Wire Ropes, Elements and Definitions - Wire Ropes: Tension, Endurance, Reliability - page 10

Fig. 1.7 Haigh-diagram with
some definitions

Goodman-line

˃ Alt

˃ A

˃ Rep /2

middle stress ˃ m R m

0

cycle with the stress amplitude r a and the middle stress r m for general cases. In a
fatigue test, the endurance of the wire is counted by the number of load cycles N it
takes.
Figure 1.7 shows a Haigh-diagram with the abscissa for the constant middle
stress r m and the ordinate for the fluctuating strength r A as amplitude around the
middle stress r m . The special cases alternate and repetitive stresses are inserted.
The alternate strength r Alt is the amplitude for a middle stress r m = 0. The
repetitive strength r Rep = 2r A is the strength range for a middle stress r m = r A .
That means for the repetitive strength r Rep the lower stress is r lower = 0.
The two basic stresses are tensile stress

r t ¼ S = A ð 1 : 1a Þ

and bending stress according Reuleaux ( 1861 )

r b ¼ d

D E :

ð 1 : 1b Þ

In these equations S is the tensile force, A the wire cross-section and d the wire
diameter. D is the curvature diameter of the wire centre on the sheave, which
means D = D 0 + d, with the contact diameter D 0 between wire and sheave. E is
the elasticity module.

1.1.6.2 Testing Machines

Tensile fatigue test. Testing methods with fluctuating tensile forces for the testing
of materials and components are very commonly used. For rope wires, such tests
were started as early as those from Pomp and Hempel ( 1937 ). The wire termi-
nations are the main problem in carrying out these tests. If a normal press clamp is
used, the wire would mostly break in the clamp.
In order to find out the real endurance or the real tensile fatigue strength of the
wire, the wire has to be fastened in such a way that the wire breaks in the free
length. To do this, a lamella clamp is used where the tensile force is gradually
transferred from lamella to lamella. In addition the wire ends—which are fastened
in the clamps—are strain-hardened by a rolling process. During this process, the