Numerical simulation and parameter optimization of earth auger in hilly area using EDEM software

Numerical simulation and parameter optimization of earth auger in hilly area using EDEM software | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Numerical simulation and parameter optimization of earth auger in hilly area using EDEM software Guofu Wang, Wei Zhang, Min Ji, Hu Miao, Zheng Jin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1844215/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Digging in hilly regions is an important measure to promote afforestation on difficult sites. In view of the working conditions to build fish-scale pit on slope, the auger mechanism of soil lifting and throwing was investigated in this study. This study utilized EDEM software to establish the operation model of the earth auger and conduct DEM (Discrete Element Method) virtual simulation experiments. A quadratic rotating orthogonal center combination test was implemented by setting the efficiency of conveying-soil (Y1) and the distance of throwing-soil (Y2) as the evaluation indices. Variance analysis and response surface optimization were performed on the virtual experimental data. The results indicated that the weight of the factors affecting the Y1 and Y2, were feeding speed > helix angle > rotating speed > slope angle, and slope auger > rotating speed > feeding speed > helix angle. The optimal parameter combination of each influencing factor was obtained. Among them, when the slope preparation was required, the optimal operating parameter combination of the auger was: Slope of 26.467°, Helix angle of 21.567°, Feeding speed of 0.1 m/s, Rotating speed of 67.408 r/min. This research provides theoretical references for the design optimization of the earth auger in hilly regions. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction In the process of vigorously promoting large-scale land greening in the whole society, the main problem is that, at this stage, the terrain of forestry areas to be developed is complex, the slope changes are diverse, and the afforestation conditions are difficult. Afforestation mechanization level is very low, which limited the afforestation scale expansion speed. Cavernous soil preparation, also known as pit digging, is one of the essential links in the process of afforestation. It is widely used in the forestry production and operation processes such as tree planting, soil loosing, and deep fertilization[ 1 ]. At this stage, the developed earth auger has good adaptability in plain areas and has been widely popularized[ 2 , 3 ]. For hilly and mountainous areas with complex terrain, the existing augers have problems of low efficiency and low safety factor in the application process[ 4 ]. In the afforestation operation regulations, in order to overcome the unadapt ability of earth auger and other machines and tools to hilly regions, it would be solved by carrying out level bench land preparation on the slope in advance[ 5 ]. However, the land preparation work is heavy and the original landform is seriously damaged. On the other hand, due to the narrow regional space and complex terrain, large machines cannot carry out land preparation. Horizontal land preparation is obviously not the most efficient way for tree planting[ 6 ]. When planting trees are on the slope, the shaping of fish-scale pits is one of the effective ways to conserve water and soil. The fan-shaped soil collection peak after digging on the slope has the same shape as the fish-scale pit, as shown in Fig. 1 . After shaping the soil shape, it only needs the manual reinforcement[ 7 , 8 ]. By investigating the technology of artificial shaping fish-scale pit, this study explores the mechanized digging operation on the slope to provide helps for shaping fish scale pits. In the 1870s, the research on the mechanism of earth auger has begun. Chinese scholars Lian Shihua, Zhuo Fengying and others conducted early research and summary on the design theory of auger, and many empirical formulas have been used so far for researchers' reference [ 9 , 10 ]. Scholars Purtskhvanidze, Macphersonet, et al., respectively investigated the operation power consumption and bending-torsional vibration of drill bits, which contributed to the design and innovation of excavators [ 11 , 12 ]. In recent years, in order to solve the problems of blockage and excessive backfill rate in the process of soil transportation, many experts have used MATLAB, ADAMS, ANSYS and other simulation analysis software to analyze the statics and dynamics of the auger [ 13 – 15 ]. The spatial displacement and fluctuation of soil and the interaction mechanism between soil-soil and soil-tool are the key factors affecting the energy consumption and operation effect of earth auger during the process of cutting and transporting soil. Although these studies are important for auger design and parameter optimization, they are rarely documented and published. Therefore, it is particularly important to investigate the continuous process mechanism of cutting-transportation and the dynamic response of soil. Mustafa ucgul, Kojo atta aikins, Jinwu Wang and other experts applied the discrete element method to simulate the interaction between tillage components and soil, such as scarifier, rotary cultivator, plow, etc. The distribution of stress and strain in soil, dynamic soil response (such as soil displacement) and physical parameters in soil machine interface are obtained (in particular, draught, and vertical forces, energy consumption, etc.)[ 16 – 18 ]. DEM is one of the commonly used numerical methods in the modeling and full simulation of farming process (such as pit excavation)[ 19 ]. Yuan Jin et al., using EDEM, investigated the spiral soil-fertilizer mixing equipment, analyzed the uniformity of soil-fertilizer mixing, and obtained the best mixing operation parameters[ 20 ]. Therefore, in this study, the soil and slope modeling are developed using EDEM, and the process of auger cutting and transporting soil on slope is simulated. Through the simulation results, the dynamic characteristics of soil are analyzed, and the structural parameters and operation parameters of auger are optimized. 2. Material And Methods 2.1 Machine structure Figure 2 illustrates the model of auger working on slope. The earth auger consists of spiral blades, rot and tip of auger, along with other key components. The soil is cut by spiral blades and carried out by the pit to form a cylindrical pit body[ 20 ]. 2.2 Working principle The process of soil movement on the surface of spiral blades can be obtained by observing the phenomena of field pre-experiment and virtual simulation. Due to the existence of slope angle, in order to ensure the verticality of the pit, there is an angle (α༞90 。 ) between the auger and the ground surface in the vertical plane. Soil drilling can be divided into three working processes according to the depth of the auger feeding. The first process is the cutting slope. The two spiral blades alternately cut the lifted soil. The first possibility is that the soil leaves the spiral blades directly by the centrifugal force, completing the projectile motion and reaching the ground surface. When the soil cutting end of the auger leaves the high-altitude side of the slope and enters the air, the soil slides down to the ground surface along the blades surface by its gravity. The second process is the deeper digging process. The cutting side end of the spiral blade is completely immersed in the soil and continuously cutting the soil. When the soil reaches the surface, most of it drains out of the pit on the high-elevation side due to different pit wall heights at the pit mouth. A preliminary fan-shaped soil collection peak is generated. The third process is the dig of a pit similar to in the plain regions. When the height of the soil collection peak on the low altitude side is accumulated to be flush with that on the high-altitude side, the soil would be evenly sprinkled after reaching the pit mouth to form a horizontal circular soil collection peak pit mouth. It can be concluded that in terms of soil movement and distribution, auger operations in hilly areas are different from those in plain areas, as shown in Fig. 3 . Due to the existence of slope, there are following differences in the digging process. The cutting ends of the two spiral blades break the soil alternately during the slope cutting process. The shape of the pit below the ground is irregular cylinder, and the movement of soil is not uniform affected by the pit wall. At a certain instant, the soil on the auger is unevenly distributed, with more distribution on the higher elevation side. After the soil reaches the ground, it would move along the surface to the low altitude, forming a fan-shaped soil collection peak. According to the pre-experiment, the bottom area and height parameters of fan-shaped soil collection peak are very important to the construction of fish-scale pit. If the bottom area of the soil collection peak is too large, the surface soil layer would be too thin, and it will be difficult to collect the soil. Poor discharge performance (too much soil in the pit) results in too little surface soil volume. The maximum distance of throwing-soil depends mainly on the projectile motion. The soil slides down a certain distance, and then stops moving under the action of friction, as shown in Fig. 4 . According to this movement process, the distance throwing-soil can be deduced, as shown in the formula. According to the momentum theorem, it can be deduced that the absolute velocity of the soil when leaving the spiral blades is: $$\left\{\begin{array}{c}{v}_{0}=\frac{{\int }_{t}^{{t}_{2}}\left[mr{\left(\omega -\frac{{v}_{r}\text{cos}\beta }{r}\right)}^{2}-\sum _{j=1}^{4}{\int }_{{\phi }_{1}}^{{\phi }_{2}}2{N}_{\dot{j}}{\mu }_{j}(r-{r}_{0})d\phi +{f}_{1}+{f}_{2}\right]{d}_{t}}{m}+{v}_{a}\\ {v}_{a}=\frac{(r-{r}_{0})\omega b}{2PC\text{sin}\beta }\left[AB-\sqrt{(A{B)}^{2}-4C\left({A}^{2}\phi -\frac{E}{{N}_{j}}\right)}\right]\end{array}\right.$$ 1 After the soil leaves the spiral blades, it is mainly affected by gravity G = mg and air resistance \({F}_{d}=kmv\) influence. According to the differential equation of motion: Up projectile motion of soil: After the soil leaves the spiral blades, it is mainly affected by gravity G = mg and air resistance \({F}_{d}=kmv\) influence. According to the differential equation of motion: Up projectile motion of soil: $$\left\{\begin{array}{c}{v}_{1}^{x}={v}_{0}{e}^{-kt}\\ {v}_{1}^{y}={e}^{kt}{v}_{0}^{y}+\frac{g}{k}\left({e}^{kt}-1\right)\end{array}\right.$$ 2 $$\left\{\begin{array}{c}{x}_{1}={v}_{0}^{x}\left(1-{e}^{-kt}\right)/\mu \\ {y}_{1}=\frac{\left({v}_{0}^{y}+g\right)\left({e}^{kt}-1\right)-gt}{k}\end{array}\right.$$ 3 Downward projectile motion of soil: $$\left\{\begin{array}{c}{v}_{2}^{x}={v}_{1}^{x}{e}^{-kt}\\ {v}_{2}^{y}=g\left({e}^{-kt}-1\right)/k\end{array}\right.$$ 4 $$\left\{\begin{array}{c}{x}_{2}={\nu }_{0}\left(1-{e}^{-kt}\right)∕k\\ {y}_{2}=\frac{{g}_{t}}{k}-\frac{g}{{k}^{2}}\left(1-{e}^{-kt}\right)\end{array}\right.$$ 5 The soil slides down on the slope: $$\left\{\begin{array}{c}{v}_{t}=\frac{{v}_{2}e{Y}_{2}}{\sqrt{{X}_{2}^{2}+{Y}_{2}^{2}}}\\ \varDelta x=\frac{{v}_{t}^{2}m\text{sin}\alpha }{2\left(mg-{\mu }_{1}{F}_{N}\text{sin}\alpha \right)}\end{array}\right.$$ 6 The distance of throwing-soil: $$S=\frac{{x}_{1}+{x}_{2}}{cos\alpha }+\varDelta x$$ 7 Base on the auger material and other structural parameters (tip and rod, et al.) are the same. According to the above formula, the distance of throwing-soil is mainly related to the surface slope, the helix angle of auger, the rotational speed of auger, and the air resistance. Under the same conditions, the greater the surface slope, the longer the time of soil throwing movement stage. The rotational speed and helix angle of auger are mainly related to the centrifugal force, which determines the initial velocity (kinetic energy) of the projectile motion. Where, v 0 is the absolute velocity of the soil as it leaves the spiral blade. t is the time. m is the mass of soil. r is the radius of auger. ω is the angular velocity of auger. v r is the vertical velocity of soil. ꞵ is the helix angle of auger. N i is the force of friction on soil particles (including the up-down and left-right four directions). µ is the coefficient of friction. r 0 is the radius of rod. φ is the Angle of rotation of soil motion. f 1 is the driving force of subsequent soil. f 2 is the resistance from the soil ahead. v a is the vertical velocity of soil movement[ 21 ]. A, B, C, E, P is the constant coefficients. \({\text{v}}_{1}^{\text{x}}\) ,is, the horizontal velocity of soil during the up projectile motion. \({\text{v}}_{1}^{\text{y}}\) ༌is th, vertical velocity of soil during the up projectile motion. v 2 is the velocity of soil during the downward projectile motion. k is the coefficient of air resistance. g is the acceleration of gravity. α is the angle of slope. x 1 , y 1 , is the soil displacements in the horizontal and vertical directions during the up-projectile motion. x 2 , y 2 , are the soil displacements in the horizontal and vertical directions during the downward projectile motion Δx is the soil displacements during the soil slides down on the slope. v r is the velocity of the soil relative to the surface of the blade. Ignoring the intermediate process of the soil lifting, on the whole, under the condition of smooth soil lifting, the important condition for the surface of the spiral blade to prevent clogging is that in the spiral blade space can continuously dig and discharge the soil. When the digging depth reaches H 1 , after the auger has rotated through the angle \({\phi }\) , the amount of soil at each position should meet the following conditions, expressed in Eq. ( 8 ): $${K}_{1}{Q}_{0}+{k}_{2}{Q}_{1}-{K}_{3}{Q}_{2}\le 0.5{Q}_{3}$$ 8 Where, \({Q}_{0}\) is the volume of the original soil in pit. \({Q}_{1}\) is the volume of soil cut by auger after turning the angle \(\phi\) . \({Q}_{2}\) is the volume of soil discharged at the discharge end of the auger, after turning the angle \(\phi\) . \({Q}_{3}\) is the space where soil can be stored on the auger. \({K}_{1},{K}_{2},{K}_{3}\) is the bulk coefficients of soil at this location. In Eq. 8 , the following relations are also included as shown in Eq. 9 – 11 : $${Q}_{0}=2r\left(\pi {H}_{1}-r\text{tan}\beta \right)$$ 9 $$\left\{\begin{array}{c}{Q}_{1}=\frac{\left(r-{r}_{0}\right)\left(\sqrt{{\left(\pi r\right)}^{2}+{{H}_{1}}^{2}}+\sqrt{{\left(\pi {r}_{0}\right)}^{2}+{{H}_{1}}^{2}}\right)h}{2}\\ h=\frac{2\pi {V}_{r}\phi \text{sin}\beta -S\phi \omega }{2\pi \omega }\end{array}\right.$$ 10 $${Q}_{2}={\delta }^{2}\left(r-{r}_{0}\right)\left(\frac{\omega {V}_{0}^{2}\text{sin}\beta -g\phi }{{\omega }^{3}}\right)$$ 11 $${Q}_{3}=\left(r-{r}_{0}\right)\left\{H\pi \left(r+{r}_{0}\right)-\frac{1}{z}d\left(\sqrt{{\left(\pi r\right)}^{2}+{H}^{2}}+\sqrt{{\left(\pi {r}_{0}\right)}^{2}+{H}^{2}}\right)\right\}$$ 12 Where, h is the thickness of cut down the soil after turning the angle φ. H is the total depth of pit. d is the thickness of the spiral blade. The thickness of the soil under cutting cannot be ignored. it would affect the interaction of the drilling forces and the size of the soil movement space[ 22 ]. For Q 1 , the value is mainly related to the thickness h of the soil dug per unit time. The value should be increased as much as possible to improve the efficiency of digging. However, if h is too large, the congestion would occur due to space limitation of two spiral blades Q 3 . As for Q 2 , the smoothness of the discharge-soil determines the steady supply of the subsequent soil force and the size of space of auger. To avoid clogging, Q 2 should be increased as much as possible. For Q 2 , the value is mainly related to the velocity v 0 , when the soil reaches the upper edge of the pit opening and leaves the spiral blade. For \({\text{Q}}_{3}\) , the auger in the deep digging process generally uses a double-headed spiral blade with better stability. The space of soil movement on the double blade is half of the single. Therefore, if the soil blocks are too thick, the upper surface of the soil is likely to touch the lower surface of the spiral blade, which is not conducive to soil improvement. In conclusion, the performance of auger working on the slope can be evaluated by monitoring the efficiency of conveying-soil and the distance of throwing-soil. 2.3 Establishment of EDEM simulation model DEM simulations were run using the EDEM software. The EDEM software was installed on a computer with Intel(R) Core (TM) i7-8700 CPU @ 3.20 GHz and 32 GB RAM. 2.3.1 DEM parameters and virtual soil bin The effect of auger geometric features and operating parameters on the performance was evaluated by simulating the operation of the auger in a virtual soil bin using DEM, as shown in Fig. 5 . The virtual soil bin was filled with spherical particles of nominal radius 7 mm. Input parameters used to describe the DEM particles and tool material properties are presented in Table 1 [ 17 , 23 ]. Table 1 Material Properties of Soil and Tool. Parameter Soil Tool Diameter particle (mm) 7 - Contact Radius(mm) 8.5 - Particle density (kg/m 3 ) 1350 7860 Shear modulus (Pa) 1×10 6 7.9×10 10 Poisson’s ratio 0.3 0.3 Coefficient of restitution of soil- 0.2 0.26 Coefficient of static friction of soil- 0.54 0.5 Coefficient of rolling friction of soil- 0.2 0.04 The 3D model of the slope was established by the SOLIDWORKS software and imported into the EDEM software as a pellet factory. The DEM particles were packed to a bulk voidage of 33.3705% as measured for the soil in the field. Table 1 also lists input parameters used to define soil-soil and soil-tool interactions. 2.3.2 Contact model The contact model is an important basis for analyzing the adhesion between mechanical parts and soil particles. During the digging operation, the soil particle is subjected to a variety of compound forces[ 24 , 25 ]. According to Newton's second law, the linear motion and rotation equation of the soil particle p can be expressed as Eq. ( 13 ). $$\left\{\begin{array}{c}\left\{\begin{array}{c}{F}_{n,Pq}^{JKR}=-4\sqrt{\pi \gamma {E}^{*}{\xi }^{\frac{3}{2}}}\\ {F}_{coh,pq}={k}_{coh,pq}{A}_{coh,pq}\end{array}\right.+\frac{4{E}^{*}}{3{R}^{*}}{\xi }^{3}\\ \left\{\begin{array}{c}{m}_{p}\frac{d{v}_{p}}{{d}_{t}}={m}_{p}g+\sum _{q=1}^{{n}_{p}}\left\{\begin{array}{c}-4\sqrt{\pi \gamma {E}^{*}{\alpha }^{\frac{3}{2}}}+\frac{4{E}^{*}}{3{R}^{*}}{\alpha }^{3}+{F}_{n,pq}^{d}+{F}_{\tau ,pq}+{F}_{\tau ,pq}^{d}+{k}_{coh,pq}{A}_{coh,pq})\end{array}\right.\\ {I}_{p}\frac{d{\omega }_{p}}{{d}_{t}}=\sum _{q=1}^{{n}_{p}}\left({T}_{\tau ,pq}+{T}_{\gamma ,pq}\right)\end{array}\right.\end{array}\right.$$ 13 Where, \({F}_{n,Pq}^{JKR}\) is the normal contact force between particles or between particles and equipment parts; \({F}_{n,pq}^{d}\) is the normal damping; \({F}_{\tau ,pq}\) is the tangential contact force; \({F}_{\tau ,pq}^{d}\) is the tangential damping; \({F}_{coh,p q}\) is the internal particle adhesion; \({I}_{p}\) is the moment of inertia of the soil particle \(p\) ; \({n}_{p}\) is the oil particles \(p\) total number of particles in contact; \({\omega }_{p}\) is the rotational angular velocity of the soil particle \(p\) ; \({T}_{\tau ,pq}\) is the tangential moment of the soil particle \(p\) ; \({T}_{\gamma ,pq}\) is the rolling moment of the soil particle \(p\) ; \({k}_{coh,pq}\) is the soil particle adhesion energy density; \({A}_{coh,pq}\) is the soil particle contact area; \(\gamma\) is the surface energy; \({E}^{\text{*}}\) is the equivalent Young's modulus; \({R}^{\text{*}}\) is the equivalent radius; \(\xi\) is the interaction parameter. The soil of afforestation land generally has a higher moisture content. Here there is cohesive and adhesive nature between the soil-soil and soil-tool. The cohesive force \({F}_{coh,pq}\) of soil particles is mainly set according to its internal cohesion characteristics. A Hertz-Mindlin with JKR and additional model-bounding contact model was adopted as the primary contact model for both particle-particle and particle-tool interactions. This model is suitable for simulating materials that have obvious adhesion and agglomeration between particles due to static electricity, moisture and other reasons. Table 2 lists the input parameters required for the contact models[ 26 , 27 ]. Table 2 Parameters of contact model. Parameter Value Normal Stiffness per unit area 2.1×10 8 N·m − 2 Shear Stiffness per unit area 8×10 7 N·m − 2 Critical Normal Stress 1.5×10 6 Pa Critical Shear Stress 8×10 5 Pa Bonded Disk Radius 2.5 mm Surface energy of soil-soil 7.46 J·m − 3 Surface energy of soil-tool 5.5 J·m − 3 2.3.3 Scheme of simulation experiment Virtual experiments on the quadratic rotating orthogonal center combination with four factors and five levels were carried out to evaluate the working performance of the auger. Based on previous experimental studies, practical experience and mechanism analysis, the appropriate levels of the experiment factors were established as indicated in Table 3 . The slope angle X1, the helix angle of auger X2, the feeding speed X3 and the rotating speed of auger X4 were selected as experimental factors, while the efficiency of conveying-soil Y1 and the distance of throwing-soil Y2 set as experimental indicators. According to the accuracy in the practical application, the value in the virtual experiment retains two significant digits. As shown in Fig. 6 , in the EDEM software analyst module, Grid Bin Group and Clipping Plane are added to measure the amount of soil outside the pit and the distance of throwing-soil. Table 3 Factors and levels of virtual experiment. Coded value Experiment factors X 1 / ( \(^\circ\) ) X 2 / ( \(^\circ\) ) X 3 / (m/s) X 4 / (r/min) 2 45 22 0.1 120 1 40 19 0.085 97.5 0 35 16 0.07 75 -1 30 13 0.055 52.5 -2 25 10 0.04 30 3. Results And Discussion 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: Table 4 Experiment schemes and results. NO. Factors Evaluation Indices X 1 X 2 X 3 X 4 Y 1 Y 2 1 -1 -1 -1 -1 1243 1246 2 1 -1 -1 -1 1143 2435 3 -1 1 -1 -1 1572 1023 4 1 1 -1 -1 1330 2517 5 -1 -1 1 -1 1502 1150 6 1 -1 1 -1 1672 2633 7 -1 1 1 -1 2039 1186 8 1 1 1 -1 1973 2619 9 -1 -1 -1 1 1376 1432 10 1 -1 -1 1 1096 2625 11 -1 1 -1 1 1469 1480 12 1 1 -1 1 1378 2763 13 -1 -1 1 1 2111 1545 14 1 -1 1 1 1926 2683 15 -1 1 1 1 2351 1580 16 1 1 1 1 2006 2831 17 -2 0 0 0 1971 1024 18 2 0 0 0 1769 3429 19 0 -2 0 0 1255 1830 20 0 2 0 0 1640 2118 21 0 0 -2 0 1021 1496 22 0 0 2 0 2428 1935 23 0 0 0 -2 1225 2092 24 0 0 0 2 1900 2409 25 0 0 0 0 1780 1988 26 0 0 0 0 1800 1994 27 0 0 0 0 1822 2015 28 0 0 0 0 1870 2086 29 0 0 0 0 1676 1856 30 0 0 0 0 1689 1889 31 0 0 0 0 1736 1949 Table 5. ANOVA results of regression model. Indicator Source of variance Sum of Squares df Mean Square F-value p-value Significant Y1 Model 3.686E + 06 14 2.633E + 05 27.92 < 0.0001 *** X 1 99202.04 1 99202.04 10.52 0.0051 *** X 2 3.311E + 05 1 3.311E + 05 35.12 < 0.0001 *** X 3 2.527E + 06 1 2.527E + 06 267.97 < 0.0001 *** X 4 2.793E + 05 1 2.793E + 05 29.62 < 0.0001 *** X 1 X 2 7612.56 1 7612.56 0.8074 0.3822 X 1 X 3 5148.06 1 5148.06 0.5460 0.4707 X 1 X 4 27473.06 1 27473.06 2.91 0.1072 * X 2 X 3 4455.56 1 4455.56 0.4726 0.5017 X 2 X 4 27142.56 1 27142.56 2.88 0.1091 * X 3 X 4 86583.06 1 86583.06 9.18 0.0080 *** X 1 2 15392.56 1 15392.56 1.63 0.2196 X 2 2 1.943E + 05 1 1.943E + 05 20.60 0.0003 *** X 3 2 4962.99 1 4962.99 0.5264 0.4786 X 4 2 82381.76 1 82381.76 8.74 0.0093 *** Residual 1.509E + 05 16 9428.56 Lack of Fit 1.206E + 05 10 12064.13 2.40 0.1485 not significant Pure Error 30215.71 6 5035.95 Cor Total 3.837E + 06 30 Y2 Model 1.062E + 07 14 7.586E + 05 81.87 < 0.0001 *** X 1 9.721E + 06 1 9.721E + 06 1049.03 < 0.0001 *** X 2 28428.17 1 28428.17 3.07 0.0990 * X 3 1.045E + 05 1 1.045E + 05 11.28 0.0040 *** X 4 3.183E + 05 1 3.183E + 05 34.35 < 0.0001 *** X 1 X 2 13110.25 1 13110.25 1.41 0.2516 X 1 X 3 1332.25 1 1332.25 0.1438 0.7095 X 1 X 4 33672.25 1 33672.25 3.63 0.0747 * X 2 X 3 1600.00 1 1600.00 0.1727 0.6833 X 2 X 4 14884.00 1 14884.00 1.61 0.2232 X 3 X 4 49.00 1 49.00 0.0053 0.9429 X 1 2 86586.40 1 86586.40 9.34 0.0075 *** X 2 2 1875.34 1 1875.34 0.2024 0.6588 X 3 2 1.512E + 05 1 1.512E + 05 16.32 0.0009 *** X 4 2 1.065E + 05 1 1.065E + 05 11.49 0.0037 *** Residual 1.483E + 05 16 9266.33 Lack of Fit 1.119E + 05 10 11190.65 1.85 0.2337 not significant Pure Error 36354.86 6 6059.14 Cor Total 1.077E + 07 30 Note: “***” means extremely significant(P < 0.01); “**” means very significant(0.01 ≤ P < 0.05); “*” means significant(0.05 ≤ P < 0.1). Y1 = 1767.57-64.29X1 + 117.46X2 + 324.46X3 + 107.87X4-21.81X1X2 + 17.94X1X3-41.44X1X4 + 16.69X2X3-41.19X2X4 + 73.56X3X4 + 23.2X12-82.42X22-13.17X32-53.67X42 Y2 = 1968.14 + 636.42X1 + 34.42X2 + 66X3 + 115.17X4 + 28.63X1X2 + 9.13X1X3-45.87X1X4 + 10X2X3 + 30.5X2X4-1.75X3X4 + 55.03X12+-8.1X22-72.72X32 + 61.03X42 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. 3.1 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, PL 1 = 0.1485 > 0.05 and PL 2 = 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 determined[ 28 ]. For the evaluation index Y1, the factors X1, X2, X3, X4, X3X4, X2 2 , X4 2 had extremely significant influences, while the factor X1X4, X2X4 had a significant influence. For the evaluation index Y2, the factors X1, X3, X4, X1X4, X1 2 , X3 2 , X4 2 had extremely significant influences, and the factor 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. 