Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 293

Table 3.16 Constants for calculating the number of reverse bending, ( 3.89 )

Factor Breaking number Discarding number

N 10 N a10

N N A

a 0 9.026 6.680 3.635 2.670

a 1 0.618 0.618 0.671 0.671

a 2 0.424 0.424 0.499 0.499

The constants b i are listed in Table 3.14 and a 1 in Table 3.16 .
In an other form the Eq. ( 3.93 ) is to find in DIN 15020 with the exponent
p = 3. The exponent p reaches such a high number only for about D/d = 40.
For rope drives with simple and reverse bendings a common exponent can be
composed. No big failure will be made if in this case the Eq. ( 3.93b ) is used.
As a first recommendation for cranes a load collective factor is listed in
Table 3.11 .

3.4.5 Limits

The following limits have to be respected for rope drives according to Table 3.9 :

• The rope tensile force must be smaller than the Donandt force S \ S D .
• In case safety requirements have to be met, the expected number of wire breaks
should be greater than the given limiting number of wire breaks or alternatively
the rope tensile force should be smaller than the discard limiting force S \ S G .
• For economic reasons, the rope diameter should be smaller than the optimal
rope diameter d \ dopt.
• Extreme forces (only for special applications).

3.4.5.1 Donandt-Force

The method of endurance calculation presented here is limited by the Donandt
force at which point the yielding stress of the wires is reached. For simple bending,
the Donandt force is according to Sect. 3.2.7
S D ; sim ¼ q 0 F min þ q 1 d

D F min

ð 3 : 71 Þ

and the Donandt force for reverse bending is

S D ; rev ¼ ð q 0 0 : 035 Þ F min þð q 1 0 : 25 Þ d

D F min :

ð 3 : 72 Þ