Study of strain-stress state of flat knives for cutting thin-walled pipes

2021 ◽  
Vol 77 (9) ◽  
pp. 1039-1046
Author(s):  
S. P. Eron’ko ◽  
E. V. Oshovskaya ◽  
O. A. Kovaleva
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Stress State ◽  
Mathematical Simulation ◽  
Cross Section ◽  
Cutting Tool ◽  
Small Diameter ◽  
Pipe Welding ◽  
Strain Stress ◽  
Thin Walled

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.

scholarly journals Plastic Deformation of Metal Tubes Subjected to Lateral Blast Loads

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Kejian Song ◽  
Yuan Long ◽  
Chong Ji ◽  
Fuyin Gao
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Plastic Flow ◽  
Cross Section ◽  
Circular Tube ◽  
Circular Tubes ◽  
Simply Supported ◽  
Different Dimensions ◽  
Thin Walled ◽  
Wave Induced

When subjected to the dynamic load, the behavior of the structures is complex and makes it difficult to describe the process of the deformation. In the paper, an analytical model is presented to analyze the plastic deformation of the steel circular tubes. The aim of the research is to calculate the deflection and the deformation angle of the tubes. A series of assumptions are made to achieve the objective. During the research, we build a mathematical model for simply supported thin-walled metal tubes with finite length. At a specified distance above the tube, a TNT charge explodes and generates a plastic shock wave. The wave can be seen as uniformly distributed over the upper semicircle of the cross-section. The simplified Tresca yield domain can be used to describe the plastic flow of the circular tube. The yield domain together with the plastic flow law and other assumptions can finally lead to the solving of the deflection. In the end, tubes with different dimensions subjected to blast wave induced by the TNT charge are observed in experiments. Comparison shows that the numerical results agree well with experiment observations.

Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

2020 ◽  
Vol 10 (6) ◽  
pp. 599-609
Author(s):  
Valery А. Gruzdev ◽  
◽  
Georgy V. Mosolov ◽  
Ekaterina A. Sabayda ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Roughness Coefficient ◽  
Computational Domain ◽  
Channel Deformations ◽  
Geological Surveys ◽  
Kuban River ◽  
The Stability ◽  
Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

Modeling the interaction of a beam of elastic vibrations with the surface of an object under acoustic non-destructive testing

2020 ◽  
pp. 55-57
Author(s):  
N.P. Aleshin ◽  
M.V. Grigorev ◽  
N.V. Kryisko ◽  
A.G. Kusyiy
Keyword(s):  
Mathematical Model ◽  
Transverse Wave ◽  
Small Diameter ◽  
Non Destructive Testing ◽  
Destructive Testing ◽  
Liquid Immersion ◽  
Elastic Transverse ◽  
Elastic Transverse Wave ◽  
Physical And Mathematical Models ◽  
Non Destructive

Physical and mathematical models are developed that describe the refraction by a concave cylindrical surface of a field of an elastic transverse wave arbitrarily incident on a surface from a liquid. Immersion control of a small-diameter pipeline is considered. Keywords acoustics, ultrasound, immersion control, physical and mathematical model, bent surface, small-diameter pipeline. [email protected]

On the displacements of the contours of the optic-electronic space images. Mathematical modeling of displacement

2017 ◽  
Vol 992 (4) ◽  
pp. 32-38 ◽  
Author(s):  
E.G. Voronin
Keyword(s):  
Mathematical Modeling ◽  
Remote Sensing ◽  
Mathematical Model ◽  
Point Of View ◽  
Design Features ◽  
Space Images ◽  
Electronic Imaging ◽  
Measuring Accuracy ◽  
Physical Laws

The article opens a cycle of three consecutive publications dedicated to the phenomenon of the displacement of the same points in overlapping scans obtained adjacent CCD matrices with opto-electronic imagery. This phenomenon was noticed by other authors, but the proposed explanation for the origin of displacements and the resulting estimates are insufficient, and developed their solutions seem controversial from the point of view of recovery of the measuring accuracy of opticalelectronic space images, determined by the physical laws of their formation. In the first article the mathematical modeling of the expected displacements based on the design features of a scanning opto-electronic imaging equipment. It is shown that actual bias cannot be forecast, because they include additional terms, which may be gross, systematic and random values. The proposed algorithm for computing the most probable values of the additional displacement and ways to address some of the systematic components of these displacements in a mathematical model of optical-electronic remote sensing.

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