# Multibody Dynamics Simulation and Vibration Test for High Clearance Orchard Sprayer
## 3 Results
### Transient Dynamics Analysis of Sprayer Frame  
A displacement load perpendicular to the ground was applied to the sprayer wheels, as shown in Figure 5, and transient dynamics analysis was performed. The obtained overall stresses of the sprayer frame as a function of time are shown in Figure 10.  
From Figure 10, it can be seen that the maximum stress occurs at 0.93 s during the whole process of the sprayer frame crossing the barrier, and the stress distribution diagram for 0.93 s is extracted, as shown in Figure 11. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Equipment Name** & **Performance Index** & **Parameter Values** \\ \hline \multirow{4}{*}{Three direction acceleration sensor of 356A16} & Sensitivity & 100 mV g\({}^{-1}\) \\  & Frequency response & 0.3–6 kHz \\  & Range & \(\pm\)50 g pk \\  & Lateral sensitivity & \(<\)5\% \\  & Channel & 32 \\  & Sampling bandwidth & 100 kHz \\  & End scale value & \(\pm\)20 mv \(\pm\)20 V \\  & Distortion factor & \(<\)0.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance parameters of vibration test instruments. Figure 8: [PERSON] stresses diagram of the frame with full load bending condition. Figure 11: [PERSON] stresses the distribution diagram of the 0.93 s frame. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Order** & **Frequency/Hz** & **Order** & **Frequency/Hz** \\ \hline
1 & 2.10 & 7 & 10.27 \\
2 & 3.15 & 8 & 11.88 \\
3 & 3.93 & 9 & 12.44 \\
4 & 5.31 & 10 & 14.06 \\
5 & 6.14 & 11 & 14.2 \\
6 & 10.21 & 12 & 14.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: First 12 orders of inherent frequency. Figure 10: Simulated stress result diagram for the sprayer frame. Figure 9: [PERSON] stresses diagram of the frame with extreme torsional condition. In Figure 11, it can be found that the maximum stress value is located in the middle spray boom and the connection of the single spray boom, the maximum stress value of 266.2 MPa. When a load of 1.5 times is applied, the stress extremes of the whole vehicle do not exceed the permissible stresses of the frame material and are within safe limits [14]. The main reason is the existence of gaps between the parts of the spray boom connection and the collision occurred in the process of the sprayer over the barrier, resulting in a large impact load. We can also find that most of the time, the stress of the sprayer frame in the process of crossing the barrier is below 250 MPa, the maximum stress is 266 MPa, the whole process of the spray frame is in a relatively safe state, and the design of the sprayer frame does not have serious problems. The time variation of the maximum displacement of the sprayer frame throughout is shown in Figure 12.  
The peak points in Figure 12 are extracted to generate a displacement deformation diagram. We can find that these peak points are all at the ends of the single spray boom; as can be seen in Figure 12, spray boom vibration at the beginning of the sprayer frame over the barrier, the spray boom reaches its maximum displacement deformation at the end of the front wheel over the barrier, after which the vibration starts to decay, and the displacement deformation of the spray boom gradually becomes smaller. When the rear wheels start to cross the barrier, the vibration of the spray boom starts to become larger, and the displacement deformation also starts to become larger, at which time the maximum displacement deformation occurs. Extract the displacement deformation at both ends of the spray boom, as shown in Figures 13 and 14. Figure 12: Simulated displacement results for the sprayer frame. Figure 13: Simulated displacement results of the left end of spray boom. Due to many measurement points, the time domain and frequency domain diagram obtained from the analysis of measurement point 1 is used as an example (shown in Figure 15).