Ilyashenko A.V. - Associate Professor of the Department "Construction Mechanics"
Moscow State Construction University,
Candidate of Technical Sciences
The study of the bearing capacity of compressed elastic thin-walled rods with the initial dawning and undergoing local loss of stability is associated with the definition of the reduced cross section of the rod. The main provisions adopted for the study of a stress-deformed state in the cratery stage of compressed nonideal thin-walled rods are given in the works. This article discusses the core behavior of the rods, which are presented in the form of a set of jointly working elements - plates with the initial dilution that imitates the work of the shelves of corner, taving and cruciform profiles. These are the so-called plates-plates with one elastically squeezed edge and other free (see Sync). In the works such a plate refers to type II.
It was found that the destructive load characterizing the carrying ability of the rod significantly exceeds the load r (M) load, at which the local loss of stability of the imperfect profile occurs. From the graphs represented by B, it can be seen that the deformations of the longitudinal fibers along the perimeter of the cross section in the crate stage become extremely unequal. In the fibers removed from the roiber, the deformation of compression with an increase in the load decreases, and with loads close to the limit, due to the sharp twist of these fibers due to the initial dilutions and the increasing arrows of longitudinal semi-fellows, which were formed after the local loss of stability, appear and intensively grow deformations. stretching.
The cross-sectional sections with spinning longitudinal fibers are discharged by voltages, as if turn off from the rod operation, weakening the effective cross section and reducing its rigidity. So, the carrying ability of the thin-walled profile is not limited to the local loss of stability. The full load perceived by more rigid (less curved) cross-sectional areas can significantly exceed the value of r (m).
We obtain an effective, reduced section, eliminating non-working areas of the profile. To do this, use the expression for the function of the voltage F K (x, y), which describes the stress state of the K-oh plate type II (see).
Let us turn to the cylinder stresses σ kh (in the direction of the outer compressive force), determined in the most unfavorable cross section of the rod (x \u003d 0). We write them in general:
Σ kx \u003d ∂ 2 Ф k (a km, y, f kj, f koj, β c, d, β c, d, j, β, s) / ∂ y 2, (1)
where constant integration A Km (m \u003d 1.2, ..., 6) and the arrows of the components of the acquired deflections F kj (j \u003d 1.2) are determined from the solution of the system of resolution equations. This system of equations includes non-linear variational equations and boundary conditions describing the joint work of nonideal profile records. Arrows f koj (j \u003d 1,2, ..., 5) components of the initial deflection of the K-th record are determined for each type of profile experimentally;
ℓ - the length of the sustainability of the half-wave formed during the local loss;
S - plate width;
β c, d \u003d cs 2 + dℓ 2;
β c, d, j \u003d cs 4 + dℓ 2 s 2 + gℓ 4;
c, D, J - whole positive numbers.
The reduced or effective width of the reduced cross section of the plate-shelf (type II) is denoted by s p. To determine it, we repel the conditions for the transition from the actual cross section of the rod to the reduced:
1. Voltages in longitudinal fibers at the initial face of the plate (at y \u003d 0), adjacent to the edge (see the sinokun), remain the same as those obtained by nonlinear theory (1):
where f 2 kr \u003d f 2 kr + 2f k0r f kr.
To determine the voltage σ k2 \u003d σ k Max, it is necessary to substitute in (1) the ordinate of the most loaded longitudinal fiber, which is from the condition: ∂σ kx / ∂y \u003d 0.
2. The sum of internal efforts in the plate during the transition to a reduced section in the direction of the compressive force does not change:
3. The moment of inner effort relative to the axis passing through the initial face (y \u003d 0) perpendicular to the plane of the plate, remains the same:
It is obvious from the drawing that
σ 'k2 \u003d σ k1 + y n (σ k2 -σ k1) / (y p + s n). (five)
We write a system of equations to determine the reduced plate width S p. To do this, we substitute (1) and (5) in (3) and (4):
where α \u003d πs / ℓ; F kr, ξ \u003d f kr f koξ + f kr f kξ + f kor f kξ;
R, ξ - whole positive numbers.
The resulting system of equations (6) and (7) makes it possible to define the reduced width S p each of the shelves of the components of the compressed undergoing local stability loss thin-walled rod. Thus, the actual cross section of the profile was replaced by the reduced.
