Duchemin, M., Tugui, C., and Collee, V., "Optimization of Contact Profiles using Super-Ellipse," SAE Int. J. Mater. Manf. 10(2):2017.
In many rolling or sliding contact mechanisms, like roller bearings, journal bearings, gearings or any contact between two semi-infinite bodies, concentrated stress occurs at the edges of the contact. This stress, due to what is called edge effect, is known to be very fatigue damaging. To avoid this concentrated stress in common roller bearings, the rolling surface of the roller and/or of the track is crowned. The crowning shapes usually include a straight line and one or several circular arcs. Even if such crowning profiles are efficient in avoiding edge effects, they are far from being optimized in terms of contact pressure distribution. In recent years, crowning shapes based on a logarithmic function developed by Lundberg have been improved and optimized for the purpose of industrialization. However, the resulting profiles are fairly complex and have only been developed for roller bearings and not for other types of rolling or sliding contacts. This paper presents a new profile type based on a super-ellipse equation (ellipse generalized to the order n). With this profile, it is quite straightforward to set parameters according to the intended application. It can be simply adapted to all kinds of contact by modifying the order of the super-elliptic profile. The benefits of the super-elliptic profile are an even contact pressure distribution and no edge effect, while it remains easy to manufacture. Several practical applications are presented, all of them related to the VCRi variable compression ratio technology developed by MCE-5 DEVELOPMENT. This technology features a wide range of contact mechanisms of various shapes, either sliding (side-pusher contact, journal bearings), rolling (synchronized roller contact), or both rolling and sliding (gear mesh contact).