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

Abstract

Presented in this paper is a set of modern tools for the design of gearing: kinematic optimisation (minimisation and balancing of specific sliding), static stress analysis (to minimise stress concentrations) and crack propagation studies (to estimate fatigue life under a pre-existing defect). All three aspects are integrated in a software package developed by the authors. In particular, Boundary Element (BE) and Finite Element (FE) grids are automatically generated corresponding to gears manufactured by means of user defined tools with known shape and cutting parameters. BE models are used for a complete and automatic subcritical propagation analysis of cracks. FE models are used mostly for cases without crack propagation but requiring a greater versatility.
Tests conducted on cases found in the literature demonstrate the accuracy of the methods used and the effects of rack shift factors and of rim thickness are studied in example cases.
It is found that the fatigue life depends significantly on the cracking path mode, which in turn is particularly sensitive to the rim thickness in gears manufactured on thin hollow shafts as are typical in aeronautical applications. Further, the rack shift factors significantly change the stress concentrations (and therefore the maximum torque transmittable, in general in a beneficial manner). However, for designs with same concentration factor the fatigue life is considerably different, and in particular is lower on gears with a low number of teeth. This clearly indicates that the use of a complete crack propagation analysis from the early stages of the design process is highly recommended.

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