Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 205

The friction coefficient of the groove, traditionally written f(l), is
f ð l Þ ¼ q 0
q

l : ð 3 : 31a Þ

In this, the line pressure on both sides of the groove is
q 0 ¼ 2 Z

c 2

2 dc ¼ k 0 d Z

c 2

k d cos c dc

c 1 c 1

or

q 0 ¼ k 0 d ð sin c 2 sin c 1 Þ: ð 3 : 31b Þ

From ( 3.30a ), ( 3.31a ) and ( 3.31b ), the friction coefficient for the undercut
groove is

4 ð sin c 2 sin c 1 Þ
sin 2c 2 sin 2c 1 þ 2 c 2 2 c 1

f ð l Þ ¼ l : ð 3 : 32 Þ

For grooves which are not undercut, c 1 = 0 and c 2 = 60, the maximum spe-
cific pressure (at the bottom of the groove) is k max = 1.351(2 S max )/(dD) and the
friction coefficient of the groove is f(l) = 1.170 l.

Example 3.4 Undercut groove

Data:
Groove angles c 1 = 47.5 ? 0.829 rad
c 2 = 80 ? 1.396 rad

Results:
The maximum specific pressure according to ( 3.31 )is

cos 0 : 829

2 S max
d D

k max ¼ :

1

4 sin ð 2 1 : 396 Þþ 1 2 1 : 396 1 4 sin ð 2 0829 Þ 1 2 0 : 829

k max ¼ 5 : 627 2 S max
d D

:

The friction coefficient of the undercut groove according to ( 3.32 )is

f ð l Þ ¼ 4 ð sin 1 : 396 sin 0 : 829 Þ

sin ð 2 1 : 396 Þ sin ð 2 0 : 829 Þþ 2 1 : 398 2 0 : 829 l
f ð l Þ ¼2 : 062 l :