This research analyses the mechanical behaviour of the insertion process between two cylinders that are commonly employed in non-rigid joints. Through comprehensive analysis, the study reveals the dynamics of insertion force, particularly by highlighting the impact of initial collisions on subsequent deformations and the ultimate evolution of insertion forces. Contrary to intuitive assumptions, our findings reveal that higher interference levels between cylinders do not uniformly correlate with increased maximum insertion force levels; instead, for certain cylinder combinations, higher interference generates lower maximum insertion force levels. Additionally, the significance of the thickness ratio as a pivotal determinant in predicting overall behaviour and insertion force, which is a variable that is often overlooked in conventional analyses, has been underscored. Furthermore, it has been demonstrated that the applicability of analytical equations that were developed as part of thick-walled cylinder theory diminishes when mechanical joints undergo plasticity, which underscores the need for alternative modelling approaches. Through finite element simulations, fidelity when representing insertion processes, with errors below 15%, not only capturing peak insertion forces but also delineating the nuanced evolution of forces and cylinder deformations, has been attained. Conversely, the analytical method employed from the examined literature yielded unrealistic insertion force estimations that proved inadequate for scenarios that involve substantial interference.
Llavori et al. (Sun,) studied this question.