Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 251

3.2.6 Palmgren-Miner Rule

According to the damage accumulation hypothesis of Palmgren ( 1924 ) and Miner
( 1945 ), the endurance of specimen ropes under different loads can be calculated
using the basic equation

X n i
N i

¼ 1 : ð 3 : 70 Þ

where n i is the number of cycles under the load i and N i is the endurance number
under the load i.
Dragone ( 1973 ) and Rossetti ( 1975 ) were the first to carry out bending fatigue
tests to check whether the Palmgren-Miner Rule could be used for running ropes.
From the results of their bending fatigue tests with different tensile forces, they
found that the Palmgren-Miner Rule is fulfilled quite well. Ciuffi ( 1979 ) reported
about a block load programme that had been done in various institutes. From these
bending tests, they found damage sums between 0.8 and 1.2. Wohlrab and
Jehmlich ( 1980 ) calculated mean damage sums of 0.96 up to discarding and of
0.91 up to breakage of the ropes with only a small standard deviation. All this
research shows that the Palmgren-Miner-Rule is valid for running ropes.

3.2.7 Limiting Factors

3.2.7.1 Donandt-Force

If a certain limiting tensile force is exceeded in a series of wire rope bending
fatigue tests, the number of bending cycles drops abruptly. This force, which is the
absolute limit of the usable tensile force, is called Donandt force. Schmidt ( 1965 )
was the first do research on this force after taking up an idea coming originally
from Donandt. Above the Donandt force, an increasing part of the wires cross-
section exceeds the yielding strength which then causes an abrupt breakdown in
the number of bending cycles.
In Fig. 3.34 , the beginning of the abrupt breakdown of the number of bending
cycles (and with that the Donandt force) can clearly be seen. The lines for the usuable
region of rope endurance have been taken from test results found in the endurance
regression calculation. In addition lines have also been drawn for the test results in the
yielding region. The intersection of the two lines is known as the Donandt force.
In the case of simple bending, the Donandt forces S D,sim for ropes of the same
construction have been evaluated by regression calculation with the basis equation

d

S D ; sim ¼ q 0 0

F e þ q 0 1

D F e :