Experiment results and regression model
The simulation experiment results based on the design scheme are presented in Table 4, including 24 analysis factors and 7 zero-point experiments for estimating the errors. Quadratic multiple regression analysis of the results in Table 4 was performed using the Design-Expert software, and the regression models between the influencing factors and evaluation indices were established as follows:
$$ Y_{{1}} = {1767.57} – {64.29}X_{{1}} + {117.46}X_{{2}} + {324.46}X_{{3}} + {107.87}X_{{4}} – {21.81}X_{{1}} X_{{2}} + {17.94}X_{{1}} X_{{3}} – {41.44}X_{{1}} X_{{4}} + {16.69}X_{{2}} X_{{3}} – {41.19}X_{{2}} X_{{4}} + {73.56}X_{{3}} X_{{4}} + {23.2}{X_{{1}}^{{2}}} – {82.42}{{X_{{2}}}^{{2}}} – {13.17}{{X_{{3}}}^{{2}}} – {53.67}{{X_{{4}}}^{{2}}} $$
$$ Y_{{2}} = {1968.14} + {636.42}X_{1} + {34.42}X_{2} + {66}X_{3} + {115.17}X_{{4}} + {28.63}X_{{1}} X_{{2}} + {9.13}X_{{1}} X_{{3}} – { 45.87}X_{{1}} X_{{4}} + {1}0X_{{2}} X_{{3}} + {30.5}X_{{2}} X_{{4}} – {1.75}X_{{3}} X_{{4}} + {55.03}{X_{{1}}^{{2}}} – {8.1}{{X_{{2}}}^{{2}}} – {72.72}{{X_{{3}}}^{2}} + {61.03}{{X_{{4}}}^{{2}}} $$
The relationship between the actual values of the efficiency of conveying-soil and the distance of throwing-soil and the predicted values of the regression model is shown in Fig. 7. It can be seen from Fig. 7 that the actual values are basically distributed on the predicted curve, consistent with the trend of the predicted values, and linearly distributed.
Scatter plot. (a) Scatter plot of actual and predicted distance of throwing-soil. (b) Scatter plot of actual and predicted efficiency of conveying-soil.
Variance analysis and discussion
The F-test and analysis of variance (ANOVA) were performed on the regression coefficients in the regression models of the evaluation indices Y1 and Y2, and the results are shown in Table 5. According to the significance values P of the lack of fitting in the regression models of the objective functions Y1 and Y2 in Table 5, PL1 = 0.1485 > 0.05 and PL2 = 0.2337 > 0.05 (both were not significant), indicating that no loss factor existed in the regression analysis, and the regression model exhibited a high fitting degree.
According to the ANOVA, the significance values P of each influencing factor in the test could be determined28. For the evaluation index Y1, the factors X1, X2, X3, X4, X3X4, X22, X42 had extremely significant influences, while the factors X1X4, X2X4 had a significant influence. For the evaluation index Y2, the factors X1, X3, X4, X1X4, X12, X32, X42 had extremely significant influences, and the factors X2, X1X4 had a significant influence. Within the level range of the selected factors, according to the F value of each factor as shown in Table 5, the weight of the factors affecting the efficiency of conveying-soil is feeding speed > helix angle of auger > rotating speed of auger > slope angle. And the weight of the factors affecting the distance of throwing-soil is slope auger > rotating speed of auger > feeding speed > helix angle of auger.
In addition, it is obvious that there are interactions between the feeding speed and rotating speed of the auger, slope auger and rotating speed of auger, helix angle of the auger and rotating speed of the auger on the efficiency of conveying-soil Y1. For the distance of throwing-soil Y2, there is an interaction between the slope angle and the rotating speed of the auger.
Analysis of response surface
The fitting coefficient of the efficiency of conveying-soil is R2 = 0.9714, R2adjust = 0.9263, R2pred = 0.8082, the difference between R2adjust and R2pred is less than 0.2. The fitting coefficient of the distance of throwing-soil is R2 = 0.9873, R2adjust = 0.9742, R2pred = 0.9355, the difference between R2adjust and R2pred is smaller than 0.2. It is indicated that the response surfaces of the two models established have good consistency and predictability for the experimental results29.
