Civil Engineering Reference
In-Depth Information
rope length has been at least partly taken into consideration. In (
2.107
), the
constant a
6c
for this together with the constants from Tables
2.8
and
2.9
are
listed in Table
2.11
.
2.6.4.4 Palmgren-Miner Rule (Damage Accumulation Hypothesis)
For roller bearings loaded by a series of load cycles with different loads, Palmgren
(
1924
) stated the hypothesis that the sum of ratios n
i
/N
i
(called damage sum) will
be 1. That means
X
m
n
i
N
i
¼ 1
:
ð
2
:
108
Þ
i¼1
In this, n
i
is the number of load cycles under the load i (load defined by i) and N
i
is the endurance under the load i. Miner (
1945
) found that this rule is also valid for
other elements and special kinds of loads.
According to (
2.108a
) the endurance Z of an element under a series of different
loads i will be
1
P
i¼1
Z
¼
:
ð
2
:
108a
Þ
w
i
N
i
Here w
i
= n
i
/Z is the portion of the number of load cycles n
i
under the load i.
However, this rule is only a hypothesis and it must be checked to see whether it
can be used for wire ropes under fluctuating tension. From the results of tension-
tension tests in four series of block loads, Chaplin (
1988
) found damage sums
between 0.897 and 1.109, and Rossetti and Maradei (
1992
) found damage sums
between 1.24 and 1.28. From similar tests with Warrington-Seale ropes, Casey
(
1993
) got damage sums between 0.6022 and 1.2584.
All these results show that the Palmgren-Miner rule can be used for wire ropes
under fluctuating tension.
2.6.4.5 Discard Criteria
The amplitude stresses for the inner wires are normally greater than in the outer
wires, Sects. 2.12-2.14. Therefore, outside wire breaks cannot be detected in most
cases during tension-tension tests, Wehking and Klöpfer (
2000
). That means, the
point at which the wire rope requires replacement is not defined by the number of
outer wire breaks. Wehking and Klöpfer therefore recommend inspecting wire
ropes under fluctuating tension by means of a magnet inductive test. Because a
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