Research On an Equivalent Continuous Contact Force Model for Oblique Impact Considering the Normal - Tangential Coupling Relationship

To address the challenge of characterizing the normal–tangential coupling relationship in dynamic oblique impact, a unified equivalent continuous contact force model incorporating hysteretic damping and microscopic slip behavior is established in this research. Based on the nonlinear spring–damper contact theory and Mindlin tangential contact mechanism, the coupled relationships between the normal and tangential contact forces in the stick and slip states are formulated through energy conservation and momentum theorems. By integrating the proposed oblique impact contact force model with a coefficient of restitution model dependent on the initial normal relative velocity, quantitative relationships are established between the tangential damping coefficient, tangential restitution coefficient, normal restitution coefficient, and tangential contact stiffness. As a key geometric parameter, the impact angle governs the contact state transition: at small angles, the contact tends to adhere with tangential energy dissipation dominated by material damping; as the angle increases, the contact shifts to sliding, where Coulomb friction governs the dissipation. The model effectively captures the strain rate and inertial effects in large-scale multibody systems with clearance under high impact velocities, simulates velocity-dependent energy dissipation and maintains high computational efficiency while accurately representing normal–tangential coupling and slip–adhesion transitions. The findings provide a theoretical foundation for elucidating failure mechanisms, such as jamming and microvibrations caused by dynamic coupling instability in sliding joint structure with clearance, and offer parameter tuning strategies for impact protection and energy management design in engineering applications.