A Thesis Submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, South Africa for the Degree of Doctor of Philosophy. / The dynamic analysis of catenary vibration of mine hoist ropes on South African mines is examined. This research has been preceded by studies in the mining industry, which have laid the foundation fot the definition of design guidelines of hoist systems to avoid catenary vibrations or rope whip. These guidelines are based on a classical linear analysis of a taut string, and in essence rely on ensuring that the frequency of excitation at the winder drum due to the coilingmechanism, does not coincide with the linear transverse natural frequency of the taut catenary. Such an approach neglects the nonlinear coupling between the lateral catenary motion and the longitudinal systern response. Although previous research sug gested the possibility of autoparametric coupling between the catenary and vertical rope, this was not developed further on a theoretical level.. The possibility of such behaviour is defined by considering the equations of motion of the coupled system. A design methodology is developed for determining the parameters of a mine hoist systern so as to avoid rope whip. The methodology accounts for the nonlinear coupling between the catenary and longitudinal system. In order to implement the proposed methodology, two phases of the analysis are developed. In the first phase the stability of the linear steady state motion is examined in the context of the nonlinear equations of motion, by applying a harmonic balance method. The stability analysis defines regions of secondary resonance, where it is shown that such regions may arise at sum and difference combinations of the linear lateral and longitudinal natural frequencies due to autoparametric excitation. Prior to this research, this phenomenon had not been appreciated in the context of the mine hoist system. A laboratory experiment was conducted to confirm the existence of these regions experimentally. In reality, the system is non-stationary since the dynamic characteristics of the system change during the winding cycle, and hence the steady state stability analysis can only describe potential regions of nonlinear interaction on a qualitative basis. The second phase of the analysis deals with a non-linear numerical simulation of the hoist system, which accounts for the non-stationary nature of the systems dynamic characteristics, and includes transient excitations induced during the wind. The methodology developed is assessed by considering the Kloof mine rope system, where rope whip was observed. This study demonstrates that although an appreciation of the steady state system characteristics is useful, the stability analysis alone is not sufficient. It is necessary to account for the non-stationary aspects of the winding cycle if a realistic interpretation of the observed behavlcur is to be achieved. To compliment this study, a motion analysis system was developed to record catenary response on an existing mine hoist installation. Such data has not been recorded before. This data provides direct evidence of the autoparametric nature of the coupled catenary/vertical rope system. / AC2017

A dissertation submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Master of Science in Engineering / It has been said that experimental modal analysis (EMA) "grew to prominence because the engineering community was incapable of properly analyzing the dynamics of commercially significant structures" [24]. The advent of powerful theoretical methods, such as the Finite Element Method (FEM) has not, however, resulted in the demise of EMA. In fact both FEM and EMA have undergone rapid growth and the merging of the two into an effective design and diagnostic tool has had a major impact on the engineering community's approach to dynamics related problems. In this study, the term dual has no mathematical connotations and is used to describe the complementary use of the techniques of EMA and FEM. The mining industry, worldwide, has experienced dynamics related problems in the operation of conveyances in vertical shafts. A study undertaken in South Africa investigated the behaviour of shaft steelwork and skips, resulting in a set of design guidelines for future shaft steelwork designs. This work only investigated the dynamic behaviour of skips. In this project, the ABAQUS and MODEL SOLUTION FEM codes were used to construct models of a. mine cage. An impact modal test was carried ant on the cage, using a GenRad 2515 CAT system, An impact hammer, suitable for exciting large structures, and a strain gauge force transducer were designed and built for the purpose of the test. The natural frequencies and mode shapes obtained from both FEM and EMA are compared by means of the modal assurance criterion (MAC). The test data is used to tune the model to produce accurate results. The model Could then be used (with minimal further test work) for predicting the response of the structure to dynamic loading or the effects of structural modifications. / Andrew Chakane 2020