# Analysis of Vibration Characteristics of the Grading Belt in Wolfberry Sorting Machines
## 2 Materials and Methods
### Graded Flat-Band Dynamics Analysis  
Belt Drive Modeling  
The Recur Dyn software, founded on relative coordinate system modeling and recursive algorithms, is capable of solving large-scale multi-body system dynamics issues [25; 26; 27]. Combining the structural principle and mathematical model of the fresh wolfberry sorter, in the process of establishing the finite element model of the grading belt transmission system, to reduce the calculation amount and error during the simulation of the system model, with the main motion system remaining unchanged as the prerequisite, an appropriate simplification of the grading device was carried out, thereby reducing the number of elements generated during the dynamic characteristic analysis. The following hypotheses are made [28; 29]:  
1. The vibration of the motor on the transmission device is relatively small and can be disregarded.
2. The fixed device beneath the flexible belt has a considerable influence on the lateral vibration of the belt. The lateral vibration characteristics of the belt without this device added are mainly considered. It is simplified into two parts, namely, the driving wheel and the transmission belt [30]. The simplified model is shown in Figure 6.  
In the establishment of the belt drive model, as the silicone rubber belt is a flexible body, it is necessary to create a finite element flexible body calculation model of the belt. The flexible body creation method based on the geometrical shape of the rigid body component is adopted to discretize the space occupied by the component through finite elements for the creation of the flexible body. The boundary conditions are defined as where no displacement occurs in the RX, RY, and RZ directions; the contact between the flat belt and the transmission shaft is of the type FSurface To Surface Contact; the material properties and main contact parameters are presented in Table 1.  
In the dynamic modeling of the flat belt system, revolute joint constraints are applied to both the driving and driven wheels. The rotational speed of the driving wheel is specified within the range of 60 to 180 min\({}^{-1}\). An initial tension force ranging from 170 to 570 N is applied to the flat belt, with the maximum allowable deflection angle of the belt set between 4\({}^{\circ}\) and 6\({}^{\circ}\). The simulation is conducted for a duration of 1 s, with the step size configured at 1000 steps [31; 32]. To analyze the lateral vibration characteristics of the grading belt, three lateral vibration amplitude measurement points were establ  
\begin{table}
\begin{tabular}{c c c c} \hline
**Name** & **Density** & **Poisson’s Ratio** & **Young’s Modulus** \\ \hline
**Parameters** & **1.15 g/cm\({}^{3}\)** & **0.48** & **22 MPa** \\ \hline Damping coefficient & Stiffness coefficient & Dynamic friction coefficient & Static friction coefficient \\ \hline \(1\times 10^{-4}\) N\(\cdot\)s/mm & 1000 N/mm & 0.4 & 0.65 \\ \hline \end{tabular}
\end{table}
Table 1: Material Properties and Exposure Parameters.  
Figure 6: Schematic diagram of amplitude measurement points with fixtures.  
belt were collected via a laser displacement sensor. Three lateral vibration amplitude measurement points were respectively set on the upper and lower sides of the flat belt.  
The collected voltage was subsequently converted into the corresponding vibration displacement values using a digital signal collector. The data were then analyzed through the computer's image processing model to generate the vibration displacement visualization, and the maximum amplitude of the stabilized curve was recorded.