## 2 Materials and Methods  
### Polymer Gears and Hybrid Polymer Gears  
This research involves the experimental investigation of polymer gears and hybrid polymer gears operating under different loads. The polymer gear and hybrid polymer gear hub geometry were defined, and a 3D CAD model was generated. Afterwards, gears were produced with the FDM method and tested on an in-house-developed test rig. A detailed description of the experimental setup and testing conditions is provided in the following section, and the implemented methodology is presented in Figure 1.  
Figure 1: Flowchart of the implemented methodology. A pair of spur gears with an involute gear geometry were designed to investigate their thermal behavior and wear. A three-dimensional computer-aided design (3D CAD) model of the gear was designed using Autodesk Inventor Professional 2025 software, and the specifications of the test gear parameters are presented in Table 1. A standard basic rack tooth profile [54] was used, and the gear teeth were designed without a profile shift, addendum or tip relief profile modification. The backlash required to allow for the thermal expansion of the gear teeth was achieved by reducing the tooth thickness. According to DIN 3967 [55], the prescribed tooth thickness tolerance was e28, with an upper tooth thickness allowance of \(-0.040\) mm and a lower tooth thickness allowance of \(-0.200\) mm. The normal backlash allowances were within the limits of 0.391 mm to 0.059 mm, and the circumferential backlash allowances were between 0.416 mm and 0.063 mm, with respect to the standard center distance deviation of \(\pm 0.023\) mm (with a tolerance zone js of 8) according to DIN 3964 [56]. The designed 3D CAD model of the gears with their associated geometry was subsequently converted into the appropriate format required for manufacturing the gear using the FDM method. The gears were initially connected to a hexagonal shaft with a main diameter of 17 mm, but, due to the heating and softening of the material, this connection was poor. The gears were eventually connected to the P4C 28 polygonal shaft with an outer diameter of 28 mm and inner diameter of 24 mm. The polygonal profile, the shape that provides the greatest torque transmission when compared to all of the other shaft connections, ensured that the gear hub would not be affected by the heating and the resulting softening of the polymer material. In this study, polymer gears and hybrid polymer gears have been investigated. Both the polymer gears and the hybrid polymer gears have the same tooth profile geometry, with a difference in the gear hub design. Compared to the polymer gears with a simple solid inner hub (Figure 2a), the hub of the hybrid polymer gears is more complex and has radial slots extending outwards from the central hub (Figure 2b). The slotted hub design enables the housing of metal inserts into the polymer matrix, which together form a hybrid polymer gear. The number of inserts corresponds to the number of teeth on the gear. Metal inserts were introduced to improve the heat transfer from the teeth to the gear hub, and also to the environment. In this study, metal inserts made of aluminum and steel were used. Alongside the thermal behavior, metal inserts with superior mechanical properties also improve the mechanical resistance and stiffness of the gears. Aluminum has the highest of thermal conductivity coefficients (237 W/m-K), followed by steel (41.8 W/m-K) and PA (0.25 W/m-K), for materials with a low thermal conductivity coefficient. Steel has the highest tensile (Young's) modulus of elasticity (206 GPa), about 3 times higher than aluminum (69 GPa) and about 100 times higher than PA (2 GPa). The radial slot in the hub has a matching geometry with a metal insert that has a rectangular plate-like shape with the following geometric characteristics: the thickness of the metal insert a, the width of the