Modeling and verification of an improved contact force in multibody systems

In many engineering applications, contact and collision phenomena are commonly observed in multibody systems, which can lead to issues such as dynamic output oscillations, reduced motion accuracy, decreased reliability and lifespan, and even functional failures in mechanical systems. To more accurately describe common collision phenomena and their impact on the dynamic characteristics of multibody systems, this paper introduces a contact force model with improved nonlinear stiffness and damping coefficients. This model is based on Hertz theory and considering the relationship between indentation and velocity during the collision process by incorporating a nonlinear index factor, m. Additionally, the Newton restitution coefficient is used as an evaluation criterion to verify the effectiveness of the improved model. Numerical analyses were conducted on single collisions between joints at different initial collision velocities and restitution coefficients, using both the proposed improved contact force model and existing classical models. Further numerical simulations of steel ball collisions were performed using the improved model, and the results were compared with experimental test data. Ultimately, the study results demonstrate that the improved contact force model is more accurate and effective than existing classical models under various restitution coefficients and collision velocity conditions, and has a wider range of applicability.