## 3 Simulation Test Analysis of Sorting and Conveying Process
### Parameterization and Modeling for Simulations  
To fulfill [PERSON] simulation criteria and lower the computer's running burden, the sorting and conveying model must be properly reduced. The simulation primarily examines the sugarcane conveying process and the collision process that occurs after the sugarcane falls. During the conveying process, sugarcane is mostly susceptible to contact force between the cane stems, which is insufficient to cause the cane stems to undergo significant deformation. With a length of 2500 mm, a diameter of 30 mm, a density of \(1.1\times 10^{-6}\) kg/mm\({}^{3}\), a modulus of elasticity of 1310 Mpa, a Poisson's ratio of 0.33 [23], and a set of stacking contact between the cane stems, the cane is simplified as a cane stem model because the collision force after the cane falls is primarily related to cane mass and geometry and has nothing to do with material flexibility. The sorting and conveying device has a lot of pieces, and its structure has been streamlined to save simulation time while still satisfying virtual test criteria. To conceal the wire mesh of the sorting mechanism, the rows of canes on the cane collecting plate are arranged horizontally, and 40 cane are pre-installed on the lifting conveyor belt. Thissimplifies the lifting conveyor belt by using a conveyor model with baffles. Steel material with a density of 7850 kg/cm\({}^{3}\), a Young's modulus of 20,700 MPa, and a Poisson's ratio of 0.3 is used for the frame, sprocket, cane collection plate, and sorting mechanism [24]. Figure 6 displays the simplified simulation model. For cane-lifting conveyor belt, cane-collecting plate, cane-sorting claw, cane-cane, and chain-link contact, the appropriate contact parameters are determined. The collision force between two elements is determined using the IMPACT function and is composed of two components: a dampening force caused by the relative velocity [25] and an elastic force resulting from the mutual incision between the two members. It is stated as follows:  
\[F\_impact=\left\{ \begin{array}{ll}0&q>q_{0}\\ k(q_{0}-q)^{e}-c_{\max}\cdot(dq/dt)\cdot step(q,q_{0}-d,1,q_{0,0})&q\leq q_{0} \end{array} \right. \tag{7}\]  
where \(q_{0}\) is the initial distance between the two objects to collide, \(q\) is the actual distance between the two objects during the collision, \(dq/dt\) is the rate of the change in the distance between the two objects with time, i.e., the velocity, \(k\) is the stiffness coefficient, \(e\) is the collision index, \(c_{\max}\) is the maximum damping coefficient, and \(d\) is the depth of incision, which determines when the damping force reaches its maximum. To prevent a discontinuity of the damping force in the process of a collision, use Eq. _step_ function [26] in the form of \(step(x,x_{0},h_{0},x_{1},h_{1})\):  
\[step=\left\{ \begin{array}{ll}h_{0}&x\leq x_{0}\\ h_{0}+a\cdot\Delta^{2}(3-2\Delta)&x_{0}<x<x_{1}\\ h_{1}&x\geq x_{1}\end{array} \right. \tag{8}\]  
where  
\[\left\{ \begin{array}{ll}a=h_{1}-h_{0}\\ \Delta=\frac{x-x_{0}}{x_{1}-x_{0}}\end{array} \right. \tag{9}\]  
For collisions of rotating objects, the stiffness coefficient can be approximated by approximating the following equation:  
\[k=\frac{16 RE^{2}}{9} \tag{10}\]  
where  
\[\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}} \tag{11}\]  
\[\frac{1}{E}=\frac{1-\mu_{1}^{2}}{E_{1}}+\frac{1-\mu_{2}^{2}}{E_{2}} \tag{12}\]  
where \(R_{1}\) and \(R_{2}\) are the radii of the two objects at the collision, respectively; \(\mu_{1}\) and \(\mu_{2}\) are the Poisson's ratios of the two objects, respectively; and \(E_{1}\) and \(E_{2}\) are the elastic moduli of the two objects, respectively. Figure 6: Simulation model for sorting and conveying. The default value in ADAMS can be used to compute the stiffness factor for collisions with non-rotating bodies [27]. The loss of impact energy is described by the maximum damping factor (Damping), which is typically set between 0.1 and 1% of the stiffness factor. The depth of the incursion at which dampening is the greatest is described as penetration depth.