Multi-Stage Gearbox Transmission System and Design Variables

Gear trains are transmission systems generated by the serial connection of simple gear pairs. The architecture and the system's layout extremely influence the gear train's performance. However, even the macrogeometry of single gears plays a crucial role in power loss. For this reason, it is necessary to consider the geometrical entities of each stage gear at the optimization level.

According to ISO 21771 (Ref. 18), each involute spur gear is defined by its module, which represents one of the most essential parameters in gears. The tip and root diameters determine the shape of the involute tooth profile, hence the addendum and dedendum factors. Furthermore, the design pressure angle and the value of the manufacturing shift coefficient also influence the tooth profile. With the rise of electric vehicles, gearbox compactness has become increasingly important. Consequently, in the discussed algorithm implementation, the pitch diameters were selected as design variables to address spatial constraints explicitly and to facilitate the definition of domain boundaries. Thus, to uniquely determine the module for each gear stage, whether composed of two gears or including idlers, the number of teeth and the pitch diameter are specified for at least one gear per stage, especially where specific dimensional requirements are present. Moreover, to better accommodate dimensional constraints, instead of directly specifying internal gear ratios or the number of teeth for each gear, a variable is introduced representing the sum of the nominal center distances of the gearbox stages. By specifying the total gear ratio as part of the design input, this approach enables the algorithm to derive the key geometric and kinematic parameters for the remaining gears in the assembly, ensuring consistency with overall layout requirements.

Finally, for each gear, the pressure angles, profile factors, shift coefficients, and face widths are defined as design variables. Each of these design variables is subject to specific boundaries, which are established by design constraints or informed by the designer's expertise. A comprehensive list of all design variables considered is provided in the accompanying Table 1.