A mathematical approach regarding a better geometry of the root fillet of symmetric and asymmetric gears with the main scope of increasing the fatigue strength of gear teeth and avoiding the occurrence of cracks

The main topic of the present paper consists of two main ideas: on one side, there is presented a mathematical approach on fatigue strength of a gear tooth and, on the other side, there is applied this mathematical approach on a particular case regarding a better fillet geometry of symmetric and asymmetric gears. In this mathematical approach, there is illustrated the planar curves theory and their planar contact. Then, there will be presented some theory regarding the gear failure and the appearance of cracks that generates tooth base fatigue. In the end, there will be presented some graphical results using Matlab programming language.