The proposed method seems to be useful both in theoretical and practical plan when calculating the carrying capacity of compressed pre-sparkled thin-walled rods in which local wave formation is permissible.
where, p is the number of current iteration; VT - complete metal sliding speed on the surface of the tool; Vn is the normal movement speed of the metal; WN is the normal speed of the tool; ST - rubbing voltage;
- yield voltage as a function of the deformable metal parameters, at a given point; - average voltage; - the intensity of the rate of deformation; x0 - the rate of deformation of comprehensive compression; KT is a penalty factor on the slide rate of the metal according to the instrument (specified by the method of iterations) KN - a penalty factory for the penetration of metal into the tool; M is the conditional viscosity of the metal, is specified by the method of hydrodynamic approximations; - tension voltage or backrest during rolling; Fn is the cross-sectional area of \u200b\u200bthe end of the pipe to which the tension or the sub-station is applied.
The calculation of the deformation and speed mode includes the distribution of the deformation states by the diameter, the necessary value of the plastic tension coefficient by the state of the Zob, the calculation of the hood coefficients, roll the diameters of the rolls and the speed of rotation of the main drive engines, taking into account the characteristics of its design.
For the first cells of the mill, including the first crate, which rolls, and for the latter, placed after the last crate, rolls, the plastic tension coefficients in them zr.i less than the required Zob. Through such a distribution of plastic tension coefficients over all cages, the calculated wall thickness at the output of it is greater than necessary on the reduction route. To compensate for the insufficient pulling ability of the tanks located in the first and after the last cells, which ride, it is necessary using an iterative calculation to find such a value of the Zob, so that the calculated and specified wall thickness at the outlet from the state were the same. The greater the magnitude of the required total plastic tension coefficient at the state of Zob, the greater the error in its definition without iterative calculation.
After the iterative calculations calculated the coefficients of the front and rear plastic tension, the thickness of the pipe wall at the inlet and output of the deformation cells along the cities of the reducing mill, we finally determine the position of the first and last cells, which ride.
Of course, the diameter is determined through the central angle qk.p. Between the vertical axis of symmetry of the roll of the roll and the line conducted from the center of the caliber coincides with the axle of rolling into the point on the surface of the caliber stream, where the neutral line of the deformation center is located on its surface, is conditionally located parallel to the rolling axis. The magnitude of the angle of the QK.P., first of all, depends on the value of the rear zado coefficient. and front zer. tension, as well as coefficient
Hood.
Determination of rolling diameter in the magnitude of the angle QK.P. Usually performed for the caliber, has a circle shape with a center in the rolling axis and a diameter equal to the average diameter of the DSR caliber.
The greatest errors in determining the quantity of the diameter without taking into account the actual geometric size of the caliber will be for the case when the rolling conditions determine its position or at the bottom or at the caliber reservation. The greater the real form of caliber will differ from the circle accepted in the calculations, the more so this error will be.
The maximum possible range of changes in the actual diameter value, the caliber roller is a roll of roll stream. The greater the amount of rolls forms a caliber, the more relative error of determining the diameter without taking into account the actual geometric size of the caliber.
With increasing partial compression of the pipe diameter in caliber, it grows the difference of its shape from the circular. So, with an increase in the compression of the pipe diameter of 1 to 10%, the relative error in determining the quantity of the diameter without taking into account the actual geometric sizes of caliber increases from 0.7 to 6.3% for two-color, 7.1% - for trival and 7.4% - For chotirohipwalkovoy "Katya" Tilt when kinematic rolling conditions, rolling diameter located along the bottom of the caliber.
Simultaneous increase in the same
3.2 Calculation Table Rolling
The main principle of constructing the technological process in modern installations is to obtain on a continuous mill of the pipes of one permanent diameter, which allows the use of a blank and a sleeve is also a permanent diameter. Obtaining the pipes of the required diameter is ensured by the reduction. Such a work system makes it much easier and simplifies the setting of the mill, reduces the tool park and, most importantly, it allows you to maintain high performance of the entire unit even when rolling pipes of the minimum (after reduction) diameter.
The rolling table is counting against the rolling stroke according to the method described in. The outer diameter of the pipe after the reduction is determined by the size of the last pair of rolls.
D p 3 \u003d (1,010..1,015) * d o \u003d 1.01 * 33.7 \u003d 34 mm
where D p is the finished pipe after the reducing mill.
