Hindawi Applied Bionics and Biomechanics Volume 2018, Article ID 7854052, 11 pages https://doi.org/10.1155/2018/7854052 Research Article Study on the Interaction between Soil and the Five-Claw Combination of a Mole Using the Discrete Element Method 1,2 1,2 1,2 1,2 Yuwan Yang , Mo Li, Jin Tong , and Yunhai Ma The Key Laboratory of Bionic Engineering, Jilin University, 5988 Renmin Street, Changchun 130022, China The College of Biological and Agricultural Engineering, Jilin University, 5988 Renmin Street, Changchun 130022, China Correspondence should be addressed to Jin Tong; jtong@jlu.edu.cn Received 12 April 2018; Accepted 11 July 2018; Published 6 August 2018 Academic Editor: Jose Merodio Copyright © 2018 Yuwan Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A mole is a born digger spending its entire existence digging tunnels. The ﬁve claws of a mole’s hand are combinative to cut soil powerfully and eﬃciently. However, little was known in detail about the interaction between the soil and the ﬁve-claw combination. In this study, we simulated the soil cutting process of the ﬁve-claw combination using the discrete element method (DEM) as an attempt for the potential design of soil-engaging tools to reduce soil resistance. The ﬁve-claw combination moved horizontally in the soil bin. Soil forces (draught and vertical forces) and soil failure (soil rupture distance ratio) were measured at diﬀerent rake angles and speeds. Results showed that the draught and vertical forces varied nonlinearly as the rake angle increased from 10 to 90 , and both changed linearly with the speed increasing from 1 to 5 m/s. The curve of the soil rupture distance ratio with rake angles could be better described using a quadric function, but the speed had little eﬀect on the soil rupture distance ratio. Notably, the soil rupture distance ratio of the ﬁve-claw combination in simulation was on average 19.6% lower than the predicted ratio of simple blades at diﬀerent rake angles indicating that the ﬁve-claw combination could make less soil failure and thereby produce lower soil resistance. Given the draught and vertical forces, the performance of the ﬁve-claw combination was optimized at the rake angle of 30 . Li et al. [5] showed that a biomimetic disc designed based 1. Introduction on the proﬁle curves of the second claw performed better Animals have many complex and clever geometric structures in structural strength and cutting eﬃciency using ﬁnite ele- that help them adapt well to diverse circumstances in nature. ment analysis. Tong et al. [6] found out that the torque of For example, the embossed textured surfaces on the prono- the optimal biomimetic blades designed based on the geom- etries of the tips of claws was lower during soil-rototilling tum, clypeus, and elytra of dung beetles reduce cohesion between the body and bung; the riblet structure on the skin and stubble-breaking operations compared with the conven- of sharks reduces skin friction drag and makes the movement tional universal blade. As is well known, the mole has evolved more eﬃcient and fast. Based on bionic methods, the unique into the structure of ﬁve-claw combination to self-adapt to its structures are utilized to design agricultural soil-engaging living circumstances. The ﬁve claws work together to com- tools to reduce soil resistance [1, 2]. Mole rats are a plete the digging task. In this study, the interaction between completely subterranean fossorial animal and a born digger soil and ﬁve-claw combination was investigated with the spending the entire existence in burrowing only to construct aim of further optimizing soil-engaging tools for minimizing their own life systems. Their strong and powerful claws cut energy consumption. soil eﬃciently [3]. In previous articles, the geometrical char- During the interaction between soil and tools, soil failure acteristics of claws were studied for optimizing agricultural is intentionally caused by the applied force of tools [7]. The tillage tools and improving working eﬃciency. For example, soil rupture distance ratio (m) is an important parameter to Ji et al. [4] studied that the geometrical characteristics of characterize the soil failure. It was deﬁned as the ratio of the second claw had a signiﬁcant soil-cutting performance. the rupture distance of blade (f ) on the soil surface to the 2 Applied Bionics and Biomechanics 훼v 훽 F Figure 1: Soil failure and soil forces according to Wheeler and Godwin [30]. 