Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 250

The middle stresses r mB and r m, comb are not very different and do not have any
great influence on the endurance of the rope. The main influence on rope endur-
ance under combined loading is rather the ratio of the stress amplitudes r a,comb /
r aB . The factor f S5 is therefore based on this ratio supplemented by correcting
factor k S . This correcting factor k S will be found by comparing bending fatigue
tests. With it, the equivalent force factor is
f S5 ¼ 1 þ k S 1 : 1 Dr z 0 : 1 r z
2 r aB

: ð 3 : 67 Þ

Bending fatigue tests have been carried out on two wire ropes, Filler 8 9 19 -
SFC - sZ and Warrington 8 9 19 - IWRC - sZ. The diameter ratios of sheave
and rope were D/d = 12.5, 25 and 63. In one type of test, the wire rope was bent,
stressed with tensile force S, and reduced by DS before and after bending. In the
other type of test constant tensile forces (forces S equ ) were used. Correcting factor
k S was found by comparing tensile forces S and DS, respectively, S equ and for this
the number of bending cycles was the same in the two types of tests. The mean of
the correcting factors found—valid for both the breaking and discarding number of
bending cycles—has been found by regression calculation to be
k S ¼ 1 : 31 0 : 0014 Dr z :

ð 3 : 68 Þ

At s = 0.19, the standard deviation for the correcting factor is relatively large.
In the regression calculation, some comparative tests carried out by DEMAG and
the R: STAHL with Warr.-Seale ropes in their rope hoists have also been included.
Dudde ( 1991 ) found that the equation can also be used for lang lay ropes for the
breaking number of bending cycles.
With ( 3.63 ), ( 3.65 ), ( 3.67 ) and ( 3.68 ) and the relation r z = aS/d 2 , the equiv-
alent force factor is

a

1 : 31 0 : 0014 a DS
d 2

1 : 1 DS

d 2 0 : 1 S d 2

f S5 ¼ 1 þ :

145 ; 000 d

d d D þ 600 d d þ 0 : 2 a S

d 2

The constants for ( 3.69 ) are listed in Table 3.13 (Sect. 3.4.2 ).
An alternative method of evaluating the number of bending cycles under
combined tension and bending based on an equivalent diameter ratio (D/d) equ
instead of an equivalent tensile force is described in Feyrer ( 1993 ). However, this
method does not provide a better result.