Modélisation du contact avec microglissement dans les cannelures désalignées

Abstract

Spline couplings are widely used in industrial mechanical systems to transmit torque while allowing relative axial motion between the shaft and the hub. In service, angular or parallel misalignment between the axes is virtually unavoidable. Such misalignment concentrates the load at the ends of the engaged teeth, thereby accelerating surface degradation mechanisms such as fretting and wear. The conforming geometry of spline teeth makes Hertz contact theory unsuited to the prediction of the contact pressure, and although the finite element method remains the reference approach for such problems, its computational cost is prohibitive for parametric studies covering a large number of configurations. The objective of this work is to develop a fast and accurate numerical model for the prediction of the contact pressure distribution and the localization of fretting-prone regions in misaligned spline couplings. The proposed approach is based on a semi-analytical contact algorithm formulated on Boussinesq’s theory. This formulation is adapted to conforming contact through the introduction of a correction for the edge effects associated with the half-space assumption. Cerruti’s formulation is incorporated to account for the tangential friction tractions. The three sources of deformation contributing to the contact are modelled in parallel. A set of artificial neural networks, trained on a database of finite element simulations, is used in place of the direct evaluation of the tooth bending, torsion, shear and compression contributions, significantly reducing the computation time. The global torsion of the shaft and of the hub is treated through a classical beam-theory formulation. Fretting prediction is then obtained by applying an approximation of the Archard’s law locally, which provides a comparative map of the regions of the tooth most exposed under a given load. The validation of the algorithm is performed through comparison with two distinct cases from the literature. For each of these configurations, the algorithm successfully reproduces the essential features reported in the literature, thereby demonstrating its validity. Consequently, the developed tool provides a faster semi-analytical alternative to the finite element method for predicting the contact pressure and displacement fields, as well as for mapping fretting in misaligned spline couplings. Its computational efficiency makes it highly suitable for parametric sizing studies and the evaluation of various configurations.

Date	21 Jul 2026
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Raynald Guilbault (Supervisor) & Luc Amar (Co-supervisor)