## 3 Results
### Development of a Method for Repairing Main Pipelines
Further, in accordance with Figures 3-5, installation of two or more fixing and centering devices, the design of which was developed in the scope of this study by authors, is carried out using a handling device on both sides of the cut-out section on the upper generatrix of the pipeline in selected sections, in which the corresponding cross markers are installed [51]. At least two fixing and centering devices are installed on the defective section of the pipeline that needs to be cut out. At the edges of each pipeline cutting place, there must be at least one fixing and centering device at a distance of no more than 0.5 m from the cutting point. After that, the pipeline is wrapped around by the grip flaps (5). Next, installation and drilling into the ground is carried out by drilling anchors (9) using a drilling rotator installed on a hexagon. After that, the current position of the pistons of large hydraulic cylinders (3) of the fixing and centering devices is fixed by closing the hydraulic locks of the hydraulic system, thereby fixing the position of the ends of the pipeline during and after cutting. The next step is the installation of cutting equipment (17) in the cutting places of the pipeline (13), after which the pipeline is cut. Next, the cut out defective section of the pipeline is lowered to the bottom of the trench by the fixing and centering devices installed on it, after which their drill anchors (9) and the fixing and centering devices themselves, installed on the cut out defective section (16) of the pipeline, are dismantled using a handling device. In addition, lifting from the bottom of the trench and dismantling the cut section of the pipeline are carried out with the help of a handling device. Further, with the help of a handling device, a new section is mounted to the place of welding of its ends with the ends of the pipeline, and the pipeline ends are centered with the ends of the defect-free section by applying the previously calculated forces for centering the ends of the pipeline to large hydraulic cylinders (30 of the corresponding fixing and centering devices. Figure 4: Side view of the device in the process of centering the pipeline after cutting out the defective section: 1—the base of the grip; 3—large power cylinder; 4—small power cylinder; 5—grip flap; 6—grip roller; 9—drill anchor; 10—platform; 11—hexagon; 12—guide cylinder; 13—pipeline; 14—arc of grip; 15–cutting place; 16—cut out section of the pipeline; 17—pipeline cutting machine. Figure 3: Device for fixing and centering the ends of the pipeline when cutting out its defective section: 1—the base of the grip; 2—grip axis; 3—large power cylinder; 4—small power cylinder; 5—grip flap; 6—grip roller; 7—roller stop; 8—grip lock; 9—drill anchor; 10—platform; 11—hexagon; 12—guide cylinder; 13—pipeline; 14—arc of grip. After that, the ends of the defect-free section are welded with the ends of the pipeline, and the drill anchors (9) of the fixing and centering devices are dismantled by means of a hydraulic rotator and the fixing and centering devices themselves. Next, the quality of the welded joints is checked and their isolation, as well as the burying of the repaired section of the pipeline, is carried out. The control of the hydraulic cylinders of the devices is carried out by the automation system by adjusting the pistons of the hydraulic cylinders in accordance with the calculated values of the forces for centering the ends of the pipeline or by remote control. Development of a Mathematical Model for Assessing the Loads Taken up by the Devices and the Forces Required for Centering the Ends of the Pipeline  
The initial data for the proposed mathematical model are data on the spatial position of the pipeline in the repair trench, the outer and inner diameters of the pipeline, the Young's modulus of its wall material as well as the coordinates of the location of the grips along the pipeline.