## 1 Introduction  
Additive manufacturing is crucial to the national development strategy of China. The large-scale development and utilization of inkjet 3D printing for sand mold production are important for the transformation and sustainable development of the foundry industry in China. Significant study topics include inkjet printing's techniques, equipment, forming quality, and quality control. In particular, high-precision sand casting molds should be produced using 3D printing technology in order to eliminate secondary processing [1]. The forming precision of printed sand molds can be improved by improving the structural design of the printhead [2], increasing the number of arrayed printheads [3], and enabling the inter-nozzle spacing to be mechanically altered [4]. However, improving the forming precision by these means inevitably leads to two new problems: first, multiplying the number of printheads to create arrayed printheads greatly increases the overall cost of the 3D printing system. The consequent increase in weight also decreases mechanical precision. Second, increasing the liquid-to-solid ratio of the feed fluid causes the mechanical strength of the sand mold to greatly exceed standard strength values, which makes it difficult to remove the sand mold from complex casted cavities and causes surface defects, such as pores and sand inclusions [5]. These issues significantly curtail the strengths of the 3D inkjet printing technique. Recently, it has been shown that forming precision can be improved significantly by tuning the volumetric dimensions and jetting velocities of the jetted microdroplets according to the specific requirements of the task at hand [6,7]. Therefore, some scholars have concluded that the tuning of microdroplet jetting characteristics to solve the sand mold printing problems is essential for the overall optimization and operation of 3D sand printing systems [8, 9, 10]. To optimize process parameters, the effects of jetting frequency, standoff distance (distance between the nozzle and printing substrate), and printing speed on inkjet printing precision were studied [11]. Presently, there is a substantial body of research on the relationship between printing parameters and printing quality. [PERSON] et al. [12] from the University of Louisville experimentally studied the effects of printing speed on printing quality and found that increasing printing speed always decreases precision owing to the intensification of inertial effects, regardless of standoff distance. [PERSON] et al. [13] studied spray-printed straight lines to construct a model that predicts the effects of printing speed on forming dimensions, and they performed simulations to validate the ability of their model to predict the dimensions of 3D printed products accurately. Although jetting frequency is an important process parameter that affects forming efficiency, it is inversely related to printing speed. Printing resolution is maximized when jetting frequency is increased and printing speed is reduced, and vice versa; forming precision is also affected by jetting frequency [14]. [PERSON] et al. [15] studied the effects of process parameters on the quality and anisotropic properties of 3D printed casting sand molds and used an experimentally validated mathematical model to show that printing quality is strongly dependent on the selection of process parameters. The aforementioned studies show that the effects of each process parameter on printing quality are well established, which is critical for the development of optimal process routes. However, a profound understanding of the basic characteristics of microdroplet jetting and the combined effects of all process parameters is necessary to homogenize and stabilize inkjet performance. Because microdroplet characteristics are affected by many parameters, determining the relationship between jetting and forming and their effects on the quality of printed sand molds are crucial.