Wire Ropes, Elements and Definitions - Wire Ropes: Tension, Endurance, Reliability - page 18

Fig. 1.13 Number of
bending cycles of a wire with
different bending lengths,
Feyrer ( 1981 )

10 5

S=175 N

steel wire
ʴ =0.75 mm

N 90

7 D

˃ B =1570 N/mm 2

D=115.75 mm
r=2.6 mm

5
4
3

-

N 10

2

l 0.9 =0

10 4
0.01 0.02

0.05 0.1
bending length l

0.2 0.5 1.0m 2.0

90 % of the total one. The curves in Fig. 1.13 are calculated using standard
deviation lg s = 0.086 of the logarithm normal distribution derived from the 13
bending cycles found for the wire bending length l 0 = 2 9 96 mm. More infor-
mation on this method of calculation is presented for wire ropes in Sect. 3.2.2
where the influence of the bending length is of practical interest.
In principle, the findings of Luo's ( 2002 ) tensile fatigue tests produced the same
result. For his tests with different stressing lengths, he used a wire with diameter
d = 2 mm, made of material X5CrNi18-10, No. 4301 and having tensile strength
R m = 840 N/mm 2 . He did 60 tensile fatigue tests for each of the wire lengths
l = 25, 125 and 250 mm with the middle stress r t,m = 356.5 N/mm 2 and the
stress amplitude r t,a = ± 290 N/mm 2 only a little above the infinite tensile fati-
gue strength. For the short wire length of 25 mm there are five run-outs with more
than N = 2 9 10 6 . For the wire length l = 250 mm, the param et ers for the log-
arithm normal distribution are the mean number of tensile cycles N ¼ 238,000 and
the standard deviation lg s = 0.136.

1.1.6.5 Infinite Wire Endurance

The fatigue strengths (infinite life fatigue strengths) have been evaluated using
Wöhler-diagrams. As before, the fatigue strengths are characterized by indices in
capital letters and the stresses by indices with small letters.
For his tensile fatigue tests, Unterberg ( 1967 ) used short wire pieces with a
length between 15 and 35 mm so that he could start—without the risk of buck-
ling—with the middle stress r m = 0. The test results are shown in Fig. 1.14 . The
mean relative tensile strength amplitude is

¼ 0 : 313 R m 0 : 249 r t ; m

r t ; A R 0 ¼ 1,770; d ¼ 2 : 7 ð 1 : 3 Þ

and related to the lower stress r t,lower