3.2 Analysis of response surface The fitting coefficient of the efficiency of conveying-soil is R 2 = 0.9714, R 2 adjust = 0.9263, R 2 pred = 0.8082, the difference between R 2 adjust and R 2 pred is less than 0.2. The fitting coefficient of the distance of throwing-soil is R 2 = 0.9873, R 2 adjust = 0.9742, R 2 pred = 0.9355, the difference between R 2 adjust and R 2 pred 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 results[ 29 ]. 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 Y1and Y2, and the corresponding response surfaces were generated, as illustrated in Fig. 8 . It can be seen in Fig. 8 (a), 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. 8 (b), 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. As can be seen in Fig. 8 (c), 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. 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. As can be seen in Fig. 8 (d), 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. 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. 3.3 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 consideration[ 30 ]. The optimization equation is obtained by the Design-Expert software multi-objective optimization method with Y1and Y2 as the optimization objective function. $$\left\{\begin{array}{c}25\le X1\le 45\\ 10\le X2\le 22\\ 0.04\le X1\le 0.1\\ 30\le X1\le 120\\ {Y1}_{\text{m}\text{a}\text{x}}(X1,X2,X3,X4)\\ {Y2}_{min}(X1,X2,X3,X4)\end{array}\right.$$ 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 . Table 6 Optimal parameter combinations of several terrain slopes NO. Slope (°) Helix angle (°) Feeding speed (m/s) Rotating speed (r/min) Efficiency of conveying-soil (Num/s) Distance of throwing-soil (mm) 1 25 21.371 0.094 91.639 2622.162 997.673 2 30 20.863 0.1 58.091 2274.818 1108.703 3 35 15.563 0.1 69.303 2270.547 1777.915 4 40 10 0.1 85.486 1897.109 2335.958 5 45 10 0.1 85.379 1961.625 3076.999 6 26.467 21.567 0.1 67.408 2450.607 762.168 3.4 Disturbance of soil A soil disturbance is defined as the loosening, movement and mixing of soil caused by an auger passing through the soil[ 16 ]. 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 bin [ 31 , 32 ], as shown in Fig. 9 . 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. Table 7. Results and comparison of validation test. Text Efficiency of conveying-soil （Num/s） Relative error（%） Distance of throwing-soil（mm） Relative error（%） Theoretical value Text value Theoretical value Text value 1 2622 2739 4.4% 998 1025 2.8% 2 2275 2327 2.3% 1109 1187 7.0% 3 2271 2221 2.2% 1778 1689 5.0% 4 1897 1945 2.5% 2336 2769 18.5% 5 1962 1763 10.1% 3077 3166 2.9% 6 2451 2576 5.1% 762 900 18.1% Average / / 4.4% / / 9.1% 4. 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. 5. Conclusions In the process of digging pits in hilly regions to assist in the construction of fish-scale pits: (1) The performance of auger working on slope can be evaluated by monitoring the efficiency of conveying-soil and the distance of the throwing-soil. (2) The weight of the factors affecting the efficiency of conveying-soil is feeding speed༞helix angle of auger༞rotating speed of auger༞slope angle. The weight of the factors affecting the distance of throwing-soil is slope auger༞rotating speed of auger༞feeding speed༞helix angle of auger. (3) According to the optimization results, the optimal parameter combination can be obtained in different slope operations. The optimized results show that if the slope preparation is required before the digging operation, the optimal operating parameter combination of the auger is: Slope of 26.467°, Helix angle of 21.567°, Feeding speed of 0.1 m/s, Rotating speed of 67.408 r/min. (4) Compared with the plain area, the variation law of soil displacement and velocity is different in hilly regions. The errors between the results from the developed DEM simulation modeling and virtual experiments’ results are in the acceptable accuracy, confirming the effectiveness of the DEM model for estimating the working efficiency of the earth auger in hilly area. Declarations Acknowledgements The authors acknowledge the financial support provided by Forestry Science and Technology Promotion Project of State Forestry and Grassland Administration of China (Grant No. (2019)35) and Key R&D and Transformation Program of Qinghai Province - Special Project of Transformation of Scientific and Technological Achievements (Grant No. 2022-NK-128) Author contributions statement W.G. methodology, investigation, analysis, statistics, writing—original draft, review and editing. Z.W. funding acquisition, writing—review and editing. J.M. writing—review and editing. M.H. statistics. J.Z. supervision. All authors have read and agreed to the published version of the manuscript. Competing interests The authors declare no competing interests. Additional information Correspondence and requests for materials should be addressed to Z.W. Data Availability Statement The data that support the findings of this study are available from the corresponding author. 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Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Major revision 30 Sep, 2022 Reviews received at journal 22 Sep, 2022 Reviews received at journal 21 Sep, 2022 Reviewers agreed at journal 12 Sep, 2022 Reviewers agreed at journal 12 Sep, 2022 Reviewers invited by journal 11 Sep, 2022 Editor assigned by journal 05 Sep, 2022 Editor invited by journal 15 Jul, 2022 Submission checks completed at journal 14 Jul, 2022 First submitted to journal 10 Jul, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1844215","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":125315853,"identity":"b55e54d1-d965-41a0-a671-d116a91f739e","order_by":0,"name":"Guofu Wang","email":"","orcid":"","institution":"Research Institute of Wood Industry, Chinese Academy of Forestry","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Guofu","middleName":"","lastName":"Wang","suffix":""},{"id":125315856,"identity":"3b9c17a7-bb53-4c3d-b1c2-918480265bba","order_by":1,"name":"Wei 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plot.\u003c/p\u003e\u003cp\u003e(a) Scatter plot of actual and predicted distance of throwing-soil.\u003c/p\u003e\u003cp\u003e(b) Scatter plot of actual and predicted efficiency of conveying-soil.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure7.png","url":"https://assets-eu.researchsquare.com/files/rs-1844215/v1/72c7ec8d76a585f6213c7c62.png"},{"id":24858349,"identity":"0055a1a2-dc48-45e1-9075-f7d04d15eaaa","added_by":"auto","created_at":"2022-08-05 23:45:07","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":4425512,"visible":true,"origin":"","legend":"\u003cp\u003e3D response diagram effect of evaluation indices.\u003c/p\u003e\u003cp\u003e(a) Effect of interaction between X1 and X2 on efficiency of conveying-soil.\u003c/p\u003e\u003cp\u003e(b) Effect of interaction between X2 and X4 on efficiency of conveying-soil.\u003c/p\u003e\u003cp\u003e(c) Effect of interaction between X3 and X4 on efficiency of conveying-soil.\u003c/p\u003e\u003cp\u003e(a) Effect of interaction between X3 and X4 on distance of throwing-soil.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure8.png","url":"https://assets-eu.researchsquare.com/files/rs-1844215/v1/1cebee4c5d359e8856a39137.png"},{"id":24859081,"identity":"abbbfbe4-3588-40f3-b440-63161d289036","added_by":"auto","created_at":"2022-08-05 23:50:07","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":8142931,"visible":true,"origin":"","legend":"\u003cp\u003eThe disturbance of the soil effect by spiral blade.\u003c/p\u003e","description":"","filename":"Figure9.png","url":"https://assets-eu.researchsquare.com/files/rs-1844215/v1/4cf0271ee247a0c2e3241e35.png"},{"id":24858351,"identity":"95b4c798-8665-4bd8-a346-c04d38c73285","added_by":"auto","created_at":"2022-08-05 23:45:07","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":12686325,"visible":true,"origin":"","legend":"\u003cp\u003eOperation diagram at the experiment site.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure10.png","url":"https://assets-eu.researchsquare.com/files/rs-1844215/v1/ff90d8bba3a71757687b7ecc.png"},{"id":24859755,"identity":"e04932ec-2639-4201-8b6a-52a8dbac3e58","added_by":"auto","created_at":"2022-08-05 23:55:11","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":537934,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1844215/v1/14eb66aa-e8c3-4499-9188-a454051b7f03.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Numerical simulation and parameter optimization of earth auger in hilly area using EDEM software","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn the process of vigorously promoting large-scale land greening in the whole society, the main problem is that, at this stage, the terrain of forestry areas to be developed is complex, the slope changes are diverse, and the afforestation conditions are difficult. Afforestation mechanization level is very low, which limited the afforestation scale expansion speed.\u003c/p\u003e \u003cp\u003eCavernous soil preparation, also known as pit digging, is one of the essential links in the process of afforestation. It is widely used in the forestry production and operation processes such as tree planting, soil loosing, and deep fertilization[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. At this stage, the developed earth auger has good adaptability in plain areas and has been widely popularized[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. For hilly and mountainous areas with complex terrain, the existing augers have problems of low efficiency and low safety factor in the application process[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn the afforestation operation regulations, in order to overcome the unadapt ability of earth auger and other machines and tools to hilly regions, it would be solved by carrying out level bench land preparation on the slope in advance[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. However, the land preparation work is heavy and the original landform is seriously damaged. On the other hand, due to the narrow regional space and complex terrain, large machines cannot carry out land preparation. Horizontal land preparation is obviously not the most efficient way for tree planting[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. When planting trees are on the slope, the shaping of fish-scale pits is one of the effective ways to conserve water and soil. The fan-shaped soil collection peak after digging on the slope has the same shape as the fish-scale pit, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. After shaping the soil shape, it only needs the manual reinforcement[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. By investigating the technology of artificial shaping fish-scale pit, this study explores the mechanized digging operation on the slope to provide helps for shaping fish scale pits.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the 1870s, the research on the mechanism of earth auger has begun. Chinese scholars Lian Shihua, Zhuo Fengying and others conducted early research and summary on the design theory of auger, and many empirical formulas have been used so far for researchers' reference [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Scholars Purtskhvanidze, Macphersonet, et al., respectively investigated the operation power consumption and bending-torsional vibration of drill bits, which contributed to the design and innovation of excavators [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. In recent years, in order to solve the problems of blockage and excessive backfill rate in the process of soil transportation, many experts have used MATLAB, ADAMS, ANSYS and other simulation analysis software to analyze the statics and dynamics of the auger [\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe spatial displacement and fluctuation of soil and the interaction mechanism between soil-soil and soil-tool are the key factors affecting the energy consumption and operation effect of earth auger during the process of cutting and transporting soil. Although these studies are important for auger design and parameter optimization, they are rarely documented and published. Therefore, it is particularly important to investigate the continuous process mechanism of cutting-transportation and the dynamic response of soil.\u003c/p\u003e \u003cp\u003eMustafa ucgul, Kojo atta aikins, Jinwu Wang and other experts applied the discrete element method to simulate the interaction between tillage components and soil, such as scarifier, rotary cultivator, plow, etc. The distribution of stress and strain in soil, dynamic soil response (such as soil displacement) and physical parameters in soil machine interface are obtained (in particular, draught, and vertical forces, energy consumption, etc.)