# CNN-Based Ti-6242 Impeller Forging Process Design for Uniform Strain Distribution
## 2 Theoretical Background for Designing New Forging Process  
Conventional design approaches to impeller forging of titanium alloys include direct forging of the billet into an impeller [28; 29] or designing a preform prior to impeller forging to develop the quality of the forged product. The conventional preform design approach for impeller forging typically involves an iterative process based on finite element analysis or experimentation for a specific impeller. In the conventional forging process, a preform is first designed, followed by the sequential steps of billet preform forging and target impeller forging [30; 32; 35]. This method is defined as Method I in this study. However, in the case of Method I, material and time consumption may occur due to the iterative process, and to overcome this, a design method based on CNN can be used to design preforms [25]. This method is defined as Method II in this study. Method II has been studied for materials such as AISI 1060, which is relatively easier to process than Ti-6242, and shapes that are easier than an impeller to process, such as h-shapes. To assess the effects of Method I and Method II on various impeller shapes based on Ti-6242, the results of forging were compared in terms of maximum strain, average strain, and strain standard deviation, using three different target impeller shapes, denoted as Figure 1a-c, respectively, as investigated in [30; 32; 35]. In this study, we defined the three target impeller geometries shown in Figure 1a-c as Target Impeller I, Target Impeller II, and Target Impeller III, respectively.  
The results of applying Method I and Method II to each shape are shown in Figure 2. For all three shapes, both the maximum strain and the average strain were lower for Method II, indicating that the concentration of strain in the regions where the CNN was applied was reduced, resulting in overall lower strain. However, the standard deviation was higher for Target Impeller I [32] and Target Impeller II [30] when using Method II, suggesting that Method I could achieve better results in terms of strain uniformity. Both methods show results where the maximum strain is always greater than 3, which can act as a factor causing cracks in Ti-6242 material [36]. The concentration of strain can increase internal stress, leading to reduced fatigue life due to stress concentration [37]. In particular, components exposed to situations with high strain and stress concentration, such as gas turbine impellers, may result in defects caused by microcrack formation [38]. The results of applying each method to the impeller shapes are shown in Figure 2d in terms of strain range (\(\Delta\epsilon\)). Strain range is observed to be greater than 1.2 for all impeller designs, which could lead to the occurrence of low cycle fatigue in Ti-6242 material [39; 40].  
Therefore, in this study, a three-step forging process of upsetting preform forging--target impeller forging was designed to reduce the possibility of defect in the impeller by decreasing the maximum strain and homogenizing the strain, although the process cost increases. For efficient design of impeller shapes in each step, CNN-based shape learning was conducted to reduce the design time via trial-and-error. The detailed CNN training procedure is described in Section 3.2.  
Figure 1: Target impeller shapes studied by: (**a**) [PERSON] [32]; (**b**) [PERSON] et al. [30]; (**c**) [PERSON] [35]. From left to right, the shapes were defined as Target Impeller I, Target Impeller II, and Target Impeller III, respectively.