4 1 mm (a) (b) Figure 2: (a) A mole and (b) the ﬁve-claw combination. working depth (d) (see Figure 1) according to Godwin and behaviors of soil and its interaction with a tillage tool by Spoor [8], and it was presented as Ucgul et al. [18–20]. Direct shear tests were used to calibrate the model parameters [19]. The good correlations give conﬁ- dence to recommend further investigation of the use of the m = hysteretic spring contact model for a wider range of soil con- ditions and types of tillage tools [18]. In this study, the DEM The soil rupture distance ratio of blades and tines had simulation model studied by Ucgul et al. would be considered been studied as inﬂuenced by diﬀerent rake angles, respec- to simulate the soil failure and predict the soil force of the tively [8, 9]. Soil forces of blades and tines including draught structure of the multiclaw combination of a mole. (F ) and vertical (F ) forces (see Figure 1) have been pre- d v Here, the soil forces and soil failure of the ﬁve-claw com- dicted using the passive earth pressure theory [8, 10–12]. bination of a mole were studied during the interaction with However, the analytical models are not suitable to compli- soil using the discrete element method. The aim was to inves- cated models. Also, the empirical method is costly and tigate the possibility of applying the structure of a ﬁve-claw time-consuming. As a consequence, numerical methods such combination to agricultural soil-engaging tools to minimize as ﬁnite element method (FEM) and discrete element method energy consumption. (DEM), which save the experiment time and cost and also can solve the complex situations, have been successfully applied to the analysis of the soil-tool interactions [13, 14]. 2. Materials and Methods FEM is excellent for continuum analysis; while soil deforma- tion involves the formation of cracks, the movement of soil 2.1. Model Five-Claw Combination particles and separation and mixture of soil layers are diﬃcult to simulate [15]. Conversely, DEM is particularly suitable to 2.1.1. Description of Five-Claw Combination of a Mole. The model the soil deformation and forces of soil-tool interac- mole rats (Scaptochirus, Talpidae) were obtained in the tions, and it may serve as a predictive simulation tool in the northeast of China where they are most common and inhabit process of designing the tillage tool’s shape [16]. mostly underground. Their broad and strong hands which Accurate simulation of soil failure depends on deﬁning consist of ﬁve diﬀerent claws (see Figure 2) were scanned and calibrating the soil particle model. Ucgul et al. [17] used by a three-dimensional laser scanner (Handyscan700, Crea- a hysteretic spring (plastic) contact model (HSCM) for a form, Canada), and the point cloud (see Figure 3) was created sweep tool operated in a cohesionless soil with a good corre- with the reverse engineering software program of Image- lation between the predicted and measured tillage forces for Ware (version 13, Siemens PLM software, Germany). After both draught and vertical forces (R =0 95 – 0 99). The a series of procedures, such as smoothing, reducing, and sim- model parameters were calibrated by the angle of repose test pliﬁcation, the ﬁve-claw combination was reconstructed into and penetration test. Then a linear cohesion model was inte- a surface, and then it was generated as an entity from a sur- grated with the HSCM to model the plastic and cohesive face on SolidWorks software. It was considered as 5 times Applied Bionics and Biomechanics 3 Table 2: DEM parameters used in the simulations. Property Value Density of soil particles (kg/m ) 2600 [31] Density of steel (kg/m ) 7820 [32] Shear modulus of soil (Pa) 5 × 10 [33] Shear modulus of steel (Pa) 7.9 × 10 [32] Yield strength of the soil (Pa) 5.88 × 10 [17] Poisson’s ratio of soil 0.3 [33] Poisson’s ratio of steel 0.3 [32] Coeﬃcient of restitution of soil-soil 0.6 [31] Coeﬃcient of restitution of soil-steel 0.6 [31] Coeﬃcient of friction of soil-soil 0.57 [17] Coeﬃcient of friction of soil-steel 0.5 [17] Coeﬃcient of rolling friction of soil-soil 0.16 [17] Figure 3: The point cloud of the ﬁve-claw combination. Coeﬃcient of rolling friction of soil-steel 0.05 [17] Cohesive energy density between soil-soil (J/m ) 5000 [19] n —the stiﬀness factor 0.95 [17] Table 1: Characteristics of the ﬁve-claw combination. n —the damping factor 0.05 [17] Interval between two Claw L (mm) W (mm) W/L Δ (mm) adjacent claws 2.2. EDEM Simulations. The DEM was undertaken using 1st 