Numerical methods for the optimisation of specific sliding, stress concentration and fatigue life of gears

Presented in this paper is a set of modern tools for the design of gearing: kinematic optimisation (minimisation and balancing of specific sliding), s tatic stress analysis (to minimise stress concentrations) and crack propaga tion studies (to estimate fatigue life under a pre-existing defect). All th ree aspects are integrated in a software package developed by the authors. In particular, Boundary Element (BE) and Finite Element (FE) grids are auto matically generated corresponding to gears manufactured by means of user de fined tools with known shape and cutting parameters. BE models are used for a complete and automatic subcritical propagation analysis of cracks. FE mo dels are used mostly for cases without crack propagation but requiring a gr eater versatility. Tests conducted on cases found in the literature demonstrate the accuracy o f the methods used and the effects of rack shift factors and of rim thickne ss are studied in example cases. It is found that the fatigue life depends significantly on the cracking pat h mode, which in turn is particularly sensitive to the rim thickness in gea rs manufactured on thin hollow shafts as are typical in aeronautical applic ations. Further, the rack shift factors significantly change the stress con centrations (and therefore the maximum torque transmittable, in general in a beneficial manner). However, for designs with same concentration factor t he fatigue life is considerably different, and in particular is lower on ge ars with a low number of teeth. This clearly indicates that the use of a co mplete crack propagation analysis from the early stages of the design proce ss is highly recommended. (C) 1999 Elsevier Science Ltd. All rights reserve d.