[\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. DEM is one of the commonly used numerical methods in the modeling and full simulation of farming process (such as pit excavation)[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Yuan Jin et al., using EDEM, investigated the spiral soil-fertilizer mixing equipment, analyzed the uniformity of soil-fertilizer mixing, and obtained the best mixing operation parameters[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Therefore, in this study, the soil and slope modeling are developed using EDEM, and the process of auger cutting and transporting soil on slope is simulated. Through the simulation results, the dynamic characteristics of soil are analyzed, and the structural parameters and operation parameters of auger are optimized.\u003c/p\u003e"},{"header":"2. Material And Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Machine structure\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the model of auger working on slope. The earth auger consists of spiral blades, rot and tip of auger, along with other key components. The soil is cut by spiral blades and carried out by the pit to form a cylindrical pit body[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Working principle\u003c/h2\u003e \u003cp\u003eThe process of soil movement on the surface of spiral blades can be obtained by observing the phenomena of field pre-experiment and virtual simulation.\u003c/p\u003e \u003cp\u003eDue to the existence of slope angle, in order to ensure the verticality of the pit, there is an angle (α༞90\u003csup\u003e。\u003c/sup\u003e) between the auger and the ground surface in the vertical plane. Soil drilling can be divided into three working processes according to the depth of the auger feeding.\u003c/p\u003e \u003cp\u003eThe first process is the cutting slope. The two spiral blades alternately cut the lifted soil. The first possibility is that the soil leaves the spiral blades directly by the centrifugal force, completing the projectile motion and reaching the ground surface. When the soil cutting end of the auger leaves the high-altitude side of the slope and enters the air, the soil slides down to the ground surface along the blades surface by its gravity.\u003c/p\u003e \u003cp\u003eThe second process is the deeper digging process. The cutting side end of the spiral blade is completely immersed in the soil and continuously cutting the soil. When the soil reaches the surface, most of it drains out of the pit on the high-elevation side due to different pit wall heights at the pit mouth. A preliminary fan-shaped soil collection peak is generated.\u003c/p\u003e \u003cp\u003eThe third process is the dig of a pit similar to in the plain regions. When the height of the soil collection peak on the low altitude side is accumulated to be flush with that on the high-altitude side, the soil would be evenly sprinkled after reaching the pit mouth to form a horizontal circular soil collection peak pit mouth.\u003c/p\u003e \u003cp\u003eIt can be concluded that in terms of soil movement and distribution, auger operations in hilly areas are different from those in plain areas, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Due to the existence of slope, there are following differences in the digging process. The cutting ends of the two spiral blades break the soil alternately during the slope cutting process. The shape of the pit below the ground is irregular cylinder, and the movement of soil is not uniform affected by the pit wall. At a certain instant, the soil on the auger is unevenly distributed, with more distribution on the higher elevation side. After the soil reaches the ground, it would move along the surface to the low altitude, forming a fan-shaped soil collection peak.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to the pre-experiment, the bottom area and height parameters of fan-shaped soil collection peak are very important to the construction of fish-scale pit. If the bottom area of the soil collection peak is too large, the surface soil layer would be too thin, and it will be difficult to collect the soil. Poor discharge performance (too much soil in the pit) results in too little surface soil volume.\u003c/p\u003e \u003cp\u003eThe maximum distance of throwing-soil depends mainly on the projectile motion. The soil slides down a certain distance, and then stops moving under the action of friction, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. According to this movement process, the distance throwing-soil can be deduced, as shown in the formula.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to the momentum theorem, it can be deduced that the absolute velocity of the soil when leaving the spiral blades is:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\left\\{\\begin{array}{c}{v}_{0}=\\frac{{\\int }_{t}^{{t}_{2}}\\left[mr{\\left(\\omega -\\frac{{v}_{r}\\text{cos}\\beta }{r}\\right)}^{2}-\\sum _{j=1}^{4}{\\int }_{{\\phi }_{1}}^{{\\phi }_{2}}2{N}_{\\dot{j}}{\\mu }_{j}(r-{r}_{0})d\\phi +{f}_{1}+{f}_{2}\\right]{d}_{t}}{m}+{v}_{a}\\\\ {v}_{a}=\\frac{(r-{r}_{0})\\omega b}{2PC\\text{sin}\\beta }\\left[AB-\\sqrt{(A{B)}^{2}-4C\\left({A}^{2}\\phi -\\frac{E}{{N}_{j}}\\right)}\\right]\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAfter the soil leaves the spiral blades, it is mainly affected by gravity G\u0026thinsp;=\u0026thinsp;mg and air resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{d}=kmv\\)\u003c/span\u003e\u003c/span\u003e influence. According to the differential equation of motion:\u003c/p\u003e \u003cp\u003eUp projectile motion of soil:\u003c/p\u003e \u003cp\u003eAfter the soil leaves the spiral blades, it is mainly affected by gravity G\u0026thinsp;=\u0026thinsp;mg and air resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{d}=kmv\\)\u003c/span\u003e\u003c/span\u003e influence. According to the differential equation of motion:\u003c/p\u003e \u003cp\u003eUp projectile motion of soil:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\left\\{\\begin{array}{c}{v}_{1}^{x}={v}_{0}{e}^{-kt}\\\\ {v}_{1}^{y}={e}^{kt}{v}_{0}^{y}+\\frac{g}{k}\\left({e}^{kt}-1\\right)\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\left\\{\\begin{array}{c}{x}_{1}={v}_{0}^{x}\\left(1-{e}^{-kt}\\right)/\\mu \\\\ {y}_{1}=\\frac{\\left({v}_{0}^{y}+g\\right)\\left({e}^{kt}-1\\right)-gt}{k}\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eDownward projectile motion of soil:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\left\\{\\begin{array}{c}{v}_{2}^{x}={v}_{1}^{x}{e}^{-kt}\\\\ {v}_{2}^{y}=g\\left({e}^{-kt}-1\\right)/k\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\left\\{\\begin{array}{c}{x}_{2}={\\nu }_{0}\\left(1-{e}^{-kt}\\right)∕k\\\\ {y}_{2}=\\frac{{g}_{t}}{k}-\\frac{g}{{k}^{2}}\\left(1-{e}^{-kt}\\right)\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe soil slides down on the slope:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\left\\{\\begin{array}{c}{v}_{t}=\\frac{{v}_{2}e{Y}_{2}}{\\sqrt{{X}_{2}^{2}+{Y}_{2}^{2}}}\\\\ \\varDelta x=\\frac{{v}_{t}^{2}m\\text{sin}\\alpha }{2\\left(mg-{\\mu }_{1}{F}_{N}\\text{sin}\\alpha \\right)}\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe distance of throwing-soil:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$S=\\frac{{x}_{1}+{x}_{2}}{cos\\alpha }+\\varDelta x$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eBase on the auger material and other structural parameters (tip and rod, et al.) are the same. According to the above formula, the distance of throwing-soil is mainly related to the surface slope, the helix angle of auger, the rotational speed of auger, and the air resistance. Under the same conditions, the greater the surface slope, the longer the time of soil throwing movement stage. The rotational speed and helix angle of auger are mainly related to the centrifugal force, which determines the initial velocity (kinetic energy) of the projectile motion.\u003c/p\u003e \u003cp\u003eWhere, v\u003csub\u003e0\u003c/sub\u003e is the absolute velocity of the soil as it leaves the spiral blade. t is the time. m is the mass of soil. r is the radius of auger. ω is the angular velocity of auger. v\u003csub\u003er\u003c/sub\u003e is the vertical velocity of soil. ꞵ is the helix angle of auger. N\u003csub\u003ei\u003c/sub\u003e is the force of friction on soil particles (including the up-down and left-right four directions). \u0026micro; is the coefficient of friction. r\u003csub\u003e0\u003c/sub\u003e is the radius of rod. φ is the Angle of rotation of soil motion. f\u003csub\u003e1\u003c/sub\u003e is the driving force of subsequent soil. f\u003csub\u003e2\u003c/sub\u003e is the resistance from the soil ahead. v\u003csub\u003ea\u003c/sub\u003e is the vertical velocity of soil movement[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. A, B, C, E, P is the constant coefficients. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{v}}_{1}^{\\text{x}}\\)\u003c/span\u003e\u003c/span\u003e,is, the horizontal velocity of soil during the up projectile motion. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{v}}_{1}^{\\text{y}}\\)\u003c/span\u003e\u003c/span\u003e༌is th, vertical velocity of soil during the up projectile motion. v\u003csub\u003e2\u003c/sub\u003e is the velocity of soil during the downward projectile motion. k is the coefficient of air resistance. g is the acceleration of gravity. α is the angle of slope. x\u003csub\u003e1\u003c/sub\u003e, y\u003csub\u003e1\u003c/sub\u003e, is the soil displacements in the horizontal and vertical directions during the up-projectile motion. x\u003csub\u003e2\u003c/sub\u003e, y\u003csub\u003e2\u003c/sub\u003e, are the soil displacements in the horizontal and vertical directions during the downward projectile motion Δx is the soil displacements during the soil slides down on the slope. v\u003csub\u003er\u003c/sub\u003e is the velocity of the soil relative to the surface of the blade.\u003c/p\u003e \u003cp\u003eIgnoring the intermediate process of the soil lifting, on the whole, under the condition of smooth soil lifting, the important condition for the surface of the spiral blade to prevent clogging is that in the spiral blade space can continuously dig and discharge the soil. When the digging depth reaches H\u003csub\u003e1\u003c/sub\u003e, after the auger has rotated through the angle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\phi }\\)\u003c/span\u003e\u003c/span\u003e, the amount of soil at each position should meet the following conditions, expressed in Eq.\u0026nbsp;(\u003cspan refid=\"Equ8\" class=\"InternalRef\"\u003e8\u003c/span\u003e):\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$${K}_{1}{Q}_{0}+{k}_{2}{Q}_{1}-{K}_{3}{Q}_{2}\\le 0.5{Q}_{3}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q}_{0}\\)\u003c/span\u003e\u003c/span\u003e is the volume of the original soil in pit. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q}_{1}\\)\u003c/span\u003e\u003c/span\u003e is the volume of soil cut by auger after turning the angle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\phi\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q}_{2}\\)\u003c/span\u003e\u003c/span\u003e is the volume of soil discharged at the discharge end of the auger, after turning the angle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\phi\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q}_{3}\\)\u003c/span\u003e\u003c/span\u003e is the space where soil can be stored on the auger. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{1},{K}_{2},{K}_{3}\\)\u003c/span\u003e\u003c/span\u003eis the bulk coefficients of soil at this location.\u003c/p\u003e \u003cp\u003eIn Eq.\u0026nbsp;\u003cspan refid=\"Equ8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, the following relations are also included as shown in Eq.\u0026nbsp;\u003cspan refid=\"Equ9\" class=\"InternalRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Equ11\" class=\"InternalRef\"\u003e11\u003c/span\u003e:\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$${Q}_{0}=2r\\left(\\pi {H}_{1}-r\\text{tan}\\beta \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\left\\{\\begin{array}{c}{Q}_{1}=\\frac{\\left(r-{r}_{0}\\right)\\left(\\sqrt{{\\left(\\pi r\\right)}^{2}+{{H}_{1}}^{2}}+\\sqrt{{\\left(\\pi {r}_{0}\\right)}^{2}+{{H}_{1}}^{2}}\\right)h}{2}\\\\ h=\\frac{2\\pi {V}_{r}\\phi \\text{sin}\\beta -S\\phi \\omega }{2\\pi \\omega }\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$${Q}_{2}={\\delta }^{2}\\left(r-{r}_{0}\\right)\\left(\\frac{\\omega {V}_{0}^{2}\\text{sin}\\beta -g\\phi }{{\\omega }^{3}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$${Q}_{3}=\\left(r-{r}_{0}\\right)\\left\\{H\\pi \\left(r+{r}_{0}\\right)-\\frac{1}{z}d\\left(\\sqrt{{\\left(\\pi r\\right)}^{2}+{H}^{2}}+\\sqrt{{\\left(\\pi {r}_{0}\\right)}^{2}+{H}^{2}}\\right)\\right\\}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cem\u003eh\u003c/em\u003e is the thickness of cut down the soil after turning the angle \u003cem\u003eφ. H\u003c/em\u003e is the total depth of pit. \u003cem\u003ed\u003c/em\u003e is the thickness of the spiral blade.