On calculation of stress-strain state of steel closed ropes in extension and twisting. Part 1. Determination of generalized stiffness and deformation coefficients

Closed hoisting ropes are related to multi-layer ropes with single laying and they are used as a motive component in lifting and transportation machines and mechanisms. It is known that closed hoisting ropes are used as a rod core for transmission of reciprocating and rotating motion from a surface drive to an operating body of well pump in oil production from wells [1, 2]. Closed ropes are often failing to operate owing to structure violation, such as buckling, lamination, unlocking and destruction of external Z-shape wires etc. [2–6]. To provide reliable and safe rope operation, it is necessary to have trustworthy methods for determination of stress-strain state (SSS) of role elements (wires and layers). The main approaches to theoretical SSS investigation for rope elements were discussed in the works [3, 4, 7–10]. The paper [7] attract attention to the techniques providing higher calculation precision and maximal approximation to construction of the real rope. These techniques are based on the following ideas: a) discrete model where rope is presented as a complicated and statically undefined rod system that can be subjected to calculation by the methods of building mechanics [3]; b) the theory of fiber composites and solution of the SaintVenant problem for a cylinder with screw anisotropy [8]. The mathematical model, where each rope layer is considered from the point of view of energetic approach as anisotropic cylinder shell equivalent with its elastic properties, while a rope in general is considered as the system of cylinder shells inserted inside each other and mutually contacting due to contact pressure and friction, is suggested in the works [11, 12]. Independently of the used techniques, the expressions for determination of force parameters in cross section of rope elements during joint extension and rotation are described as the system including two equations [3]: