Abstract
This article proposes a universal procedure for efficiently modelling the flexible behaviour of pre-stressed cables, guided by multiple pulleys. Such cable-pulley systems usually connect various structural components, which often feature additional flexibility. One concern in holistic system analyses is to correctly describe the elasticity of the entire assembly for one particular spatial configuration. This can be achieved in terms of a linear stiffness matrix that accounts for the kinematics of the assembly. In this article, parametric stiffness matrices for arbitrary cable-pulley arrangements are derived. A reduction scheme is used to facilitate the integration of the derived stiffness matrix into superordinate finite element models. The method is validated with a non-linear finite element model and applied to a complex hoisting cable system connecting multiple large steel structures.
Highlights
Cables, especially those made from twisted or braided steel wire and referred to as wire rope, are basic mechanical elements of great significance in material handling tech- KForsch Ingenieurwes (2021) 85:67–75 lization of smaller drives and cables of reduced diameter
The stiffness between arbitrary points of the cable system is no longer exclusively depending on the stiffness of the individual segments
If cables modelled by means of finite elements are undergoing large deflection in multi-body simulations, the absolute nodal coordinate formulation (ANCF) provides a suitable method to include the non-linear dynamical behaviour
Summary
Especially those made from twisted or braided steel wire and referred to as wire rope, are basic mechanical elements of great significance in material handling tech-. If cables modelled by means of finite elements are undergoing large deflection in multi-body simulations, the absolute nodal coordinate formulation (ANCF) provides a suitable method to include the non-linear dynamical behaviour. A cable-system model derived using the introduced method allows to couple multiple compliant structural components in holistic simulations, focussing on the static and lower frequency dynamic behaviour of the entire system. The initially introduced coordinates, which describe the sheaves’ rotations, are eliminated by means of a reduction scheme, leading to a reduced order stiffness matrix As this reduced matrix does only contain the translational degrees of freedom associated with the attachment points, integration in finite element software is facilitated. As the presented holistic simulation model sufficiently describes the dynamics in the frequency range of interest, control strategies for the active suppression of unwanted vibrations during normal operation can be analysed and evaluated in future work
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