Stefan Kaczmarczyk

Transient vibration phenomena in deep mine hoisting cables. Part 1: Mathematical model

Abstract The classical moving co-ordinate frame approach and Hamiltons principle are employed to derive a distributed-parameter mathematical model to investigate the dynamic behaviour of deep mine hoisting cables. This model describes the coupled lateral–longitudinal dynamic response of the cables in terms of non–linear partial differential equations that accommodate the non-stationary nature of the system. Subsequently, the Rayleigh–Ritz procedure is applied to formulate a discrete mathematical model. Consequently, a system of non-linear non-stationary coupled second order ordinary differential equations arises to govern the temporal behaviour of the cable system. This discrete model with quadratic and cubic non-linear terms describes the modal interactions between lateral oscillations of the catenary cable and longitudinal oscillations of the vertical rope. It is shown that the response of the catenary–vertical rope system may feature a number of resonance phenomena, including external, parametric and autoparametric resonances. The parameters of a typical deep mine winder are used to identify the depth locations of the resonance regions during the ascending cycles with various winding velocities.

Transient vibration phenomena in deep mine hoisting cables. Part 2: Numerical simulation of the dynamic response

A simulation model is presented which investigates the dynamic response of a deep mine hoisting cable system during a winding cycle. The response, namely the lateral motions of the catenary cable and the longitudinal motion of the vertical rope with conveyance is observed on the fast time scale, and the slow time scale is introduced to monitor the variation of slowly varying parameters of the system. The cable equivalent proportional damping parameters, and periodic excitation functions resulting from the cross-over cable motion on the winder drum are identified. Subsequently, the model is solved numerically using parameters of a double-drum multi-rope system. Since the system eigenvalues are widely spread and the problem is of stiff nature, the numerical simulation is conducted using a stiff solver. The results of the simulation demonstrate various transient non-linear resonance phenomena arising in the system during the wind. The nominal ascending cycle simulation results reveal adverse dynamic behaviour of the catenary largely due to the autoparametric interactions between the in- and out-of-plane modes. Principal parametric resonances of the lateral modes also occur, and conditions for autoparametric interactions between the lateral and longitudinal modes arise. Additionally, a transition through a number of primary longitudinal resonances takes place during the wind. The adverse dynamic motions in the system promote large oscillations in the cable tension which must be considered significant with respect to fatigue of the cable. It is noted that a small change in the winding velocity may cause large changes in the dynamic response due to the resonance region shifts. Consequently, the resonance modal interactions can be avoided, to a large extent, if the winding velocity is increased to an appropriate level.

Vibrations of composite plates with SMA fibres in a gas stream with defects of the type of delamination

The dynamics of a multi-layer composite plate with delaminations subjected to an aerodynamic load is analysed. A finite element model to predict the dynamic response of the system with embedded shape memory alloys (SMA) fibres is proposed. The effect of delamination on the natural frequencies of the plate subjected to supersonic flow is studied, and the flutter instability boundaries are determined. The numerical model developed is applied to show that the SMA fibres can be applied to modify these boundaries. Thus, a SMA-based control system can be designed to reduce the adverse dynamic response of composite structures due to flutter phenomena.

Problem solving and creativity in engineering: conclusions of a three year project involving reusable learning objects and robots

Abstract The necessity for creative problem solving skills within the sciences and engineering are highlighted in benchmark and policy statements as essential abilities. None of these statements, however, offer any guidance on how these skills might be fostered, let alone assessed. This paper presents findings from the second cycle of an action research project to develop a dedicated creative problem solving module for first year engineering undergraduates. In the module problem based learning (PBL) techniques have been used with Lego Mindstorm NXT robots to develop creative problem solving skills. The focus of the module has been on developing process skills as opposed to the simple methodical solving of routine problems. Process skills have been introduced and mediated by the use of reusable learning objects (RLOs) within a virtual learning environment (VLE). Separate RLOs have also been used to develop skills in using the robots. The action research cycle has been informed by a parallel project involving interviews designed to explore the perceptions of students, academics and professional engineers of creative problem solving. Phenomenography has been used as the main research tool. Student feedback through online questionnaires, focus groups, classroom-based observation and interviews indicates that the module, and its means of delivery, has proven successful in improving creative problem solving skills. It also highlights the value of developing process skills within a practical and motivational environment.

