Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 238

Berner ( 2011 ) introduces an uniform definition for the pressure, following an early
idea of Donandt ( 1927 ). With that the pressure in undercut grooves is as up to now

D d 8 cos ð b = 2 Þ

S

k max ¼ ð 3 : 57a Þ

p b sin b

and in V grooves in a new form

D d 3 p

S

k max ¼

2 sin ð c = 2 Þ :

ð 3 : 57b Þ

For consideration the influence of the rope slip on the rope endurance, Berner
introduces the traction grade

g ¼ T B 1
T K 1

ð 3 : 57c Þ

with the traction demand (ratio of the rope forces) T B = S 1 /S 2 and the traction
capacity T K = e f(l)b .
Berner has made a number of rope bending tests with or without traction .
Thereby the aim was to find out the ratio

f N3 ¼ N Form
N Round

ð 3 : 57d Þ

of the number of bending cycles in form and in round grooves. In bending tests
without traction, Berner ( 2011 ) found

• The ratio f N3 is relative big.
• The ratio f N3 is for wire ropes with fibre core much bigger than for those with
steel core.
• The numbers of bending cycles from the tests justify the calculation of the
pressure with the Eqs. ( 3.57a ) and ( 3.57b ).
• In bending tests, in that the wire rope runs in all cycles over a sheave with form
groove and than over one with round groove, leads the repeated ovalisation of
the rope—that thereby occurs—not to the expected additional reduction of the
rope endurance. The number of double bendings can therefore calculate with
the Palmgren-Miner-Rule, Sect. 3.4.4 .
For the endurance tests Berner constructed a test machine which works like an
elevator with traction sheave but with a single rope. With that test machine the
influence of rope pressure and the rope slip on the rope endurance can be detected.
The work of Berner ( 2011 ) is more looking on the principle relations between
the pressure, the rope slip and the rope endurance. The evaluated endurance factor
f N3 cannot be used for an elevator in practice because the forced slip between the
parallel bearing ropes and the load collective should be known. For the time being
the endurance factor f N3 from Holeschak ( 1987 ) should be used like now.