Wire Ropes, Elements and Definitions - Wire Ropes: Tension, Endurance, Reliability - page 20

1500

N/mm 2

1000

700

500

R o
N/mm 2

400

1570

300

1770

Unterberg (1967)

1960

1570 Matsukawa et al

(1988)
Birkenmaier (1980)
Dillmann and
Gabriel (1982)

200

1770

1670
1470
1670

100

5mm 6 7

0 1 2 3

wire diameter ʴ

4

Fig. 1.15 Repetitive tensile strength for different wire diameters d for a mean nominal tensile
strength R 0 = 1,720 N/mm 2

strength amplitude according to ( 1.3a ) although there the stress gradient is 0.
Because of this and also as a result of other observations, Unterberg ( 1967 ) stated
that the theory of stress gradient does not exist for rope wires.
In Fig. 1.15 the influence of the wire diameter d is shown using the results from
different authors. In this figure the mean repetitive fatigue strength r t ; Rep ¼ 2 r t ; A
is used. As a reminder, repetitive strength means that the middle stress is
r t,m = r t,A and the lower stress is 0. As an equation using the results in Fig. 1.15 ,
the repetitive strength is expressed as

r t ; Rep ¼ 2 r t ; A ð r lower ¼ 0 Þ¼ 1,200 e 0 : 122 d : ð 1 : 3b Þ

The influence of the other size parameter, the stressed wire length l, can be
evaluated for the fatigue strength amplitude in the same way as for a number of
load cycles N if the standard deviation of the fatigue strength amplitude for one
and the same wire were known.
The influence of the tensile strength R m on the rotary bending strength r Rot is
shown in Fig. 1.16 from Wolf ( 1987 ). In this diagram, Wolf put in the results
gained by Buchholz ( 1965 ) wires with lower tensile strength to get an overview for
a greater strength range. For small tensile strengths, the rotary bending strength
increases almost proportionally with tensile strength R m . The rotary bending
strength does not increase as much for rope wires (wires with tensile strength
between 1,300 and 2,200 N/mm 2 ). According to Wolf ( 1987 ), it is