Optimization of asymmetric tooth root generated with protuberance hob

The Direct Gear Design method optimizes various parameters and elements of gear tooth geometry to achieve the required gear drive performance. One such critical element of the tooth profile is the root fillet. Previous publications had considered asymmetric tooth root fillet optimization assuming that the tooth involute flanks and root fillets are processed (machined) simultaneously. However, there are many applications that require high gear tooth flank accuracy and high load capacity in combination with minimized gear production cost. In order to satisfy these requirements, the tooth involute flanks and root fillets are processed separately. A gear blank is machined by a topping protuberance hob that finalizes the root fillet, tooth tip diameter and chamfers, leaving stock for the tooth flank grinding. Then, after the gear’s heat treatment (carburizing + case hardening) and in some cases shot peening of the tooth root, the tooth flanks are processed using highly productive generating grinding, removing the grinding stock. As a result, the full residual stress developed by case hardening is retained. This fabrication sequence is most typical for automotive transmission gears.

Since the tooth root load capacity is a major contributor to gear transmission performance, reducing the tooth bending stress concentration for asymmetric gears generated with a protuberance hob is critically important.

The paper demonstrates the construction and optimization of the tooth root fillet while leaving required grinding stock on the involute tooth flanks. It describes a reversed generation of the protuberance hob tooth profile by the completely defined gear tooth profile, which includes the optimized root fillet and grinding stock on the tooth flanks. It also considers the limitations of protuberance hob tooth root generation for asymmetric gears with low numbers of teeth.

The paper presents a numerical comparison of the tooth root stresses for the trochoidal root fillet generated by the full radius protuberance hob tooth tip and the optimized root fillet produced by the protuberance hob with the tooth tip reverse-generated from this optimized root fillet.

The substantial tooth root stress reduction that can be achieved by optimizing asymmetric tooth roots generated with a protuberance hob makes asymmetric gears highly attractive for automotive transmissions.