Contact stress analysis of skew conical involute gear drives in approximate line contact Szu-Han Wu, Shyi-Jeng Tsai * Department of Mechanical Engineering, National Central University, Jhong-Li 32001, Taiwan article info Article history: Received 16 April 2008 Received in revised form 15 December 2008 Accepted 23 January 2009 Available online 3 March 2009 Keywords: Conical gears Approximate line contact Loaded tooth contact analysis Non-Herzian contact Tooth contact deformation Tooth bending deflection abstract An approach for loaded tooth contact analysis of skew conical gear drives in approximate line contact is proposed. The meshing analysis is based on the characteristic of the line of action of involute gearing. The contact problem is solved numerically giving due consider- ation to the influences of the tooth contact deformation and tooth bending deflection. The proposed approach is efficient and practical not only for cases of non-Hertzian contact, but also for gear drives with end-relieved or modified flanks. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Of all the different types of gears, conical gears as the special type of general spatial gearing makes them not only suitable for parallel axis transmission, but also to cases with intersecting or skew axes. Since Beam [1] first proposed the so-called ‘‘Bevloid gears”, many studies detailing their geometry, design, manufacturing and inspection have appeared [2–7]. How- ever, one of the weak spots of conical gears is less surface durability in spatial applications due to point contact problems, although transmission accuracy is not correspondingly sensitive to assembly error. There have been few studies dedicated to developing new concepts, design and analysis approaches to overcome this restriction on power transmission. A research team from the German ZF company came up with a novel conical gear drive design for high power transmission in which they applied flank modification [8,9]. Mitome proposed a new type of conical gear with a concave tooth surface designed to increase surface durability [10], and applied these concave conical gears for marine power transmission [11]. Li et al. [12] suggested a modification of the teeth of conical gears based on a mathematical model of the conjugate surface generated by a conical gear. All the studies discussed above were derived from the viewpoint of manufacturing. Tsai and Wu on the other hand worked from the viewpoint of design. They suggested two concepts to increase the surface durability of conical gears. Skew conical gear drives can be designed as gear pairs, with either approximate line contact, or profile-shifted transmission, or both. Tsai and Roth first developed the line contact conditions for skew conical gear drives [5,13]. However, such line contact gear drives are not really practical, because they are very sensitive to edge contact, and thus prone to assembly problems. Wu and Tsai proposed a design approach for a skew conical gear drive with point contact but having a larger major-to-minor- 0094-114X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2009.01.010 * Corresponding author. Tel.: +886 3 4267301; fax: +886 3 4254501. E-mail address: sjtsai@cc.ncu.edu.tw (S.-J. Tsai). Mechanism and Machine Theory 44 (2009) 1658–1676 Contents lists available at ScienceDirect Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmt