Cutting of pipes into measured lengths on-line of pipe welding mill by disc saws and by facilities of abrasive cutting requires special measures of safety of personal. Besides, the necessity of frequent change of cutting instrument results in losses of production time. To eliminate the drawbacks, a study was initiated related to creation of shears which could enable to accomplish a quality transverse cutting of thin-walled pipes of small diameter by flat knives with various form of the working edges. A methodology and the results of study of strain-stress state of flat knives with application of physical and mathematical simulation of the process of transverse cutting of thin-walled pipes of small diameter presented. At the physical simulation using a polarization-optical installation, the pictures of deformation centers arising in the lower part of the knife in the zone of contact of its cutting edges with the body of the hollow circular profile being cut by it were obtained. In the experiment, models of three types of knives made of organic glass on a scale of 1:1 were used. Cutting edges of the knives for cutting pipes of 25 mm outer diameter, wall thickness of 2 mm were wedge-shaped, convex semicircular and concave. The data from studies of the loaded state of transparent knife models served as the basis for mathematical simulation of the strain-stress state of the shears cutting tool in the SolidWork application package using a strength analysis module that implements the finite element method in the form of tetrahedrons. The current values of the pipe cutting force used in the mathematical model were preliminarily calculated according to the previously proposed dependence, taking into account the strength of the hollow profile material and the area of the cut layer of its cross section for a given relative displacement of the cutting edges of the knife. The results of mathematical modeling were the pictures of deformations and equivalent stresses of the cutting part of the knife, determined according to the third theory of strength. A qualitative similarity has been established for the distribution patterns of stress fields recorded using the polarization-optical method on knife models and obtained in mathematical modeling for working samples of the shears cutting tool operated under the conditions of pipe welding mills. The proposed mathematical model makes it possible to estimate the values of the maximum equivalent stresses in the working part of a flat knife, taking into account the shape of its cutting edges, as well as the force required for cutting a thin-walled pipe into measured lengths with the corresponding dimensions of its cross-section and the strength of the material.
MATHEMATICAL MODELING OF PLASTICITY CONDITIONS FOR PROBLEMS OF ZERO GAUSSIAN CURVATURE OF THE STRESS STATE OF PLATES UNDER VARIABLE LOADS
