Wire Ropes, Elements and Definitions - Wire Ropes: Tension, Endurance, Reliability - page 13

Fig. 1.9 Bending stress
along the wire bending
length, Wolf ( 1987 )

˃ b Stuttgart rotary bending machine

b

˃ b mion

rotary bending
machine Schenck

0 1

free wire length

Therefore the bending stress on the terminations is only slightly smaller than in the
middle of the bending length. This means that wire breakage in or close to the
terminations is almost certainly avoided and the bending stress is nearly constant
over the whole of the bending length. Figure 1.9 shows the bending stress along
the bending length in the Schenck machine and the Stuttgart machine.
The bending stress amplitude in the middle of the bending length l (free wire
length) is

r a ¼ r b ¼ k d E
C

ð 1 : 1c Þ

This bending stress, the maximum stress, is taken as the nominal bending stress of
the wire in the Stuttgart rotary bending machine. The minimum bending stress on
both of the wire terminations is
r b ; min ¼ k 0 d E
C

: ð 1 : 1d Þ

For both equations: k and k 0 are constants in Table 1.4 , d is the wire diameter, E is
the elasticity module and C is the distance between the parallel axes of the wire
terminations.
Furthermore, in Table 1.4 , the ratio of the minimum and the nominal bending
stress r b,min /r b is listed. For his tests Wolf ( 1987 ) used the ratio l/C = 1.6 instead
of p/2 with the minimum stress r b,min = 0.883 r b or a 11.7 % smaller stress at

Table 1.4 Constants k, k 0 and the ratio of wire bending stresses r b,min /r b in the Stuttgart rotary
bending machine
l/C p/2 1.58 1.59 1.60

k 1.0 1.008 1.017 1.026

k 0 1.0 0.969 0.936 0.906

r b,min /r b 1.0 0.961 0.921 0.883