Minimizing tooth bending stress in spur gears with simplified shapes of fillet and tool shape determination

The strength of a gear is typically defined relative to durability (pitting) and load capacity (tooth-breakage). Tooth-breakage is controlled by the root shape and this gear part can be designed because there is no contact between gear pairs here. The shape of gears is generally defined by different standards, with the ISO standard probably being the most common one. Gears are manufactured using two principally different tools: rack tools and gear tools. In this work, the bending stress of involute teeth is minimized by shape optimization made directly on the final gear. This optimized shape is then used to find the cutting tool (the gear envelope) that can create this optimized gear shape.A simple but sufficiently flexible root parameterization is applied and emphasis is put on the importance of separating the shape parameterization from the finite element analysis of stresses. Large improvements in the stress level are found.