Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 226

with d in mm. For this equation the graph is drawn in Fig. 3.39 . An approximate
equation in the former manner is with an exponent of nearly double size

0 : 63

d
16

f d : ð 3 : 52c Þ

For small rope diameters for d = 2 mm and a little for d = 4 mm, the endurance
factor depends on the endurance level and shows a big scatter. Therefore the
Eqs. ( 3.52b ) and ( 3.52c ) should be only used for diameters d C 6mm.

3.2.2.4 Bending Length, Size Effect

Müller (1961) was the first to carry out a number of bending fatigue tests on a wire
rope with different bending length. He found that the number of bending cycles
N decreases up to the bending length l =8d and remains more or less constant for
greater bending lengths. However as can be seen in Fig. 3.40 , numerous bending tests
up to a bending length l = 1,000d show that the number of bending cycles decreases
permanantly with the ben di ng length. In Fig. 3.40 , curves are drawn for the mean
number of bending cycles N and for the number of bending cycles N 10 and N 90 as the
limit for 10 % of the number of bending cycles being smaller respectively greater.
The curves are calculated from the 13 numbers of bending cycles for the bending
length l =45d using the method described in the following Fig. 3.40 .

10 5

S = 23,4KN

Seale 8 × 19 − FNC − sZ

7 N 90

R 0 = 1370 N/mm 2

D

_

D/d = 25, r = 0.53 d
steel, hardened
lubricated with mineral oil
visc. 1370 - 1520 mm 2 /s, 40 ° C

5 N

4

N 10

3

2

l 0.9 =0

10 4

1000

2 45 7 10 20 30

bending length l/d

50 100 200 500

Fig. 3.40 Number of bending cycles for different rope bending lengths, Feyrer (1981)