# Investigation of Roller-Tape Contact Pair Used in Precision Mechatronic System
## 4 Numerical Investigation of Tape Displacement  
A model for calculating mechanical properties (Figure 10) was developed for the tape displacement measurement system, which was one of the most important components of a raster generation device. It should be noted that the numerical simulation model presents one very important node in the experimental setup illustrated in Figure 4c. Five Hypalon plates were affixed to the bottom and top of the steel tape. Both top and bottom contact pairs were monitored during simulation. Figure 11 illustrates the contact pairs. The iterative solution method was selected. Two selections of boundaries that could not penetrate each other under deformation were chosen for the analysis of the contact pair boundary condition. The contact pairs defined boundaries for parts that could come into contact as shown in Figure 11a,b, for upside and downside contacts, respectively. The augmented Lagrangian was selected as the algorithm for computing contact in the normal direction. Characteristic stiffness in current simulation was equivalent to [PERSON]'s modulus. Penalty factor controls the stability and stiffness of the interface surface during iterations. Moreover, an additional control over solver cutbacks, such as trigger cutback criterion in numerical simulation, was not used because there was no destination boundary movement history. The exponential dynamic Coulomb friction model using both static and dynamic friction coefficients were included in the time dependent study for both contact pairs (Figure 11). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**Displacement of the Tape-angle Transducer Contact Point**} \\  & & \multicolumn{3}{c}{**Statistical Parameters, \(\upmu\)m**} \\
**Mean** & **Standard Deviation** & **Minimum** & **Maximum** & **Range** \\
0.0122 & 0.0244 & \(-\)0.0777 & 0.0859 & 0.163 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical parameters of the results of the measurement of the displacement of the steel tape–angle transducer contact point and velocity in the longitudinal direction Y.  
Two-point probes similar to the experimental setup sensor position (Figure 4c) were chosen for postprocessor analysis after simulation. They are illustrated in Figure 10 as points A and B. Figure 13 illustrates fixed constraints and the body load of the current model. Five contact zones between the steel tape and support from Hypalon material are presented in Figure 13a. Dynamic friction and gravity of these contact pairs only were taken into consideration during simulation. DOF (Degree of Freedom) by \(z\) and \(x\) axes in contact zones was restricted. Two coordinated restrict the set velocity (Figure 10), and the steel tape had a freedom of movement along the length only. Gravity was also included in the simulation. The simulation was based on the parametric sweep of the top roller preload by-\(z\) axes (Figure 13b) and a change from 10 to 40 N with 10-N steps. This range was chosen based on the experimental 30-N preload setup. Mechanical properties of materials used in numerical simulation are presented in Table 3.  
Figure 14 below presents a compiled mesh of finite elements. The steel tape unit was modeled using COMSOL Multiphysics software. The quality of mesh elements maximizes in the contact zone. In the simulation, 0.48 and 0.93, respectively, were the minimum and the average element qualities. \begin{table}
\begin{tabular}{c c c c} \hline  & **Structural Steel** & **Hypalon SH90** & **Aisi 420** \\ \hline Density, kg/m\({}^{3}\) & 7850 & 1200 & 7700 \\ Young’s modulus, & 200e9 & 20e6 & 215e9 \\ Pa & 0.30 & 0.40 & 0.28 \\ Poisson’s ratio & 0.30 & 0.40 & 0.28 \\ \hline \end{tabular}
\end{table} 
Table 3: Mechanical properties of used materials. Figure 14: Finite element mesh of the steel tape unit in the contact zone between the rollers and the steel tape (**a**) and Hypalon plates and steel tape contact pairs (**b**). Figure 13: Fixed constraints (**a**) and body load (**b**).