Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 111

2.4.2.2 Calculation of the Torque for Wire Ropes

The results of the torque measurements with the round strand wire ropes with one
strand layer can be very good evaluated by a regression calculation. Kollros ( 1974 ,
1976 ) evaluated first his torque measurements with such a regression. Based
on theoretical considerations he creates an equation with two constants for
the regression. Forerunner of these constants are the torque constant l =
M/S = c 1 d and the torsional stiffness D = M/x from Engel ( 1957 , 1958 , 1966 ).
The torque measurements with many wire ropes by Feyrer and Schiffner ( 1986 )
show that two constants are not enough to describe the results with good precision.
Therefore the regression for the results of these measurements has been made
practically with the equation of Kollros but with three constants. The torque is then

M ¼ c 1 d S þ c 2 d 2

S x þ c 3 G d 4 x : ð 2 : 77 Þ

Therein M is the torque;

u the rotary angle in rad;

d the rope diameter;

x = u/L the twist angle;

S the tensile force;

L the rope length;

G the shear module;

and, c 1 c 2 , c 3 , are constants.
The twist angle x has to set positive for turning off the rope and negative for
turning on the rope. The constants c and their standard deviation are listed in
Table 2.6 . These constants have been found by regression of Feyrer and Schiffner
( 1986 ) with their own test results, with many test results of students and with the
test results of Kollros ( 1974 ) and Unterberg ( 1972 ). As limit for the use of ( 2.77 )
with the constants c, the maximum allowed twist angle x max = u max /100d (angle
for a rope length of 100 times rope diameter) is also given in Table 2.6 .
By measurements with wire ropes of diameters 55.6 and 76 mm Kraincanic and
Hobbs ( 1997 ) evaluated torque constants c 1 that corresponds respecting the stan-
dard deviation with those in Table 2.6 . Cantin et al. ( 1993 ) found in measurements
with a 6-strand rope constants c 1 and c 2 comparable with that of Table 2.6 but the
constant c 3 deviates more than 30 %. For lang's lay triangular strand ropes Rebel
( 1997 ) found that ( 2.77 ) cannot describe satisfactory the measured torques.
Therefore Rebel established an equation with nine constants what he evaluated out
of his measurements.