A Set-valued Impact Law Approach for Modeling and Analysis of Rigid Contact Universal Joint with Clearance

Abstract

This study presents a dynamic model of a universal joint (U-Joint) with radial clearance, focusing on the rigid unilateral frictional contacts at the crosspiece and yoke interfaces. Unlike previous models that neglect crosspiece inertia and interface friction, this work incorporates these effects using a set-valued impact law based on Signorini's condition with Coulomb friction, capturing the complex non-smooth dynamics introduced by radial clearance. Numerical simulations of a 2 degrees-of-freedom (DOF) shaft system reveal the critical influence of clearance on U-Joint dynamic behavior, including impact-induced oscillations, quasi-periodic motion, and chaotic dynamics, which are essential for accurate driveline modeling and real-time control in automotive, aerospace, and precision medical applications.