Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 149

open spiral ropes having larger diameters. The wire ropes have different numbers
of wires. The wire ropes with the diameters d = 40 mm and 127 mm have the
biggest number of wires with the construction 1 + 7 + 7/7 + 14 + 19 + 25 +
31 + 42 + 48 + 49 = 292, Casey ( 1993 ).
The constants a i and other results of the regression calculation for these spiral
ropes are listed in Table 2.8 . The results of Casey, and Paton and others are used
for the regression again up to the number of load cycles N B 1.75 9 10 6 . The
lower specific force is at maximum S lower /d 2 = 84 N/mm 2 . Therefore, with the
constants a i of these wire ropes, ( 2.102 ) is only valid up to this lower specific
force.
A common regression calculation has been carried out using the results of
Wehking and Klöpfer, Casey, and Paton and others. Because of the very different
numbers of wires z, the regression equation has been—compared with Feyrer
( 2003 )—complemented here by the number of wires z.

2

lg N ¼ a 0 þ a 1 lg 2 S a d e
d 2

þ a 2 S lower d e
d 2

S lower d e
d 2

þ a 3

S e S e S e

ð 2 : 102a Þ

d
d e

þ a 4 lg þ a 5 lg z :

The constants a i from the common regression are also listed in Table 2.8 .
According to the ropes used, the mean number of load cycles is given with these
constants and ( 2.102a ) for open spiral ropes with the diameter d = 4-127 mm and
with the number of wires z = 37-292. The standard deviation is lg s = 0.214.
Using the constants k T10 = 1.69 respectively k T1 = 2.93, with a certainty of 95 %
at the most 10 % respectively 1 % of the wire ropes are broken at the number of
load cycles

N 10 ¼ 0 : 435 N respectively N 1 ¼ 0 : 236 N :

For open spiral ropes, the relation between the wire rope stress and the specific
force is about

r z ¼ 1 : 70 S

d 2 :

With an increasing rope diameter, the endurance decreases. On the other hand
the endurance increases with the number of wires. Thereby the influence of the
rope diameter predominates. In the range tested, the number of load cycles
decreases with the rope diameter exponent a 4 = -0.793 and increases with the
number of wires exponent a 5 = 0.399. All the spiral ropes tested were zinc coated
and lubricated. It is not possible to evaluate the influence of the nominal strength
on the rope endurance from the existing database. The constants in Table 2.8 are
therefore valid for wire ropes with a nominal strength between 1,370 and 1,770 N/
mm 2 .