Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 292

with X n

1
P

Z ¼

i¼1 u i ¼ 1

n

u Z i

i¼1

and complemented by the nominal number of working cycles Z 0

Z ¼ X

n

with X

n

Z 0

u i Z 0
Z i

u i ¼ 1 ð 3 : 93 Þ

i¼1 i¼1

In that is

u i relative part of total number of working cycles Z

Z i number of working cycles under the force S i resp. k i

Z number of working cycles under the force S resp. k

Z 0 number of working cycles under the nominal force S 0 resp. k = 1

For a given ratio of tensile forces the ratio of working cycles is

p
¼ k i :

Z 0
Z i

S i
S 0

¼

Introduced in Eq. ( 3.93 ) the collective factor is

! p

k ¼ X with X

n n

u i k i

u i ¼ 1 : ð 3 : 93a Þ

i¼1 i¼1

The number of working cycles loaded by a collective can be calculated with the
tensile force S, reduced by the collective factor k

S ¼ k S 0 :

The exponent p can be taken from the endurance Eqs. ( 3.55 ) and ( 3.61 ).
If the wire rope is only loaded by simple bendings, the exponent is

:

p ¼ b 1 þ b 3 lg D
d

ð 3 : 93b Þ

and if only reverse bendings occur

:

b 1 þ b 3 lg D
d

p ¼ a 1

ð 3 : 93c Þ