Optimization of the Parameters in the Xylem

Based on the results of the xylem Plackett–Burman and steepest ascent test, the ranges of *X*<sup>3</sup> , *X*<sup>5</sup> , and *X*<sup>6</sup> were 0.028–0.074, 0.22–0.45, and 0.013–0.028, respectively. Taking the physical test value of the xylem stacking angle as the optimization objective, using the parameter Optimization module built into the Design-expert software, the nonsignificant factors were taken as the physics test values, and the rest were taken as the middle values of the steepest ascent test level to determine the optimal combination of the xylem–Q235A steel rolling friction coefficient (*X*3 ), static friction coefficient (*X*5 ) of the xylem–xylem, and rolling friction coefficient (*X*6 ) of the xylem–xylem; the optimization objective function and constraints are shown in Equation (11):

$$\begin{cases} \text{tar}\,\text{Y}\_2 = 27.17\\ 0.028 \le X\_{3'} \le 0.074\\ 0.22 \le X\_{5'} \le 0.45\\ 0.013 \le X\_{6'} \le 0.028 \end{cases} \tag{11}$$

After solving, 100 sets of optimized solutions were obtained. The simulated results of the optimized parameter group were compared with the physical test results. The optimized solution with the most similar shape of the xylem stacking physical test angle was found. The rolling friction coefficient (*X*3 ) between the xylem and Q235A steel was determined to be 0.033, the static friction coefficient (*X*5 ) between the xylem and xylem was 0.44, and the rolling friction coefficient (*X*6 ) between the xylem and xylem was 0.016.

### Determination and Validation of the Optimal Parameter Combination

The optimized solutions for the phloem were subjected to simulation tests, and the simulated stacking angles were 38.23◦, 38.06◦, 37.84◦, 37.93◦, and 38.12◦. The simulated results were close to the cylindrical lifting physical test angle, as shown in Figure 18, with relative errors of 0.79%, 0.34%, 0.24%, 0.11%, and 0.5%, respectively.

**Figure 18.** Comparison of the physical test and simulation test of the ramie phloem stacking angle: (**a**) physical test; (**b**) simulation test.

To evaluate the difference between the simulation and physical results of the phloem stacking angles, a two-sample *t*-test was conducted. Before conducting the two-sample *t*-test, the existence of significant differences in the variance between the two samples needed to be determined. Therefore, an *F*-test was conducted on the physical stacking angle results to test the simulation results. Table 19 shows the *F*-test results of the phloem.

**Table 19.** Results of the phloem *F*-test.


The phloem samples showed a significant difference between the two variances, with a two-tailed probability of 2*p* < 0.01. Therefore, a two-sample heteroskedasticity *t*-test was conducted to assess the significance between the simulation and physical results. Table 20 displays the results of the two-sample heteroskedasticity *t*-test of the phloem.


**Table 20.** Results of the phloem two-sample heteroskedasticity *t*-test.

According to Table 20, |*t*|<"*t* two-tailed critical" and "*p* two-tailed critical" > 0.05, indicating that there was no significant difference between the phloem simulation and physical results after calibrating the simulation parameters.

The simulated accumulation angles of the xylem were 27.13◦, 27.3◦, 27.38◦, 27.05◦, and 27.12◦. The simulated results were close to the physical results, as shown in Figure 19, with relative errors of 0.15%, 0.48%, 0.77%, 0.44%, and 0.18%, respectively.

To evaluate the difference between the simulation and physical results of the xylem stacking angles, a two-sample *t*-test was conducted. Before performing the two-sample *t*-test, it was important to assess the variance between the two samples to determine if there was a significant difference. Therefore, an *F*-test was performed on the simulation results based on the physical stacking angle results, and Table 21 shows the *F*-test results for the xylem.

**Table 21.** Results of the xylem *F*-test.


The xylem samples showed a significant difference between the two variances, with a two-tailed probability of 2*p* < 0.01. Therefore, a two-sample heteroskedasticity *t*-test was conducted to assess the significance between the simulation and physical results. Table 22 displays the results of the two-sample heteroskedasticity *t*-test of the xylem.

According to Table 22, |*t*|<"*t* two-tailed critical" value and "*p* two-tailed" > 0.05, indicating no significant difference between the xylem simulated and physical results after calibrating the simulation parameters.


**Table 22.** Results of the xylem two-sample heteroskedasticity *t*-test.

The results show that after optimizing the simulation parameters, the optimal parameter combination for the stacking angle simulation test and the physical test was when: the static friction coefficient (*X*5) between the phloem and phloem was 0.41; rolling friction coefficient between the phloem and phloem (*X*6) was 0.056; rolling friction coefficient (*X*3 ) between the xylem and Q235A steel was 0.033; the static friction coefficient (X5 ) between the xylem and xylem was 0.44; and rolling friction coefficient (*X*6 ) between the xylem and xylem was 0.016. There was no significant difference between the stacking angle simulation test results and the physical test results. The similarity in the shape and result of the stacking angle between the two indicates that the simulation parameters were accurately set. In addition, the maximum relative error between the simulated and physical results for the phloem was 0.79%, and for the xylem it was 0.77%. The average relative error between the two was only 0.4%. This further verifies the reliability and authenticity of the simulation test. The obtained parameters can be used for subsequent simulation tests on calibrating the ramie stalk's bonding parameters and the ramie stalk's discrete element decorticating simulation test.
