Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 137

RO is run out. Then M20 LR22 means as example a mean load of 20 % and a load
range of 22 % of the measured rope breaking force.
Figure 2.34 shows a trend line that represents the numbers of load cycles that
have been get under
• load range 18-36 % UBL (2S a d 2 = 125-250 N/mm 2 )
• twist angle (amplitude of the cyclic rotation) x = 140/100d to 1,400/100d.

In this field the number of load cycles of the wire rope—stressed by different
fluctuating tensile forces—depends to the main part on the fluctuating twist angle.
As example the number of load cycles is N = 10,000 for x = 1,000/100d and
N = 100,000 for x = 300/100d.
For smaller cyclic rotation, the rope endurance is dominated by the fluctuating
tensile force. In case of no or very small twist, the number of load cycles to
breakage can be calculated with the equations of Sect. 2.8 for 6-strand Warr.-
Seale—IWRC—sZ. For the untwisted 77 mm wire rope, the calculated mean
number of load cycles is N = 220,000 with the given 2Sa/d 2 = 180 N/mm 2 and

S u /d 2 = 48.5 N/mm 2 as can be seen in Fig. 2.34 for the same endurance region.

2.4.7.3 Stationary Wire Ropes

A wire rope supported non-rotated at the upper and the lower ends rotates with a
rotary angle u as can be seen in Fig. 2.29 . The twist angle on the upper and the
lower rope ends are expressed accurately enough by the simplified Eqs. ( 2.91a )
and ( 2.91b ). The fluctuating twist angle depends on the sum of the constant force
from the rope mass and the fluctuating force S 0 . In most cases these fluctuating
twist angles and the fluctuating stresses from that are relative small.

2.4.7.4 Running Ropes

Fluctuating twist angles occur in running ropes of elevators, mine hoistings and
rope ways. Between the guided car and the drum or traction sheave, the wire rope
is twisted as a hanging stationary rope. When the car mounts, the twist angles—
caused by the rope weight—in the remaining rope length will be continually
reduced. In addition to the variable twist angle, there is also a constant twist angle
x con —constant over the rope length—which usually arises from the installation
itself and its loading history. A third twist angle x side can be produced, when the
wire rope is wound in the groove of the sheave or drum. This occurs especially if
the wire rope moves under side deflection sliding and rolling over the groove flank
in the groove, Neumann ( 1987 ) and Schönherr ( 2005 ).
The maximum fluctuating twist angle and therefore the maximum fluctuating
stress occurs in the rope piece above the car or the counter weight. The twist angles in
that rope piece can be calculated under the supposition that no twist angle exists from
installing the rope and its loading history and that no further twist angle is introduced