Efficient Stick-Slip Friction Modeling for the Sliding Cable Systems Integrating ALE Formulation and Lugre Model

Sliding cables, characterized by their lightweight, high flexibility, high tensile strength, low damping, and capability to transmit loads through complex geometric paths over long distances, are extensively employed in diverse industrial applications. However, multibody dynamics analysis of sliding cable systems faces a challenge in balancing model accuracy and computational efficiency, caused by moving frictional contacts. Conventional simplified modeling approaches based on the Arbitrary Lagrangian-Eulerian (ALE) description, simplify frictional contact interactions to positional constraints. Then, cable motion is described as time-varying material coordinate and approximating friction via tension abatement, the stick slip effect is ignored. Addressing this limitation, this study proposes an enhanced dynamic mesh model within the ALE framework, integrating the LuGre friction model to explicitly capture presliding, stick-slip transitions, and Stribeck effects. By deriving a material-coordinate-based formulation of the LuGre friction force and its analytical Jacobian matrix, the method enables seamless incorporation into multibody dynamics equations while preserving the ALE framework's advantages in handling large displacements without remeshing. Numerical simulations of a cable-pulley transmission system validate the model's capability to accurately reproduce stick-slip behavior, demonstrating significant improvements over traditional tension-decay approximations. The proposed approach resolves abrupt friction transitions and enhances prediction accuracy for systems exhibiting intermittent stick-slip motion, yet maintains computational tractability through efficient Jacobian implementation. These advancements bridge a critical gap in sliding cable dynamics simulations, offering a robust tool for applications where friction-induced nonlinearities dominate, such as crane operations, robotic manipulators, and aerospace deployable mechanisms.