本研究針對磁吸式壓電獵能器，提出一個基於升頻轉換概念的新型設計機構，並提出數學模型，包括以壓電力學及振動學建立之運動模型以及三維磁力模型，預測獵能器作用時所輸出之電壓與功率。本研究建立有限元素分析模型，並實作原型，以確認設計概念之可行性以及數學模型之正確性。在磁力實驗方面，結果顯示3D模型對於兩磁鐵間距較大的情況下能有效的預估磁力曲線，此外，旋轉角的影響經實驗後僅造成7%的差距，故在數值模擬上忽略旋轉角所帶來的影響，將結果匯入有限元素軟體ANSYS，以暫態分析模擬獵能器之暫態響應。經過實驗、ANSYS與數學模型比對，雖然數學模型在基頻頻率上有8.63%之誤差，但仍可預測其大致之趨勢。從有限元素分析模擬結果可知此設計在最佳阻抗10k歐姆下可以產生0.645mJ的電能，在點亮LED實驗中，獵能器可提供瞬間最大功率774 W，足以點亮一顆LED燈。本研究最後利用數學模型針對幾個重要的幾何參數，包含壓電懸臂樑尺寸、金屬裸露長度、以及磁鐵間距等進行最佳化探討，分析結果可做為後續優化獵能器設計之參考。

Based on the frequency up-conversion, a novel PEH composed of a piezoelectric cantilever beam and plural magnets is proposed. The output voltage and power can be analyzed and predicted by mathematical models including 3D magnetic force model and dynamic model derived from the piezoelectricity and vibration theory. The model is validated by the finite element analysis and experiments. In the experiment regarding to the magnetic force measurement, the results show that the 3D force model provides more accurate magnetic force calculation for large distance between two magnets. In addition, the tilt angle of the magnet has a little effect of 7% difference from the case of no tilt angle, indicating that the tilt angle can be neglected in the dynamic model. The magnetic force distribution is imported into ANSYS, a finite element analysis software, to compute the transient responses of the PEH. The natural frequency of the beam determined by the mathematical model has a 8.63% difference lower than that observed by experiments. However, the overall trend of the responses can be obtained from the mathematical model. By the mathematical model, the PEH can harvest a power of 0.645 mJ under an optimum load of 10 k. In the experiments of connecting an LED to the PEH, a pulse current with a peak power of 774 W is observed, which is sufficient to lighten the LED. After validating the mathematical model, it is used to investigate the optimization of some geometric parameters such as the size of the cantilever and the gap between magnets. The results are helpful for improvements to the PEH design in the future.

[1] N. Elvin and A. Erturk, Advances in energy harvesting methods. Springer Science & Business Media, 2013.
[2] P. Glynne-Jones, M. J. Tudor, S. P. Beeby, and N. M. White, "An electromagnetic, vibration-powered generator for intelligent sensor systems," Sensors and Actuators A: Physical, vol. 110, no. 1-3, pp. 344-349, 2004.
[3] S. Meninger, J. O. Mur-Miranda, R. Amirtharajah, A. Chandrakasan, and J. H. Lang, "Vibration-to-electric energy conversion," IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 9, no. 1, pp. 64-76, 2001.
[4] G. Zhu et al., "Toward large-scale energy harvesting by a nanoparticle-enhanced triboelectric nanogenerator," Nano letters, vol. 13, no. 2, pp. 847-853, 2013.
[5] S. R. Anton and H. A. Sodano, "A review of power harvesting using piezoelectric materials (2003–2006)," Smart materials and Structures, vol. 16, no. 3, p. R1, 2007.
[6] A. Erturk and D. J. Inman, Piezoelectric energy harvesting. John Wiley & Sons, 2011.
[7] S. Roundy, P. K. Wright, and J. Rabaey, "A study of low level vibrations as a power source for wireless sensor nodes," Computer communications, vol. 26, no. 11, pp. 1131-1144, 2003.
[8] S. Roundy and P. K. Wright, "A piezoelectric vibration based generator for wireless electronics," Smart Materials and structures, vol. 13, no. 5, p. 1131, 2004.
[9] D. Charnegie, "Frequency tuning concepts for piezoelectric cantilever beams and plates for energy harvesting," University of Pittsburgh, 2007.
[10] Y.-J. Wang, C.-D. Chen, and C.-K. Sung, "Design of a frequency-adjusting device for harvesting energy from a rotating wheel," Sensors and Actuators A: Physical, vol. 159, no. 2, pp. 196-203, 2010.
[11] H. Wu, L. Tang, Y. Yang, and C. K. Soh, "A novel two-degrees-of-freedom piezoelectric energy harvester," Journal of Intelligent Material Systems and Structures, vol. 24, no. 3, pp. 357-368, 2013.
[12] I. Sari, T. Balkan, and H. Kulah, "A wideband electromagnetic micro power generator for wireless microsystems," in TRANSDUCERS 2007-2007 International Solid-State Sensors, Actuators and Microsystems Conference, 2007: IEEE, pp. 275-278.
