Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 204

Fig. 3.22 Pressure between
rope and undercut groove,
k = k 0 cos c

ʳ

ʳ 2

k v

k =
k 0 ·cos

ʳ

k o

ʳ 1

the maximum tensile force S max has to be introduced as the maximum rope tensile
force over the whole length of the groove. The part of the pressure in the direction
to the sheave axis is

k v ¼ k cos c ¼ k 0 cos 2 c :

The integral of this part of the pressure over the groove angle c is equal to the
line pressure

q ¼ 2 c2
c1

k v d

2 dc ¼ k 0 d c2
c1

cos 2 c dc

or

:

1

4 sin 2c 2 þ 1 2 c 2 1 4 sin 2c 1 1

q ¼ k 0 d

2 c 1

ð 3 : 30a Þ

With this and q = 2S max /D and according to ( 3.30 ) for the groove angle c, the
rope pressure is

cos c

2 S max
d D

k ¼ :

1

4 sin 2c 2 þ 1 2 c 2 1 4 sin 2c 1 1 2 c 1

The maximum specific pressure existing for the groove angle c = c 1 is

cos c 1

2 S max
d D

k max ¼ : ð 3 : 31 Þ

1

4 sin 2c 2 þ 1 2 c 2 1 4 sin 2c 1 1

2 c 1