Modelling and numerical simulation of vertical transportation systems

Dynamic phenomena such as transient and steady-state resonant vibrations in vertical transportation systems deployed in the modern built environment and underground mining applications affect the performance of the entire installation. In extreme high rise structures and deep underground mines traction drive elevator systems and drum-driven lifting installations employ long ropes and cables that exhibit low-frequency modes and nonlinear modal interactions. This results in the need to develop mathematical models in order to simulate their dynamic behaviour to predict and control their non-linear stationary and non-stationary dynamic responses; the coupled vibrations of a car/ conveyance and counterweight; as well as motions of other components present in the system, such as compensating sheave assemblies and diverter pulleys. The underlying causes of these dynamic responses / vibrations are varied. They include low frequency sway motions of the host structure induced by high winds and seismic activities, poorly aligned guide rail joints and guide rail imperfections, eccentric / out-of-balance pulleys and sheaves, systematic resonance in the electronic drive control system, motor torque ripple and aerodynamic effects that occur in the hoistway. Consequently, conditions for external, parametric and autoparametric resonances can readily arise during the operation of such installations. In this context, this paper will demonstrate a general approach to model the dynamic behaviour of typical vertical transportation and lifting installations. Subsequently, dynamic models and simulation techniques for the prediction of their non-stationary / nonlinear dynamic responses are discussed and the effectiveness of these techniques are demonstrated. Then, suitable strategies can be proposed to minimize the effects of adverse dynamic responses of the system so that the installation can operate under these conditions safely.