3.3.3. Phloem–Xylem Rolling Friction Coefficient

The coefficient of the rolling friction was measured similarly to that of the coefficient of static friction. The xylem was placed radially on the surface of the phloem, and the inclined device was slowly and uniformly raised to gradually increase the phloem plate's inclination angle. When the xylem began to roll, the raising was immediately stopped, and the inclination device was fixed. The rolling angle (*β*) was measured and recorded by an angle display device. The test was repeated ten times, and the average rolling angle between the phloem and xylem was measured to be 3.91◦.

In the DEM simulation test, the values of the restitution coefficient and static friction coefficient that had been calibrated were input. The range of the rolling friction coefficient was set to 0.01–0.04 with an interval of 0.005, and all other contact parameters were set to 0. The simulation test for the rolling friction coefficient was designed as shown in Table 6, and each group of tests was repeated three times to obtain the average value.


**Table 6.** Simulation test results for the rolling friction coefficient between the xylem and phloem.

The simulation test results in Table 6 were plotted as a scatter plot and fitted, and the fitting curve is shown in Figure 13. The fitting equation for the rolling friction coefficient between the ramie phloem–xylem (*μ*r) and the rolling angle (*β*) is provided by Equation (7):

$$
\beta = 2.031 + 88.99\mu\_r - 57\mu\_r \tag{7}
$$

where *β* represents the rolling angle in degrees, mm; and *μ<sup>r</sup>* represents the rolling friction coefficient between the xylem and phloem.

**Figure 13.** Fitting curve for the rolling friction coefficient and rolling angle.

The fitting result indicates that the determination coefficient (R2) of the fitting equation is 0.999, thereby indicating a high reliability of the fitting equation. By substituting the measured rolling angle into Equation (7), *μ*<sup>r</sup> was calculated to be 0.021. Through simulation verification tests conducted five times and taking the average value, the rolling angle was found to be 3.90◦, with a relative error of 0.3% compared to the physical test results. This shows that the simulated test results after calibration were consistent with the physical test results, thus confirming the rolling friction coefficient between the phloem and xylem as 0.021.

Thus, the calibration of the contact parameters between the phloem and xylem of the ramie stalk by the discrete element method was completed, and the calibrated coefficients of restitution (*e*1), coefficient of the static friction (*μ*s), and coefficient of the rolling friction (*μ*r) between the phloem and xylem were 0.60, 0.53, and 0.021, respectively.

### *3.4. Plackett–Burman Parameter Significance Analysis*

#### 3.4.1. Significance Analysis of Phloem Parameters

The Plackett–Burman test results for the phloem are shown in Table 7, and the Design-Expert software was used to perform a significance analysis of the results, as shown in Table 8.




**Table 8.** Parameter significance analysis of the Plackett–Burman test in the phloem.

The *p*-values of the static friction coefficient between the phloem and phloem (*X*5) and the rolling friction coefficient between the phloem and phloem (*X*6) were less than 0.05, indicating that *X*<sup>5</sup> and *X*<sup>6</sup> have a significant effect on the stacking angle of the phloem. In contrast, the other factors have a relatively small effect. Therefore, only significant factors (i.e., *X*<sup>5</sup> and *X*6) were considered for the subsequent steepest ascent test and response surface design of the phloem.

#### 3.4.2. Significance Analysis of the Xylem Parameters

The Plackett–Burman test results for the xylem are shown in Table 9, and the Design-Expert software was used to perform a significance analysis of the results, as shown in Table 10.

**Table 9.** Xylem Plackett–Burman test results.


**Table 10.** Parameter significance analysis of the Plackett–Burman test in the xylem.


The results show that the *p*-values of the rolling friction coefficient between the xylem and Q235A steel (*X*3 ), the static friction coefficient between the xylem and xylem (*X*5 ), and the rolling friction coefficient between the xylem and xylem (*X*6 ) were all less than 0.05. Thus, it can be concluded that these three factors are the most critical factors affecting the stacking angle of the xylem, while other factors have relatively small effects. As a

result, only the significant factors (i.e., *X*<sup>3</sup> , *X*<sup>5</sup> , and *X*<sup>6</sup> ) were considered for the subsequent steepest ascent test and response surface design of the xylem.
