This work is a contribution to optimize the size of gears, by studying the variations of spur gear contact stress. The formulation is based on the virtual work principal and the classical contact law. Such contact problem is non-linear and is generally treated through the Newton-Raphson’s method, which is a robust method but nevertheless requires high computational resources. In this work and as an alternative the used methodology jointly applies the asymptotic numerical method and the finite element method that is a good compromise between efficiency and computational resources. It consists in rewriting the different dependent variables as an asymptotic development which transforms a non-linear problem into a succession of linear ones. The contact is formulated by Hertz theory which assimilate teeth contact to a contact between two cylinders; by applying the classical contact law we take into account the real geometry profile of the teeth.

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