Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 308

(Because of the large numbers of simple bending cycles, the synthetic material
of the groove of the traction sheave does not exert any influence on the endurance
of the rope.).
Number of working cycles:
According the Palmgren-Miner Eq. ( 3.92 ) the 10 %-limit and the mean number
of working cycles (The small influence of the endurance factor f N4 = 0, 984 for
the loss by the rope twist angle x = -284/100d from Table 3.15 is considered) is

Z A10 ¼ 41,600 Z A ¼ 100,600

and the load trips of the ca ge s l an d ll up to the ropes being discarded is
T A10 ¼ 2 Z A10 ¼ 83 ; 200 T A ¼ 2 Z A ¼ 201 ; 200
The rope mass investment for one load trip is s = T A ¼ 0 : 0657 kg/load trip
(The s = T A ¼ theoretical minimum rope mass investment for one trip

0 : 0572 kg = trip can get for the rope diameter d = 72 mm.)
The acceleration has a remarkable influence on rope endurance. For a slightly
reduced acceleration to a 0 = 1 m/s 2 the mean number of trips is T A ¼ 245,000.
The loss of endurance by the rope twisting is still unknown. For the present
hoisting distance a relative small endurance loss has to be expected.
Alternative construction:
In the present example, a traction sheave installation with one bearing rope has
been chosen for direct comparison with the drum installation in the following
Example 3.15. It is preferable to use parallel bearing ropes for new traction sheave
installations.
An installation with four parallel bearing ropes with the rope diameter
d = 30 mm and the sheave diameters D = 3,000 mm produces the same stresses
as the present one rope installation. Because of the size effect, the rope endurance
of this four rope installation would have slightly better endurance that of a one
rope installation, if—in the not very realistic case—the four ropes had the same
tensile force. If the rope with the greatest stresses only has an 8 % higher tensile
force than the mean of the four ropes, then the endurance of this rope will be about
the same as the rope in the one rope installation.

Example 3.14 Mining installation with drum
The wire rope is wound in only one layer on the drum in a fitted groove. The
drum winder is moved in the direction of the drum axis, strictly geared in relation
to the drum rotation in such a way that the wire rope always runs in the same
position in relation to the shaft on or off the drum. Therefore virtually no side
deflection of the rope exists, Feyrer (2002).