# Analysis of Vibration Characteristics of the Grading Belt in Wolfberry Sorting Machines
## 4 Conclusions  
1. To address the vibration issue of the transmission belt in the fresh wolfberry sorting machine, the lateral vibration theory was employed to develop relevant models and derive theoretical formulas. The analysis revealed that the primary factors influencing lateral vibration are initial tension, rotational speed, and center distance.
2. The feasibility of the model was validated through field experiments. The average error between the maximum amplitude in the simulation results and the actual measured maximum amplitude was 3%, indicating that the established dynamic model is reliable.
3. Based on the single-factor experiments, the response surface methodology (RSM) was employed to optimize the grading flat belt of the wolfberry sorter. The factors influencing the lateral vibration of the grading flat belt were ranked in descending order of their comprehensive impact as follows: initial tension > bias angle > rotational speed. In this study, a quadratic polynomial regression model to obtain a comprehensive score was established through response surface experiments. The results indicate that the lateral vibration displacement is minimized when the initial tensile force is 520 N/mm, the rotational speed of the transmission shaft is 60 min\({}^{-1}\), and the deflection angle of the transmission mechanism is 5\({}^{\circ}\).
4. Under the working conditions of an initial tension of 520 N/mm, a transmission shaft speed of 60 r/min, a transmission mechanism deflection angle of 5\({}^{\circ}\), and a belt center distance of 2200 mm, harmonic response analysis was performed using the modal superposition method. Significant resonance responses were observed at excitation frequencies of 4 Hz and 8 Hz. Under these conditions, both the pulley structure and the fixing device were optimized. When the fillet radius of the pulley was set to 10 mm and the length of the fixing device was adjusted to 1600 mm, the lateral vibration of the belt was minimized, thereby reducing the impact of lateral vibration and improving the reliability of the goji berry sorter.  
This article presents a dynamic analysis of general transmission systems based on a dynamic simulation model. However, the results obtained from this model still exhibit significant discrepancies compared to real-world conditions. Subsequently, an investigation into the vibration characteristics during the fresh wolfberry screening process will be carried out. This aims to refine the simulation model for better alignment with real-world conditions and enhance the precision of the acquired data. Simultaneously, in partnership with wolfberry processing enterprises, the virtual prototype model will be further refined and enhanced by integrating experimental and field data. Through the iterative optimization approach of \"simulation-experimentation-enhancement\", the engineering applicability of the model will be significantly improved, thereby offering more precise theoretical guidance for the design and performance optimization of the transmission system in fresh wolfberry sorting machines.  
Conceptualization, Y.Y. and Z.S.; methodology, Y.Y.; software, Z.S.; validation, Y.Y. and Z.S.; formal analysis, J.Z.; investigation, J.L.; resources, W.Q.; data curation, J.L.; writing--original draft preparation, J.Z.; writing--review and editing, Z.S.; visualization, Z.S.; supervision, W.Q.; project administration, Y.Y. All authors have read and agreed to the published version of the manuscript. This research was funded by the Key Research and Development Program of Shaanxi Province (2018 GY-077), Shaanxi Province Qin Chuang Yuan Science and Technology Innovation Special Project (2021 ZDZX-GY-0006).  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data are contained within the article.  
**Conflicts of Interest:** The authors declare no conflicts of interest.