6.47 2.34 0.362 1st and 2nd 3.86 EDEM 2.7 software. Soil particles were represented by spher- 2nd 7.83 2.42 0.309 2nd and 3rd 2.79 ical particles with a 4 mm radius particle size which was 3rd 8.82 2.586 0.293 3rd and 4th 3.04 selected to reduce the computation time. The particle size 4th 7.99 2.46 0.308 4th and 5th 3.12 was randomly generated in the range of 0.95–1.05 times the 5th 5.43 2.06 0.380 4 mm size. Particles were conﬁned in a soil bin constructed by ﬁve EDEM walls. The dimensions of the soil bin were 400 mm long × 200 mm wide × 150 mm deep, which allowed the ﬁve-claw combination to have enough distances to avoid the size of the prototype which was too small to model. The any edge eﬀects from the soil bin walls. The total number of parasolid text format was saved and imported to the EDEM™ soil particles produced was 10,000. The ﬁnal bulk density of software for simulation. The horizontal movement of the the particles was 1283 kg/m . A linear cohesion integrated ﬁve-claw combination in soil was evaluated as this movement hysteretic spring contact model suggested by Ucgul et al. is common in soil-engaging tools. [18–20] was used to model the cohesive behavior of soil. The material of the claws was considered as steel-like tillage 2.1.2. Characteristics of the Five-Claw Combination. Every tools. A Hertz-Mindlin contact model (HMCM) was used hand of a mole has ﬁve diﬀerent claws. From Figures 2(b) to model the interaction between soil and claws. The model and 3(a), the 3rd claw was considerably longer than the 1st, assumed a nonlinear elastic manner to predict the behavior 2nd, 4th, and 5th claws with the 5th claw being very small. between soil and ﬁve-claw combination. All related parame- The length (L) and width (W) of each claw were measured ters are shown in Table 2. and displayed in Table 1. The ratio of width to length of each The ﬁve-claw combination was positioned at the end of claw was calculated. It was found out that all the ratios of the the soil bin at a speciﬁed rake angle and working speed main three claws (i.e., the 2nd, 3rd, and 4th claws) were near before the model travelling (see Figure 4(a)). The working 0.3, while the other two claws (i.e., 1st and 5th claws) with depth was ﬁxed at 45 mm in order to assure claws interact larger ratios indicated their thinness and weakness, which with the soil particles as fully as possible. To investigate proved again that the middle three claws played the main the eﬀects of the rake angle (α) and working speed (v)on roles in digging. Moreover, the ﬁve-claw combination always the soil forces and soil failure, the simulations were run for ° ° engages soils with a spaced arrangement. Thereby, the inter- rake angles from 10 to 90 at 20 intervals and working val (Δ) between two adjacent claws (Figure 3) was also an speeds from 1 to 5 m/s at an interval of 1 m/s. When the important parameter to determine the structure of the ﬁve- working speed was varied, the rake angle was kept constant claw combination. They were measured for characterizing (α =90 ). When the rake angle was varied, the working the structure of ﬁve-claw combination (Table 1). It was speed was kept constant (v =3 m/s). Each simulation was observed that the middle three claws were arranged more repeated three times as there was always a variation in closely than the other two claws of 1st and 5th claws. In our results, and the average value of the simulation results was study, the model of ﬁve-claw combination would present taken as the ﬁnal result. The ﬁve-claw combination inter- these characteristics. acted with soil particles as it traveled (see Figure 4(b)), and L 4 Applied Bionics and Biomechanics (a) (b) Figure 4: Interaction of soil and the ﬁve-claw combination: (a) at the initial state; (b) travelling in the soil bin. w = blade width; d = working depth; α = rake angle; v = working speed. 3000 Distance = 0.06 m Velocity (m/s) 0.6 0.5 Distance = 0.13 m 0.4 0.3 0 0.2 Distance = 0.26 m 0 50 100 150 200 250 300 350 Distance (mm) 0.1 Draught force Vertical force 0.0 Figure 5: An example of force curves from the simulation. Working speed = 3 m/s; rake angle = 90 . Figure 6: Snapshots of the top view of soil failure during the simulations of the velocity ﬁeld. f = soil rupture distance; red the resultant soil forces and soil failure were conducted as zone = soil failure region. described in the following section. 