# Profile Design of the Grooved Die and Rolling Force Prediction in the Cold Pilger Rolling Process
## 4 Experimental Conditions and Pilger Rolling Test Results
### Experimental Results  
#### 4.2.1 Analysis of the Results and a Load Comparison  
Cold pilger rolling experiments were performed to analyze the load distribution and Q factor values according to the working zone. In the cold pilger rolling process, the load distributions and Q factor were found to vary according to the die groove shape. For the working zone, the load values measured by the cold pilger rolling experiment and the load values predicted by Equation (9) are shown in the comparison in Figure 17. When the die groove shape was linear, the experimentally measured loads and the load distributions obtained through the predictive equations tended to coincide. The load gradually increased from the inlet to converge to the maximum load value of 9.11 tons in front of the outlet. This is because the deformation amount is not constant in the pilger rolling process; rather, it increases toward the process end. Accordingly, if a considerable portion of the tube is formed at the outlet, there is a risk of mandrel breakage and product quality degradation.  
In the case where the die groove shape has a parabolic profile, the experimentally measured loads and the load distributions obtained through the predictive equations show similar tendencies from the forming inlet to the center part. Hence, the load difference is observed at the outlet. A maximum load of 10.53 tons in the forming inlet due to the variable die (roll, mandrel) shape is evident. The load decreases more than predicted by the model, from its maximum value onward, and this can be due to the predominance of longitudinal deformation over circumferential deformation.  
Figure 16: Cold pilger rolling mill.  
Figure 17: Comparison of theoretical and experimental results for rolling force under different surface profile: (**a**) linear profile; (**b**) parabolic profile.  
Figure 18 shows the variation of the Q factor according to the working zone during the pilger rolling process. In the case where the die groove shape is linear, the result is satisfactory. It has a value of one or more from the inlet where the forming starts to the outlet where the forming ends. However, the Q factor value continuously increases until the forming ends due to an increase in the wall thickness reduction in the outlet. In this case, it can have a negative impact on the final product shape. In the case where the die groove shape is parabolic, the Q factor values from the inlet, where the cross-section reduction begins, to the outlet where the forming ends are all one or higher.  
By examining the Q factor distribution over the entire working zone, it is observed that the Q factor value increases up to the forming center and then decreases thereafter. However, since the change of Q factor value is not large, it does not have a significant impact on the final product shape. Nevertheless, the smaller Q factor value at the outlet will have a positive effect on the final product shape because there is less thickness deformation and a longer consolidating interval.