Abstract: Background Worm gear sets are used in many applications of the transmission field. These mechanisms have interesting advantages. Despite this, its modelization is still challenging. This is due to its complex geometry. The goal behind this is to have an accurate model that allows improvement of the design of worm gear sets. Purpose In this context, the paper presents a new mathematical model of a worm gear drive under rotational external excitations. Methods Dynamic model is defined by fourteen degrees of freedom describing all rotations and translations of worm gear set, AQ1 bearings, a motor and a receiver connected together. First, equations of motion are developed to describe the dynamic behavior. Lagrange formula is, thus, employed. Elastic deformations of meshed teeth are considered. The normal load associated with the meshing is established as function of the model degrees of freedom through the elastic deflection. Second, a numerical simulation is carried out. Newmark Beta method is used to solve equations. Results Numerical results are presented to discuss the model accuracy. The impact of the variation of friction coefficient and the stiffness of the worm gear is finally studied to discuss the consistency of the new formulation developed through this work.

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