging with shoe-mounted piezoelectrics”, IEEE Micro, vol. 21, pp. 30-42, May-June 2001. [3] E.M. Yeatman, “Rotating and gyroscopic MEMS energy scavenging”, Proceedings of the International Workshop on Wearable and Implantable Body Sensor Networks (BSN’06), Apr. 2006. [4] J. A. Paradiso, and T. Starner, “Energy scavenging for mobile and wireless electronics,” IEEE Pervasive Compt., 4 (2005) (1), pp. 18-27 [5] T. Starner and J. A. Paradiso, “Human generated power for mobile electronics”, Low-Power Electronics Design, C. Piquet, Ed., CRC Press, 2004, ch. 45, pp. 1-35. [6] S. Roundy, P.K Wright, and J. Rabaey, “A study of low level vibrations as a power source for wireless sensor nodes”, Comput. Commun., 26 (2003), pp. 1131-1144. [7] E.S. Leland, E. M. Lai, and P.K Wright, “A self-powered wireless sensor for indoor environmental monitoring”, Wireless Networking Symposium, University of Texas, Austin, Oct. 2004. [8] D. P. Arnold, S. Das, F. Cros, I. Zana, M. G. Allen and J. H. Lang, “Magnetic induction machines integrated into bulk-micromachined silicon”, Journal of microelectromechanical systems, vol. 15, pp. 406414, Apr. 2006. [9] E. M. Yeatman, “Applications of MEMS in power sources and circuits”, Journal of micromechanics and microengineering, 17 (2007), pp. S184-S188. [10] Y. H. Chee, A. M. Niknejad and J. M. Rabaey, “An ultra-low-power injection locked transmitter for wireless sensor networks”, IEEE Journal of Solid-State Circuits, vol. 41, no. 8, pp. 1740-1748, Aug. 2006. [11] P. Niu, and P. Chapman, “Design and performance of linear biomechanical energy conversion devices”, Power Electronics Specialists Conference (PESC’06), June 2006, pp. 1-6. [12] J. Kymissis, C. Kendall, J. Paradiso and N. Gershenfeld, “Parasitic power harvesting in shoes”, Second Symposium on Wearable Computers, Oct. 1998, pp. 132-139. [13] P. Niu, “Biomechanical energy conversion”, Ph.D. Dissertation, University of Illinois at Urbana-Champaign, Urbana, Illinois, Sept. 2007. [14] S. Roundy and P.K Wright, “A piezoelectric vibration based generator for wireless electronics”, Smart Materials and Structures, 13 (2004), pp. 1131-1142. [15] S. Roundy, E.S. Leland, J. Baker, E. Carleton, E. Reilly, E. Lai, B. Otis, J. Rabaey, P.K Wright and V. Sundararajan, “Improving power output for vibration-based energy scavengers”, IEEE Pervasive Compt., 4 (2005) (1), pp. 28-36. [16] C.B. Williams and R.B. Yates, “Analysis of a micro-electric generator for microsystems”, Proceedings of the Transducers 95/Eurosensors IX, (1995), pp. 369-372.
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Modeling, Design and Optimization of Hybrid Electromagnetic and Piezoelectric MEMS Energy Scavengers Xiaochun Wu, Alireza Khaligh, Yang Xu Electrical and Computer Engineering Department, Illinois Institute of Technology 3301 South Dearborn Street Chicago, IL 60616 Abstract-A hybrid energy scavenging technique is introduced to harness ambient energy through electromagnetic and piezoelectric mechanisms to achieve higher power density and higher energy conversion efficiency in a high mechanical damping MEMS structure. By inspecting the second-order mechanical dynamic system for electromagnetic and piezoelectric energy conversions, a unified model is proposed to capture the relation of the recoverable hybrid energy and the input vibration frequency as well as the amplitude. Design trade-offs are considered for the hybrid scavenger size and power maximization. A hybrid MEMS energy scavenger design with optimization results for implementation is shown as an example. Keywords: energy scavenging, harvesting, piezoelectric, MEMS, hybrid energy conversion
battery. The battery supplies the power for the sensor, DSP, and low-power RF transceiver circuits. This paper presents a hybrid MEMS energy scavenging technique that coverts ambient kinetic energy to electricity both electromagnetically and piezoelectrically. The technique makes use of the commonality of ambient kinetic energy sources and has the advantage of improving the energy conversion efficiency, when the mechanical damping coefficient is high and the amounts of the two kinds of converted energy are comparable.
