# Optimal Design of Droplet Ejection for PZT Printhead Based on Surrogate Model
## 6 Summary  
In this study, the stability ejection of droplets of the PZT printhead was the purpose, and the design and optimization of the droplet ejection process were optimized. Specifically, we focused on the establishment of the CFD and surrogate model of the droplet ejection process, the sensitivity analysis of the influencing droplet ejection parameters and the optimization process analysis. The summary is as follows:  
(1) The working principle of the droplet ejection process of the PZT printhead and the influencing factors of the ejection parameters were explained. We established the CFD numerical simulation model of a single droplet ejection process, and the feasibility of the proposed CFD model was verified by comparing the experimental results. Our results provide a basis for building the surrogate model.  
(2) Based on the LHS method, the CFD simulation results were used to proceed to conduct DoE, and the accuracy of the four surrogate models of PRS, RBF, KRG and SRV was verified by using the generated verification points. The validation results show that the KRG model has the largest \(R^{2}\) value, indicating that the KRG model in this study was more suitable for the study of the droplet ejection process.  
(3) According to the KRG surrogate model established, the sensitivity analysis of the four parameters of ink density, viscosity, surface tension and driving pulse period was carried out by the Sobol method, and the influence of the above parameters on droplet ejection was determined. The results showed that the influence of ink density on droplet stability ejection was the largest, followed by ink viscosity and surface tension, and finally, the driving pulse period value.  
(4) Based on the GA algorithm, the surrogate model design parameters were optimized. The optimization process took the droplet column length, Hd, as the objective and with no satellite droplets as the constraint condition. The optimized liquid column length was reduced compared with the original length, which verified the feasibility and effectiveness of the optimization method proposed in this paper.  
This study aimed to propose a method to optimize the droplet ejection parameters more efficiently and directly so as to provide a reference for the optimization and design of the droplet ejection technology. At the same time, this study also has some limitations: In  
Figure 15: Comparison between the optimized model and the original model. (**a**) Droplet ejection counters of the optimized model. (**b**) Droplet ejection counters of the original Model 1. (**c**) Droplet ejection counters of the original Model 2. (**d**) Comparison of the droplet length.  
this paper, only four influencing parameters were selected for optimization and sensitivity analysis. Other influencing parameters, such as nozzle structure size and driving signal amplitude, need to be studied further. The sensitivity analysis of the influencing parameters showed that the ink density had the greatest influence, but under the comprehensive influence mechanism, the emergence of this result also needs further verification and analysis. The limitations listed above will be further addressed in future studies.  
Conceptualization, T.L. and J.H.; methodology, T.L. and H.L.; software, T.L. and C.M.; validation, H.L., T.L. and C.M.; formal analysis, H.L.; investigation, C.M.; data curation, H.L.; writing--original draft preparation, T.L.; writing--review and editing, H.L.; visualization, C.M.; supervision, J.H.; project administration, T.L. and H.L.; funding acquisition, T.L. All authors have read and agreed to the published version of the manuscript.  
This research is supported by the Ningxia Natural Science Foundation (Grant No. 2021 AAC03196), the National Natural Science Foundation of China (Grant No. 51965001) and the Important Science and Technology Specific Projects of Anhui Province (S202003a05020087).  
Not applicable.  
The authors declare no conflict of interest.