壓電技術運用於列印噴嘴已發展到一個段落，近幾年來更是由原本利用壓電噴頭進行2D列印中更進一步將其使用在3D列印中，例子之一即為以光固化樹酯為基材之材料噴塗成型技術(Material Jetting, MJ)。在本研究中，藉由模擬推擠式壓電噴頭噴出高黏度之光固化樹酯形成墨滴的過程，能夠針對列印之效率以及實驗中難以觀測之殘留墨水做探討。本研究利用COMSOL模擬軟體配合實際量測市售3D列印多孔噴頭之單一噴孔模組尺寸建立數值模型，並以光固化樹脂材料之流體性質為模擬參數。在本研究中，將壓電噴頭噴墨完整過程中拆為兩部分模擬，以簡化模擬複雜度與增快計算速度。第一部分利用層流與網格變形模擬驅動電壓波形使壓電元件產生之形變，並使噴頭流道腔室體積變化產生墨水流動，求得噴孔入口處隨時間變化的平均速度；第二部分則使用層流與等位函數法模擬空氣與墨水的兩相流流動，並藉由第一部分之結果作為入口條件，模擬墨水受壓電元件致動後，墨水從噴孔噴出至環境空氣時墨滴之形成與狀況。模擬結果與相同墨水與驅動參數下之實際實驗結果比較得到相符之結果。
模擬結果顯示單一波形下可得出在t_r 、t_f=2,3μs下，和V_(p.p)為20V至28V時每增加1V可以增加0.68和0.54pL，而在固定V_(p.p)=24,26,28V時，t_r 、t_f=2至3μs每減少1μs會增加3.43、3.82和4.14pL的墨滴體積，並得出以t_r 、t_f=2.0μs進行噴墨時，當t=75μs時，壓電噴頭內噴孔入口處的墨水速度會有15.24m/s的最大速度，但t=200μs時，壓電噴頭內噴孔入口處的墨水速度即降至0.04m/s，且在V_(p.p)分別為20、22、24、26與28V時可以產生15.19、16.25、18.29、20.10和21.25pL體積之墨滴。最後以t_r 、t_f=2.0μs做連續兩次的噴墨模擬，可得出在1000μs的噴墨過程中平均有3.98pL的墨水自然地從噴頭微流道內流出噴孔外，而V_(p.p)每增加1V會增加1.67pL的殘留於噴孔的墨水量。

Piezo-electric actuators have been applied to printerhead technology for the past decades. Recently, the technique has been extended from 2-D printing to 3-D printing technology, such as Material Jetting (MJ) technology with UV Curable Resin. In this study, a numerical simulation of the liquid jetting and droplet forming process of a push-mode piezoelectric printerhead using high viscosity fluid is developed to investigate the effects of driving waveform on ink residue and droplet formation. The simulation is performed with COMSOL, and the geometry of the model and the fluid properties are obtained from the actual MJP module on the market and UV curable resin. The simulation is a two-step process: First part is to simulate the deformation of piezoelectric material driven by a specific waveform, and with grid deformation and laminar flow assumption to obtain the inlet velocity profile into the nozzle. Second part is to apply the results of the first part as the inlet boundary condition to simulate the droplet formation by laminar flow and the level set method. The simulation results are in a reasonable agreement compared with the experimental data. This method successfully couples the characteristics of the piezoelectric component driven by specific input waveform with the formation of the jetted droplet. Under a single waveform and constant t_r=t_f=2,3μs and V_(p.p)=20~28V, the droplet size increases at a rate of 0.68pL/V and 0.54pL/V. For fixed V_(p.p) at 24, 26, 28V, the droplet volume increases 3.43, 3.82, 4.14pL per 1μs decrease on the rise-fall time, respectively. With the rise and fall time both set to 2μs, the flow velocity inside the nozzle drops from 15.24m/s at t=75μs to 0.04m/s at t=200μs, and the droplet volumes generated are 15.19、16.25、18.29、20.10 and 21.25pL at V_(p.p)=20,22,24,26,28V, respectively. Simulation of two successive jetting process shows that there is an averaged total volume of 3.98pL of the ink residue during a 1000μs jetting process, and the residue volume increases with V_(p.p) by a rate of 1.67pL/V.

