# Research on the Prediction of Insertion Resistance of Wheel Loader Based on PSO-LSTM
## 2 Experimental Data Acquisition and Analysis
### Resistance
The comparison between the insertion resistance calculated by the empirical formula and the actual insertion resistance is shown in Figure 8. Among them, the actual insertion resistance of gravel fluctuates from the calculated resistance, while the actual insertion resistance of sand is higher than the calculated resistance. This is related to the environment in which the experiment was conducted, which has high humidity due to the climate. The cohesion and adhesion of the sand increase due to the humidity, which makes the resistance to the bucket greater [28; 29]. The two different types of materials exhibit different characteristics of resistance. The insertion resistance of gravel shows a greater randomness and a greater variation in resistance. In contrast, the insertion resistance of sand changes more smoothly and increases gradually. Moreover, the value of resistance generated by each insertion is unique, and the empirical formula does not accurately reflect the trend of insertion resistance. For the soil mechanics method, the pile develops a virtual surface and a slip surface as the bucket moves inside the pile. This breaks the material pile into three parts, as shown in Figure 9. Area A is the material inside the bucket, area B is the material being shoveled, and area C is the unshoveled material. The wheel loader insertion process is divided into two phases. These include the pre-insertion phase and the late-insertion phase. In these two phases, the forces on the bucket are not the same, as shown in Figure 10, and the forces are calculated as shown in Equation (4). A number of these parameters need to be selected empirically, some of them need to be determined experimentally, and others need to be measured instantly. Meanwhile, the definition of the two phases is not clear. The above reasons lead to the insertion resistance, which is difficult to calculate according to the soil mechanics method, and the insertion resistance is not accurate compared to the real resistance. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type** & \(K_{1}\) & \(K_{2}\) & \(K_{3}\) & \(K_{4}\) & \(B\) (cm) & \(L\) (cm) \\ \hline Gravel & 0.75 & 0.12 & & & & \\ Sand & 0.5 & 0.1 & 1.1 & 1.4 & 290 &
\begin{tabular}{c} Insertion \\ depth \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the empirical formula. \[\left\{ \begin{array}{l}F_{1}=k\rho gSH\cos\alpha\\ F_{2}=\mu F_{4}\cos\beta+\mu F_{3}\cos(\varphi-\beta)\\ F_{3}=-F_{p}\\ F_{4}=Mg\end{array} \right. \tag{4}\]  
where \(F_{1}\) is the resistance of the bucket tip and edge; \(k\) is the resistance influence coefficient; \(\rho\) is the density of material; \(g\) is the acceleration of gravity; \(S\) is the shovel area; \(H\) is the vertical height of the bucket tip and the pile; \(\alpha\) is the angle between the bucket movement direction and the horizontal direction; \(F_{2}\) is the friction force exerted on the bucket by the material inside the bucket; \(\mu\) is the friction coefficient; \(\varphi\) is the angle of internal friction; \(\beta\) is the angle between the bucket tip and the horizontal direction; \(F_{3}\) is the force generated by the slip of the pile on the bucket; \(F_{p}\) is the Coulomb pressure, and it is shown in the Equation (5); \(F_{4}\) is the gravitational force exerted by the material inside the bucket; \(M\) is the weight of the material in the bucket. \[F_{p}=\frac{\rho H^{2}}{2\sin^{2}\varepsilon\sin(\varepsilon-\delta)}.\frac{ \sin^{2}(\varphi+\varepsilon)}{\left[1+\sqrt{\frac{\sin(\varphi+\delta)\sin( \varphi-\gamma)}{\sin(\varepsilon-\delta)\sin(\varepsilon+\gamma)}}\right]^{ 2}} \tag{5}\]  
where \(\varepsilon\) is the angle between the virtual surface and the vertical direction; \(\gamma\) is the angle of repose of the pile; \(\delta\) is the angle between \(F_{p}\) and the normal vector of the virtual surface, and the angle is acute. Figure 8: Insertion resistance.