# Analysis of Dynamic Behavior of Spray Boom under Step Excitation
## 3 Results and Discussion  
### Model Validation  
Vertical vibration of the extremity of the spray boom was tested on the ground (Figure 7), and 18 groups of response data were obtained. The effective data time is less than 5 s. Results show that the spray boom is affected by engine vibration and other external factors when the boom sprayer is running on horizontal ground. The maximum allowable vibration error at the extremity tested by the ultrasonic sensor is \(\pm\)0.05 m. The typical vibration response curves of the spray boom at the first 5 s of three speeds are illustrated in Figure 8. When the boom sprayer passes through obstacles at a traveling speed of 4 km\(\cdot\)h\({}^{-1}\), the vibration at the extremity of the spray boom maximizes, which is about 0.628 m upward vibration. With an increase in the traveling speed, the vibration amplitude of the extremity decreases and is reduced obviously, especially when the speed is accelerated from 4 to 6 km\(\cdot\)h\({}^{-1}\). Under the three speeds, the maximum amplitude of downward vibration at the extremity changes very little and is about 0.537 m. As the traveling speed of the boom sprayer rises, the frequency of the extremity of the spray boom is increasing, further proving that the spray boom and suspension can drive the spray boom to follow the low-frequency components of the ground, while isolating the fluctuation and inclination of high-frequency components. The vibration curve shows that the spray boom during vibration is affected by different parts of the boom sprayer body, spray boom suspension and vibration frequency, resulting in the interval small amplitude vibration. Due to the relative friction caused by the relative motion of each part of the boom sprayer in the vibration, the vibration waveform clips and distorts. The vibration of the spray boom is mainly concentrated in the first 3 s and decays rapidly after 3 s.  
Figures 9-11 compare the measured vibration response of the spray boom with the model predicted results when the boom sprayer passes through the obstacle at the speeds of 4, 6, and 8 km\(\cdot\)h\({}^{-1}\). Among the three vehicle speeds, the correlation coefficient between the model simulation results and the measured results minimizes to 0.917 at 8 km\(\cdot\)h\({}^{-1}\). Clearly, the measured vibration distortion waveform at the extremity of the spray boom is larger, and each peak and valley have obvious friction peak shaving. The model prediction curve distortion waveform is less but has friction peak shaving at each peak and valley. Figure 8: Vibration response curves of the extremity of the spray boom when the boom sprayer passes through obstacles at three speeds. The main reason for this difference is that when the boom sprayer passes through the obstacle, an unpredictable random collision friction occurs between relevant components. The maximum error between the model prediction and the measured values occurs when the boom sprayer passes through the obstacle at the speed of 8 km\(\cdot\)h\({}^{-1}\). The upward and downward errors are 0.0618 and 0.0238 m, respectively, which are within a reasonable range. Thus, the model can effectively predict the vertical vibration of the spray boom. Figure 10: Model predicted values and experimental values of vibration response of the extremity of the spray boom when the boom sprayer passes through obstacles at 6 km\(\cdot\)h\({}^{-1}\). Figure 9: Model predicted values and experimental values of vibration response of the extremity of the spray boom when the boom sprayer passes through obstacles at 4 km\(\cdot\)h\({}^{-1}\). Through experimental comparison, the model can effectively predict the vertical vibration of the spray boom. The geometric continuous model of the spray boom based on multi-body vibration can improve the efficiency of the parameterized design of the boom sprayer and improve the running stability of the boom sprayer. At the same time, it can be found that there is still room for further improvement in the microscopic accuracy of the model established in this paper.