2.3. Calibration of the Model Soil Particles. Calibration was increased when the ﬁve-claw combination began to contact done through the simulation and matching of the soil rup- with the soil particles and then ﬂuctuated around a constant ture distance ratio (m) with the values predicted by an value when the ﬁve-claw combination advanced through the analytical method. This similar approach has been used soil particles. The average values of draught and vertical by Mak et al. [21] and Li et al. [22] for calibrating a PFC forces were taken over the constant section of the force curve model. The blade was a wall with a width of 75 mm and trav- (corresponding to the midsection of the soil bin between 50 eled at a speed of 3 m/s with a working depth of 45 mm ° ° and 250 mm). through the soil particles model. The rake angles of 30 ,50 , ° ° Snapshots of the top view taken during the simulations of 70 , and 90 were used in the calibration. The soil rupture dis- the velocity ﬁeld are presented in Figure 6. The diﬀerent color tance ratio (m) was calculated according to (1). The soil rup- levels presented the diﬀerent velocities of soil particles. The ture distance of soil failure (f ) made by the blade travelling red color meant the larger velocity of soil particles, the green was measured on the soil surface. The soil rupture distance color meant very small velocity of soil particles, and the blue ratio was compared with the prediction of the values by color meant that the state of soil particles was static. The soil Hettiaratchi et al. [9]. The soil particles model parameters failure boundary was mainly in the section of the red zone. were conﬁrmed when these simulation results matched The soil rupture distance (f ) was the maximum longitudinal with the prediction by Hettiaratchi et al. [9]. distance from the model surface to the front of soil failure 2.4. Data Collection and Processing. During the travelling of boundary (see Figure 1). Three stages (i.e., original stage, middle stage, and end stage) during the travelling of ﬁve- ﬁve-claw combination in the soil bin, the draught and vertical forces were monitored over the length of the soil bin. The claw combination were displayed in Figure 6. It was sug- forces ﬂuctuated due to the random nature of soil particle gested that the soil rupture distance at the original stage of disturbance (see Figure 5). The draught and vertical forces the simulation was obtained to be the ﬁnal result which was Forces (N) Applied Bionics and Biomechanics 5 3.75 300 3.50 3.25 y = 0.99203x R = 0.99 100 3.00 2.75 0 10 20 30 40 50 60 70 80 90 −50 Rake angle (deg) 2.50 2.50 2.75 3.00 3.25 3.50 3.75 Draught force Prediction Vertical force Figure 7: The correlation of the soil rupture distance ratio (m) Figure 8: The draught and vertical forces of the ﬁve-claw between the simulation and prediction. combination aﬀected by the rake angle. consistent with the study by Shmulevich et al. [23]. Then of 67.5 . The negative vertical forces meant that the tools the soil rupture distance ratio (m) was calculated accord- had a noticeable behavior of penetrating into the soil. There- ing to (1). fore, the ﬁve-claw combination had a better penetration per- formance at the rake angle of 30 . Overall, the rake angle of 30 was the optimal operating condition for the ﬁve-claw 3. Results and Discussion combination to produce lower draught forces and better soil 3.1. Soil Particles Model Calibration Results. The soil rupture penetration performance. This rake angle was also recom- distance ratio (m) of simulations was matched with the cor- mended by Li et al. [22] who studied the eﬀects of rake angles responding values predicted by Hettiaratchi et al. [9] at dif- of a bear claw on the soil cutting forces. ferent rake angles in Figure 7. The simulated results slightly Soil ﬂow in the vicinity of the ﬁve-claw combination at underestimated the soil rupture distance ratio of prediction diﬀerent rake angles was observed in the simulation results, (y =0 99203x). However, the value of the coeﬃcient of deter- as presented in Figure 9. The simulation results of the veloc- ity ﬁeld of soil particles were schematically described. The mination (R =0 99) showed that the examined data pairs were close to the correlated line. Furthermore, the average velocity of each particle was marked by an arrow, of which, the length and direction indicate the magnitude and direc- error of the soil rupture distance ratio in simulation com- pared with the corresponding values of prediction at diﬀerent tion of the velocity, respectively. At the rake