Since after a continuous mill, a pipe of one diameter comes out, then we accept D H \u003d 94 mm. In continuous mills, the roll calibration ensures the obtainment in the last steam rolls of the inner diameter of the pipe larger than 1-2 mm diameter, so that the mandrel diameter will be equal to:
H \u003d D H - (1..2) \u003d D H -2S N -2 \u003d 94-2 * 3.2-2 \u003d 85.6 mm.
We adopt the diameter of the mandrel equal to 85 mm.
The inner diameter of the sleeve must provide free administration of the mandrel and takes 5-10 mm larger than the diameter of the mandrel
d r \u003d n + (5..10) \u003d 85 + 10 \u003d 95 mm.
The wall of the sleeve accept:
S r \u003d s H + (11..14) \u003d 3.2 + 11.8 \u003d 15 mm.
The outer diameter of the sleeves is determined based on the size of the inner diameter and the wall thickness:
D r \u003d D g + 2s g \u003d 95 + 2 * 15 \u003d 125 mm.
The diameter of the used billet D З \u003d 120 mm.
The diameter of the mandrel of the firmware is selected taking into account the magnitude of the rolling, i.e. Lifting the inner diameter of the sleeve constituting from 3% to 7% of the inner diameter:
N \u003d (0.92 ... 0.97) D g \u003d 0.93 * 95 \u003d 88 mm.
The coefficients of drawing for the firmware, continuous and reduction mills are determined by formulas:
,
Common hood coefficient is:
Similarly, a rolling table for pipes with a size of 48.3 × 4.0 mm and 60.3 × 5,0mm is calculated.
The rolling table is presented in Table. 3.1.
|
The size of finished pipes, mm |
Diameter of the workpiece, mm |
Firmware Stan. |
Continuous Stan. |
Reducing Stan. |
Common hood coefficient |
||||||||||
|
Outside diameter |
Wall thickness |
Size of the sleeve, mm |
Mandrel diameter, mm |
Extrase coefficient |
Pipe sizes, mm |
Mandrel diameter, mm |
Extrase coefficient |
Pipe size, mm |
Number of cells |
Extrase coefficient |
|||||
|
Wall thickness |
Wall thickness |
Wall thickness |
|||||||||||||
3.3 Calibration of reducing mill rolls
Calibration of rolls is important part of Calculation of the mode of operation of the mill. It largely determines the quality of the pipes, the durability of the tool, the distribution of loads in working cells and drive.
Calibration calculation of rolls includes:
the distribution of private deformations in the cities of the mill and counting the average diameters of calibers;
determination of the size of the valve calibers.
3.3.1 Distribution of private deformations
According to the nature of the changes in private deformations of the cage of the reduction mill can be divided into three groups: the head at the beginning of the mill, in which the compresses are intensively increasing in the course of rolling; calibrating (at the end of the mill), in which deformations decrease to minimum meaning, and a group of centes between them (middle), in which private deformations are maximal or close to them.
When rolling pipes with a tension of the size of private deformations, it is taken on the basis of the condition of the stability of the pipe profile with the magnitude of the plastic tension that provides a predetermined pipe.
The coefficient of general plastic tension can be determined by the formula:
,
where 
- axial and tangential deformations taken in logarithmic form; The value is determined in the case of trivial caliber by the formula
where (S / D) Cp is the mean ratio of the wall thickness to the diameter for the period of strain of the pipe in the mill; K-coefficient taking into account the change in the degree of thickness of the pipe.
,
,
where M is the value of the total deformation of the pipe in diameter.
.
The magnitude of the critical private compression with this coefficient of plastic tension, according to, can reach 6% in the second crate, 7.5% in the third cage and 10% in the fourth cage. In the first crates it is recommended to receive in the range of 2.5-3%. However, to ensure a stable capture, the magnitude of the compression is usually reduced.
In the premeditone and fines of the mill, the compression is also reduced, but to reduce loads on the rolls and increase the accuracy of finished pipes. In the last cage of the calibrating group, the compression is taken equal to zero, the penultimate-up to 0.2 of the compression in the last cage of the middle group.
IN medium group Celes are practiced a uniform and uneven distribution of private deformations. With a uniform distribution of compression in all cells of this group, they are permanent. The uneven distribution of private deformations may have several options and be characterized by the following laws:
compression in the middle group is proportionally reduced from the first cells to the latter - the falling mode;
in several first cells of the middle group, private deformations are reduced, and the rest are permanent;
compression in the middle group first increase, and then reduce;
in several first cells of the middle group, private deformations are left permanent, and in the rest reduce.
