*3.4. Outer Surface Quality of Drawn Tubes*

Figure 9 shows the height maps of the outer surface of the drawn tubes. Since the outer diameter was estimated to be much smaller than the die diameter before the tube drawing test, tube drawing at a drawing speed ratio of 1.50 was not performed at a die reduction of 0.05. Asterisks indicate that the tube drawing was not performed for this reason. The minimum drawing speed ratio for each die reduction is shown in Table 3. The symbol \*\* indicates drawing experiments that were impossible to perform because the drawing speed ratio was less than the minimum value. The number of areas with regions of particularly high (red) or low (blue) heights increased as the drawing speed ratio increased for each material. The proportion of low-height and the high-height parts decreased in the order of the copper, the aluminum alloy, and the stainless-steel tube. Therefore, the outer surfaces of the materials were rougher in the order of the copper, the aluminum alloy, and the stainless-steel tube for drawing conditions.

**Figure 9.** *Cont.*

**Figure 9.** Height maps of the outer surface of the drawn tubes. (**a**) Stainless-steel, (**b**) copper [10], and (**c**) aluminum alloy tubes. 1-chuck implies that only the tube on the exit side was chucked. 2-chucks means that both the tubes on the die entrance and exit sides were chucked. The symbol \* indicates that the drawing experiment was not performed. The symbol \*\* indicates that the drawing experiment was impossible because the drawing speed ratio is less than the minimum value.

## *3.5. Drawing Stress during Drawing*

The mechanism causing the excessive thinning of the diameter was discussed based on the drawing stress, calculated from the load measured by the load cell affixed to the chucks of the draw-bench machine. Therefore, the load measurement accuracy of the draw-bench machine was investigated. The load measured by each load cell affixed to chucks A and B should match when a tube is simply stretched. It was confirmed that the two load cells affixed to chucks A and B measured an equivalent load, as shown in Figure 10. The load measurement accuracy of the draw-bench machine was evaluated by comparing the load obtained by the universal testing machine and the draw-bench machine. The load of the chuck A was applied for comparison. Figure 11 shows a comparison of the load measured by the universal testing machine and the draw-bench machine. In the true strain range larger than 0.4, the load of the draw-bench machine was up to 2% smaller than that of the universal testing machine. However, the drawing tension under most of the experimental conditions in this study was in a strain range smaller than 0.4. Therefore, the load measurement accuracy of the draw bench was allowed when compared to the universal testing machine.

Figure 12 shows measurement results of the copper tube's load at the die reduction *R*e of 0.17 and the drawing speed ratio of 1.10. The drawing force was calculated as the average load within 3% of the maximum. Figure 13 shows the measured drawing stress at the die reduction of 0.17 and 0.29 for each material. The tubes were drawn without contacting the die during drawing under an increased drawing speed ratio when the die reduction was 0.05. Therefore, the results of the drawing stress at the die reduction *R*<sup>e</sup> of 0.05 are not shown. The drawing stress increased as the drawing speed ratio increased for each material. The drawing stress was large in the order of the stainless-steel, the copper, and the aluminum alloy tubes. This order corresponded to the fracture stress of the stress-strain curves in Figure 5.

**Figure 10.** Measurement results of the load obtained by the tensile test of the copper tube using the draw-bench machine without the die. Chucks A and B indicate the chuck of the draw-bench machine on the die's entrance and exit sides, respectively.

**Figure 11.** Comparison of the load obtained by the tensile test using the universal testing machine and the draw-bench machine without the die.

*β* **Figure 12.** Load during drawing of the copper tube at the die reduction *R*e of 0.17 and the drawing speed ratio β of 1.10.

*β*

**Figure 13.** Drawing stress during drawing for each material. (**a**) Die reduction was 0.17 and (**b**) 0.29. The dotted lines indicate the eye guide.

#### **4. Discussion**
