Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 102

and with ( 2.65 )

r

m r
S

T ¼ 2 L
i

: ð 2 : 66 Þ

In this i is the number of the antinodes of vibration on the rope length. The
frequency is

r

S
m r

f ¼ 1

i
2 L T ¼

: ð 2 : 67 Þ

In rope fields which are not too long i.e. about 100 m, it is possible to make the
rope vibrate, Zweifel ( 1961 ). Using the frequency f observed here, the rope tensile
force S can be calculated according to the converted ( 2.67 )
S ¼ m r 2 f L
i

2

: ð 2 : 68 Þ

There are strong variations of the rope tensile force in rope-ways due to
braking. The movements of the ropes and their connected masses in such systems
can only be calculated with large-scale methods. Such methods are presented by
Czitary ( 1975 ), Engel ( 1977 ), Schlauderer ( 1990 ) and Beha ( 1994 ). For transverse
vibrations, the damping depends on the rope construction, the rope tensile force
and the amplitude. Raoof and Huang ( 1993 ) reported investigating into the
damping of spiral ropes.
The basic frequency of transversal vibration (string) of a wire rope can be
calculated with the help of the Excel-program SEILELA2.XLS.

Example 2.7: Frequency of transverse vibration (string)

Data from Example 2.5.
According to Table 1.9 , the length-related rope mass is

1
100 W 2

1
100 0 : 4 10 2 ¼ 0 : 40 kg/m

d 2 ¼

m r ¼

The frequency of the transverse vibration with one antinode of vibration i = 1

is

r

1 ; 000 9 : 81
0 : 40

r

S
m r

i
2 L

1
2 50

f ¼ ¼ ¼ 1 : 5661 1 = s :