Bending of helically twisted cables under variable ... - Pfisterer

As As is well well known known from earlier observations observations [EPRI, 1979], and and also also intuitive, intuitive, the wires in a cable beg begin to
move on their underlying layer when a certain curvature is exceeded - Fig. 2.8.:
Fig. 2.8 Wire displacement during bending
The position on the cable cross-section section where the displacement starts starts and the affected length of of the
specific wire depend on whether the secondary stress in the non-displaced displaced wire, as calculated in (2.22),
exceeds the maximum value that can be resisted by friction (2.17).
By equating the abovementioned equations (2.17) and (2.22) for ϕ → π/2 /2 and solving for the curvature,
we find:
Thus σzus,L (2.22) > σzus,L (2.17), which is valid also for all wires of the considered cross
therefore therefore assumed that that the the specific specific individual individual wire wire will slide over its entire length length once this this “final”
“final”
curvature is exceeded.
The displacement starts at position ϕϕ,
, however, where the slope of (2.22) exceeds the slope of (2.17) for
the the first time, Fig. 2.9. As As shown shown earlier earlier [Leider, [Leider, 1973], this this is the case almost almost exactly where ϕ = 0, (also
see Fig. 2.7). The curvature associated with the start of slipping is:
With With partial partial slippage slippage therefore, the secondary stress stress in in a a wire wire is is governed in sections by the two curves
of of equation equation (2.17) (2.17) and and (2.22), (2.22), Fig. 2.9. 2.9. The bending bending region region where both stress conditions “coexist” along
the wire is called the transition region. This region will be dealt with later.
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(2.17), which is valid also for all wires of the considered cross-section. It is