With falling deformation modes in the average group of cells, the differences in the value of rolling power and the load load are reduced, caused by the growth of metal deformation resistance as rolling, due to the decrease in its temperature and increase the deformation rate. It is believed that a decrease in compression by the end of the mill also allows you to improve the quality of the outer surface of the pipes and reduce the transverse difference.
When calculating the calibration of rolls we accept the uniform distribution of compounds.
The magnitudes of private deformations in the mills are shown in Fig. 3.1.
Distribution of compounds
Based on the adopted values \u200b\u200bof private deformations, the average diameters of calibers can be calculated by formulation pipeand, directly, ... failures) during production Foam concrete. For production Foam concrete applied various ... workers directly related to production Foam concrete, special clothing, ...
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Introduction
1 State of the issue on the theory and technology of profiling of multifaceted pipes by displeasure drawing (literary review).
1.1 Sort of profile pipes with flat faces and their use in the technique.
1.2 Main ways to produce profile pipes with flat faces.
1.4 Still shaped tool.
1.5 The drawing of multifaceted vintage-shaped pipes.
1.6 Conclusions. The purpose and objectives of the research.
2 Development of a mathematical model profiling pipes with dragging.
2.1 Basic provisions and assumptions.
2.2 Description of the geometry of the deformation focus.
2.3 Description of the strength parameters of the process of profiling.
2.4 Evaluation of the fill in the corners of the wolves and tias of the facelights of the profile.
2.5 Description of the algorithm for calculating profiling parameters.
2.6 Computer analysis of power conditions for profiling square pipes with irrelevant drawing.
2.7 Conclusions.
3 Calculation of the tool for strength for drawing profile pipes.
3.1 Setting the problem.
3.2 Determination of the intense status of the Volley.
3.3 Construction of displaying functions.
3.3.1 Square hole.
3.3.2 Rectangular hole.
3.3.3 Plane tank.
3.4 Example of calculating the intense state of wolves with a square hole.
3.5 Example of calculating the intense status of wolves with a circular opening.
3.6 Analysis of the results obtained.
3.7 Conclusions.
4 Experimental studies for profiling square and rectangular pipes with dragging.
4.1 Methodology for the experiment.
4.2 Profiling square tube with dragging in one transition to one volt.
4.3 Profiling square tube with dragging for one transition with anti-antipaty.
4.4 Three-factor linear mathematical model Profiling square pipes.
4.5 Determination of the fill in the corners of the wolves and tias.
4.6 Improving Channel Calibration Wolves for rectangular pipes.
4.7 Conclusions.
5 Drawing of profile screw-like swirling pipes.
5.1 Selection of technological parameters of drawing with molding.
5.2 Definition of torque.
5.3 Determining the effort of stretching.
5.4 Experimental studies.
5.5 Conclusions.
Relevance of the topic. The active development of the production sector of the economy, strict requirements for the efficiency and reliability of products, as well as the efficiency of production require the use of resource-saving types of equipment and technology. For many industries of the construction industry, mechanical engineering, instrument making, the radio engineering industry, one of the solutions is the use of pipes of economical species (heat exchange and radiator pipes, waveguides, etc.), which allows: increase the power of installations, strength and durability of structures, reduce their metal consistency, save materials Improved appearance. Wide nomenclature and considerable amount of consumption of profile pipes made the development of their production in Russia necessary. Currently, the bulk of the shaped pipes is manufactured in pipe-operated workshops, as the operations of cold rolling and drawing are sufficiently developed in the domestic industry. In this regard, the improvement of existing production is especially important: the development and manufacture of equipment, the introduction of new technologies and methods.
The most common types of shaped pipes are multifaceted (square, rectangular, hex, etc.) of high accuracy pipes obtained by irrelevant drawing in one pass.
The urgency of the topic of the thesis is determined by the need to improve the quality of multifaceted pipes by improving the process of their profiling without mandrel.
The aim of the work is to improve the process of profiling of multi-faceted pipes by displeasure drawing by developing techniques for calculating technological parameters and tool geometry.
To achieve the goal, it is necessary to solve the following tasks:
1. Create a mathematical model for profiling multifaceted pipes by displeasant drawing to assess the power conditions, taking into account the non-aluminous law of hardening, the anisotropy of the properties and the complex geometry of the Volley channel.
