# Research on Rollover Stability and an Anti-Rollover Warning System for the Vibroseis Truck
## 2 Rollover Stability Analysis for Vibroseis Truck
### Stability of the Vibroseis Truck on a Sloping Road  
To analyze the driving process of the vibroseis truck on a sloping road, a simulation analysis model, a lateral slope road upward turning analysis, and a sloping road downward turning analysis were established, as shown in Figure 8a-c, respectively. As shown in Figure 8b, the process of turning upwards on a sloping road involves driving on a horizontal road to a sloping road (stage one), going straight on the slope and turning to the right (stage two), going straight up the slope and turning upwards (stage three), and turning up the slope and going straight (stage four). As shown in Figure 8c, the downward turning process on the sloping road involves driving on the horizontal road to the slope road stage (stage one), going straight up the slope and turning to the right (stage two), turning straight on the slope and turning downward (stage three), and going straight down the slope (stage four). In the simulation, the driving speed was 7 m/s (25.2 km/h), the maximum steering angle was 25\({}^{\circ}\), and the slope angle was 15\({}^{\circ}\).  
A comparative analysis of the speed changes of the front and rear bodies of the vibroseis truck during the upward and the downward steering on the lateral slope was carried out to determine the changes in the speed of the vibroseis truck during the turning process. The speed comparison curve of the front and rear car bodies is shown in Figure 9.  
Figure 8: (**a**) Simulation analysis model, (**b**) sloping-road upward turning, and (**c**) sloping-road downward turning.  
Figure 9: The speed comparison curve of the front and rear car bodies.  
It can be seen in Figure 9 that in 3-4 s, the vibroseis truck reached the longitudinal slope from the horizontal road. During this process, the speed decreased significantly. The reason is that when the front and rear wheels leave the horizontal road, an impact is generated at the boundary between the slope and the horizontal road, resulting in a decrease in speed. The vibroseis truck required 7-11 s to turn right on the longitudinal slope. During this process, the speed of the front and rear car bodies decreased first and then increased with the continuous increase of the steering angle, and the speed of the rear car body was lower than that of the front car body. At t = 13 s, the vibroseis truck began to turn from the lateral slope. During the upward and downward steering, the speed of the front body was greater than the speed of the rear body. When turning downward, the speed of the front and rear car bodies was greater than the speed when turning upward. The reason is that the distance between the front and rear axles and the hinge point was not equal, and the front body was equipped with a swing bridge structure, which caused the speed of the front body to be slightly higher than that of the rear body. At the same time, during the upward turning process of the source vehicle, the gravity component along the slope was opposite to the direction of the speed. This produced a negative work, which reduced the speed of the vehicle. When turning downward, the component of gravity along the slope was the same as the speed direction; this produced a positive work and accelerated the speed of the vehicle.  
Based on the above analysis, during the longitudinal and lateral turning of the vibroseis truck on the examined slope, the speed of the front body was greater than the speed of the rear body, and the lateral downward turning had a higher driving speed than the upward turning, which indicated the steering angle and slope angle. They have a certain influence on the speed of the vibroseis truck's turning process and have a greater influence on the speed when turning laterally upwards.