3.1.2. ANOVA for Quadratic Model

According to the data samples in Table 6, the quadratic model of power (P), rate of crushed soil (RC), and straw burial rate (RB) was calculated by Design-Expert 12.0 software:

• Power (P)

According to the ANOVA results in Table 7, the Model F-value of 135.01 implies the model is significant. There is only a 0.01% chance that an F-value this large could occur due to noise. *p*-values less than 0.0500 indicate model terms are significant. In this case, *A*, *B*, *D*, *A2*, *B2* are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. Removing the insignificant term, the regression equation of the power consumption model in this study.

$$P = 1.22 + 0.6875A + 0.1242B - 0.0492D + 0.9322A^2 + 0.0697B^2 \tag{24}$$

The ANOVA results showed that the interaction of the factors in this model was not significant, and only the radius (R), the end cutter height (H), and the bending angle (β) were significant among the factors. It can be found from Figure 10a that when H = 45, α = 45, β = 120, the power consumption value is the lowest when R is 180, which is 1.12 kW, and as the radius R gradually increases, the power consumption increases significantly, and the analysis of the reason is due to the increase of torque, which leads to the increase of power consumption; when the radius R is lower than 180 and starts to decrease, the reason for the increase of power consumption is that the center of the blade sinks too deep into the tillage layer, which causes the blade to repeatedly Cutting soil, unable to throw out the soil fully, causing an increase in power consumption. Figure 8b,c show that

the power consumption decreases with the increase of H and increases with the decrease of β, respectively.


**Table 7.** ANOVA for Quadratic model of Power.

\*\* indicates highly significant (*p* < 0.01), \* indicates significant (*p* < 0.05), and *p*-values greater than 0.1000 indicate the model terms are not significant.

**Figure 10.** Power consumption value at different factors.

• Rate of crushed soil (RC)

According to the ANOVA results in Table 8, the Model F-value of 4.00 implies the model is significant. There is only a 0.70% chance that an F-value this large could occur due to noise. *p*-values less than 0.0500 indicate model terms are significant. In this case, *A*, *B*, *A*2, *B*<sup>2</sup> are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. Removing the insignificant term, the regression equation of the rate of crushed soil model in this study.

$$R\mathcal{C} = 67.31 + 4.82A + 5.97B - 5.52A^2 - 6.22B^2 \tag{25}$$


**Table 8.** ANOVA for Quadratic model of Rate of crushed soil.

\*\* indicates highly significant (*p* < 0.01), and *p*-values greater than 0.1000 indicate the model terms are not significant.

The ANOVA results showed that the interaction of the factors in this model was not significant. The radius (R) and the end cutter height (H) were significant among the factors. It can be found from Figure 11 that when H = 45, α = 45, β = 120, RC gradually increases with the increase of R and H. The curve stops growing at R = 195 and H = 45, respectively. The value of RC hovers around 68%. It indicates that the space for disturbing the soil at the same tillage depth under the action of a single blade is limited, and the scanning trajectory formed by its rotation is approximated.

**Figure 11.** Rate of crushed soil value at different factors.

• Rate of straw burial (RB)

According to the ANOVA results in Table 9, the Model F-value of 11.95 implies the model is significant. There is only a 0.01% chance that an F-value this large could occur due to noise. *p*-values less than 0.0500 indicate model terms are significant. In this case, *A*, *AD*, *BC*, *A*2, *D*<sup>2</sup> are significant model terms. Values greater than 0.1000 indicate the model

terms are not significant. Removing the insignificant term, the regression equation of the rate of crushed soil model in this study is:

$$RB = 17.80 + 2.68A + 1.58AD - 1.91BC - 5.60A^2 - 1.44D^2 \tag{26}$$

**Table 9.** ANOVA for Quadratic model of Rate of straw burial.


\*\* indicates highly significant (*p* < 0.01), \* indicates significant (*p* < 0.05), and *p*-values greater than 0.1000 indicate the model terms are not significant.

The ANOVA results showed that the interaction of the factors in this model was significant. The R, Rβ, and Hα were significant among the factors. The trend of RB with R is shown in Figure 12a, which shows that the RB value increases and then decreases, with a maximum at R = 200 and a model prediction of 17.78%. This is due to the upper limit of the maximum straw burial capacity of a single blade role at the same tillage depth. Too small a blade radius causes the straw not to be fully tilled into the ground, and conversely, too large a radius causes the straw to be thrown farther by the blade, also preventing effective mulching. Figure 12b presents the interaction between R and β. It is clear that the effect of changing R on RB is similar to that shown in Figure 12a. Changing the value of β, when β is 110, the maximum value of RB is slightly less than that at 120. When β increases to 130, the extreme value of the variation curve decreases further, and the value of R is taken to 217.5. Figure 12c presents the interaction curve of H with α. It can be seen that the magnitude of α affects the trend of RB with H. This is because α affects the position of the bending line and, thus, the direction of the end line. α is 35, and RB decreases with increasing H. It can be seen that the larger H is at this angle, the more straw can be buried by a single blade. On the contrary, for α of 55, RB behaves in the opposite way to the above. The intersection points of the two are near H = 45.

#### *3.2. Parameter Optimization and Comparison Test*

The optimization function in Design-Expert 12.0 software was applied for the quadratic model in this study. The optimal parameters of the blade were obtained by solving the regression model with the conditions that the broken soil rate was taken as the minimum value of 65%, the minimum straw burial rate was 15%, and the power consumption was the lowest, as shown in Figure 13. The theoretical optimal parameters were obtained as the combination of radius (R) 209.761 mm, end face height (H) 45.8743 mm, pinch angle (α) 37.607◦, and bending angle (β) 113.209◦. In accordance with the actual fabrication

process and practice, the values were taken as R = 210 mm, H = 45 mm, α = 37◦, and β = 115◦, etc.

**Figure 12.** Rate of straw burial value at different factors.

**Figure 13.** Parameter optimization of theoretical values.

A comparison test between the EDEM simulation and field was conducted under the optimal parameters to verify the reliability of the optimized parameters. Table 10 shows the results of this comparative test. The simulation test results showed that the power, soil breakage rate, and straw burial rate were 1.62 kW, 67.47%, and 17.21%, respectively; the field results showed that the power, soil breakage rate, and straw burial rate were 1.73 kW, 71.34% and 18.89%, respectively. The average error rates of the simulated and field test values were 6.36%, 5.42%, and 8.89%, respectively, which indicated that the model was a decent fit.


**Table 10.** Comparison of simulation and test results under optimal parameters.