angle of 10 , rake angles was −3%; therefore, the simulation model of soil many soil particles that moved forward and upward existed above the ﬁve-claw combination. The largest velocity which particles behaved fairly well regarding the estimation of the soil rupture distance ratio at diﬀerent rake angles. Ucgul was corresponding to the longest arrow appeared in front of the ﬁve-claw combination. Also, many soil particles mov- et al. [18–20] also recommended that the DEM simulation parameters had good potential to model tillage forces in a ing forward and downward appeared under the ﬁve-claw range of soil and operating conditions. combination. As a result, the ﬁve-claw combination would suﬀer larger crowding and soil gravity. Therefore, the 3.2. Soil Forces Aﬀected by Rake Angles. The draught and ver- draught and vertical forces of the ﬁve-claw combination were tical forces of ﬁve-claw combination aﬀected by rake angles very large as described in Figure 8 at the rake angle of 10 .At are shown in Figure 8. On average, the draught forces were the rake angle of 30 , the number of soil particles moving for- 12 times the magnitude of vertical forces. All the draught ward and upward above the ﬁve-claw combination declined. Also, a smaller number of soil particles under the ﬁve-claw and vertical forces varied nonlinearly with the rake angle in the range of 10 to 90 . All forces ﬁrst decreased with the rake combination moved forward and downward, which meant the ﬁve-claw combination would not compact the tillage angle increasing from 10 to 30 , and then increased from 30 to 90 . Thereby, the draught forces and vertical forces all pan and could better penetrate into soils. Thus, the vertical minimized at the rake angle of 30 . Interestingly, the vertical forces of the ﬁve-claw combination were negative and the draught forces were weakened. Then, with the increasing forces were negative at the rake angle of 30 . Godwin [24] summarized that the draught and vertical forces of the tine rake angle, the number of disturbed soil particles increased and the velocity gradually increased. Evidently, at the rake were aﬀected by rake angles of 22.5 to 112.5 and found out that the draught and vertical forces increased with rake angle. angle of 90 , the number of soil particles at larger velocity He stated that there was a crossover value for the vertical maximized and the region of evenly-disturbed soil particles expanded to the bottom of the ﬁve-claw combination. forces upward to downward force at the critical rake angle Simulation Forces (N) 6 Applied Bionics and Biomechanics o o Velocity (m/s) Rake angle = 10 Rake angle = 30 0.60 0.48 o o Rake angle = 50 Rake angle = 70 0.36 0.24 Rake angle = 90 0.12 0.00 Figure 9: Velocity ﬁeld in the vicinity of the ﬁve-claw combination at diﬀerent rake angles. Overall, the variation trend of draught and vertical forces observed in Figure 8 was in parallel with the situation of soil 400 ﬂow in the vicinity of the ﬁve-claw combination. 3.3. Soil Forces Aﬀected by Speeds. The draught and vertical y = 79.3x + 12.7 forces of the ﬁve-claw combination aﬀected by speeds are dis- R = 0.99 played in Figure 10. On average, the draught forces always surpassed the vertical forces. The ﬁtted curves indicated the draught and vertical forces were enlarged linearly when the speed increased from 1 to 5 m/s. But the variation rate of y = 11.7x + 9.88 draught forces against speeds was larger than that of vertical R = 0.99 forces. The two coeﬃcients of determination (R ) of the ﬁtted 50 curves both reached 0.99, which meant the data were close to the correlated line. This variation trend accorded with the 0 1 23 456 relationship of draught and vertical forces of tine and the Speed (m/s) speed in the range of 0 to 12 km/h which was summarized Draught force by Godwin [24]. Vertical force The soil ﬂows in the vicinity of the ﬁve-claw combination at diﬀerent speeds were observed in the simulation results as Figure 10: The draught and vertical forces of the ﬁve-claw shown in Figure 11. At the speed of 1 m/s, a smaller number combination aﬀected by speed. of soil particles moved forward and upward in front of the ﬁve-claw combination. The largest velocity mainly appeared At the speed of 5 m/s, the number of soil particles at larger on the soil surface. Fewer soil particles moved forward and velocity maximized and mainly assembled in front of the downward under the ﬁve-claw combination. Thus, the draught and vertical forces of the ﬁve-claw