Mathematical model of splicing of steel cable

The article presents materials on the study of mathematical modeling of jointing (splicing) of a steel rope used to transfer the traction force by friction forces. The developed mathematical model of jointing describes the stress-strain state of strands (wires) from quasi-static loads arising in the process of cyclic stretching and bending of the steel rope on the traction pulley, in which the resultant force in the pop-river section of the steel rope shifts relative to the central axis, causing its bending and twisting. Using experimental data, it is established that the torsion and bending of the steel rope is called the technology of jointing in the nodes where the replacement of strands occurs. It is experimentally established that defects in the area of jointing (splicing) are manifested as a result of cyclic tensile and bending loads on the pulley, which is associated with limited mobility of the strands in the nodes due to a violation of the symmetry of the cross section. When stretching and bending on the pulley, the load between the strands of the rope is distributed very unequally, which ultimately leads to its out-of-center stretching and the formation of a «wavy» defect. The mathematical model describes the process of jointing (splicing) of the steel plate, taking into account the existing technology that violates the symmetry of the cross section in the nodes, which, as a result of quasi-static loads, develops to critical values of the rejection index «waviness».