ORIGINALARBEITEN/ORIGINALS DOI 10.1007/s10010-017-0233-1 Forsch Ingenieurwes (2017) 81:337–347 Theoretical investigations of the load distribution of small sized crown gear sets different material pairings Markus Baar 1 · Peter Oster 1 · Thomas Tobie 1 · Karsten Stahl 1 Received: 31 March 2017 © Springer-Verlag GmbH Deutschland 2017 Abstract An analytical approach for the calculation of the load distribution on the flank of crown gears, based on the theory according Placzek, is proposed. The teeth of the face gear and the pinion are divided into equidistant slices perpendicular to the normal plane, where the local forces, resulting from the acting torque, are calculated un- der consideration of the local deformation behavior of the gear system. By considering the geometrical conditions like radii of curvature, etc., the local Hertian stresses can be de- termined. Based on these considerations, the impact of the stiffness, the helix angle and the offset on the local force or load distribution is illustrated. Finally the lubricant film thickness is calculated by using the EHD-theory. Keywords Face gear · Crown gear · Contact pattern · Load distribution 1 Introduction For transformation of torque and speed along two crossing axes it is usually used a bevel- or worm-gear set. Due to The results shown in this paper are based on the research project “Tragfähigkeit Kronenradverzahnung” (AZ: 981-11) at the gear rechearch center (FZG) funded by the “Bayerische Forschungsstiftung” in collaboration with “ebm-Papst Zeitlauf antriebstechnik” (Lauf a. d. Pegnitz). The content of this paper accords to extractions of the dissertation “Kennwerte zur Tragfähigkeit kleinmoduliger Kronenradverzahnungen unterschiedlicher Werkstoffpaarung” (TU München, Baar).  Markus Baar markus.baar@mytum.de 1 Gear Research Centre (FZG), Munich, Germany the configuration, these types of gear sets show different disadvantages. Bevel gear sets for example need an exact adjustment of the axes to reach an optimized contact pat- tern. The geometry of the gear wheels leads to axial forces and linked to this to complex bearing constructions. The mesh of worm gear sets is afflicted with high sliding. In a first step this leads to a running in and linked to that to an optimized contact pattern under load, but in a second step it can cause increased wear and reduced efficiency up to self- locking. A rather unknown alternative angular gear set is a crown gear set, combining a cylindrical gear with a plane/face gear wheel. Different to bevel gears only the plane gear wheel has to be exactly adjusted for an optimized contact pattern; the axial position of the pinion has no influence on an exact meshing. In case of straight teeth there are no axial forces on the pinion (like a bevel gear pinion has); this allows simple bearing constructions. Crown gear sets show compact design in combination with high gear ratio and efficiency in one gear stage. This type of gear set can be used as alternative to common used bevel and worm gear sets and show high potential for innovative and efficient drive system and component solutions. Different to common and widely used cylindrical, bevel, hypoid or worm gear sets, there are no publicly and gener- ally verified guidelines or standards for the calculation of crown gears. Up to now the calculation for a crown gear set bases on experimental or FEM based in-house know-how of individual companies. Existing approximations for the calculation reduce the crown gear to a sum of infinitesimal meshes of a cylindrical pinion with a tooth rack varies pro- file angle along the tooth width or use modified equations for bevel gears. For this approach the special geometry of crown gears stays unconsidered. K