Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 261

Fig. 3.71 Number of wire
breaks B 360 and the maximum
number of wire breaks
B 22.5, max , Feyrer ( 1983c )

600

300

200

B 360

100

50

B 22.5

counted

30

20

B 22.5

10

calculated

from B 360

5

3

2

1

2x10 4 10 5

4x10 5 3456 2 3

number of bending cycles N

Gräbner ( 1968 ) found that the increase in the number of wire breaks could be
divided into three phases. In phase I, the total number or, out of this, a mean
number of wire breaks on a reference length L as a section of the rope bending
length l increases exponentially. In phase II, the increase in the number of wire
breaks is reduced. Then in phase III, the number of wire breaks increase again, but
progressively. The findings of bending fatigue tests with relatively large rope
bending lengths, Ren ( 1996 , 1998 ) have frequently confirmed this three-phase
model.
The same total number of wire breaks B 360 as in Fig. 3.70 for the bending
length l = 16 9 22.5 d = 360 d are now shown in Fig. 3.71 in a double logarithm
scaled diagram. Supplementary to this, the maximum numbers of wire breaks
counted B 22.5,max on a bending length L = 22.5 d have been introduced in
Fig. 3.71 . The increase in the maximum number of wire breaks is described very
well by a straight line in the diagram 3.68, that is, by the equation

B L ; max ¼ c 0 N c 1 : ð 3 : 76 Þ

In her bending fatigue tests with large bending lengths, Jahne ( 1992 ) confirmed
that the increase in the mean number of wire breaks in the first phase can normally
be described by ( 3.75 ) and the maximum number of wire breaks by ( 3.76 ).
In Fig. 3.71 , there is also a line going up in steps. This stepped line has been
calculated with ( 3.77 ) from the total number of wire breaks, respectively, the mean
number of wire breaks on a reference length. Equation ( 3.77 ) requires a Poisson
distribution for the wire breaks. Figure 3.71 shows that the maximum number of
wire breaks calculated in this manner comes very close to the findings of the
bending fatigue tests.