## 2 Materials and Methods
### Design of Simulation Experiments  
There are four primary design variables for the bionic potato digging shovel, i.e., the length \(l\), height \(h\), and arranged spacing \(S_{i}\) (\(i\) = 1, 2) of the bionic structure. Each variable can have multiple levels. That design will lead to a large number of trials for a fully aligned combination design, which greatly increases the simulation workload. Among the influencing factors of the reduction of tillage resistance, the influence of the bionic structural parameters on the tillage resistance is significantly greater than that of the arrangement spacing. With the best drag reduction biomimetic structure parameters (\(l\), \(h\)), if the shovel with the arrangement spacings (\(S_{1}\), \(S_{2}\)) does not reduce the resistance, then, for the bionic structural parameters (\(l\), \(h\)) with non-resistance-reduction, which are under the same arrangement spacing combination (\(S_{1}\), \(S_{2}\)), it should be non-resistance-reduction as well. This factor finding order can reduce unnecessary simulations. Hence, a preliminary simulation experiment was performed in this paper by using the control variables and parallel comparison methods. The specific method was as follows. First, we set a uniform arrangement spacing and then, studied the effect of the biomimetic structure parameters \(l\) and \(h\) on the drag reduction performance. The biomimetic structural parameters with the optimal drag reduction performance were obtained through simulations. Then, assuming that the optimal drag reduction structure is known, the influence of the arrangement of the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Property** & **Value** & **Source** \\ \hline Density of soil particles (kg\(\cdot\)m\({}^{-3}\)) & 2550 & [25] \\ Density of steel (kg\(\cdot\)m\({}^{-3}\)) & 7850 & [20] \\ Poisson’s ratio of soil & 0.35 & [25] \\ Poisson’s ratio of steel & 0.29 & [20] \\ Shear modulus of soil (Pa) & \(1\times 10^{6}\) & [27] \\ Shear modulus of steel (Pa) & \(7.9\times 10^{10}\) & [20] \\ Coefficient of static friction for soil-soil & 0.83 & [27] \\ Coefficient of rolling friction for soil-soil & 0.25 & [27] \\ Coefficient of restitution for soil-soil & 0.66 & [27] \\ Coefficient of static friction for soil–steel & 0.56 & [28] \\ Coefficient of rolling friction for soil–steel & 0.18 & [28] \\ Coefficient of restitution for soil–steel & 0.60 & [28] \\ Cohesion interaction of soil–soil (J\(\cdot\)m\({}^{-2}\)) & 7.91 & [27] \\ Cohesion interaction of soil–steel (J\(\cdot\)m\({}^{-2}\)) & 6 & [28] \\ Particle radius & 4–6 mm (random) & [31] \\ Simulation speed (km/h) & 3 (or 0.84 m/s) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters used in the discrete element method (DEM) simulation. bionic structure on the drag reduction performance was simulated. Finally, the structural parameters and the arrangement spacing parameters with the best drag reduction performance were obtained. Hence, the effects of the biomimetic structural parameters as well as the transversal and longitudinally arranged spacings on the drag reduction performance of potato digging shovel under clayey soil conditions were discussed. The purpose was to obtain a suitable range of the bionic drag reduction structure parameters and their arrangement spacing, which provided basic parameters for subsequent design optimization and physical experiment. The engineering application range of the parameters and the range of optimization parameters are given. First, the arrangement spacing between the scalelike unit structures was set as \(S_{1}=S_{2}=1\) mm. The parameters for length \(l\) and height \(h\) were set as the design variables. Thus, the effects of the bionic structure on the drag reduction performance were compared. The design of the simulations for the S-U-S are listed in Table 2.  
Second, after the previous simulations on the basis of the first step, the optimal solution for drag reduction regarding the height and length parameters of the scalelike unit structure can be obtained.