combination were ﬁve-claw combination. Even the region of disturbed soil par- ticles expanded to the bottom of the ﬁve-claw combination. weakened at the speed of 1 m/s as described in Figure 10. Therefore, the draught and vertical forces were enhanced Then with the increasing speed, the number of disturbed soil rapidly as shown in Figure 10. particles increased and the velocity was gradually accelerated. Forces (N) Applied Bionics and Biomechanics 7 Velocity (m/s) Speed = 1 m/s Speed = 2 m/s 0.60 0.48 Speed = 3 m/s Speed = 4 m/s 0.36 0.24 Speed = 5 m/s 0.12 0.00 Figure 11: Velocity ﬁeld in the vicinity of the ﬁve-claw combination at diﬀerent speeds. o o Rake angle = 30 Rake angle = 50 Velocity (m/s) 0.60 0.48 0.36 o o Rake angle = 70 Rake angle = 90 0.24 0.12 0.00 Figure 12: Soil failure of the ﬁve-claw combination in the top view of the velocity ﬁeld at diﬀerent rake angles. 3.4. Soil Rupture Distance Ratio Aﬀected by Rake Angle. and shown in Figure 13. The soil rupture distance ratio was signiﬁcantly aﬀected by the rake angle and described nonli- Figure 12 shows the variation of soil rupture distance with rake angle. The red zone of the velocity ﬁeld was narrowed nearly as the rake angle rose from 30 to 90 . This nonlinear down in the front of the ﬁve-claw combination. Since the soil trend was well described by a quadratic function with a coef- rupture distance ratio (m) was proportional to the soil rup- ﬁcient of determination (R ) of 0.99. ture distance (f ) according to (1), the variation trend of soil This variation trend underlying the soil rupture distance rupture distance with rake angles meant the soil rupture dis- ratio of the ﬁve-claw combination aﬀected by rake angles was tance ratio would diminish with rake angles. It was calculated similar to the study of simple blades by Hettiaratchi et al. [9]. 8 Applied Bionics and Biomechanics d4 d5 d1 d2 d3 y = 0.0006x −0.083x + 5.4175 R = 0.99 (a) y = 0.0003x −0.06x + 4.7438 R = 0.99 30 40 50 60 70 80 90 Rake angle (deg) Prediction Simulation (b) Figure 13: The soil rupture distance ratio of the ﬁve-claw Figure 14: The comparison of the working depth between the ﬁve- combination aﬀected by rake angle. claw combination and the blade in the soil-cutting process: (a) the ﬁve-claw combination working at varying depths (d , d , d , d , 1 2 3 4 and d are the working depths of the corresponding claw, resp.); Table 3: Comparison of the soil rupture distance ratio by (b) the blade working at a ﬁxed depth (d is the working depth of simulation of the ﬁve-claw combination and prediction of simple the blade). blades by Hettiaratchi et al. [9]. Soil rupture distance Rake angle Average ratio (m) Error (%) (deg) error (%) Simulation Prediction 30 3.2 3.5 −8.6 50 2.6 2.8 −7.1 −19.6 70 2 2.7 −25.9 90 1.9 3 −36.7 The corresponding predictions of blades were also displayed in Figure 13. Generally, the soil rupture distance ratio of the bionic model was about 19.6% lower than the predicted values of simple blades (see Table 3). When the rake angle was below 50 , the error of the soil rupture distance ratio of the ﬁve-claw combination was smaller than the correspond- 0 12 345 ing predicted values of simple blades, but the error was −1 Speed (m s ) gradually enlarged when the rake angle increased from 50 to 90 . It was implied the soil failure was aﬀected signiﬁ- Figure 15: The soil rupture distance ratio of the ﬁve-claw cantly by the structure of ﬁve-claw combination. The ﬁve- combination aﬀected by speed. claw combination would create less soil failure due to the ﬁve claws working at varying depth in the soil-cutting pro- be found from the soil rupture distance with speeds in cess (see Figure 14) and thereby got lower soil forces. The Figure 16. The red zone of the velocity ﬁeld was narrowed force reducing behavior by the structure of ﬁve-claw combi- down but concentrated in front of the ﬁve-claw combina- nation was prominent at large rake angles, which should be tion. Staﬀord [25] studied the eﬀect of speed on soil shear further studied though. Overall, the structure of ﬁve-claw strength and found out that it is diﬃcult to investigate the combination is potentially applicable to agricultural tillage variations of soil cohesion and internal friction angle with implements, aiming to minimize energy consumption by speeds. Thus, soil properties changed in a complicated way changing soil failure. as inﬂuenced by speeds, which led to the variation of the soil rupture distance ratio. 