## 3 Simulation Analysis
### Influence of Piston Effect on Pressure in Transport Lane
#### 3.3.2 Influence of Piston Effect on Measuring Point Pressure in Transport Lane  
Figure 12 shows the relationship between the pressure of measuring points in each transport lane and time under the influence of the piston effect. The position of each measuring point is shown in Figure 1. It is also assumed that the positive direction of the x-axis is the downwind direction and vice versa. From the diagram, we can see that in the same lane, the trend of the pressure change curve is essentially the same. Under the influence of a running cage, the pressure curve has a high pulsation frequency and large pulsation amplitude. The operation of the cage will cause a transient change in the pressure in the transport lane. In particular, the pressure difference caused by the cage passing through each transport lane is the largest, and the minimum pressure is generated in the lane. The piston wind area interacts with each other under the intersection of two cages, and the pressure field distribution in the transport lane is the most complex. As the cage is away from each transport lane, the pressure of the measuring points in the lane gradually recovers. Figure 13 shows the difference between the maximum and minimum pressure caused by the piston effect in each transport lane. From the figure, we can see that the pressure difference of each measuring point is linearly decreasing with the distance from the measuring point to the shaft. That is, the farther away from the shaft measuring point, the less affected by the piston effect, and the smaller the pressure difference. The measuring point distance increased from 21.7 m to 71.7 m, and the pressure in 1414.0 m, 1584.0 m and 1765.0 m transport lanes decreased by 11.08 Pa, 9.62 Pa and 8.58 Pa, respectively. Figure 11: Pressure field distribution of each transport lane in x = 1 m section. Figure 12: The time-varying curve of pressure at each measuring point in different transport lanes: (a) 1765.0 m transport lane, (b) 1584.0 m transport lane, (c) 1414.0 m transport lane. Figure 13: The pressure difference of measuring points in each transport lane. The airflow in the transport lane belongs to turbulent flow. Under the influence of piston wind, the airflow particles collide, mix and exchange with each other. Turbulence is a random motion process that changes irregularly in time, but it has a regular probability distribution. Therefore, this paper uses probability density distribution to analyze the statistical characteristics of the piston air flow in each transport lane [29]. Three feature points with different distances from the entrance of the lane were selected along the central axis of the three transport lanes of 1765.0 m, 1584.0 m and 1414.0 m, respectively, for wind speed probability density statistics, and they were compared with the probability density distribution of normal distribution function by Formula (3). The results are shown in Figures 14-16. \[p(x)=\frac{1}{\left(2\pi\sigma^{2}\right)^{1/2}}\exp\left(-\frac{\left(x-\mu \right)^{2}}{2\sigma^{2}}\right) \tag{3}\]  
Figure 16: Probability density of characteristic points of 1414.0 m transport lane: (**a**) Point one, (**b**) Point two, (**c**) Point three. Figure 14: Probability density of characteristic points of 1765.0 m transport lane: (**a**) Point one, (**b**) Point two, (**c**) Point three. Figure 15: Probability density of characteristic points of 1584.0 m transport lane: (**a**) Point one, (**b**) Point two, (**c**) Point three. In the formula, \(p(x)\) is the probability density; \(x\) is the instantaneous airflow velocity of a point; \(\mu\) is the sample average; \(\sigma\) is the standard deviation of the sample size. From the diagram, we can see that the probability density curve of the feature points in each transport lane is basically consistent with the trend of the normal distribution curve, but it does not completely coincide.