Civil Engineering Reference
In-Depth Information
diameters this is vice versa. High tensile stresses as well as high bending stresses
reduce the number of bending cycles. Consequently the greatest possible number
of bending cycles can be expected when both tensile stress and bending stress are
not too high and when they are in a reasonable relation to each other. The rope
diameter with which the greatest number of bending cycles can be expected is
called the optimal rope diameter d opt .
Müller ( 1961 ) had already drawn the attention to the existence of an optimal
rope diameter. When preparing the standard DIN 15020, on the basis of his
bending tests he proposed using coefficients c ¼ d = S
p
and diameter ratios D/d for
the different groups of rope drives, from which a relatively optimal rope diameter
would result. Clement ( 1981 ) also derived an optimal rope diameter from his
Eq. ( 3.50 ) which was developed to determine the endurance of a rope.
Here the optimal rope diameter is derived on the basis of the rope endurance
( 3.55 ). The number of bending cycles N or lg N reaches a maximum for
o lg N
o lg d ¼ 0 :
The small influence of the bending length can be neglected. Then the optimal
rope diameter for simple bending or for combined fluctuating tension and bending
(with the actual valid tensile force S = S sim or S = S equ )is
lg d opt ¼ 2 b 1 þ b 2 þ 0 : 63
4 b 3
0 : 4
4
1,770 þ lg D
R 0
þ lg S
4
lg
:
ð 3 : 55a Þ
2
Deriving the combined ( 3.55 ) and ( 3.61 ), the optimal rope diameter for reverse
bending is
lg d opt ¼ 2 a 1 b 1 þ a 2
4 a 1 b 3
þ b 2 þ 0 : 63
4 b 3
0 : 4
4
1,770 þ lg D
R 0
þ lg S
4
lg
:
ð 3 : 55b Þ
2
The constants b i are listed in Table 3.14 and constants a i in Table 3.16 , Sect.
3.4 . The constants c 0 can be added to this for standardised wire ropes and
standardised nominal rope strengths. Then the optimal rope diameter is
lg d opt ¼ lg c 0 þ lg D
2
þ lg S
4
:
or
D S
q
p
d opt ¼ c 0
:
ð 3 : 73 Þ
The constant c 0 is listed in Table 3.19 (Sect. 3.4.5 ).
In Fig. 3.62 , the number of bending cycles of a rope for the tensile force S = 10
kN and different diameters D are drawn over the rope diameter d. The optimal rope
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