# Optimization of Pin Type Single Screw Mixer for Fabrication of Functionally Graded Materials
## 4 Conclusions  
The pin-type active screw mixer, developed utilizing RSM in conjunction with a global optimization approach, has proven its efficacy in substantially reducing the distance required for the transition of material components. When compared to two other similar screw types, the optimized pin-type screw mixer reduced the transition distance by approximately 28.5% and 33.1%, respectively, in scenarios where the ratio of material component changes ranged from 9:1 to 1:9. In addition, CFD models with a high degree of accuracy have been generated in this study. These models are unquestionably capable of efficiently and economically characterizing the transition delay time for material component changes and the uniformity of mixing in extruded materials. In conjunction with the simulation results, the response function of the three control points to the transition delay time was eventually determined through the half-composite center design. In the simulation model, the particle tracking method was employed to compute the Lyapunov exponent, which serves to assess the degree of chaotic mixing in the chamber. Additionally, this method  
Figure 18: Digital image processing of print specimen.  
evaluates the radial dispersive mixing capability of the mixer through the Poincare map. Numerical validation results indicate that the Lyapunov exponent of the optimized pin-type screw mixer is 4.3 times higher than that of the mixer lacking pins and 3.5 times higher than that of the cylindrical pinned mixer. The Poincare map further confirms that the optimized pin-type screw offers superior radial dispersion mixing capabilities. These findings provide evidence that the optimized pin-type screw mixer enhances the chaotic mixing effect by increasing radial mixing while decreasing axial mixing. Through experimental research, the double-extruder printing system, combined with the optimized screw mixer, has successfully prepared FGM parts with smooth variations. Moreover, the gradient change process can be effectively characterized through digital image processing.  
In this work, the researchers extensively studied a singular instance of transition delay distance associated with a change in material components. In addition, the CFD model can be employed to explore additional transition delay distances arising from various changes in material components. To streamline the experimental data, this study utilized a quadratic B-spline to characterize the pin's geometry. Subsequent research may involve the utilization of higher-degree B-splines to extend the scope of design possibilities. It is worth noting that nearly all paste-like materials are amenable to the DIW process. This presents exciting opportunities for further exploration into the regulation of printing parameters for pastes exhibiting diverse rheological properties, such as ceramics, polymers, and other non-Newtonian fluids. This exploration holds the potential to unlock a wider array of performance of FGM parts. Regarding the study of print path strategies, future research directions may consist of the consideration of the spatial deployment of the transition region. The objective would be to achieve a transition while minimizing any negative effects on material properties.  
All authors contributed to the study conception and design; The draft of the manuscript was written by [PERSON]; All authors were involved in analysing the data. [PERSON] reviewed this paper; [PERSON] provided the management for the work. All authors have read and agreed to the published version of the manuscript.  
This project was supported by the Central Guidance for Local Science and Technology Development Fund Project, Hebei Provincial Department of Science and Technology, China (Grant No. 216Z1804G).  
Not applicable.  
Data are contained within the article.  
The authors declare no conflicts of interest.