# Research on the Prediction of Insertion Resistance of Wheel Loader Based on PSO-LSTM
## 2 Experimental Data Acquisition and Analysis
### Resistance  
The wheel loader insertion resistance comes from the combined force, consisting of three shaft-pin-type sensors. Taking the forward direction of the wheel loader as the positive direction, the shaft-pin-type sensor at the lift arm and bucket on the right side of the wheel loader is noted as P1, the shaft-pin-type sensor at the lift arm and bucket on the left side of the wheel loader is noted as P2, and the shaft-pin-type sensor at the connecting rod and bucket is noted as Q, as shown in Figure 4. Due to the influence of the structure of the wheel loader, these three sensors are not installed parallel to the horizontal direction, but at a certain angle to the horizontal direction, as shown in Figure 5. The angle between the Y-axis direction and horizontal direction of P2 is 70\({}^{\circ}\); Q is in the same direction as P2, but its installation angle is different from P2, and the angle between its Y-axis direction and the horizontal direction is 43.85\({}^{\circ}\); and P1 is in the opposite direction of P2 because it is installed on the other side of the wheel loader. The resistance of gravel and sand in the X direction and Y direction measured by P1, P2, and Q, respectively, for an insertion depth of 600 mm is shown in Figure 6. Among them, P1 and P2 have almost the same magnitude but opposite directions in the X direction, where P2 is negative and P1 is positive. The resistance of gravel has a greater variation, while the resistance of sand has a smoother variation. The partial force in the Y direction is always positive and has almost the same trend, but the resistance value of P2 is slightly  
Figure 4: Shaft-pin-type sensor. Figure 5: The installed angle of the shaft-pin-type sensor. larger than P1 due to the uneven force on the left and right sides of the bucket, which is more obvious in the sand. As for Q, although its installation direction is the same as P2, its force direction is opposite to P1 and P2, and the bucket force schematic is shown in Figure 7. Therefore, the resistance values in the X direction and Y direction of Q are negative, and the absolute value of resistance in the Y direction is always higher than that in the X direction. Since the installation angle of P1, P2, and Q are not parallel to the horizontal direction, the resistance direction of the three shaft-pin-type sensors needs to be corrected to make  
Figure 6: Resistance by shaft-pin-type sensor. (**a**) X direction resistance of gravel sample; (**b**) Y direction resistance of gravel sample; (**c**) X direction resistance of sand sample; (**d**) Y direction resistance of the sand sample. Figure 7: Bucket force diagram. the direction horizontal. \(F_{YQ}\), \(F_{XQ}\), \(F_{YP}\), and \(F_{XP}\) are the resistance values measured by the shaft-pin-type sensors, and \(F_{QX}\) and \(F_{PX}\) are the resistance values after correction. The calculation formula is shown in Equation (1). \[\left\{ \begin{array}{l}F_{PX1}=F_{XP1}\cos\alpha-F_{YP1}\sin\alpha\\ F_{PX2}=F_{XP2}\cos\alpha-F_{YP2}\sin\alpha\\ F_{QX}=F_{XQ}\cos\alpha-F_{YQ}\sin\alpha\end{array} \right. \tag{1}\]  
Following this, the insertion resistance of the bucket, \(F\), can be expressed as:  
\[F=F_{PX1}+F_{PX2}-F_{QX} \tag{2}\]  
To verify the reliability of the insertion resistance, a comparison with the resistance calculated by the empirical formula is chosen in this paper. The empirical formula for insertion resistance is shown in Equation (3) [3], and the influence coefficients and parameters are shown in Table 1[27]. \[F_{c}=9.8K_{1}K_{2}K_{3}K_{4}BL^{1.25} \tag{3}\]  
where \(K_{1}\) is the influence coefficient of pile looseness; \(K_{2}\) is the influence coefficient of pile type; \(K_{3}\) is the influence coefficient of pile shape and height; \(K_{4}\) is the influence coefficient of the bucket; \(B\) is the width of the bucket; \(L\) is the insertion depth.