## 3 Experimental Setup  
The mathematical tension model of the roll-to-roll gravure printed electronics system shows that the temperature affects the web tension between two adjacent rollers by the web Young's modulus at room temperature (\(E_{E}\)), and the web Young's modulus at drying temperature (\(E_{D}\)). The web material (PET) is sensitive to temperature, so the web Young's modulus \(E_{E}\) will change with the room temperature, and the web Young's modulus \(E_{D}\) will change with the drying temperature.  
For further studying the thermal characteristics of the plastic film tension in roll-to-roll printed electronics, the relations between the inputs and the outputs, including the room temperature and drying temperature, are researched through numerical simulations by using MATLAB/Simulink, and through experiments by using a gravure printing setup.  
Figure 3 shows the gravure printed electronics experimental setup, which consists of three sections: unwinding, printing, and rewinding. In the printing section, all of the driving shafts are driven by servo motors (YASKAWA SGMGH-44), and the speeds of the printing rollers are obtained by the position encoders on the servo motor. Tension signals are picked up by load cells (MITSUBISHI LX-030 TD) mounted on the idle rollers and then amplified by the tension amplifiers (MITSUBISHI LM-10 TA).  
The whole system is controlled by a multi-axis controller (GOOGOOLTECH T8 VME). The web material is PET.  
In order to study the thermal characteristics, an open loop control system is adopted in order to control the printing roller speeds, and there is no tension controller in this section. There is a tension compensation setup near the load cell for compensating the decrease of the tension caused by the mechanical system (such as friction forces). The adjustment work occurs before production, and the compensation setup is not adjusted during production.  
In Figure 2, setting \(i=2\), the model of the two adjacent printing rollers subsystems can be expressed as follows:  
\[[L_{2}+L_{D2}(\frac{E_{E}}{E_{D}}-1)]\frac{\mathrm{d}T_{2}(t)}{\mathrm{d}t}=[ AE_{E}-T_{2}(t)]v_{2}(t)-[AE_{E}-T_{1}(t)]v_{1}(t). \tag{18}\]  
The mechanical parameters of the printing subsystem are summarized in Table 1.  
The room temperature range of the workshop is usually between \(\sim\)10-30 \({}^{\circ}\)C, and the drying temperature range is usually from \(\sim\)120-150 \({}^{\circ}\)C. As the web material is Polyethylene terephthalate (PET), the relations between web temperature and the Young's modulus are shown in Table 2.  
The process parameters are as follows: the steady-state value of upstream web tension \(T_{1}^{*}=100\) N, the steady speeds of the printing rollers \(v_{1}^{*}=v_{2}^{*}=10\) m/min.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Values** & **Units** \\ \hline web length of a web span (\(L_{2}\)) & 9.1 & m \\ web length inside the drying device (\(L_{D2}\)) & 3.5 & m \\ web cross-sectional area (\(A\)) & \(1\times 10^{-4}\) & m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical Parameters of the Printing Subsystem.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Web Temperate (\({}^{\circ}\)C)** & **10** & **20** & **30** & **120** & **135** & **150** \\ \hline
**Young’s Modulus (10\({}^{9}\) Pa)** & 5.200 & 4.890 & 4.590 & 0.622 & 0.463 & 0.365 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Relations between Temperature and the Young’s modulus of Polyethylene terephthalate (PET).  
Figure 3: Gravure printed electronics experimental setup.