軸向激擾之拍擊式能量擷取系統

Axial Excited Slapping Energy Harvesting System

郭俊孝(Chun-Hsiao Kuo)

指導教授 ： 王怡仁

淡江大學/工學院/航空太空工程學系碩士班/碩士(2023年)

https://doi.org/10.6846/tku202300092

摘要

VEH 的傳統電能轉換方式有兩種，其一是將壓電片放置於一Fixed-Free彈性鋼片的根部，利用彈性鋼片的振動對根部的 PZT 產生形變，以轉換振動能為電能，另外是利用雙彈性鋼片的方式，將壓電片放置於單層彈性鋼片的自由端，並由另一片單層彈性鋼片拍擊此壓電片，獲得另一鋼片的拍擊力，此類系統裝置於彈性鋼自由端的 PZT 其形變量有限，雖然有拍擊的效果，相對於第一種將 PZT 置於彈性鋼根部的設計，卻又少了一些形變造成的電能轉換效益。而本研究針對上述兩種例子進行改良，將壓電片放置於一Fixed-Fixed彈性鋼片的中間，接著在此彈性鋼片的一端施加一軸向 (Axial) 的簡諧外力 (Simple Harmonic force) 使其產生橫向 (Transversal) 的振動及形變，並且在最大變形處加裝擋板 (Baffle)，如此，可獲得一般的 PZT形變產生的電能轉換，也可獲得額外的拍擊力產生的電能轉換，除了改良傳統既有設計，且兼具“單層彈性鋼片獵能系統 (Single Elastic Steel VEH system (SES-VEH) )”和“雙層彈性鋼片獵能系統 (Double Elastic Steel VEH system (DES-VEH) )”兩者發電的效果。本研究不僅改善了SES-VEH的缺點，還結合了DES-VEH的優點，完美的將發電效益最大化。本研究將針對此系統建立一套完整的理論模式，並將理論及數值兩相互驗證，其中，彈性鋼片的形變已達到非線性的範圍，且此軸向激擾的模式為典型的參數激擾 (Parametric Excitation) 型態，因此理論的模擬及解析，將以非線性的方法執行之。
本研究並以實驗印證理論之正確性。利用彈性鋼片藉此模擬彈性樑之情形，將彈性鋼片兩端之邊界條件以 C型裝置固定，其一端固定不動，在其另一端設置可水平移動之滑軌以及振動器 (Actuator) 以模擬出彈性鋼片發生挫曲時之振動方式。此實驗分為兩組，吾人利用彈性樑模態 (Mode shape) 分析，分析彈性鋼片發生最大形變之位置，並將壓電片分別放置於彈性樑根部及最大形變處，比較發電效益。其次，將壓電片放置於形變最大處並且在此加裝擋板增加拍擊力(不僅有形變力也具有拍擊力)，藉此找出最大發電效益，根據實驗結果第一模態無拍擊力實驗電壓值約為1.9V，增加拍擊力後電壓值增加到約2.7V，而第二模態從原本約2.7V增加到約3.8V，證實了將形變與拍擊力兩相結合確實有較高之發電效益。最後實驗在與理論值互相驗證，以獲得最後之結論。

關鍵字

非線性振動 ； 參數激擾 ； 獵能 ； 壓電片 ； 多尺度法

並列摘要

The traditional method for electric energy conversion in a VEH involves placing a piezoelectric-patch (PZT) on the root of a Fixed-Free elastic steel sheet. The vibration of the elastic steel sheet induces deformation on the PZT, thereby converting the mechanical energy to electrical energy. This system is known as the "Single Elastic Steel VEH system (SES-VEH)". Another method involves using a Double Elastic Steel sheet, where the PZT is placed at the free end of one elastic steel sheet and another elastic steel sheet slaps the PZT, generating a slap force. This system is known as the "Double Elastic Steel VEH system (DES-VEH)". The PZT deformation in a DES-VEH system placed at the free end of the elastic steel sheet is limited. Although there is a slap force generated, this design lacks the benefit of additional deformation for energy conversion compared to the traditional design of placing the PZT at the root of the elastic steel sheet.
This study improves upon the above two examples by placing the PZT in the middle of a Fixed-Fixed elastic steel sheet and applying a simple harmonic force in the axial direction on one end of the sheet to induce transverse vibration and deformation. Additionally, a baffle is installed at the maximum deformation position to generate a slap force from the elastic deformation of the steel sheet, resulting in a slap force on the PZT. This design achieves both the traditional PZT deformation for energy conversion and the additional slap force for energy conversion, combining the benefits of SES-VEH and DES-VEH. The study also establishes a complete theoretical model for this system, with both theoretical and numerical verification. The deformation of the elastic steel sheet is in the nonlinear range, and the axial excitation mode is a typical parametric excitation type. Therefore, the theoretical simulation and analysis will be carried out in a nonlinear manner. This study was conducted to validate the correctness of the theory through experiments. An elastic steel sheet was used to simulate the situation of an elastic beam. The C-shaped device was used to fix the boundary conditions of the elastic steel sheet at both ends, with one end fixed and the other end equipped with a horizontal sliding track and an actuator to simulate the vibration mode of the elastic steel sheet when it undergoes buckling.
The experiment was divided into two groups. In the first group, we used mode shape analysis of the elastic beam to determine the position of maximum deformation of the elastic steel sheet. We placed PTZ at the root of the elastic steel sheet and at the position of maximum deformation, respectively, to compare their power generation efficiency. In the second group, we placed the PZT at the position of maximum deformation and added a baffle to increase the slap force (not only deformation force but also slap force) to find the maximum power generation efficiency. The experimental results showed that the experimental voltage value of the first mode without slap force was approximately 1.9V, which increased to approximately 2.7V after increasing the slap force. The voltage value of the second mode increased from the original value of approximately 2.7V to approximately 3.8V, confirming that the combination of deformation and slap force indeed has higher power generation efficiency.

並列關鍵字

Nonlinear Vibrations ； Parametric Excitation ； Energy Harvester ； Piezoelectric patch ； Method of Multiple Scales

參考文獻

[1] H. A. Sodano and D. J. Inman, “Estimation of electric charge output for piezoelectric energy harvesting,” Strain Journal, Vol.40, Issue.2, pp.49-58, 2004.

[2] A. Rajora, et al, “Energy harvesting estimation from the vibration of a simply supported beam,” International Journal of Acoustics Vibration, Vol.22, Issue.2, pp.186-193, 2017.

[3] R. Masana and M. F. Daqaq, “Electromechanical Modeling and Nonlinear Analysis of Axially Loaded Energy Harvesters,” Journal of Vibration and Acoustics, Vol.133, Issue.1, pp.10, 2011.

[4] Y. H. Li, et al, “Nonlinear forced vibration and stability of an axially moving viscoelastic sandwich beam,” International Journal of Mechanical Sciences, Vol.138, pp.131-145, 2018.

[5] Q. Yan, H. Ding, L. Chen, “Nonlinear dynamics of axially moving viscoelastic Timoshenko beam under parametric and external excitations,” Applied Mathematics and Mechanics (Engilsh Edition), Vol.36, Issue.8, pp.971-984, 2015.