# A Predictive Multibody Model of Paper Applied to Cash Recycling
## 4 Results and Discussion
### High-Fidelity Cash Recycler Model  
In this section, the simulation of banknote transport through a high-fidelity model of a cash recycler is analysed. Although the whole transportation system has been simulated, this section will focus on a critical part of the cash recycler, i.e., the feeder group. The purpose of the feeder is to convey the banknote past the rejection unit. The rejection unit is composed of the pulling system. The rejection rollers play the key role of allowing only one banknote at a time to pass. They are mounted with an interference of 0.2 mm with the feeding rollers, as visible in Figure 15.  
Figure 15: High-fidelity model of the cash recycler. Focus on the feeder and the rejection unit. In this context, it is critical to select the correct interference. If it were too large, the banknote would not be able to pass; if too small, more than one banknote would pass simultaneously. However, setting the right interference is not sufficient. It is also crucial to use the right materials so as to ensure a specific balance of friction. The friction between banknote and feeding rollers should be higher than that between banknote and rejection rollers. Furthermore, the friction between two overlapping banknotes should be less than that of the top banknote with the rejection rollers. The purpose of the skimmer rollers is twofold, as follows:  
1. They align the banknote by pivoting if it arrives tilted;
2. They press down on the banknote by providing the necessary drag force to get the banknote just below the rejection rollers but not past them (the feeding rollers are in charge of that). The pulling system aims to advance the banknote quickly toward the exit. A spring with a preload of 15 N is used for this, so that the pulling force is increased. The rollers can rotate around the pulling axis, which can translate relative to the support on which it is mounted. The MB model of the cash recycler was built on MotionView(r) by importing the CAD file. All the bodies are treated as rigid, so information on the material they are made of is not relevant to the bodies' global deformations but rather to the contact parameters (contact stiffness and coefficient of friction). Motion, which in reality is transmitted by a motor to the pre-feeding and feeding rollers via a belt mechanism, is here imposed directly. Three different EUR 10 banknote models have been tested on the present cash recycler MB model as follows:  
1. 200 boxes banknote model with center-to-center connections;
2. 200 boxes banknote model with edge-to-edge connections;
3. 600 boxes banknote model with edge-to-edge connections. All investigated models manage to capture the macro-behavior of the banknote correctly. However, the first model, i.e., 200 boxes with center-to-center connections, shows some drawbacks. More specifically, as shown in Figure 16a, some boxes have angular positions radically different with respect to adjacent boxes. The cohesion between neighboring boxes is insufficient at some locations. This incorrect configuration may cause deviations of the banknote from the predetermined path and is, therefore, not deemed acceptable. The problem is completely overcome when using the edge-to-edge banknote model, which ensures a sufficient level of cohesion between neighboring boxes. Furthermore, this second investigated model exhibits an additional advantage. During the simulation the banknote is supposed to remain in the same position when it is touching the rejection  
Figure 16: Frames showing the incorrect configuration of the center-to-center banknote model (**a**), and the correct configuration of the edge-to-edge banknote model (**b**). rollers but not yet in grip with the toothed rubber of the feeding rollers. This happens at around 400 ms from the start of the simulation. Figure 17 shows the comparison between the displacement of one representative box coming from the two models, i.e., center-to-center vs. edge-to-edge.