Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 191

r b ; ov ¼ 134 N mm 2 :

Part of the rope ovalisation will be permanent and it will increase slowly with
the number of times the rope runs over the sheave, Bechtloff ( 1969 ) and Dietz
( 1971 ). However, of all the bending stress arising due to ovalisation, a great deal
will be fluctuating stress. Wire ropes with a fibre core are easily ovalised which
means that they will have wide contact with the groove even if the groove has a
large radius. The great influence exerted by the groove radius is demonstrated in
Fig. 3.49 which shows test results from different authors.

3.1.4 Secondary Bending Stress

In cross lay strands, the outside wires are only supported by inner wires at single
points. Due to this, the outside wires are already bent a little, reducing the small
wire bow by the rope's tensile force. The bending stress resulting from the
compressive forces from the groove is much greater, Fig. 3.11 . This bending stress
is called secondary bending stress.
The pressure from the compressive forces on the wires depend mainly on the
tensile force of the wire rope, the sheave diameter, the groove radius and the form
elasticity of the wire rope and the groove. The compressive force on a wire can be
estimated using ( 3.37a ). In most cases the secondary bending stress and the
pressure will be reduced after the first loading by plastification of small regions of
contact. This reduced secondary bending stress and pressure then works as fluc-
tuating stresses in every bending cycle of the wire rope.
Müller ( 1966 ) found in bending tests that wire ropes with cross lay strands have
only about one third of the endurance of those with parallel lay strands. The reason
for this lies mainly in the secondary bending stress. In addition to the cross lay
strands, the outside wires are loaded by secondary bending stress in compound
strands. Nevertheless, ropes constructed with these strands can be used success-
fully in mining hoisting installations as, due to the great sheave diameters and
smooth groove material used here, the secondary bending stress is small.

Fig. 3.11 Secondary
bending of a wire

F

F

N