\u003c/p\u003e \u003cp\u003eThe thickness of the soil under cutting cannot be ignored. it would affect the interaction of the drilling forces and the size of the soil movement space[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. For Q\u003csub\u003e1\u003c/sub\u003e, the value is mainly related to the thickness h of the soil dug per unit time. The value should be increased as much as possible to improve the efficiency of digging. However, if h is too large, the congestion would occur due to space limitation of two spiral blades Q\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eAs for Q\u003csub\u003e2\u003c/sub\u003e, the smoothness of the discharge-soil determines the steady supply of the subsequent soil force and the size of space of auger. To avoid clogging, Q\u003csub\u003e2\u003c/sub\u003e should be increased as much as possible. For Q\u003csub\u003e2\u003c/sub\u003e, the value is mainly related to the velocity v\u003csub\u003e0\u003c/sub\u003e, when the soil reaches the upper edge of the pit opening and leaves the spiral blade.\u003c/p\u003e \u003cp\u003eFor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{Q}}_{3}\\)\u003c/span\u003e\u003c/span\u003e, the auger in the deep digging process generally uses a double-headed spiral blade with better stability. The space of soil movement on the double blade is half of the single. Therefore, if the soil blocks are too thick, the upper surface of the soil is likely to touch the lower surface of the spiral blade, which is not conducive to soil improvement.\u003c/p\u003e \u003cp\u003eIn conclusion, the performance of auger working on the slope can be evaluated by monitoring the efficiency of conveying-soil and the distance of throwing-soil.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Establishment of EDEM simulation model\u003c/h2\u003e \u003cp\u003eDEM simulations were run using the EDEM software. The EDEM software was installed on a computer with Intel(R) Core (TM) i7-8700 CPU @ 3.20 GHz and 32 GB RAM.\u003c/p\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.3.1 DEM parameters and virtual soil bin\u003c/h2\u003e \u003cp\u003eThe effect of auger geometric features and operating parameters on the performance was evaluated by simulating the operation of the auger in a virtual soil bin using DEM, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The virtual soil bin was filled with spherical particles of nominal radius 7 mm. Input parameters used to describe the DEM particles and tool material properties are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMaterial Properties of Soil and Tool.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSoil\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTool\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDiameter particle (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eContact Radius(mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParticle density (kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1350\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7860\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShear modulus (Pa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u0026times;10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.9\u0026times;10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePoisson\u0026rsquo;s ratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCoefficient of restitution of soil-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCoefficient of static friction of soil-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCoefficient of rolling friction of soil-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe 3D model of the slope was established by the SOLIDWORKS software and imported into the EDEM software as a pellet factory. The DEM particles were packed to a bulk voidage of 33.3705% as measured for the soil in the field. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e also lists input parameters used to define soil-soil and soil-tool interactions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.3.2 Contact model\u003c/h2\u003e \u003cp\u003eThe contact model is an important basis for analyzing the adhesion between mechanical parts and soil particles. During the digging operation, the soil particle is subjected to a variety of compound forces[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. According to Newton's second law, the linear motion and rotation equation of the soil particle p can be expressed as Eq.\u0026nbsp;(\u003cspan refid=\"Equ13\" class=\"InternalRef\"\u003e13\u003c/span\u003e).\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$$\\left\\{\\begin{array}{c}\\left\\{\\begin{array}{c}{F}_{n,Pq}^{JKR}=-4\\sqrt{\\pi \\gamma {E}^{*}{\\xi }^{\\frac{3}{2}}}\\\\ {F}_{coh,pq}={k}_{coh,pq}{A}_{coh,pq}\\end{array}\\right.+\\frac{4{E}^{*}}{3{R}^{*}}{\\xi }^{3}\\\\ \\left\\{\\begin{array}{c}{m}_{p}\\frac{d{v}_{p}}{{d}_{t}}={m}_{p}g+\\sum _{q=1}^{{n}_{p}}\\left\\{\\begin{array}{c}-4\\sqrt{\\pi \\gamma {E}^{*}{\\alpha }^{\\frac{3}{2}}}+\\frac{4{E}^{*}}{3{R}^{*}}{\\alpha }^{3}+{F}_{n,pq}^{d}+{F}_{\\tau ,pq}+{F}_{\\tau ,pq}^{d}+{k}_{coh,pq}{A}_{coh,pq})\\end{array}\\right.\\\\ {I}_{p}\\frac{d{\\omega }_{p}}{{d}_{t}}=\\sum _{q=1}^{{n}_{p}}\\left({T}_{\\tau ,pq}+{T}_{\\gamma ,pq}\\right)\\end{array}\\right.\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{n,Pq}^{JKR}\\)\u003c/span\u003e\u003c/span\u003e is the normal contact force between particles or between particles and equipment parts; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{n,pq}^{d}\\)\u003c/span\u003e\u003c/span\u003e is the normal damping; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{\\tau ,pq}\\)\u003c/span\u003e\u003c/span\u003e is the tangential contact force; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{\\tau ,pq}^{d}\\)\u003c/span\u003e\u003c/span\u003e is the tangential damping; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{coh,p q}\\)\u003c/span\u003e\u003c/span\u003e is the internal particle adhesion; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{p}\\)\u003c/span\u003e\u003c/span\u003e is the moment of inertia of the soil particle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(p\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({n}_{p}\\)\u003c/span\u003e\u003c/span\u003e is the oil particles\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(p\\)\u003c/span\u003e\u003c/span\u003e total number of particles in contact; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\omega }_{p}\\)\u003c/span\u003e\u003c/span\u003e is the rotational angular velocity of the soil particle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(p\\)\u003c/span\u003e\u003c/span\u003e;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{\\tau ,pq}\\)\u003c/span\u003e\u003c/span\u003e is the tangential moment of the soil particle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(p\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{\\gamma ,pq}\\)\u003c/span\u003e\u003c/span\u003e is the rolling moment of the soil particle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(p\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({k}_{coh,pq}\\)\u003c/span\u003e\u003c/span\u003e is the soil particle adhesion energy density; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({A}_{coh,pq}\\)\u003c/span\u003e\u003c/span\u003e is the soil particle contact area; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\gamma\\)\u003c/span\u003e\u003c/span\u003e is the surface energy; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({E}^{\\text{*}}\\)\u003c/span\u003e\u003c/span\u003e is the equivalent Young's modulus; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}^{\\text{*}}\\)\u003c/span\u003e\u003c/span\u003e is the equivalent radius; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\xi\\)\u003c/span\u003e\u003c/span\u003e is the interaction parameter.\u003c/p\u003e \u003cp\u003eThe soil of afforestation land generally has a higher moisture content. Here there is cohesive and adhesive nature between the soil-soil and soil-tool. The cohesive force \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{coh,pq}\\)\u003c/span\u003e\u003c/span\u003e of soil particles is mainly set according to its internal cohesion characteristics. A Hertz-Mindlin with JKR and additional model-bounding contact model was adopted as the primary contact model for both particle-particle and particle-tool interactions. This model is suitable for simulating materials that have obvious adhesion and agglomeration between particles due to static electricity, moisture and other reasons. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e lists the input parameters required for the contact models[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParameters of contact model.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNormal Stiffness per unit area\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.1\u0026times;10\u003csup\u003e8\u003c/sup\u003e \u003cem\u003eN\u0026middot;m\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShear Stiffness per unit area\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8\u0026times;10\u003csup\u003e7\u003c/sup\u003e \u003cem\u003eN\u0026middot;m\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCritical Normal Stress\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.5\u0026times;10\u003csup\u003e6\u003c/sup\u003e \u003cem\u003ePa\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCritical Shear Stress\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8\u0026times;10\u003csup\u003e5\u003c/sup\u003e \u003cem\u003ePa\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBonded Disk Radius\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.5 \u003cem\u003emm\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSurface energy of soil-soil\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7.46 \u003cem\u003eJ\u0026middot;m\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;3\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSurface energy of soil-tool\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.5 \u003cem\u003eJ\u0026middot;m\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;3\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.3.3 Scheme of simulation experiment\u003c/h2\u003e \u003cp\u003eVirtual experiments on the quadratic rotating orthogonal center combination with four factors and five levels were carried out to evaluate the working performance of the auger. Based on previous experimental studies, practical experience and mechanism analysis, the appropriate levels of the experiment factors were established as indicated in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The slope angle X1, the helix angle of auger X2, the feeding speed X3 and the rotating speed of auger X4 were selected as experimental factors, while the efficiency of conveying-soil Y1 and the distance of throwing-soil Y2 set as experimental indicators. According to the accuracy in the practical application, the value in the virtual experiment retains two significant digits. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, in the EDEM software analyst module, Grid Bin Group and Clipping Plane are added to measure the amount of soil outside the pit and the distance of throwing-soil.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFactors and levels of virtual experiment.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eCoded value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eExperiment factors\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eX\u003csub\u003e1\u003c/sub\u003e / (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(^\\circ\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eX\u003csub\u003e2\u003c/sub\u003e/ (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(^\\circ\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eX\u003csub\u003e3\u003c/sub\u003e/ (m/s)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eX\u003csub\u003e4\u003c/sub\u003e/ (r/min)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.085\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e97.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.055\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e52.