## 1 Introduction  
Steel ropes consisting of wound strands of wires have a long history of implementation in technical installations. Steel ropes are widely used starting from static support of buildings and bridges to moving force transmission in elevators and cable cars. Due to their thin structure and the fact that ropes are the most loaded components in critical safety installations, such as passenger elevators, periodic quality control and maintenance is obligatory for installations with ropes [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. Defects of the ropes develop from exploitation based effects: mechanical wear, cracks from bending fatigue, corrosion, overload, and shear cracks. Steel rope quality degeneration process is very gradual; it never breaks instantly, wires are broken sequentially and at random places. There are plenty of methods for cable diagnostics. The oldest method of rope examination is optical inspection, which is still in use, but it remains expensive and inefficient with modern applications. There are more methods, such as acoustic field, electromagnetic [1; 4; 5; 12; 13] and X-ray, but they are hardly applicable for broken wire defects. The above mentioned diagnostic methods often fail at finding broken wires on steel rope surfaces. Dirty and oily ropes in real applications can be inspected much more efficiently using transversal vibrations of rope fragments, where the rope fragment ends are fixed. During the vibration process broken wires clean themselves and can be noticed by using vibration sensors. The analysis of the rope defects and its diagnostics are impossible without a proper understanding of the rope mechanics and the development of realistic models. There are many analytical and numerical models; a primary role of the latter belongs to the method of finite element modeling (FEM). The proposed models of the rope evaluate different phenomena. [PERSON] and [PERSON] developed a model for seven rope strands with an independent core, evaluating stresses and fatigue, but omitting contact and friction influences [14]. There is research on twisted \(6\times 36\) IWRC and straight \(18\times 7\) IWRC structure of the rope, where stresses and torque are evaluated, but the contact influence was neglected with infinite friction [15]. An improved model of the \(6\times 19\) rope strand contacts and friction evaluated the mechanism of heat generation in the rope [16], but general behavior of the rope was left behind. Modern FEM model of two-layered rope fragments evaluated all possible contacts between wires, dry friction, small deflections and deformations, torque, and bending moments [17], thus explaining behavior of the rope structure using static loads. Further analysis of the rope dynamics is required to decrease amount of calculation, therefore a 3D linear FEM element for the definition of friction between wires and the rope core was developed [18; 19]. Development of more comprehensive FEM models of one strand of the rope in the mode of elastic deformation really diminished differences between numerical calculations and experimental research. Using such analysis, promising results with strong correlation between them and experimental measurements were obtained [20]. Influence of variable strand pitch to other rope mechanical properties was successfully modeled and tested using factory-produced rope [21], thus proving optimal strand pitch value. Material properties as well as polymer use in the steel ropes with a polymer core influences rope exploitation process, and a proposed methodology of fault finding in the internal layer brings new perspectives to the field of rope diagnostics [22]. A significant amount of research has been performed in the field of practical defectoscopy, i.e. the research and development of rope defect detecting equipment. A well-known rope control device, which implemented magnetic field analysis, is presented in [23]. A magnetic field delivers comprehensive information about ferromagnetic media; this way various defects of the rope can be detected.