## 2 Materials and Methods
### Polymer Gears and Hybrid Polymer Gears
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Pinion and Wheel** \\ \hline Module, m [mm] & 3 \\ Number of teeth, z & 26 \\ Pressure angle, \(\alpha\) [deg] & 20 \\ Pitch diameter, d [mm] & 78 \\ Outside diameter, d\({}_{\alpha}\) [mm] & 84 \\ Root diameter, d\({}_{\alpha}\) [mm] & 70.5 \\ Center distance, a [mm] & 78 \\ Contact ratio, \(\epsilon\)\({}_{\alpha}\) & 1.621 \\ Base tangent length over 4 teeth, W\({}_{4}\) [mm] & \(32.09^{-0.04}_{-0.19}\) \\ Thinning for backlash, \(f_{\alpha}\) [mm] & 0.120 \\ Normal backlash, j\({}_{\alpha}\) [mm] & 0.240 \\ Material & PA \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the test gear. metal insert b, the length of the metal insert c and the distance of the metal insert from the top of the tooth x. Four different hybrid polymer gear hub designs were investigated in this study. Figure 3 shows a single tooth with the parameters specified for each of the four designs of the hybrid polymer gear hub. For all four hub designs, the insert thickness a and the insert width b have fixed values. The width of the insert b is identical to the width of the gear, 12 mm for the pinion and 10 mm for the wheel, respectively. The remaining parameters are represented in relation to the module m, a standard parameter used to designate the size of the gears. The thickness of the insert is a = m/3 = 1 mm and has the same value for all hub designs. The length of the insert in the first hub design (Figure 3a) is c\({}_{1}\) = 8\(\cdot\)m = 24 mm, and the distance of the insert from the tooth tip is x\({}_{1}\) = m = 3 mm; in the second hub design (Figure 3b), the length of the insert is c\({}_{2}\) = 4\(\cdot\)m = 12 mm, with the same distance from the tooth tip as for the first hub design, x\({}_{2}\) = m = 3 mm. The length of the metal insert for the third hub design (Figure 3c) is the same as in the second hub design, c\({}_{3}\) = 4\(\cdot\)m = 12 mm, and the distance of the insert from the tooth tip is x\({}_{3}\) = 3\(\cdot\)m = 9 mm. For the first three hub designs, the heat is mainly transferred from the gear teeth to the shaft by thermal conduction, whereby the surface area that transfers heat to the environment by convection or thermal radiation is expected to be negligibly small. The fourth hub design (Figure 3d) has the same geometric characteristics as the third design (c\({}_{4}\) = 4\(\cdot\)m = 12 mm; x\({}_{4}\) = 3\(\cdot\)m = 9 mm), but also has a thin rim with a depth of t = m = 3 mm, which enables greater heat exchange by  
Figure 3: Geometric characteristics: (**a**) first, (**b**) second, (**c**) third and (**d**) fourth polymer gear hubs. Figure 2: (**a**) Schematic view of the polymer gear hub and (**b**) the hybrid polymer gear hub. convection and thermal radiation. The hub design with a thin rim was built asymmetrically so that the rim with the full depth t was located only on one side of the gear. All of the inserts, whether made of aluminum or steel, were manufactured from sheet metal by laser cutting. The surfaces of the metal inserts are flat, smooth, oxide-free and press-fitted into the polymer matrix to allow for good contact between the two solids. This eliminates all of the gaps between the insert and the polymer matrix caused by surface roughness or the waviness of the contacting surfaces.