The response surface is created directly using the Design-Expert software. After entering the data, select “Analysis” module. In the “Model-Graph” menu bar, select “3D-surface” to switch to the 3D view. To express the interactive influence of each factor on the efficiency of conveying-soil Y1 and distance of the throwing-soil Y2, the above two quadratic regression equations of the evaluation indices were subjected to the dimensionality reduction treatment. Two of the factors was set to level 0, while the other two underwent interaction effect analysis to study the influence law on the evaluation indices Y1 and Y2, and the corresponding response surfaces were generated, as illustrated in Fig. 8.
3D response diagram effect of evaluation indices. (a) Effect of interaction between X1 and X2 on efficiency of conveying-soil. (b) Effect of interaction between X2 and X4 on efficiency of conveying-soil. (c) Effect of interaction between X3 and X4 on efficiency of conveying-soil. (d) Effect of interaction between X3 and X4 on distance of throwing-soil.
It can be seen in Fig. 8a, when the slope angle was constant, the efficiency of conveying-soil increased with the rotating speed of the auger to a certain value, then the efficiency increase changed more gently. The reasons for this phenomenon are described as follows. On the one hand, the greater the kinetic energy of the soil when leaving the original position, and the thinner the soil was cut, resulting in the smaller the probability of blockage in the spiral blade space. On the other hand, the centrifugal force of soil arriving at the pit mouth is greater, so it does not obstruct in the pit mouth. However, if the rotation speed of the auger was too high and the soil layer cut was too thin, the subsequent soil’s driving effect to the front would be weakened, or even the flow would be interrupted, so the vertical rising speed of the soil would be reduced. When the rotational speed of the auger was constant, the efficiency of conveying-soil decreased with the increase of slope and then slightly increased. With the increase of slope, the time of slope cutting process increased, and there was more soil backfilling on the side of high altitude, which leaded to the reduction of soil discharge efficiency. However, with the increase of slope, the amount of soil slide at the pit mouth was increased, improving the efficiency of soil discharge. Further analysis demonstrated that the response surface for Y1 changed more rapidly in the direction of the rotating speed than in that of the slope angle, indicating that the rotating speed of auger X4 had a more significant influence than the slope angle X1.
As can be seen in Fig. 8b, when the helix angle of the auger was fixed, the efficiency of conveying-soil continued to increase with the increase of the rotation speed. When the rotating speed of auger was fixed, the efficiency of conveying-soil increased with the increase of the helix angle and tends to decrease when it reached a certain value. The spiral blades space was the channel of soil movement. This phenomenon was caused by the increase of the gap between the two spiral blades with the increase of the helix angle of the auger, the soil was not easy to produce blockage. Meanwhile, the movement distance of soil was shorter, and the soil with higher kinetic energy was discharged more quickly from the pit. When reaching the pit mouth, the angle of soil throwing was larger and the soil backfilling rate was reduced. However, if the helix angle of auger was too large, the upward support ability and friction of the spiral blade surface to the soil would be reduced. Further analysis demonstrated that the response surface for Y1 changed more rapidly in the direction of the helix angle than the rotating speed of the auger, indicating that the helix angle of the auger X2 had a more significant influence than the rotating speed of the auger X4.
When the feeding speed was fixed, the efficiency of throwing-soil continued to increase with the increase of the rotating speed. When the rotating speed of auger was fixed, the efficiency of the throwing-soil with the increase of the feeding speed (see in Fig. 8c). The phenomenon was caused by the faster the feeding speed of the auger, the thickness of soil cut per unit time increased. Furthermore, the subsequent driving force of soil increased, and the soil kinetic energy increased. However, in the actual production, excessive feeding speed would cause soil blockage on the surface of spiral blades. The reason is due to in the simulation process, the soil would not stop moving because of blockage. Further analysis demonstrated that the response surface for Y1 changed more rapidly in the direction of the rotating speed than in that of the feeding speed, indicating that the rotating speed of auger X4 had a more significant influence than the feeding speed X3.
