Simulation and experimental demonstration of improved efficiency in coupled piezoelectric cantilevers by extended strain distribution
Introduction
Piezoelectric energy harvesting from vibrations is cost efficient and environmentally friendly compared to batteries with limited lifetime, which make them a good alternative for powering, e.g., intelligent wireless sensors inaccessibly integrated into harsh industrial environments like engines or machines with inherent vibrations [1], [2].
A single piezoelectric cantilever used in vibration harvesters can be tuned to the most abundant vibration frequency in its environment but it will be at risk of providing insufficient electrical power if the vibration spectrum shifts or fluctuates beyond the narrow window of optimal tuning. One fundamental challenge in cantilever design is thus to widen the bandwidth without sacrificing the power output [3].
Gas turbines constitute an interesting but challenging environment for wireless sensing with high temperatures and high amplitude vibrations. The space available for harvesters to power sensors is limited, putting constrains on their total size. The harvestable frequencies change dynamically with the turbine's rotational speed. It is a design challenge to find a minimum size harvester that can utilize the broad and varying spectrum of vibrations in the whole range from startup to cruise conditions of the gas turbine.
There is a significant amount of research reported on approaches to widen the bandwidth and gaining higher harvested energy from piezoelectric cantilevers. Li et al. [4] proposed an array of structures with a different resonant frequency for each structure. Soliman et al. [5] used an amplitude limiter to gain broader bandwidth. Petropoulos et al. [6] used coupled oscillators; Spreemann et al. [7] used magnets to achieve a non-linear harvester resulting in broader bandwidth. Ramlan et al. [8] tested bi-stable structures, and Zhu et al. [3] used a large inertial mass (large device size) with a high degree of damping.
Another interesting way to increase the harvested energy and the bandwidth has been proposed by Zhou et al. [9] exploiting a primary beam multimode magnifier. In this design the secondary beam multi-mode energy harvester is attached to the primary beam multimode dynamic magnifier and this design has a broader bandwidth and the harvested energy is greatly improved. To further enhance this effect Wu et al. [10] describe two degrees of freedom piezoelectric energy harvester, where the secondary beam is cut inside the main beam. This makes the design less bulky, results in a broader bandwidth with two closely spaced peaks, and gives a high power output from both beams.
The harvester design presented in this paper is realized using commercial components and is a combination of a magnifier and two degrees of freedom harvester having a magnifier in the shape of a bimorph piezoelectric cantilever, where the secondary cantilever is also a bimorph piezoelectric cantilever. This design enhances the harvested energy and gives a broader bandwidth than an array of two tuned single cantilevers. The design gives a small increase in volume but utilizes the bottom beam more efficiently for higher power output, much due to the improved and extended strain profile of this beam.
Section snippets
Design realization and simulation of single and coupled cantilevers
The theory of piezoelectric cantilevers in the literature mainly covers single cantilevers. An extension to the single cantilever theory has to be applied in order to describe two connected beams as a couple for enhanced power output. Zhou et al. [9] extends the single cantilever theory to cover two coupled beams with a multi-mode design. This design is proved to yield a higher power output and to broaden the bandwidth. Our improved alteration of their design utilizes two piezoelectric
Measurement setup
A prototype couple harvester was built by two v21b MIDE piezoelectric cantilevers (Fig. 6). The bottom cantilever is attached to a metal box by a piece of PTFE. The top cantilever is attached at the other end of the bottom cantilever via a piece of PTFE as coupling fixture with PTFE screws and nuts to attach the cantilevers. Very thin cables are soldered to the top cantilever to minimize the mechanical influence. All protecting plastic and contact materials on the top cantilever are removed to
Result
The single and coupled cantilevers were tested in the experimental setup in the frequency range 50–200 Hz. The resonance modes for the prototype are 85.2 and 135.5 Hz with a relative deviation of 20.5% and 26.6%, respectively compared to the initial simulations (Table 2). The measured output power is lower than the simulated power output. Fig. 7 shows the voltage squared power output from the double single and coupled harvesters. The coupled harvester has 5.4 times higher power output than the
Conclusion
A compact and broadband coupled harvester based on two mechanically coupled cantilevers, intended for powering of wireless sensors in physically constrained environments has been designed, simulated, built, measured, and compared to two single cantilevers that are tuned to display the same resonance frequencies as the coupled. In simulations the coupled harvester yielded 4.7 times more harvested power than two single cantilevers, to a large part an effect of an extended stress distribution for
Acknowledgments
The Swedish Research Council and the European project STARGATE is greatly acknowledged for their financial support.
Henrik Staaf received his master's degree in physics and his teaching degree for the Swedish high school in 2003. In 2007 until 2012 he was appointed IT-pedagog within a corporate group in IT-Gymnasiet Sweden AB, where the focus was to enhance the usage of IT in the classroom and to use virtual platforms as pedagogic support and to implement new platforms. From 2008 till 2012 he was a teamleader on IT-GymnasietGöteborg. He has worked as a full time teacher until 2012, when he started his Ph. D.
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Henrik Staaf received his master's degree in physics and his teaching degree for the Swedish high school in 2003. In 2007 until 2012 he was appointed IT-pedagog within a corporate group in IT-Gymnasiet Sweden AB, where the focus was to enhance the usage of IT in the classroom and to use virtual platforms as pedagogic support and to implement new platforms. From 2008 till 2012 he was a teamleader on IT-GymnasietGöteborg. He has worked as a full time teacher until 2012, when he started his Ph. D. studies at Chalmers University of Technology through the Swedish Education Initiative and sponsored by the Swedish Council of Science. The Ph. D. studies focus on energy sources for Intelligent Wireless Sensors which is divided into energy storage and energy harvesting, where the main focus on harvesting is from piezoelectric and thermal energy harvesters and the energy storage focus on supercapacitors.
Elof Köhler is a Ph. D. student in the Micro- and Nanosystems group at the department of Microtechnology and Nanoscience at Chalmers University of Technology. He has a bachelor degree in applied physics and a master degree in nanoscience, both from Chalmers University of Technology. The main focus in his Ph. D. work is energy harvesting with high temperature thermoelectric energy harvesting as his favorite pet.
Dhasarathy Parthasarathy graduated with a Master of Science in Electrical Engineering in 2012 from Chalmers University of Technology, Sweden. He currently works in Volvo Technology AB, Göteborg, Sweden where he is researching the application of wireless sensors in commercial vehicles.
Per Lundgren has been with the Department of Microtechnology and Nanoscience at Chalmers University of Technology since 2006. His research activities are mainly related to experimental investigations of nanostructured materials intended for application in electronic devices.
Peter Enoksson received the Ph. D. 1997 from the Royal Institute of Technology, KTH, Sweden. 1997 he became assistant professor and 2000 was appointed associate professor at KTH. He was appointed Professor of MOEMS 2001 at Chalmers University of Technology, Gothenburg Sweden. In 2002 he was appointed vice dean of School of Electrical Engineering and 2003 head of the Solid State Electronics Laboratory. Currently he heads the Micro- and Nanosystems group at the department of Microtechnology and Nanoscience, MC2. His research focus on combining MEMS/NEMS with other sciences in novel dedicated and advanced systems. Prof Enoksson has published more than 200 research journal and conference papers and ten patents. He is initiator of spin-off companies, winner of the Innovation Cup, referee for several journals and also a member of the editorial board of Journal of Micromechanics and Microengineering, the steering committees of MicroMechanics Europe and of company and projects boards.