Civil Engineering Reference
In-Depth Information
(constant + fluctuating) as only one variable make it possible to achieve a result with
only a few tests. However, this method offends against the fundamental rules of
fatigue strength which means that the results gained by these equations can only be
valid for relatively small test ranges of tensile stresses and diameter ratios D/d.
In the equations listed in Table
3.4
, the number of bending cycles is given as a
function of the constant tensile force (specific tensile force S/d
2
) and separate from
the fluctuating stresses caused by the diameter ratio D/d. The degree to which the
different equations correspond can be proved by the coefficient of determination.
The regression calculation for a great number of bending tests results with a great
range of tensile stress and of diameter ratio D/d show the highest coefficient of
determination for (
3.49
) with three independent variables, Feyrer (
1981
). Just how
well the points from the test results correspond to the straight lines from (
3.49
)is
demonstrated in Fig.
3.34
.
A good predecessor was created by Calderale (
1960
) and Giovannozzi (
1967
)
and it results in a smaller coefficient of determination. However, this equation does
not consider the different gradients of the lines needed for the diameter ratios.
Only the independent equation from Clement (
1980
) with its three independent
variables—as in (
3.49
):
r
S
d
2
r
S
d
2
ln N ¼ a
0
þ
a
1
d
d
D
þ
a
3
d
d
D
D
þ
a
2
D
ð
3
:
50
Þ
shows a coefficient of determination close to that of (
3.49
), Feyrer (
1981a
).
In the following, only (
3.49
) will be used. This equation is valid both for the
breaking and the discarding number of bending cycles. In (
3.49
), the unit force
S
0
= 1 N and the unit diameter d
0
= 1 mm have been left out to simplify the
overview (knowing that the units N and mm always have to be used). Then (
3.49
)is
d
2
þ
b
2
lg
D
S
S
d
2
lg
D
d
lg N ¼ b
0
þ
b
1
lg
d
þ
b
3
lg
ð
3
:
49
Þ
There have been a great many bending fatigue tests done with most common
types wire rope, Feyrer (
1981a
,
1985a
,
b
,
1988
,
1997
). From the results of these
tests, the constants a
i
of (
3.49
) are evaluated by regression calculation for the
breaking number N and for the discarding number N
A
of bending cycles. These
constants a
i
are related to the
Mean nominal strength R
0
= 1,770 N/mm
2
Nominal rope diameter d = 16 mm
Rope bending length l = 60d.
Lubricated before the test, not relubricated during test.
These constants (changed from a
i
-b
i
) are listed in Table
3.14
, Sect.
3.4.3
, for the
extended rope endurance equation which also includes some additional influences.
As the Eq. (
3.49
) shows, the number of bending cycles is logarithm normal
distributed. The standard deviation is therefore to describe as lg s.
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