[13] A. Erturk and D. J. Inman, "Broadband piezoelectric power generation on high-energy orbits of the bistable Duffing oscillator with electromechanical coupling," Journal of Sound and Vibration, vol. 330, no. 10, pp. 2339-2353, 2011.
[14] H. W. Kim et al., "Energy harvesting using a piezoelectric “cymbal” transducer in dynamic environment," Japanese journal of applied physics, vol. 43, no. 9R, p. 6178, 2004.
[15] L. Xie and M. Cai, "An in-shoe harvester with motion magnification for scavenging energy from human foot strike," IEEE/ASME Transactions on mechatronics, vol. 20, no. 6, pp. 3264-3268, 2015.
[16] L. Gu and C. Livermore, "Impact-driven, frequency up-converting coupled vibration energy harvesting device for low frequency operation," Smart Materials and Structures, vol. 20, no. 4, p. 045004, 2011.
[17] M. Pozzi and M. Zhu, "Plucked piezoelectric bimorphs for knee-joint energy harvesting: modelling and experimental validation," Smart Materials and Structures, vol. 20, no. 5, p. 055007, 2011.
[18] P. Pillatsch, E. Yeatman, and A. Holmes, "A scalable piezoelectric impulse-excited energy harvester for human body excitation," Smart Materials and Structures, vol. 21, no. 11, p. 115018, 2012.
[19] T. Galchev, H. Kim, and K. Najafi, "Non-resonant bi-stable frequency-increased power scavenger from low-frequency ambient vibration," in TRANSDUCERS 2009-2009 International Solid-State Sensors, Actuators and Microsystems Conference, 2009: IEEE, pp. 632-635.
[20] T. Galchev, H. Kim, and K. Najafi, "Micro power generator for harvesting low-frequency and nonperiodic vibrations," Journal of Microelectromechanical Systems, vol. 20, no. 4, pp. 852-866, 2011.
[21] M. Renaud, P. Fiorini, R. van Schaijk, and C. Van Hoof, "Harvesting energy from the motion of human limbs: the design and analysis of an impact-based piezoelectric generator," Smart Materials and Structures, vol. 18, no. 3, p. 035001, 2009.
[22] Ö. Zorlu, E. T. Topal, and H. Kulah, "A vibration-based electromagnetic energy harvester using mechanical frequency up-conversion method," IEEE Sensors Journal, vol. 11, no. 2, pp. 481-488, 2010.
[23] S. Moss, A. Barry, I. Powlesland, S. Galea, and G. Carman, "A broadband vibro-impacting power harvester with symmetrical piezoelectric bimorph-stops," Smart Materials and Structures, vol. 20, no. 4, p. 045013, 2011.
[24] L. Gu, "Low-frequency piezoelectric energy harvesting prototype suitable for the MEMS implementation," Microelectronics Journal, vol. 42, no. 2, pp. 277-282, 2011.
[25] N. Yuksek, Z. Feng, and M. Almasri, "Broadband electromagnetic power harvester from vibrations via frequency conversion by impact oscillations," Applied Physics Letters, vol. 105, no. 11, p. 113902, 2014.
[26] H. Kulah and K. Najafi, "Energy scavenging from low-frequency vibrations by using frequency up-conversion for wireless sensor applications," IEEE Sensors Journal, vol. 8, no. 3, pp. 261-268, 2008.
[27] P. Pillatsch, E. Yeatman, and A. Holmes, "Magnetic plucking of piezoelectric beams for frequency up-converting energy harvesters," Smart Materials and Structures, vol. 23, no. 2, p. 025009, 2013.
[28] T. Xue and S. Roundy, "On magnetic plucking configurations for frequency up-converting mechanical energy harvesters," Sensors and Actuators A: Physical, vol. 253, pp. 101-111, 2017.
[29] T. Galchev, E. E. Aktakka, and K. Najafi, "A piezoelectric parametric frequency increased generator for harvesting low-frequency vibrations," Journal of Microelectromechanical Systems, vol. 21, no. 6, pp. 1311-1320, 2012.
[30] 李旻哲, "指壓式壓電獵能器之實做, 分析與量測," 碩士論文, 2018.
[31] 陳冠維, "有限元素-解析解法-SPICE共模擬之機電耦合系統應用於高功率密度壓電獵能模組最佳化設計," 博士論文, 國立成功大學, 2018.
[32] 吳朗, 電子陶瓷: 壓電陶瓷. 全欣, 1994.
[33] G. Akoun and J.-P. Yonnet, "3D analytical calculation of the forces exerted between two cuboidal magnets," IEEE Transactions on magnetics, vol. 20, no. 5, pp. 1962-1964, 1984.
[34] "efuda, Properties of Piezo Material Lead Zirconate Titanate (PZT-5H)." https://www.efunda.com/materials/piezo/material_data/matdata_output.cfm?Material_ID=PZT-5H, 2090626 (accessed June 26, 2019).