# Profile Design of the Grooved Die and Rolling Force Prediction in the Cold Pilger Rolling Process
## 5 Conclusions  
In this study, we developed a die groove shape design method and rolling force prediction model according to the die groove shape in the cold pilger rolling process to produce seamless pipes. A pilger rolling experiment was conducted to verify the effectiveness of the proposed design method and load prediction model. The following conclusions were drawn.  
1. Based on the Geleji equation, a rolling force prediction model was developed for the main process variables (tube feed amount 3 mm, reduction area 70%, working zone 380 mm, principal deformation zone 190 mm, maximum roll outer diameter 303 mm). The  
Figure 21: Cross-sectional shape and dimension of pilger-rolled SUS304 tube.  
Figure 20: Comparison of theoretical and experimental results for tube diameter.  
proposed predictive model was used to calculate the load change in the working zone in the cold pilger rolling process for linear and parabolic die groove shapes.  
2. The roll and mandrel shapes in the exponential function from (\(y=e^{ax+b}+c\)) were designed using the proposed pilger die groove shape design method. The exponent values \(a\), \(b\), and \(c\) used in the die groove shape design defined the variable curvature of the working zone. The exponent values used in the variable roll design were 0.0045, 0.4628, and 6.3515, respectively, and the exponent values used in the mandrel design were 0.0045, 0.3832, and 4.0130, respectively.  
3. Verification experiments were performed on the pilger die grooves in linear and parabolic shapes. The validity of the rolling force prediction model was verified by comparing the predicted and experimental values. As a result of predicting the pilger load, the maximum pilger force was found to be relatively high at 10.53 tons in the parabolic profiles. However, this profile will be helpful in decreasing the risk of mandrel breakage and product quality degradation due to the rapid reduction of the load in the outlet. As a result of calculating the Q factor for the two profiles (linear, parabolic), the Q factor values of both profiles were one or higher. It, therefore, can be applied to the production of high-pressure vessels and special steel. In particular, a parabolic-shaped die groove with a Q factor of 1 or higher and a relatively uniform distribution is advantageous for the production of SUS304 seamless pipe.  
4. As a result of the pilger rolling experiment, the load and product dimension in the working zone were measured in a way similar to the predicted values. In the case of the outer diameter, the maximum dimension error was 0.32 mm; for the inner diameter, the value was 0.28 mm. These results indicate that the values were within the dimensional error range (less than \(\pm\)0.5 mm). Therefore, using the pilger die design method and the rolling force prediction model presented in this study, a pilger-rolled SUS304 tube that satisfies the required quality standard could be manufactured.  
S.-K.L.: investigation, data curation, writing--original draft preparation; K.-H.L.: conceptualization, methodology, validation, software, writing--review and editing, supervision. All authors have read and agreed to the published version of the manuscript.  
This study has been conducted with the support of the Korea Institute of Industrial Technology as \"Development of intelligent root technology with add-on modules (KITECH EO-21-0009)\".  
Not applicable.  
Data Availability Statement: Data sharing is not applicable to this article.  
The authors declare no conflict of interest.