Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 73

Fig. 2.6 Winding angle of a
wire in the wire rope cross
section, normative phase
angle U

˕ L

˕ D

ˆ

with r S for the strand winding radius, b for the strand lay angle and u S for the
angle of rotation of the strand helix. The strand lay length is

h S ¼ 2 p r S
tan b

:

Andorfer ( 1983 ) derived analytically the equations for the space curve of the
double helix of the wire in the straight stranded rope as done before by Bock
( 1909 ) using a kinematic method and later on by Wolf ( 1984 ) using a vectoral
method. The wire winding radius r stands perpendicular on the strand axe helix
and the ratio between the wire winding angle u W and the strand winding angle u S
is constant, u W /u S = const. Schiffner ( 1986 ) pointed out that this constant ratio
practically always occurs if the clearance between the wires is—as usual—very
small.
The constant ratio between both winding angles u W and u S is only valid if they
both start from u W = u S = 0. The constant ratio of the winding angles is there-
fore better described by

h S

m ¼

cos b : h W

That means in any one strand lay length h S there are m* wire lay lengths h W .
With m = m* ± 1is

u W u S ¼ m u S ¼ U :

Bock ( 1909 ) nominated U as normative phase angle. After U = 2p, a wire
element has the same position as for U = 0, Fig. 2.6 . The positive sign has to be
set for ordinary lay ropes and the negative for lang lay ropes.
To include the case of any phase of u W and u S a constant winding angle of the
wire helix u W0 or shorter u 0 will be added. Then it is

u W u S þ u 0 ¼ m u S þ u 0 :