electromagnetic,
VDD
I. INTRODUCTION Energy scavenging from ambient energy sources is emerging as a potential solution to limited battery capacity. More and more electronics using batteries can be powered by energy from solar, electromagnetic fields, human motions, and mechanical vibrations. However, many applications are still limited by the recovered power and conversion efficiency. While low-power circuit design techniques are explored [1] to reduce the power requirements of electronics applications, it is of tremendous interest to develop new energy conversion devices to increase the power density and conversion efficiency [2-9]. Compared to the meso-scale counterparts, MEMS energy scavengers provide low power due to the small size. However, in ultra-low power applications such as wireless sensor nodes and implantable medical devices, MEMS energy scavenging becomes a plausible solution due to its small form factor and low cost in mass production. Since kinetic energy is a common source in the ambient environment, MEMS energy scavengers can be used in applications where other sources such as solar and chemical power are not available. Further, MEMS energy scavengers have the advantage of compatibility with integrated circuits. Fig. 1 shows the system diagram of an integrated selfpowered wireless sensor node. The voltage from the MEMS energy scavenger is regulated and then charges a storage
978-1-4244-2018-6/08/$25.00 ©2008 IEEE
Battery Vibration Energy Scavenger
Sensor
Power Regulation Circuit
DSP
TX RX
Fig. 1. Block diagram of an integrated self-powered wireless sensor node
II. BACKGROUND Human motions such as arm swing, horizontal foot motion, and center-of-mass motion are energy sources that have been attracting research on energy extraction for powering wearable electronic devices [11]. Energy extraction from human motion is especially useful for long-term monitoring of human body implantable devices. In [12], researchers have demonstrated a PZT unimorph piezoelectric power generator embedded in shoes with an RMS power of 1.8 mW and used it to power a digital RFID tag successfully. The authors in [13] introduced a meso-scale electro-magnetic energy scavenger for energy extraction from center-of-mass motion of human body. The scavenger has achieved a power density of 0.44 mW/cm3. But due to the large amplitude (a typical value of 4 cm – 7 cm) and low frequency (typically 2 Hz) for center-of-mass motion of human body, the power density will drop if the scavenger scales down to millimetre-
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177
scale or micro-scale, since the scavenger size will limit the amplitude of the proof mass vibration. Mechanical vibration is a common kinetic energy source in the environment, including vibrations of buildings, machine tools, and car engines. Typical ambient mechanical vibrations have a higher frequency and smaller amplitude than human motions. Researchers in [15] fabricated early prototypes of piezoelectric cantilevers (9 to 25 millimeters in length) with a relatively heavy mass on the free end, capable of generating 2 375 μW / cm 3 from a vibration source of 2.5 m/s at 120 Hz. The smaller vibration amplitude makes MEMS energy scavengers more applicable. Authors in [16] showed a conceptual design of a 5 × 5 × 1 mm 3 electromagnetic microgenerator and predicted power generation of 1 µW at 70 Hz and 0.1 mW at 330 Hz, assuming a deflection of 50 µm. To improve the power density of MEMS scavengers, hybrid energy scavenging is proposed, which has the advantage of extracting energy from multiple energy sources so that even if one energy source is not available in the environment, alternative energy sources may still supply power and the probability of “power outage” is smaller, increasing the reliability of the systems and enabling the energy diversification. Therefore, hybrid energy scavenging is a promising energy scavenger design trend. III. ANALYSIS AND MODELING A. Mass-Damper-Spring Model for Vibration Energy Scavengers Electromagnetic and piezoelectric energy scavengers based on proof mass vibration can be modelled as a second-order mass-damper-spring dynamic system. Fig. 2 demonstrates the schematic of a second-order energy scavenger model proposed by Williams and Yates [16]. The system consists a proof mass, m, a spring, k, a mechanical damping coefficient, bm, and an electrical damping coefficient, be. x and y represent the spring deflection and the input displacement, respectively. The differential equation that describes the system is given as Eqn. (1). (1) m&x& + (b m + b e )x& + kx = m&y&
