# Multibody Dynamics Simulation and Vibration Test for High Clearance Orchard Sprayer
## 4 Discussion  
1. The effect of engine vibration frequency on the frame The external excitation of the sprayer frame during operation comes mainly from the excitation of the frame by the unevenness of the road; The internal excitation comes mainly from the internal components of the sprayer during operation, such as the engine, fan, and diaphragm pump. The effect of engine operation on the spray frame is mainly considered in the modal analysis. The rotational excitation frequency of the sprayer engine during operation is calculated by the following equation [29; 30]. \[f=\frac{2 nz}{60\tau} \tag{3}\]  
where \(n\) is the number of engine revolutions, r/min; \(z\) is the number of engine cylinders, and \(\tau\) is the number of engine strokes. The engine used in the sprayer is 4G33 TC four-cylinder from CHANGCHAI COMPANY, LIMITED, four-stroke inline water-cooled diesel engine with a rated working RPM of 2400 r/min and RPM for the unloaded operation of 900 r/min. Bringing in Equation (3), we can get the rotation excitation frequency of 4G33 TC is 30 Hz at idle and 80 Hz at normal operation. According to Tables 5 and 6, it can be seen that the main vibration frequencies of the sprayer are 30 Hz and 80 Hz, and this test result proves the accuracy of the calculation results. The results in Table 5 show that in idle condition, the dominant vibration frequency at the test points is 30 Hz and the vibration amplitude is small. Test point 1 has a relatively even distribution of vibration amplitudes in the X, Y, and Z direction, while the remaining four test points have vibration amplitudes mainly in the X direction. This is because the engine is installed on the two beams in the Y direction, and the test point 1 is in the middle of the two supports. The excitation caused by the engine has little difference in the three directions, and the other four test points are all on the right side of the engine, so the vibration caused by the engine is shown in the X direction. This difference can be found in the same pattern in Table 6, and the reasons for this phenomenon are the same. From Tables 5 and 6, it can be seen that the inherent frequency of the sprayer frame gradually increases, but the value of the overall inherent frequency is small. It can be seen that the first 12 th order inherent frequency of the sprayer frame ranges from 2.1 to 14.35 Hz, which does not overlap with the engine excitation frequency of 30 or 80 Hz and will not resonate with the engine excitation. 2. Effect of step excitation on spray bar deformation From Figures 11 and 12 it can be seen that the two ends of the spray boom make a reciprocal motion when the sprayer frame crosses the barrier, and there is a trend of vibration decay between the front and rear wheels crossing the barrier; there is also a lower peak between the two peak values in the Figure, which is due to the X, Y, and Z three directions in the simulation software and the displacement is calculated as follows. \[U=\sqrt{U_{X}^{2}+U_{Y}^{2}+U_{Z}^{2}} \tag{4}\]  
As the displacement of the three directions is positive, there is no negative value, but there are positive and negative values of the displacement of a single direction, so between the other two higher crests appear to lower crests to the left end of the spray boom displacement deformation, for example, to extract the displacement of the left endpoint of the spray boom in three directions, the results are shown in Figure 13.  
According to Figures 13 and 14, it can be found that the displacement deformation of the spray bar is irregular motion, and the displacement deformation size is gradually decreasing [31]. From Figure 16, the displacement deformation of the spray bar in the X, Y and Z directions, the displacement deformation of the spray bar shows a cyclic reciprocal displacement when the sprayer is subjected to step excitation. The displacement transformation situation is based on the equilibrium position of the spray bar as the reference point, in each of the three directions of up and down movement, and cycle back and forth.