[1] T. Wohlers and T. Gornet, "History of additive manufacturing," Wohlers report, vol. 24, no. 2014, p. 118, 2014.
[2] C. K. Chua and K. F. Leong, 3D PRINTING AND ADDITIVE MANUFACTURING: Principles and Applications (with Companion Media Pack) of Rapid Prototyping. World Scientific Publishing Co Inc, 2014.
[3] Standard terminology for additive manufacturing – Coordinate systems and test methodologies, 2015.
[4] H. P. Le, "Progress and trends in ink-jet printing technology," Journal of Imaging Science and Technology, vol. 42, no. 1, pp. 49-62, 1998.
[5] H. Wijshoff, "The dynamics of the piezo inkjet printhead operation☆," Physics Reports, vol. 491, no. 4-5, pp. 77-177, 2010.
[6] N. Reis and B. Derby, "Ink jet deposition of ceramic suspensions: Modeling and experiments of droplet formation," MRS Online Proceedings Library Archive, vol. 625, 2000.
[7] P. Wang, "Numerical Analysis of Droplet Formation and Transport of a Highly Viscous Liquid," 2014.
[8] 吳鉉忠, "壓電式微液滴噴射數學模擬系統之開發與實驗研究 / Development of a Mathematical Model for Piezoelectric Micro-droplet Ejection and Its Experimental Study," ed, 2004.
[9] 林聰鎰, "壓電噴墨頭流體動態行為之模擬研究," 成功大學航空太空工程學系學位論文, pp. 1-175, 2007.
[10] C. S. Kim, S.-J. Park, W. Sim, Y.-J. Kim, and Y. Yoo, "Modeling and characterization of an industrial inkjet head for micro-patterning on printed circuit boards," Computers & Fluids, vol. 38, no. 3, pp. 602-612, 2009.
[11] 刘春格 and 唐正宁, "基於壓電墨滴速度大小的理論研究," 包裝工程, vol. 31, no. 15, pp. 36-38, 2010.
[12] Q. Guo, Z. Li, and Y. Hu, "Mathematical model of piezoelectric ejection for high-power LED phosphor coating process," in Networking, Sensing and Control (ICNSC), 2013 10th IEEE International Conference on, 2013, pp. 89-93: IEEE.
[13] P.-H. Chen, H.-Y. Peng, H.-Y. Liu, S.-L. Chang, T.-I. Wu, and C.-H. Cheng, "Pressure response and droplet ejection of a piezoelectric inkjet printhead," International Journal of Mechanical Sciences, vol. 41, no. 2, pp. 235-248, 1999.
[14] S. Kim, J. Sung, and M. H. Lee, "Pressure wave and fluid velocity in a bend-mode inkjet nozzle with double PZT actuators," Journal of Thermal Science, vol. 22, no. 1, pp. 29-35, 2013.
[15] 陳志豪 and 林振德, "噴孔流道曲率變化與表面親疏水性對噴射液滴行為影響之研究," 2007.
[16] D. Jang, D. Kim, and J. Moon, "Influence of fluid physical properties on ink-jet printability," Langmuir, vol. 25, no. 5, pp. 2629-35, Mar 3 2009.
[17] P. Shin, S. Lee, J. Sung, and J. H. Kim, "Operability diagram of drop formation and its response to temperature variation in a piezoelectric inkjet nozzle," Microelectronics Reliability, vol. 51, no. 2, pp. 437-444, 2011.
[18] P. Shin and J. Sung, "The effect of driving waveforms on droplet formation in a piezoelectric inkjet nozzle," in Electronics Packaging Technology Conference, 2009. EPTC'09. 11th, 2009, pp. 158-162: IEEE.
[19] 張益彰, "運用微視流技術觀測調變驅動脈衝與不同工作流體下之壓電噴墨液滴演化特性," 2006.
[20] J. Brünahl and A. M. Grishin, "Piezoelectric shear mode drop-on-demand inkjet actuator," Sensors and Actuators A: Physical, vol. 101, no. 3, pp. 371-382, 2002.
[21] K.-S. Kwon and W. Kim, "A waveform design method for high-speed inkjet printing based on self-sensing measurement," Sensors and Actuators A: Physical, vol. 140, no. 1, pp. 75-83, 2007.
[22] 曾子威, "多噴孔壓電噴頭之波形設計研究應用於材料噴塗基層製造," 2017.