# Effects of Solid Die Types in Complex and Large-Scale Aluminum Profile Extrusion
## 4 Results and Discussion  
### Extrusion Velocity of the Product  
The goal of the extrusion die design is to ensure the velocity in the extruded product is evenly distributed, and it is a decisive factor in the quality of the extruded product [31,32]. The velocity relative difference (VRD) shown in Equation (4) is used to assess the overall level of the velocity distribution of the extruded product [10,31,33]. \[VRD\ =\ \frac{\sum_{i=1}^{n}\frac{|V_{i}-V_{d}|}{V_{a}}}{n}\times 100\% \tag{4}\]  
where \(V_{i}\) is the speed at node \(i\); \(V_{a}\) is the average velocity of all nodes; \(n\) is the number of nodes considered in cross-section of product. The smaller the VRD value, the better the flow distribution. Smaller VRD also means that product quality is better. The value of VRD for balancing metal flow is defined by the designer, which is expected when the die design is as small as possible. In this study, if VRD is less than 2% of the metal flow is considered to be balanced [11,27]. Figure 8 shows the flow distribution in the extrudate of the conventional flat die obtained from simulation with bearing length calculated by Equation (1) with \(K_{w}\) = 2.5. The velocity distribution on the product is uneven in this case. Velocity tends to be faster and uniform in the region near the center and slow in the region far from the center (region 1 and region 2). The velocity in region 1 is slowest, which can be explained by the obstruction formed by the complex geometry. The difference between the maximum and minimum velocity in the product profile is 20.37 mm/s. The calculated VRD value is 4.23%. However, this value is too large and needs to be further improved. To balance the metal flow in the extruded product of traditional flat die, the bearing length needs to be increased. Then \(K_{w}\) coefficient should be increased accordingly. Table 5 lists bearing lengths of the regions in traditional flat dies with different \(K_{w}\) values. The simulation results of velocity distribution for \(K_{w}\) coefficient of 3.5 and 4.5 are shown in Figures 9a and 9b. It is observed that the differences between the maximum and minimum velocity are reduced from 10.37 to 5.37 mm/s. In other words, increasing \(K_{w}\) leads to the fact that the material flow becomes more balanced. Hence, the traditional flat die must use a coefficient of \(K_{w}\) = 4.5 (corresponding to the maximum bearing length of 14.2 mm) to balance the metal flow in the extrudate. Figure 10 indicates the velocity distribution in the pocket and spread dies. It shows that the velocity distribution with spread die is nearly even (Figure 10b). In this case, the calculated VRD value is 0.43%. The geometry of the product is not warped or bent. With a maximum bearing length of 7.9 mm (\(K_{w}\) = 2.5), the material flow can be balanced. However, controlling the metal flow in the spread die is more difficult compared to the other dies. Figure 8: Velocity distribution in the extrudate of the traditional flat die with the calculated bearing length of \(K_{w}\) = 2.5. Figure 10: Velocity distribution in the products at the ram speed of 1 mm/s of the dies: (**a**) The pocket die; (**b**) The spread die. Figure 9: Velocity distribution in the products of the traditional flat dies with different K\({}_{w}\) coefficients at the ram speed of 1 mm/s: (**a**) \(K_{w}\) = 3.5; (**b**) \(K_{w}\) = 4.5. To further investigate the effect of ram speed on velocity distribution on the profiles of different die types, a series of steady-state simulations were conducted with ram speeds of 3, 5, 7, and 9 mm/s. Figure 11 demonstrates the changing trend of VRD with the ram speeds. In the case of the pocket die, the velocity remains almost balance with a slight vary in VRD when changing the speed of ram. With the traditional flat die, the velocity tends to be more uniform with the increasing ram speed, indicated by a significant decrease of VRD. For the spread die, the velocity distribution becomes more uniform when the ram speed is low (at 1 mm/s) or high speed (at 9 mm/s).