Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 99

Example 2.5: Frequency of a mass hanging on a wire rope

Data:
Filler 6 9 19-IWRC-sZ (ten times loaded)
Mass M = 1,000 kg
Rope diameter d = 10 mm
Rope length L = 50 m

Results:
With A = C 2 d 2 = 45.7 mm 2

the wire rope-cross section with C 2 = 0.457

accordingly Table 1.9 , the rope tensile stress is

r m ¼ M g
A

¼ M g

C 2 d 2 ¼ 1 ; 000 9 : 81 0 : 457 10 2 ¼ 218 N/mm 2 :

According to ( 2.50 ) and ( 2.52 ), the wire rope elasticity module is

E S ¼ 119,300 N = mm 2 :

From that, according to ( 2.58 ), the spring constant is

c S ¼ 119 ; 300 44 : 9
50

¼ 107,130 N/m

and the frequency according to ( 2.57 )is

r

107,130
1,000

1
2 p

f 0 ¼ ¼ 1 : 6511 = s :

2.2.4.3 Transverse Waves

A short-time local (lateral) deflection moves as a wave along the wire rope. Czitary
( 1931 ) investigated these waves theoretically and he pointed out that the tensile
force of a wire rope can be calculated by measuring the wave running time.
According to Zweifel ( 1961 ) the velocity of a transverse wave is

s

g S
q

½1 þ EI
S

ð 2 p
k

Þ 2

t ¼ : ð 2 : 61 Þ

In this S is the rope tensile force in N;