Real-time explicit co-simulation of wire-rope systems for industrial mobile harbor cranes

Abstract

This paper presents an investigation into the real-time explicit co-simulation of mobile harbor cranes under hoisting operation. The system is divided into two subsystems, with Subsystem 1 representing the payload and Subsystem 2 encompassing the wire-rope system. To capture the real-time behavior of the wire ropes accurately, the ALEM (Arbitrary Lagrangian–Eulerian Modal) method is employed in this study. Using this formulation, the intricate behavior of the wire ropes, encompassing elasticity, bending effects, and dynamic influences, is rigorously considered. The dynamic equations governing the payload are solved using the Runge–Kutta4 method, while the Generalized Alpha method is utilized to solve the wire-rope system. Both the Gauss–Seidel and Jacobi methods are investigated as two coupling techniques to connect the subsystems. Additionally, the study delves into the impact of the extrapolation method and macro time step on results accuracy and efficiency. The findings demonstrate that co-simulation employing the Gauss–Seidel method and FOH (First-Order Hold) extrapolation yields optimum and accurate simulations. Moreover, the study successfully achieves real-time simulation by optimizing the wire-rope system simulation, accounting for all degrees of freedom inherent in a 3D system. Remarkably, the maximum error observed in the axial force amounts to a mere 0.6% when employing real-time simulation. These findings can hold practical value for employing the current wire-rope subsystem in the interface modeling of real-world industrial cranes.