| Summary: | 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
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