Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 290

firstly the number of simple bending cycles with the endurance factor f N to
on that the calculation of the number of reverse bending cycles is based
according Eq. ( 3.89 ). However there are no test results to defend this idea of the
1.edition.

3.4.3.3 Reverse Bending

Following ( 3.61 ) from Sect. 3.2.4 , the number of reverse bending cycles can be
calculated from the number of simple bending cycles with the equation

ð 3 : 89 Þ

The constants a i are listed in Table 3.16 . If the two related Sheave diameters are
not the same, a substitute diameter D m can be used

D m ¼ 2 D 1 D 2
D 1 þ D 2

: ð 3 : 90 Þ

and for different grooves the substitute endurance factor is

f N3m ¼ 2 f N3 ; 1 f N3 ; 2
f N3 ; 1 þ f N3 ; 2

: ð 3 : 91 Þ

By definition, reverse bending means that the axes of the two sheaves involved
are parallel. Up to now, there are no known fatigue tests for wire ropes running
over sheaves where the axes are not parallel. For cases where the sheave axes are
not parallel, the definition from DIN 15020 can be used, Fig. 3.83 .
If there are greater distances between the sheaves, the wire rope can be
turned—especially in the case of side deflection—so that reverse bending can
probably be avoided. Beck and Briem ( 1993 ) found a rope turn of 50 for War-
rington ropes with fibre cores in an elevator with a sheave distance of 165 d. In
current rope endurance calculations it is not possible to assume such a rope turn.

3.4.4 Palmgren-Miner Rule

3.4.4.1 Loading Sequence

With the help of the cumulative damage hypothesis of Palmgren ( 1924 ) and Miner
( 1945 ), it is possible to evaluate the number of working cycles (number of loading
sequences) F. The basic equation (Sect. 3.2.6 )is