## 4 Discussion  
A sharp displacement of the ends of the pipeline when it is cut during the repair process with replacement of the defective section is an urgent problem. The reason for this displacement is the elastic bending of the main pipeline. It should be noted that the pipeline located in the repair trench is most often in an elastically bent state. At the same time, no measures are provided to eliminate the sharp displacement. It is also important to note that, for further centering of the pipeline ends, pipelayers are used, which allow centering only by raising the pipeline ends. To ensure such centering conditions, it is often necessary to carry out additional earthworks. In addition, the transportation of pipelayers requires the payment of permits for the transport of oversized equipment, which in annual terms can reach $100,000 for one service division of the company. The solution to the above problems is the method of repair of main pipelines developed within the scope of this study. This repair method improves the efficiency of the repair process, as well as the level of industrial safety. This is achieved by using the developed fixing and centering devices during the repair process, which allow fixing of the ends of the pipeline before cutting it to eliminate their sharp displacement, as well as their further centering before welding a new section. The developed mathematical model makes it possible to carry out a preliminary assessment of the reaction forces arising in the hydraulic cylinders of devices when fixing the ends of the pipeline, the efforts of their centering as well as the stresses arising, in this case, in the body of the pipeline. The mathematical model showed a sufficient level of convergence with the results of finite element modeling of the main pipeline in the ANSYS software package. At the same time, the assessment of the reaction forces arising in the hydraulic cylinders of the devices was carried out on the basis that the oscillations of the pipeline are undamped, which simplifies the mathematical model and, as a result, gives somewhat overestimated values of the reaction forces compared to the actual ones. This excess of the calculated value over the actual value is taken as a safety factor, which makes it possible to ensure greater reliability of the operation of the hydraulic cylinders of the devices during their selection. To clarify the value of this safety factor, in the future it is planned to carry out experimental studies to measure the reaction forces that occur when the pipeline ends are displaced in fixed supports in selected sections of the pipeline. The initial data for carrying out calculations according to the proposed mathematical model are data on the spatial position of the pipeline in the trench. As a method for determining the spatial position of the pipeline, laser scanning is proposed, the result of which is a spatial point cloud of the pipeline. The developed method of pipeline point cloud processing allows obtaining of a polynomial describing the position of the central axis of the pipeline in space. According to the results of experimental studies, the polynomial obtained as a result of applying this method in comparison with the polynomial obtained as a result of photographing the cross markers glued along the side generatrix of the pipeline allows, with an accuracy of 5%, the assessment of the studied values of the reaction forces, centering forces and the resulting stresses in the pipeline wall. The developed mathematical model makes it possible to carry out calculations for pipelines with different diameters, wall thicknesses as well as wall materials with different strength parameters. The diameter and wall thickness of the pipeline are taken into account when calculating its rigidity and axial moment of inertia. As for the strength parameters of the pipeline, its plasticity plays the most important role here.