3.5. Soil Rupture Distance Ratio Aﬀected by Speed. Figure 15 shows that the soil rupture distance ratio of the ﬁve-claw 3.6. Possible Application of the Structure of the Five-Claw combination was aﬀected by speed. It decreased from 2.23 Combination. In tillage operations, the big problems to be to 1.78 as the speed increased from 1 to 5 m/s, which could solved urgently are the larger soil resistance and higher Rupture distance ratio, m = f/d Rupture distance ratio, m = f/d Applied Bionics and Biomechanics 9 Velocity (m/s) Speed = 1 m/s Speed = 2 m/s 0.60 0.48 Speed = 3 m/s Speed = 4 m/s 0.36 0.24 Speed = 5 m/s 0.12 0.00 Figure 16: Soil failure of the ﬁve-claw combination in the top view of the velocity ﬁeld at diﬀerent speeds. energy consumption. The structure of the ﬁve-claw combina- ﬁve-claw combination was 19.6% lower than the cor- tion of a mole could diminish the soil rupture distance ratio responding values of simple blades by Godwin and and thereby help to reduce soil forces, while it is diﬀerent Spoor [8] and was decreased from 2.23 to 1.78 as with other methods by varying the working operations (e.g., the speed rose from 1 to 5 m/s. vibrating tillage tools [26] and reverse-rotary tiller [27]) or Overall, the structure of the ﬁve-claw combination with by minimizing penetration resistance (optimizing the cutting varying depth of operation plays an important role in edges of tillage tools [28, 29]). Actually, the deeper working reducing soil resistance through decreasing the soil rupture central tine and shallower working wings are already used distance ratio. This study provides a novel geometry for commercially and this work validates their use. Therefore, designing soil-engaging tools with less energy consumption. the structure of the ﬁve-claw combination is potentially Of course, the eﬀect of the soil type and condition on the applicable to soil-engaging tools, such as a plough, subsoiler, interaction between soil and the ﬁve-claw combination and rotary tiller blade. needs further study. 4. Conclusions Data Availability The interaction between soil and the ﬁve-claw combination The raw data used to support the ﬁndings of this study are was simulated using the discrete element method for study- included within a supplementary information ﬁle. ing the soil forces and soil failure of the ﬁve-claw combina- tion of a mole. Simulation showed the following: Conflicts of Interest (1) The draught and vertical forces of the ﬁve-claw com- bination were nonlinearly aﬀected by rake angles. The authors declare there are no conﬂicts of interest regard- Particularly, the draught forces were reduced and ing the publication of this paper. the soil penetration performance was improved at the rake angle of 30 . And the draught and vertical Acknowledgments forces both increased linearly as the speed rose from 1 to 5 m/s. This work was supported by the National Key Research and (2) The soil rupture distance ratio changed with the rake Development Program of China (Grant no. 2017YFD0701103), angle in a nonlinear trend, which was well ﬁtted by a the National Natural Science Foundation of China (Grant power function with a coeﬃcient of determination of nos. 51505184 and 51075185), and the 111 Project (no. 0.99. On average, the soil rupture distance ratio of the B16020) of China. 10 Applied Bionics and Biomechanics Supplementary Materials References Supplementary 1. Table S1: an example of force curves from [1] L. Q. Ren, Z. W. Han, J. Q. Li, and J. Tong, “Eﬀects of non- the simulation (working speed = 3 m/s; rake angle = 90 ). smooth characteristics on bionic bulldozer blades in resistance reduction against soil,” Journal of Terramechanics, vol. 39, The draught and vertical forces recorded along the trav- no. 4, pp. 221–230, 2002. elling distance of the ﬁve-claw combination during the [2] J. Tong, B. Z. Moayad, Y. H. Ma et al., “Eﬀects of biomimetic interaction with soil at the speed of 3 m/s and rake angle surface designs on furrow opener performance,” Journal of of 90 Bionic Engineering, vol. 6, no. 3, pp. 280–289, 2009. Supplementary 2. Table S2: calibration of the model soil par- [3] R. G. Scott and R. C. Richardson, “Realities of biologically ticles. The soil rupture distance ratio (m) of a blade with the inspired design with a subterranean digging robot example,” values predicted by the analytical method from Hettiaratchi in Proceedings of the 6th IASTED international conference on et al. [9]. 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