Piezoelectric print-heads (PPHs) are used with a variety of fluid materials with specific functions; thus, matching the drive waveform of the PPH and the physical characteristics of the fluid can greatly improve deposition accuracy and quality. In this study, a distribution equation for the critical point for producing droplets defined in a dimensionless plane composed of Weber and Reynolds numbers was proposed. Computational fluid dynamics (CFD) was used to calculate the critical point distribution of the droplets generated by various materials in the dimensionless plane. Simulation results showed that the proposed distribution equation could describe the varying laws of the critical points of different materials. Process parameters in the distribution equation were identified using a fitting method based on CFD simulation results. The formula for calculating the critical characteristic velocity and dimensionless coordinates of the generated droplets was proposed based on the identified process parameters. The critical characteristic velocity and dimensionless coordinates of water, ethanol, aniline, and glycol were calculated using the proposed method. The average relative error between the calculated results and those from CFD is less than 5%. The drive waveforms of PPH are designed using the critical characteristic velocity of four different materials. Their droplet generation processes were recorded through a droplet watch system. The experimental results indicate that the flight velocity of the droplets generated at the critical characteristic velocity is close to zero, which indicates that the method proposed in this study is accurate.

中文翻译：

---

圆形喷嘴产生微滴临界速度的一种计算方法

压电打印头（PPHs）与多种具有特定功能的流体材料一起使用；因此，将PPH的驱动波形与流体的物理特性相匹配，可以大大提高沉积精度和质量。在这项研究中，提出了在由韦伯数和雷诺数组成的无量纲平面中定义的用于产生液滴的临界点的分布方程。计算流体动力学 (CFD) 用于计算无量纲平面中各种材料产生的液滴的临界点分布。仿真结果表明，所提出的分布方程能够描述不同材料临界点的变化规律。使用基于 CFD 模拟结果的拟合方法确定分布方程中的工艺参数。基于确定的工艺参数，提出了生成液滴的临界特征速度和无量纲坐标的计算公式。使用该方法计算了水、乙醇、苯胺和乙二醇的临界特征速度和无量纲坐标。计算结果与CFD计算结果的平均相对误差小于5%。PPH的驱动波形是利用四种不同材料的临界特征速度设计的。它们的液滴生成过程通过液滴观察系统记录下来。实验结果表明，在临界特征速度下产生的液滴飞行速度接近于零，表明本研究提出的方法是准确的。