The dynamic behaviour of a non-stationary elevator compensating rope system under harmonic and stochastic excitations

Moving slender elastic elements such as ropes, cables and belts are pivotal components of vertical transportation systems such as traction elevators. Their lengths vary within the host building structure during the elevator operation which results in the change of the mass and stiffness characteristics of the system. The structure of modern high-rise buildings is flexible and when subjected to loads due to strong winds and earthquakes it vibrates at low frequencies. The inertial load induced by the building motion excites the flexible components of the elevator system. The compensating ropes due to their lower tension are particularly affected and undergo large dynamic deformations. The paper focuses on the presentation of the non-stationary model of a building-compensating rope system and on the analysis to predict its dynamic response. The excitation mechanism is represented by a harmonic process and the results of computer simulations to predict transient resonance response are presented. The analysis of the simulation results leads to recommendations concerning the selection of the weight of the compensation assembly to minimize the effects of an adverse dynamic response of the system. The scenario when the excitation is represented as a narrow-band stochastic process with the state vector governed by stochastic equations is then discussed and the stochastic differential equations governing the second-order statistical moments of the state vector are developed.

Modelling, Simulation and Analysis Techniques in the Prediction of Non-Stationary Vibration Response of Hoist Ropes in Lift Systems

The paper presents the results of a study in which the non-stationary dynamic response of typical lift installations is investigated. A general approach to describe the dynamic behaviour of a vertical transport installation is presented. Subsequently, vibration models of a building elevator and a mine hoist installation are discussed. Perturbation and numerical techniques are discussed and applied to predict the non-stationary response of hoist ropes. It is shown that the method of multiple scales with non-linear scale as well as the method of characteristics can be employed to analyse a passage through resonance in a simple lift installation. Furthermore, the effectiveness of direct numerical integration of equations of motion is demonstrated in the case of a mine hoist installation.

The nonstationary, nonlinear dynamic interactions in slender continua deployed in high-rise vertical transportation systems in the modern built environment

This paper presents a nonlinear mathematical model and numerical results concerning the nonstationary lateral dynamic behaviour of long low tension slender continua deployed and moving at speed in high-rise vertical transportation systems installed in tall structures. The analysis presented in this study involves the identification of conditions for internal lateral resonances that can readily arise in the system when the slowly varying frequencies approach the fundamental or higher frequencies of the structure. The passage through the fundamental resonance leads to dangerously large displacements in the plane of the excitation. Due to the nonlinear (cubic) coupling, interactions between the in-plane modes and the out-of-plane modes occur. These interactions are studied numerically in order to predict and to examine the non-planar motions that may arise due to the autoparametric resonances. In order to suppress the internal resonance interactions higher speed levels and /or cable tension levels should be applied. Alternatively, an active tension control algorithm can be considered.

Modelling, Simulation and Experimental Validation of Nonlinear Dynamic Interactions in an Aramid Rope System

Vibration phenomena taking place in lifting and hoist installations may influence the dynamic performance of their components. For example, in an elevator system they may affect ride quality of a lift car. Lateral and longitudinal vibrations of suspension ropes and compensating cables may result in an adverse dynamic behaviour of the entire installation. Thus, there is a need to develop reliable mathematical and computer simulation models to predict the dynamic behaviour of suspension rope and compensating cable systems. The aim of this paper is to develop a model of an aramid suspension rope system in order to predict nonlinear modal interactions taking place in the installation. A laboratory model comprising an aramid suspension rope, a sheave/ pulley assembly and a rigid suspended mass has been studied. Experimental tests have been conducted to identify modal nonlinear couplings in the system. The dynamic behaviour of the model has been described by a set of nonlinear partial differential equations. The equations have been solved numerically. The numerical results have been validated by experimental tests. It has been shown that the nonlinear couplings may lead to adverse modal interactions in the system.

Nonlinear Sway and Active Stiffness Control of Long Moving Ropes in High-Rise Vertical Transportation Systems

In this paper a model to describe the lateral dynamic behaviour of long moving ropes employed in high-rise vertical transportation is developed. The model takes into account the fact that the longitudinal elastic stretching of the ropes is coupled with their transverse motions (sway) which results in cubic nonlinear terms. The governing non-stationary nonlinear equations are solved numerically to investigate the passage through resonance conditions arising during the system operation. The active stiffness control of transverse vibrations of the ropes is discussed. This involves the application of a longitudinal action at the rope end. The results of numerical simulation tests demonstrate the ability of multimodal active control to reduce non-linear low frequency sway of the ropes during and after the passage through resonance.

Non-Linear Modal Interactions in a Suspension Rope System with Time-Varying Length

This paper focuses on the investigation of the autoparametric coupling effects and modal interactions in a suspension rope system with a time varying length. Equations of motion of a multi-degree-of-freedom discrete, non-stationary and non-linear model are presented and are used to analyze the dynamic response of an elevator suspension rope system under resonance conditions. The equations of motion involve quadratic and cubic non-linear terms which are responsible for the modal interaction between the lateral and longitudinal oscillations of the rope and the car motions. The model takes into account the periodic excitations caused by motion of the host structure. The results confirm that adverse responses may arise and internal autoparametric resonance phenomena may occur.