Modeling and Simulation of the Deflection of a Telescopic Rail with variable Extension Length

Lightweight robotic systems for logistics applications face significant positioning challenges due to structural compliance, with telescopic rail mechanisms presenting a particularly complex modeling problem because of traveling contact interfaces between sliding rail bodies. As the extension length varies during operation, the contact zones migrate along the rail segments, requiring dynamic contact modeling. These moving interfaces create configuration-dependent stiffness distributions and friction behaviors that static reduced models cannot capture, while high-fidelity finite element simulations of the full contact mechanics remain computationally prohibitive for tasks such as model-based control or parametric studies. The proposed method employs high-fidelity finite element (FE) models of the individual bodies and projects them into low-dimensional subspaces using model order reduction (MOR) techniques such as Krylov subspaces and modal reduction. These projection spaces form the basis for computing nonlinear reduced elastic bodies within the floating-frame-of-reference formulation, which offers advantages for industrial applications. The resulting nonlinear reduced-order models (ROMs) are coupled via penalty-based contact, where contact forces are evaluated through a master–slave node mapping that tracks the traveling contact zones across the full motion range. The resulting simulation model retains only the necessary degrees of freedom for real-time performance while maintaining sufficient accuracy for practical use. A comprehensive sensitivity study evaluates the influence of key parameters: (i) MOR technique, (ii) reduction order, (iii) penalty factor, and (iv) integration scheme. This allows quantification of the trade-offs between accuracy loss and computational speedup. The framework ultimately enables model-based feedforward control to improve trajectory tracking in compliant logistics robots for warehouse applications under real-time constraints.