Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 118

u 90 ¼ arcsin 8 ; 000 16 ð 0 : 085 þ 1 : 282 0 : 012 Þ ¼ arcsin 0 : 4283

200 150

u 90 ¼ 25 : 4

According Eq. ( 2.81b ) the total rotary angle that the bottom sheave not exceed

is

u rtot ¼ arcsin 2 : 06 0 : 4283 ¼ arcsin 0 : 8823
u tot ¼ 61 : 9 :

An overlapping of the bearing rope traces is not to fear.

2.4.4 Rope Twist Caused by the Height-Stress

2.4.4.1 Wire Rope Supported Non-rotated at Both Ends

Because of the rope weight the tensile force in a suspending rope has on the upper
end a bigger tensile force than on the lower end. The rope stress increasing with
the height of the suspending rope is called height-stress. Because the rope torque
along the rope length must be constant, the wire rope supported non-rotated on the
upper and the lower end will twist between the both ends. The rotary angle of a
vertical hanging wire rope is demonstrated in Fig. 2.29 . The rope turns on in the
upper field and off in the lower field.
Engel ( 1957 ) and little later Hermes and Bruuens ( 1957 ) derived at first the rotary
angle caused by the height-stress, see also Gibson ( 1980 ). Engel ( 1959 ) calculated
the twist angle for haul and traction ropes of rope ways. Rebel ( 1997 ) calculated
with his own equation the rotation of triangular strand ropes in deep shafts.
Malinovsky and Tarnavskaya ( 2006 ) derived their calculation method reminding

Fig. 2.29 Rotary angle u
and twist angle x of a vertical
hanging wire rope supported
on both ends non-rotated