Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 124

Fig. 2.31 Change of rope
length by twisting the rope

u

ʔ u

ʔ L

ʔ l

ʲ

L

I

2.4.5 Change of the Rope Length by Twisting the Rope

By twisting a wire rope, the rope length and the lay length will be increased in the
''on'' rotary direction and decreased in the ''off'' rotary direction. For this problem,
Hankus ( 1997 ) remembered the equations of Glushko ( 1996 ). He measured and
calculated the rotary angles of wire ropes in mining shafts, Hankus ( 1993 , 1997 ).
In the following, the change of rope lengths will be calculated using geometric
data for wire ropes with one strand layer and a fibre core. It can be presupposed
that the strand length l and the strand winding radius r will remain constant. On the
base of Fig. 2.31 the change of the rope length is given by the equation

q

l 2 ð u Du Þ 2

L þ DL D ¼ : ð 2 : 95 Þ

In this L is the rope length and DL D is the rope elongation when the rope is
twisting.
Du is the change of the circle bow length for the strand helix. With the strand
winding radius r S = r = const. and the rotary angle u, the circle bow and the
change of the circle bow length are

u ¼ r u and Du ¼ r Du :

Then, from ( 2.95 ), the rope elongation by twisting the rope is

q

l 2 r 2 ð u Du Þ 2

DL D ¼ L : ð 2 : 96 Þ

With the strand lay angle b it is

l ¼ L = cos b ; r u ¼ L tan b and Du = L ¼ x :

Using that, the rope elongation (+) or shortening (-)is