Bending of helically twisted cables under variable ... - Pfisterer

Where µ L is is the the coefficient coefficient of of friction friction between between the the wire element element under under consideration consideration and and its subsurface,
e.g. the core wire of the cable.
Maintaining intaining the the static static balance balance of of forces forces in in the the axial axial direction of of the wire we obtain, Fig. 2.5:
Where dZL is is the the maximum maximum difference difference in in tensile tensile force a wire wire element element can resist resist through through friction.
friction.
Fig. 2.5 Force relationships in a wwire
element in layer L
Integrating (2.14) over φ and inserting the boundary condition
yields
Where Zd,L is is the the tensional tensional stress stress on on the the wire wire alone, alone, in acc. with (2.5), which is the same same for all wires wires in
layer L.
ZL, however, is the maximum (total) tension ZZL(φ)
) that can be countered by friction force at every point φ
on the wire. Apart from tension force Zd,L Z countering only tension stress therefore, friction generates a
variable tension force component along the wires of layer L, provided the relative movement is
sufficient:
13