Page 65 - Failure Analysis Case Studies II

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where C (the torque factor) and T (the torsional stiffness) are constants (in practice these are not
constants and the relationships are much more complex being highly non-linear as well as having
different slopes and significant hysteresis, consequently being affected by the amplitude of any
deformation). In this simplified form, both ‘constants’ are a function of rope diameter and
construction, C begin directly proportional to diameter and T increasing with the fourth power of
diameter for any given construction.
One example of the consequences of this type of behaviour is seen in the rotational deformation
of a rope in a very deep mine shaft where the maximum tension in the rope, at the shaft headframe,
derives from two components of similar magnitude: attached mass and rope mass. The result is a
linear fall in tension down the rope. With a rope that is not torque balanced, this would suggest a
similar gradient in torque, but that cannot be sustained so there is a counter rotation of the upper
part with respect to the bottom to provide a constant torque throughout the rope. In offshore
applications there is a need to understand such behaviour in order to anticipate when torsional
problems can arise.
A simple knowledge of torque factor (constant C in the expression above), which may be
supplied for different rope constructions by the rope manufacturer, only gives the torque generated
as a function of tension when the rope is in its manufactured state of twist and constrained from
rotation, and does not indicate torsional stiffness. A more informative way of looking at the
torsional characteristics of rope is to review the torsional stiffness as a function of tensile load,
state of rotation, and torsion amplitude. This kind of response has been modelled by Rebel [7]
who has measured torsional response in this way, as illustrated in Fig. 3, for fibre cored ropes with
six triangular strands, as used for mine hoisting in South Africa.
An alternative to Rebel’s highly complex model is another linear expression to characterise
torque/tension behaviour of six stranded rope, which has been developed by Feyrer and Schiffner
[4]. This is somewhat more sophisticated than the two term expression above, reflecting the changes
in torsional stiffness associated with changes in tension. In the expression:

d4
d4
M = ~1 Fd+ c2Fd2 - + c3Gd4 -
dz dz
where cl, c2 and c3 are constants, which have been determined for different rope constructions; d
is rope diameter; G is wire shear modulus; F and M are tension and torque respectively, as before.

5. Sensitivity of wire rope to torsional distortion

Whether a rope is torque balanced or not the manner of use can result in the imposition of
torsional distortion. Of course this is more likely for ropes that are not torque balanced, than those
which are, but torque balance is not a safeguard. In practice the feature common to most torque
balanced constructions of having concentric layers, whether of wires or strands, renders such ropes
very vulnerable to twist.
There are two classes of distortion damage that can result from twist being imposed on a rope: