In recent years, topological optimization has become a powerful tool for designers and engineers in the technical world. The principle of this method is based on optimizing a given optimization region by minimizing or maximizing one or more objective functions, e.g. stiffness, mass, or natural frequency of the structure. For this reason, software companies developing CAD or FEM software have included topological optimization in their portfolio, either as a modular part of the software or as a dedicated program. In general, users of these programs do not have a mathematical definition of the software background, and it is not clear what variations in calculations may occur when using different software. For this reason, a comparative analysis of the selected software was performed to determine the differences between the results assuming the same boundary conditions and machine parts such as computing time, weight and volume.

In this paper, root stress, manufacturing possibilities and limitations of standard and nonstandard tooth root fillet of spur gears are examined. Nowadays, standard trochoidal root fillet is used the most as an economical trade-off between tooth strength and manufacturing complexity. A disadvantage of the trochoidal root fillet, especially in spur gears with less than 17 teeth, is undercutting which minimises strength of tooth root, introduces stress concentration, and deteriorates meshing conditions. This study focuses on different root designs, namely elliptical and novel cycloidal root fillets. Root stress in gears with different root designs is analysed by FEM and compared with analytical equations according to ISO. The possibility of producing nonstandard root fillet gears by hobbing and limitations of surface finishing are considered as well. Analysis reveals stress differences between each of the root fillet shapes and their relative advantages and disadvantages.