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3. Results And Discussion","content":"\u003cp\u003eThe simulation experiment results based on the design scheme are presented in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e, including 24 analysis factors and 7 zero-point experiments for estimating the errors. Quadratic multiple regression analysis of the results in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e was performed using the Design-Expert software, and the regression models between the influencing factors and evaluation indices were established as follows:\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab4\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eExperiment schemes and results.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eNO.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"4\" align=\"left\"\u003e\n\u003cp\u003eFactors\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eEvaluation Indices\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eY\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eY\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1243\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1246\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1143\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2435\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1572\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1023\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1330\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2517\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1502\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1150\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1672\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2633\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2039\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1186\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1973\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2619\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1376\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1432\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1096\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2625\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e11\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1469\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1480\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e12\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1378\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2763\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e13\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2111\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1545\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e14\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1926\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2683\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2351\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1580\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e16\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2006\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2831\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e17\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1971\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1024\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e18\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1769\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3429\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e19\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1255\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1830\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1640\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2118\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e21\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1021\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1496\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e22\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2428\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1935\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1225\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2092\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e24\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1900\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2409\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1780\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1988\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e26\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1800\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1994\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e27\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1822\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2015\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e28\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1870\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2086\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e29\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1676\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1856\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e30\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1689\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1889\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e31\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1736\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1949\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cp\u003e\u003cstrong\u003eTable 5.\u003c/strong\u003e ANOVA results of regression model.\u003c/p\u003e\n\u003ctable id=\"Taba\" border=\"1\"\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eIndicator\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSource of\u003c/p\u003e\n\u003cp\u003evariance\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSum of\u003c/p\u003e\n\u003cp\u003eSquares\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003edf\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eMean\u003c/p\u003e\n\u003cp\u003eSquare\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eF-value\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ep-value\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSignificant\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"19\" align=\"left\"\u003e\n\u003cp\u003eY1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eModel\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.686E\u0026thinsp;+\u0026thinsp;06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e14\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.633E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e27.92\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e99202.04\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e99202.04\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e10.52\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0051\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.311E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.311E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e35.12\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.527E\u0026thinsp;+\u0026thinsp;06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.527E\u0026thinsp;+\u0026thinsp;06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e267.97\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.793E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.793E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e29.62\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e1\u003c/sub\u003eX\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7612.56\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7612.56\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.8074\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.3822\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e1\u003c/sub\u003eX\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5148.06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5148.06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.5460\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.4707\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e1\u003c/sub\u003eX\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e27473.06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e27473.06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2.91\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1072\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e*\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e2\u003c/sub\u003eX\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4455.56\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4455.56\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.4726\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.5017\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e2\u003c/sub\u003eX\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e27142.56\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e27142.56\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2.88\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1091\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e*\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e3\u003c/sub\u003eX\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e86583.06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e86583.06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e9.18\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0080\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e1\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e15392.56\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e15392.56\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.63\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.2196\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.943E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.943E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e20.60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0003\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4962.99\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4962.99\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.5264\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.4786\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e4\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e82381.76\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e82381.76\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.74\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0093\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eResidual\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.509E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e16\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9428.56\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eLack of Fit\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.206E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e12064.13\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2.40\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1485\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003enot significant\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePure Error\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e30215.71\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5035.95\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCor Total\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.837E\u0026thinsp;+\u0026thinsp;06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e30\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"19\" align=\"left\"\u003e\n\u003cp\u003eY2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eModel\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.062E\u0026thinsp;+\u0026thinsp;07\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e14\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7.586E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e81.87\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9.721E\u0026thinsp;+\u0026thinsp;06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9.721E\u0026thinsp;+\u0026thinsp;06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1049.03\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e28428.17\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e28428.17\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3.07\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0990\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e*\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.045E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.045E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e11.28\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0040\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.183E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.183E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e34.35\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e1\u003c/sub\u003eX\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e13110.25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e13110.25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.41\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.2516\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e1\u003c/sub\u003eX\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1332.25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1332.25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1438\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.7095\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e1\u003c/sub\u003eX\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e33672.25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e33672.25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3.63\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0747\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e*\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e2\u003c/sub\u003eX\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1600.