# Optimal Design of Droplet Ejection for PZT Printhead Based on Surrogate Model
## 1 Introduction
[17] proposed a method to design the driving pulse waveform based on the motion of the meniscus of the PZT printhead. For obtaining high-quality injection droplets, [PERSON] et al. [18] established a laminar flow simulation model in COMSOL software and optimized the different parameters of the driving waveform. In order to accurately control the deformation of the PZT printhead membrane, [PERSON] et al. [19] proposed a self-perception method for the deformation of the printhead membrane and iterated a new driving waveform according to this method. Experimental results showed that the control accuracy of the optimized waveform parameters was significantly higher than that of the unoptimized waveform. In order to improve the effect of residual damping of oscillation inside the ink chamber of the printhead, [PERSON] [20] proposed an input-driven waveform design method based on robust optimization, and the experimental results proved the effectiveness of the method and the consistency of the droplet ejection process. For the above studies on optimizing the driving waveform, the combined influence of other parameters (such as ink viscosity, density and surface tension) on the ejection droplet is ignored (that is, the modeled relationship between the printing parameters and droplet ejection established in the above studies are imperfect). Based on the above analysis, it can be seen that researchers have proposed different methods to achieve and find the optimized target ejection parameters, and CFD numerical simulation models or experiments are needed to verify these new methods. However, due to the experimental conditions and the large-scale calculation of the numerical model, scholars cannot easily find the optimal solution for the ejection parameters for the high-quality droplet. On the other hand, the existing optimization design is mainly based on the optimization of individual parameters, and the comprehensive effect of these influencing parameters is not mentioned. In order to solve the above problem, this paper proposed a new method, that is, utilizing the surrogate model instead of the original numerical model for calculation. In addition, for expressing the numerical relationship between the optimization goal of the ejection droplet and different optimization parameters (such as driving pulse frequency, physical ink characteristics, etc. ), the surrogate model will be established on the basis of the CFD simulation model, and the optimal solution will be obtained through the continuous optimization calculation of the surrogate model. The rest of this paper is summarized as follows: Firstly, the sand-printer PZT printhead was adopted as the study object to introduce its working principle and the influencing parameters of the ejection droplet for the optimization objective of this study. On this basis, we established the CFD numerical simulation model of the single droplet injection process and verified the effectiveness of this model, which provided a basis for the surrogate model construction. Secondly, sensitivity analysis and uncertainty optimization were carried out for the influence parameters of the droplet ejection process, and we utilized the surrogate model to optimize the influencing parameters. Finally, the optimization results of the surrogate model were discussed and summarized with relevant conclusions.