When the slope was fixed, the distance of the throwing-soil increased with the increase of rotation speed of the auger, and the increase amplitude increased gradually, as shown in Fig. 8d. The reason for this phenomenon was that the soil had more kinetic energy when it left its original position and the centrifugal force it received when it reaching the pit mouth is greater. When the rotation speed was too low, the soil layer was thin and the subsequent soil driving force was insufficient, resulting in the soil mass per unit area at the pit mouth was light and then the kinetic energy was small. When the rotating speed of auger was fixed, the distance of the throwing-soil increased continuously with the increase of the slope. As the slope increased, the time of soil swipe down process increased and then the rolling distance on the slope increased. Further analysis demonstrated that the response surface for Y2 changed more rapidly in the direction of the slope angle than in that of the rotating speed of auger, indicating that the slope angle X1 had a more significant influence than the rotating speed X3.
Comprehensive optimal design
As relative importance and influencing rules of various experimental factors on evaluation indexes were different from each other, evaluation indexes should be taken into comprehensive consideration30. The optimization equation is obtained by the Design-Expert software multi-objective optimization method with Y1 and Y2 as the optimization objective function.
$$25le {X}_{1}le 45$$
$$10le {X}_{2}le 22$$
$$0.04le {X}_{3}le 0.1$$
$$30le {X}_{4}le 120$$
$${{Y}_{1}}_{mathrm{max}}({X}_{1},{X}_{2},{X}_{3},{X}_{4})$$
$${{Y}_{2}}_{min}({X}_{1},{X}_{2},{X}_{3},{X}_{4})$$
In practice, the best combination of parameters needs to be selected according to the terrain slope. When the slope was fixed, the Design-Expert software was applied to optimize and solve the above mathematical model. The optimal combination of working parameters affecting the efficiency of conveying-soil Y1 and distance of throwing-soil Y2 for the auger were obtained and are shown in Table 6. If the ground preparation was required before the digging operation, the digging parameters can be designed according to values of Group 6 in Table 6.
Disturbance of soil
A soil disturbance is defined as the loosening, movement and mixing of soil caused by an auger passing through the soil16. In the interface of the EDEM Analyst, add a “Clipping plane” to show the movement of the auger inside the pit. The kinetic energy, soil particle velocity vector, and velocity value of soil particles is observed when the auger in the middle of the soil bin31,32, as shown in Fig. 9.
The disturbance of the soil effect by spiral blade.
The soil was lifted to the surface and then dropped to the lower side. In addition to the volume occupied by the spiral blades, the disturbed area also included the out-of-pit disturbed area caused by the compression of the cutting end of the spiral blade, as shown in the lower left corner of the auger.
The kinetic energy and velocity of soil decreased firstly and then increased along the opposite direction of the auger feeding. The cutting end of the auger and the soil-throwing section occurred in the region with high kinetic energy and velocity. This was because the maximum kinetic energy was obtained at the cutting end of the auger, which was gradually consumed in the process of rising. After reaching the dumping end, the soil lost the restraint of the pit wall. When the centrifugal force of soil lost the reaction force, the kinetic energy of soil increased. Too much kinetic energy, however, can cause the soil to spread too far, causing subsequent trouble. The kinetic energy of the soil at the cutting end was related to the rotational speed of the auger. The spiral angle affected the angle between the force and gravity, and then the kinetic energy consumption in the process of soil increased.
Verification experiments
To verify the accuracy of the optimization model for auger working, as well as to evaluate the rationality of the working parameter combination optimized by the virtual experiment, performance verification tests were carried out on the EDEM software. According to the optimized process parameter setting test (as shown in Table 6), the relative error between the theoretical value and the experimental value was obtained. The verification test results are summarized in Table 7. The average relative errors of the efficiency of conveying-soil and the distance of throwing-soil between the Theoretical value and text value were only 4.4%, 9.1%. The simulation model is fairly accurate. The field performance verification experiments were carried out in slope. Figure 10 illustrates the field test and working conditions.
Operation diagram at the experiment site.
Source: Ecology - nature.com