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1600.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1727\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.6833\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e2\u003c/sub\u003eX\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e14884.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e14884.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.61\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.2232\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e3\u003c/sub\u003eX\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e49.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e49.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0053\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.9429\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e1\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e86586.40\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e86586.40\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e9.34\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0075\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1875.34\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1875.34\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.2024\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.6588\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.512E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.512E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e16.32\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0009\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eX\u003csub\u003e4\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.065E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.065E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e11.49\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.0037\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e***\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eResidual\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.483E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e16\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9266.33\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eLack of Fit\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.119E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e11190.65\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.85\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.2337\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003enot significant\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePure Error\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e36354.86\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6059.14\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCor Total\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.077E\u0026thinsp;+\u0026thinsp;07\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e30\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003ctfoot\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"8\"\u003eNote: \u0026ldquo;***\u0026rdquo; means extremely significant(P\u0026thinsp;\u0026lt;\u0026thinsp;0.01); \u0026ldquo;**\u0026rdquo; means very significant(0.01\u0026thinsp;\u0026le;\u0026thinsp;P\u0026thinsp;\u0026lt;\u0026thinsp;0.05); \u0026ldquo;*\u0026rdquo; means significant(0.05\u0026thinsp;\u0026le;\u0026thinsp;P\u0026thinsp;\u0026lt;\u0026thinsp;0.1).\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tfoot\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eY1\u0026thinsp;=\u0026thinsp;1767.57-64.29X1\u0026thinsp;+\u0026thinsp;117.46X2\u0026thinsp;+\u0026thinsp;324.46X3\u0026thinsp;+\u0026thinsp;107.87X4-21.81X1X2\u0026thinsp;+\u0026thinsp;17.94X1X3-41.44X1X4\u0026thinsp;+\u0026thinsp;16.69X2X3-41.19X2X4\u0026thinsp;+\u0026thinsp;73.56X3X4\u0026thinsp;+\u0026thinsp;23.2X12-82.42X22-13.17X32-53.67X42\u003c/p\u003e\n\u003cp\u003eY2\u0026thinsp;=\u0026thinsp;1968.14\u0026thinsp;+\u0026thinsp;636.42X1\u0026thinsp;+\u0026thinsp;34.42X2\u0026thinsp;+\u0026thinsp;66X3\u0026thinsp;+\u0026thinsp;115.17X4\u0026thinsp;+\u0026thinsp;28.63X1X2\u0026thinsp;+\u0026thinsp;9.13X1X3-45.87X1X4\u0026thinsp;+\u0026thinsp;10X2X3\u0026thinsp;+\u0026thinsp;30.5X2X4-1.75X3X4\u0026thinsp;+\u0026thinsp;55.03X12+-8.1X22-72.72X32\u0026thinsp;+\u0026thinsp;61.03X42\u003c/p\u003e\n\u003cp\u003eThe 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.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e. It can be seen from Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e that the actual values are basically distributed on the predicted curve, consistent with the trend of the predicted values, and linearly distributed.\u003c/p\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n\u003ch2\u003e3.1 Variance analysis and discussion\u003c/h2\u003e\n\u003cp\u003eThe 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\u0026nbsp;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\u0026nbsp;5, PL\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.1485\u0026thinsp;\u0026gt;\u0026thinsp;0.05 and PL\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.2337\u0026thinsp;\u0026gt;\u0026thinsp;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.\u003c/p\u003e\n\u003cp\u003eAccording to the ANOVA, the significance values P of each influencing factor in the test could be determined[\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e]. For the evaluation index Y1, the factors X1, X2, X3, X4, X3X4, X2\u003csup\u003e2\u003c/sup\u003e, X4\u003csup\u003e2\u003c/sup\u003e had extremely significant influences, while the factor X1X4, X2X4 had a significant influence. For the evaluation index Y2, the factors X1, X3, X4, X1X4, X1\u003csup\u003e2\u003c/sup\u003e, X3\u003csup\u003e2\u003c/sup\u003e, X4\u003csup\u003e2\u003c/sup\u003e had extremely significant influences, and the factor 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\u0026nbsp;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.\u003c/p\u003e\n\u003cp\u003eIn 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.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n\u003ch2\u003e3.2 Analysis of response surface\u003c/h2\u003e\n\u003cp\u003eThe fitting coefficient of the efficiency of conveying-soil is R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.9714, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eadjust\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.9263, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003epred\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8082, the difference between R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eadjust\u003c/sub\u003e and R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003epred\u003c/sub\u003e is less than 0.2. The fitting coefficient of the distance of throwing-soil is R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.9873, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eadjust\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.9742, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003epred\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.9355, the difference between R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eadjust\u003c/sub\u003e and R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003epred\u003c/sub\u003e 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 results[\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eTo 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 Y1and Y2, and the corresponding response surfaces were generated, as illustrated in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eIt can be seen in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e(a), 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.\u003c/p\u003e\n\u003cp\u003eAs can be seen in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e(b), 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.\u003c/p\u003e\n\u003cp\u003eAs can be seen in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e(c), 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. 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.\u003c/p\u003e\n\u003cp\u003eAs can be seen in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e(d), 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. 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.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n\u003ch2\u003e3.3 Comprehensive optimal design\u003c/h2\u003e\n\u003cp\u003eAs relative importance and influencing rules of various experimental factors on evaluation indexes were different from each other, evaluation indexes should be taken into comprehensive consideration[\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e]. The optimization equation is obtained by the Design-Expert software multi-objective optimization method with Y1and Y2 as the optimization objective function.\u003c/p\u003e\n\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equa\" class=\"mathdisplay\"\u003e$$\\left\\{\\begin{array}{c}25\\le X1\\le 45\\\\ 10\\le X2\\le 22\\\\ 0.04\\le X1\\le 0.1\\\\ 30\\le X1\\le 120\\\\ {Y1}_{\\text{m}\\text{a}\\text{x}}(X1,X2,X3,X4)\\\\ {Y2}_{min}(X1,X2,X3,X4)\\end{array}\\right.$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIn 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\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e. If the ground preparation was required before the digging operation, the digging parameters can be designed according to values of Group 6 in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab5\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eOptimal parameter combinations of several terrain slopes\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eNO.\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSlope\u003c/p\u003e\n\u003cp\u003e(\u0026deg;)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eHelix angle\u003c/p\u003e\n\u003cp\u003e(\u0026deg;)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eFeeding speed\u003c/p\u003e\n\u003cp\u003e(m/s)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eRotating speed\u003c/p\u003e\n\u003cp\u003e(r/min)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eEfficiency of conveying-soil\u003c/p\u003e\n\u003cp\u003e(Num/s)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eDistance of throwing-soil\u003c/p\u003e\n\u003cp\u003e(mm)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e21.371\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.094\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e91.639\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2622.162\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e997.673\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e30\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e20.863\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e58.091\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2274.818\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1108.703\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e35\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e15.563\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e69.303\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2270.547\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1777.915\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e40\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e85.486\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1897.109\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2335.958\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e45\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e85.379\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1961.625\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3076.999\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e26.467\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e21.567\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e67.408\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2450.607\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e762.168\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n\u003ch2\u003e3.4 Disturbance of soil\u003c/h2\u003e\n\u003cp\u003eA soil disturbance is defined as the loosening, movement and mixing of soil caused by an auger passing through the soil[\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e]. In the interface of the EDEM Analyst, add a \u0026ldquo;Clipping plane\u0026rdquo; 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 bin [\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e], as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eThe 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.