Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 245

Schönherr ( 2005 ) evaluated her test results by regression calculation. From this,
the ratio of the numbers of bending cycles with side deflection to those ropes
without side deflection is

w 0 : 00103 w 2 :

N w
N 0

¼ 1 0 : 00863 þ 0 : 00243 D
d

ð 3 : 60 Þ

The side deflection angle w has to be set in degree, all with a positive sign. That
means that the influence of the direction of the side deflection in relation to the lay
direction of the outside strands has not been considered in ( 3.60 ). As is to be seen
in Fig. 3.55 , this expected influence is very small and, generally speaking, even
undetectable. Neumann's ( 1987 ) bending cycles ratios N w /N 0 tend to be smaller
than those resulting from Schönherr's Eq. ( 3.60 ), but because of the relatively
large standard deviation s = 0.185, it lies in the confidence interval.
Equation ( 3.60 ) is valid under test conditions. However, there is no great error
to be expected if it is used for lang lay ropes, which were not tested, and the
discarding numbers of bending cycles.
Because of the friction force acting on the outside, the side deflection leads to a
turn of the rope depending on the torsion stiffness and the free length of the rope.
Neumann ( 1987 ) and Schönherr ( 2005 ) observed such rope turns. Oplatka ( 1990 )
demonstrated the rope turns in an impressive video.

3.2.3.10 Twisted Wire Ropes

Weber and Wehking ( 2013 ) have been made endurance bending tests with pieces
from one wire rope with fibre FC core, three with steel core IWRC and one spiral
round strand rope.The number of bending cycles will be reduced the more the rope
is twisted in turn off (positive) or loosening turn on (negative) direction, Weber
and Wehking ( 2013 ). In Fig. 3.56 the number of bending cycles N are shown for
one of the wire ropes with steel core twisted between x = ±1,080/100d. The
diameter related tensile force is S/d 2 = 117 or 195 N/mm 2 and the bending ratio is
D/d = 16 or 25.
All five wire ropes have been tested in the same way. From the numbers of
bending cycles the ratio between the twisted and the untwisted ropes can be derive.
That rotio can be used as a first endurance factor f N4 for the twist influence on the
number of bending cycles. The endurance factor is
lg f N4 ¼ lg N x

N ¼ a 1 x þ a 2 x 2

ð 3 : 60a Þ

The constants are listed in Table 3.15 .