The extracted output power is maximized, if the resonant frequency of a mass-damper-spring system, described in Eqn. (1), is equal to the input vibration frequency [16]. In this particular case and under the assumption that the power scavenging doesn’t hamper the source vibration, the extracted power is given in Eqn. (2), or equivalently, (3) [6]. mζ e ω3 Y 2 (2) PEM = 4ζ T2 PEM =
mζ e A 2 4ωζ T2
(3)
where PEM is the magnitude of the electromagnetically generated power, Y is the magnitude of the input displacement, and ζ e is the electrical damping ratio ( b e = 2mζ e ω ), which can be controlled for output power maximization [16]. ζ T is the total damping ratio ( ζ T = ζ m + ζ e ), ω is the input frequency, ζ m is the mechanical damping ratio, and A is the input acceleration magnitude. Eqn. (2) and (3) represent the maximum recoverable power for a scavenger. And the maximum extraction power is achieved when the electrical damping ratio matches the mechanical damping ratio. C. Piezoelectric Energy Conversion Eqn. (2) and (3) also set an upper bound for piezoelectric energy conversion, where ζ e represents the effective electrical damping ratio resulting from piezoelectric energy conversion. Referred to Eqn. (15) in [6], the effective damping ratio is limited by the coupling coefficient, k31, of the piezoelectric material. When the effective electrical damping ratio is much lower than the mechanical damping ratio in MEMS structures, the piezoelectric power generation can be calculated as follows. Fig. 3 shows a piezoelectric energy scavenging structure. A piezoelectric beam with a length L, thickness t, and width of W is clamped on both ends with a seismic mass in the center. When the system resonant frequency is equal to the input vibration frequency, the power generation in the bending mode can be derived from Eqn. (47) in [14] as Eqn. (4) here. 2
PPZ
⎛ t ⎞ YPZT 2 ⎟⎟ C b ⎜⎜ A ε ⎝ 2k 2 ⎠ = 2 ⎡ ⎛ ⎤ ζ ⎞ 2ω 3 ζ m ⎢ ⎜⎜ 2m ⎟⎟ + 1 + 1⎥ ⎢ ⎝ k 31 ⎠ ⎥ ⎣ ⎦
(4)
where Ppz is the magnitude of the piezoelectric power generation, C b = 2εWL / t is the equivalent piezoelectric
Fig. 2. Schematic of a vibration energy scavenger
B. Electromagnetic Energy Conversion
capacitance, k 2 = L2 / 3t is the geometric constant relating strain to deflection for a clamped-clamped beam, ε is the dielectric constant of the piezoelectric material, Ypz is the Young’s modulus of the material. D. Hybrid MEMS Energy Conversion
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A multi-turn Cu coil and a pair of Neodymium Iron Boron (NdFeB) magnets can be mounted on the scavenger.
Fig. 3. Schematic of piezoelectric energy scavenger
PPZ =
9 ⎡ 128ζ m ⎢ ⎢ ⎣
⎛ ζm ⎞ ⎜ 2 ⎟ ⎜k ⎟ ⎝ 31 ⎠
2
⎤ + 1 + 1⎥ ⎥ ⎦
mω3 Y 2
(5)
As we can see from Eqn. (2) and (5), both the electromagnetic and piezoelectric power generations are proportional to the mass, the cube of the input frequency and the square of the vibration amplitude. Adding the two parts of energy, we have, PHB = (
ζ EM + 4ζ T2
9 ⎡ 128ζ m ⎢ ⎢ ⎣
2 ⎤ ⎛ ζm ⎞ ⎜ 2 ⎟ + 1 + 1⎥ ⎜k ⎟ ⎥ ⎝ 31 ⎠ ⎦
)mω 3 Y 2
(6)
where ζ EM is the damping ratio resulting from the electromagnetic conversion, and ζ T is the effective total damping ratio. IV. STRUCTURE DESIGN EXAMPLE
Fig. 4. Schematic of a hybrid energy scavenger
V. DESIGN CONSIDERATIONS As the energy scavenger size scales down to millimeters and microns that are the typical scales of MEMS structures, the proof mass vibration amplitude is limited if the ambient vibration amplitude is too large. So for constant acceleration vibration, meso-scale energy scavenging structures are suitable for low-frequency large-amplitude vibration applications while MEMS energy scavengers are more desirable for high-frequency small-amplitude applications, as shown in Fig. 5 (the acceleration is 12 m/s2 in this example). 3
Meso-scale Scavengers
2 Log(amplitude) [Log(mm)]
For a hybrid electromagnetic and piezoelectric MEMS energy scavenger, when the total effective damping coefficient of the system is less than the mechanical damping coefficient, the two separate energy scavengers can be modelled as a single simple system using a unified expression as follows. Substituting the expressions of the spring constant 192 t 3 W k=2 YPZT and the resonant frequency ω = k / m 12L3 into Eqn. (4), we have,
ω2Y=12 m/s2 Vibration Amplitude = 1 mm
1
MEMS Scavengers
0 -1 -2 -3
Fig. 4 shows a hybrid electromagnetic and piezoelectric energy scavenger designed for vibration energy harvesting. In the center, a movable vibration proof mass is connected to the sides of the stator frame by four piezoelectric serpentine springs. High magnetic flux density permanent magnets are placed on the mass. A copper coil is fixed relative to the stator frame in the middle of the mass. When the mass vibrates up and down, the coil generates an AC voltage, and the piezoelectric springs, electrically connected through the stator frame, convert the strain in the springs into another AC voltage. For millimetre-scale hybrid structures, silicon, tungsten or PZT can be selected as the material of the vibration mass, stator frame and serpentine springs. A silicon, tungsten or PZT wafer can be patterned to the desired shape using deep reactive ion etching (DRIE). If silicon is used, PZT needs to be deposited on the top and bottom of the serpentine springs.
-4
0
0.5
1 1.5 2 Log(frequency) [Log(Hz)]
2.5
3
Fig. 5. Design regimes for meso-scale and MEMS energy scavengers
Maximizing the scavenging power also requires the total electrical damping ratio to match the mechanical damping ratio. At meso-scale, the mechanical damping coefficient of energy scavengers is small (e.g., less than 0.1). It is easy to design an electrical damping coefficient as large as the mechanical damping coefficient using either electromagnetic conversion [16] or piezoelectric conversion [6]. In MEMS scavengers, the mechanical damping coefficient is large (e.g., higher than 0.5), and it is difficult to design an electrical damping coefficient for electromagnetic or piezoelectric scavengers as large as the mechanical coefficient, since it is
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not practical to fabricate too many turns of coils on MEMS structures for electromagnetic conversion, or the electrical damping coefficient is limited by the piezoelectric coupling coefficient. Therefore, hybrid energy scavenging technologies are suitable for MEMS scavengers, where the electromagnetic and piezoelectric power generations are comparable. With a larger total electrical damping coefficient (not exceeding the mechanical damping coefficient), hybrid energy scavenging maximizes the overall output power density and improves the energy conversion efficiency. VI. OPTIMIZATION RESULTS FOR MEMS IMPLEMENTATION Most ambient mechanical vibrations have a small acceleration, e.g., 2.25 m/s2 at a peak frequency of 121 Hz for a small microwave oven [6]. But a car engine compartment has a typical vibration acceleration of 15 m/s2 at around 50 Hz. Since the corresponding vibration amplitude is about 150 μm , MEMS hybrid energy scavengers can be designed for powering low power electronics, such as wireless sensor nodes on cars. For a volume constraint of 20 mm3 for car engine vibration energy harvesting, the dimensions of the frame in Fig. 4 are chosen as 7 × 7 × 0.4 mm 3 . The proof mass is designed as large as possible [16], as long as the left volume is enough for the serpentine springs to meet the resonant frequency matching requirement. For compact non-vacuum packaging, a mechanical damping ratio of 0.5 is assumed. But the electrical damping ratio due to the electromagnetic or piezoelectric conversion cannot be higher than 0.5. Otherwise the total damping ratio would be higher than 1. PZT is used as the proof mass and serpentine spring materials, and the thicknesses are both 0.4 mm. The dimensions of the proof mass and each serpentine and spring are designed as 5 × 5 × 0.4 mm 3 3 40 × 0.1 × 0.4 mm , respectively. A tungsten mass with dimension of 5 × 5 × 0.6 mm 3 is mounted on the PZT mass to increase the total mass. Using Eqn. (6) in [16] to select the load resistor for electromagnetic output maximization, we get an output power of 16.3 μW , or a power density of 0.83 mW / cm 3 . Here, a resistive load as low as 10 Ω is selected (lower load resistances will result in higher dissipated power), and a 400 turn coil and a flux density of 0.5 T are used. The estimated electromagnetic damping ratio is about 0.2. Based on the above parameters and assumptions, we get an output power of 6.9 μW , or a power density of 0.35 mW / cm 3 as the piezoelectric contribution. So the total power density for this MEMS scavenger would be 1.18 mW / cm 3 .