\u003c/p\u003e\n\u003cp\u003eThe 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.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 7.\u003c/strong\u003e Results and comparison of validation test.\u003c/p\u003e\n\u003ctable\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"2\" width=\"59\"\u003e\n\u003cp\u003eText\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" width=\"186\"\u003e\n\u003cp\u003eEfficiency of conveying-soil\u003c/p\u003e\n\u003cp\u003e（Num/s）\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"2\" width=\"59\"\u003e\n\u003cp\u003eRelative error（%）\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" width=\"191\"\u003e\n\u003cp\u003eDistance of throwing-soil（mm）\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"2\" width=\"59\"\u003e\n\u003cp\u003eRelative error（%）\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd width=\"111\"\u003e\n\u003cp\u003eTheoretical value\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"75\"\u003e\n\u003cp\u003eText value\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"112\"\u003e\n\u003cp\u003eTheoretical value\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"79\"\u003e\n\u003cp\u003eText value\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"111\"\u003e\n\u003cp\u003e2622\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"75\"\u003e\n\u003cp\u003e2739\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e4.4%\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"112\"\u003e\n\u003cp\u003e998\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"79\"\u003e\n\u003cp\u003e1025\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e2.8%\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"111\"\u003e\n\u003cp\u003e2275\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"75\"\u003e\n\u003cp\u003e2327\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e2.3%\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"112\"\u003e\n\u003cp\u003e1109\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"79\"\u003e\n\u003cp\u003e1187\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e7.0%\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"111\"\u003e\n\u003cp\u003e2271\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"75\"\u003e\n\u003cp\u003e2221\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e2.2%\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"112\"\u003e\n\u003cp\u003e1778\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"79\"\u003e\n\u003cp\u003e1689\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e5.0%\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"111\"\u003e\n\u003cp\u003e1897\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"75\"\u003e\n\u003cp\u003e1945\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e2.5%\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"112\"\u003e\n\u003cp\u003e2336\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"79\"\u003e\n\u003cp\u003e2769\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e18.5%\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"111\"\u003e\n\u003cp\u003e1962\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"75\"\u003e\n\u003cp\u003e1763\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e10.1%\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"112\"\u003e\n\u003cp\u003e3077\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"79\"\u003e\n\u003cp\u003e3166\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e2.9%\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"111\"\u003e\n\u003cp\u003e2451\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"75\"\u003e\n\u003cp\u003e2576\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e5.1%\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"112\"\u003e\n\u003cp\u003e762\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"79\"\u003e\n\u003cp\u003e900\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e18.1%\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003eAverage\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"111\"\u003e\n\u003cp\u003e/\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"75\"\u003e\n\u003cp\u003e/\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e4.4%\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"112\"\u003e\n\u003cp\u003e/\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"79\"\u003e\n\u003cp\u003e/\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd width=\"59\"\u003e\n\u003cp\u003e9.1%\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e"},{"header":"4. Verification Experiments","content":"\u003cp\u003eTo 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\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e6\u003c/span\u003e), the relative error between the theoretical value and the experimental value was obtained. The verification test results are summarized in Table\u0026nbsp;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\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e illustrates the field test and working conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eIn the process of digging pits in hilly regions to assist in the construction of fish-scale pits:\u003c/p\u003e \u003cp\u003e(1) The performance of auger working on slope can be evaluated by monitoring the efficiency of conveying-soil and the distance of the throwing-soil.\u003c/p\u003e \u003cp\u003e(2) The weight of the factors affecting the efficiency of conveying-soil is feeding speed༞helix angle of auger༞rotating speed of auger༞slope angle. The weight of the factors affecting the distance of throwing-soil is slope auger༞rotating speed of auger༞feeding speed༞helix angle of auger.\u003c/p\u003e \u003cp\u003e(3) According to the optimization results, the optimal parameter combination can be obtained in different slope operations. The optimized results show that if the slope preparation is required before the digging operation, the optimal operating parameter combination of the auger is: Slope of 26.467\u0026deg;, Helix angle of 21.567\u0026deg;, Feeding speed of 0.1 m/s, Rotating speed of 67.408 r/min.\u003c/p\u003e \u003cp\u003e(4) Compared with the plain area, the variation law of soil displacement and velocity is different in hilly regions. The errors between the results from the developed DEM simulation modeling and virtual experiments\u0026rsquo; results are in the acceptable accuracy, confirming the effectiveness of the DEM model for estimating the working efficiency of the earth auger in hilly area.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors acknowledge the financial support provided by Forestry Science and Technology Promotion Project of State Forestry and Grassland Administration of China (Grant No. (2019)35) and Key R\u0026amp;D and Transformation Program of Qinghai Province - Special Project of Transformation of Scientific and Technological Achievements (Grant No. 2022-NK-128)\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions statement\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eW.G. methodology, investigation, analysis, statistics, writing\u0026mdash;original draft, review and editing. Z.W. funding acquisition, writing\u0026mdash;review and editing. J.M. writing\u0026mdash;review and editing. M.H. statistics. J.Z. supervision. All authors have read and agreed to the published version of the manuscript.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional information\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCorrespondence and requests for materials should be addressed to Z.W.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eYu, J.G, Qu, J.W. 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Study on round rice straw bale wrapping silage technology and facilities, Int J Agric \u0026amp; Biol Eng,4(11): 88\u0026ndash;95(2018).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYong-Jae S. \u003cem\u003eet al.\u003c/em\u003e Interacting analysis between wheel and sand particles based on DEM and its validation with experiments, Journal of mechanical science and technology, 2020, 34(11):4537\u0026ndash;4544.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIl-Kab J. \u003cem\u003eet al.\u003c/em\u003e Effect of crushing conditions of crushing rate in process analysis of sewage-sludge organic solid-fuel crusher using the discrete element method, Journal of mechanical science and technology, 33(12):5933\u0026ndash;5942(2019).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-1844215/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1844215/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDigging in hilly regions is an important measure to promote afforestation on difficult sites. In view of the working conditions to build fish-scale pit on slope, the auger mechanism of soil lifting and throwing was investigated in this study. This study utilized EDEM software to establish the operation model of the earth auger and conduct DEM (Discrete Element Method) virtual simulation experiments. A quadratic rotating orthogonal center combination test was implemented by setting the efficiency of conveying-soil (Y1) and the distance of throwing-soil (Y2) as the evaluation indices. Variance analysis and response surface optimization were performed on the virtual experimental data. The results indicated that the weight of the factors affecting the Y1 and Y2, were feeding speed\u0026thinsp;\u0026gt;\u0026thinsp;helix angle\u0026thinsp;\u0026gt;\u0026thinsp;rotating speed\u0026thinsp;\u0026gt;\u0026thinsp;slope angle, and slope auger\u0026thinsp;\u0026gt;\u0026thinsp;rotating speed\u0026thinsp;\u0026gt;\u0026thinsp;feeding speed\u0026thinsp;\u0026gt;\u0026thinsp;helix angle. The optimal parameter combination of each influencing factor was obtained. Among them, when the slope preparation was required, the optimal operating parameter combination of the auger was: Slope of 26.467\u0026deg;, Helix angle of 21.567\u0026deg;, Feeding speed of 0.1 m/s, Rotating speed of 67.408 r/min. This research provides theoretical references for the design optimization of the earth auger in hilly regions.\u003c/p\u003e","manuscriptTitle":"Numerical simulation and parameter optimization of earth auger in hilly area using EDEM software","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-08-05 23:45:04","doi":"10.21203/rs.3.rs-1844215/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2022-09-30T06:06:39+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2022-09-22T07:21:31+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2022-09-21T05:39:31+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"6ab47c73-1297-44c2-b695-d65b6c869da6","date":"2022-09-12T06:28:13+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"edf4522c-abce-4558-9387-4ab9c15b5116","date":"2022-09-12T05:15:28+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-09-12T01:23:19+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-09-05T21:14:03+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2022-07-15T05:33:51+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2022-07-14T14:47:41+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2022-07-10T16:45:21+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f1f244da-1c5b-4e3a-b97f-4e5885aee3b5","owner":[],"postedDate":"August 5th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2022-11-07T05:44:14+00:00","versionOfRecord":[],"versionCreatedAt":"2022-08-05 23:45:04","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-1844215","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1844215","identity":"rs-1844215","version":["v1"]},"buildId":"cBFmMYwuxLRRLfASyISRj","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}