VII. CONCLUSION Hybrid energy scavenging is proposed to maximize the MEMS energy density when the vibration amplitude is
limited and the MEMS scavenger has a much higher mechanical damping coefficient. A hybrid power expression is derived for modeling hybrid electromagnetic and piezoelectric energy conversion. The hybrid power is proportional to the cube of the input vibration frequency and the square of the amplitude. Practical design considerations are discussed that when the electromagnetic power generation is comparable with the piezoelectric power generation, hybrid MEMS energy scavenging improves the output power. A MEMS energy scavenger example with optimized dimensions for car vibration energy scavenging is presented with an output power density of 1.18 mW / cm 3 . REFERENCES [1] T. Sterken, K. Baert, C. Van Hoof, R. Puers, G. Borghs, and P. Fiorini, “Comparative modelling for vibration scavengers”, Sensors, Proceedings of IEEE, Oct. 2004, vol. 3, pp. 1249-1252. [2] N. S. Shenck and J. A. Paradiso, “Energy scavenging with shoe-mounted piezoelectrics”, IEEE Micro, vol. 21, pp. 30-42, May-June 2001. [3] E.M. Yeatman, “Rotating and gyroscopic MEMS energy scavenging”, Proceedings of the International Workshop on Wearable and Implantable Body Sensor Networks (BSN’06), Apr. 2006. [4] J. A. Paradiso, and T. Starner, “Energy scavenging for mobile and wireless electronics,” IEEE Pervasive Compt., 4 (2005) (1), pp. 18-27 [5] T. Starner and J. A. Paradiso, “Human generated power for mobile electronics”, Low-Power Electronics Design, C. Piquet, Ed., CRC Press, 2004, ch. 45, pp. 1-35. [6] S. Roundy, P.K Wright, and J. Rabaey, “A study of low level vibrations as a power source for wireless sensor nodes”, Comput. Commun., 26 (2003), pp. 1131-1144. [7] E.S. Leland, E. M. Lai, and P.K Wright, “A self-powered wireless sensor for indoor environmental monitoring”, Wireless Networking Symposium, University of Texas, Austin, Oct. 2004. [8] D. P. Arnold, S. Das, F. Cros, I. Zana, M. G. Allen and J. H. Lang, “Magnetic induction machines integrated into bulk-micromachined silicon”, Journal of microelectromechanical systems, vol. 15, pp. 406414, Apr. 2006. [9] E. M. Yeatman, “Applications of MEMS in power sources and circuits”, Journal of micromechanics and microengineering, 17 (2007), pp. S184-S188. [10] Y. H. Chee, A. M. Niknejad and J. M. Rabaey, “An ultra-low-power injection locked transmitter for wireless sensor networks”, IEEE Journal of Solid-State Circuits, vol. 41, no. 8, pp. 1740-1748, Aug. 2006. [11] P. Niu, and P. Chapman, “Design and performance of linear biomechanical energy conversion devices”, Power Electronics Specialists Conference (PESC’06), June 2006, pp. 1-6. [12] J. Kymissis, C. Kendall, J. Paradiso and N. Gershenfeld, “Parasitic power harvesting in shoes”, Second Symposium on Wearable Computers, Oct. 1998, pp. 132-139. [13] P. Niu, “Biomechanical energy conversion”, Ph.D. Dissertation, University of Illinois at Urbana-Champaign, Urbana, Illinois, Sept. 2007. [14] S. Roundy and P.K Wright, “A piezoelectric vibration based generator for wireless electronics”, Smart Materials and Structures, 13 (2004), pp. 1131-1142. [15] S. Roundy, E.S. Leland, J. Baker, E. Carleton, E. Reilly, E. Lai, B. Otis, J. Rabaey, P.K Wright and V. Sundararajan, “Improving power output for vibration-based energy scavengers”, IEEE Pervasive Compt., 4 (2005) (1), pp. 28-36. [16] C.B. Williams and R.B. Yates, “Analysis of a micro-electric generator for microsystems”, Proceedings of the Transducers 95/Eurosensors IX, (1995), pp. 369-372.
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