2. To determine the power conditions depending on the physical, technological and structural parameters of the profiling in case of displeasure.
3. Develop a methodology for estimating the fill corners of the corners of the wolves and tias to the faces in the drawing of multifaceted pipes.
4. Develop a methodology for calculating the strength of the shaped wolves to determine the geometric parameters of the tool.
5. Develop a methodology for calculating technological parameters while simultaneously profiling and dry.
6. Conduct experimental studies of technological parameters of the process that ensure the high accuracy of the dimensions of multifaceted pipes and check the adequacy of the calculation of the technological parameters of profiling on the mathematical model.
Research methods. Theoretical studies were based on the basic provisions and assumptions of the theory of drawing, the theory of elasticity, the method of conformal mappings, computational mathematics.
Experimental studies were carried out in laboratory conditions Using the methods of mathematical planning of the experiment on the universal testing machine of CDMU-30.
The author protects the results of the calculation of the technological and structural parameters of the profiling of multifaceted pipes by displeasant drawing: the method of calculating the strength of the shaped wolves, taking into account normal loads in the channel; Methodology for calculating the technological parameters of the process of profiling of multifaceted pipes by displeasant drawing; methodology for calculating the technological parameters while simultaneously profiling and drying with displeasure drawing of screw thin-walled multifaceted pipes; The results of experimental studies.
Scientific novelty. The patterns of changes in the power conditions are established under the profiling of multifaceted pipes by irrelevant drawing, taking into account the nonlinear law of hardening, the anisotropy of the properties and the complex geometry of the Volley channel. The problem is solved by determining the stress state of the shaped wolves under the action of normal loads in the channel. The full record of the equations of the stress-strain state while simultaneously profiling and cutting the multifaceted pipe.
The reliability of the research results is confirmed by the strict mathematical formulation of objectives, using analytical methods for solving problems, modern methods of experimental experimental experimental data, reproducibility of the results of the experiment, satisfactory convergence of calculated, experimental data and the results of practice, compliance with the results of modeling the manufacturing technology and the characteristics of ready-made multifaceted pipes.
The practical value of the work is as follows:
1. The modes of obtaining square pipes 10x10x1mm from high precision alloy D1, increasing the yield of suitable by 5%.
2. The dimensions of the shaped wolves ensuring their performance are determined.
3. Combining profiling and twisting operations reduces the technological cycle of manufacturing screw multifaceted pipes.
4. Improved calibration of the shaped wolf channel for profiling rectangular pipes 32x18x2mm.
Approbation of work. The main provisions of the dissertation work are reported and discussed at the International Scientific and Technical Conference dedicated to the 40th anniversary of the Samara Metallurgical Plant "New Destinations of Production and Consumption of Aluminum and its Alloys" (Samara: SGAU, 2000); 11 Interuniversity Conference "Mathematical Modeling and Regional Tasks", (Samara: SSTU, 2001); Second International Scientific and Technical Conference "Metallophysics, Mechanics of Materials and Processes of Deformation" (Samara: SGAU, 2004); XIV stupid-levsk readings: International Youth Scientific Conference (Kazan: KSTU, 2006); IX Royal Readings: International Youth Scientific Conference (Samara: SGAU, 2007).
Publications Materials reflecting the main dissertation of the thesis are published in 11 works, including in the leading peer-reviewed scientific publications defined by the highest attestation commission - 4.
Structure and scope of work. The thesis consists of the main symbols, the introduction, of the five chapters, the list of literature and applications. The work is set out on 155 pages of typewritten text, including 74 drawings, 14 tables, bibliography from 114 items and an application.
The author is grateful to the team of the Department of Metal Processing Pressure For Assistance, as well as scientific leader, Professor of the Department, D.T.N. V.R. Cargin for valuable comments and practical assistance in work.
Main results and conclusions for work
1. From the analysis of scientific and technical literature it follows that one of the rational and productive processes of manufacturing thin-walled multi-faceted pipes (square, rectangular, hexagon, octamic) is the process of displeasure drawing.
2. A mathematical model has been developed for the process of profiling of multifaceted pipes by displeasant drawing, which allows determining the power conditions, taking into account the nonlinear law of hardening, the anisotropy of the properties of the pipe material and the complex geometry of the Volley channel. The model is implemented in the Delphi 7.0 programming environment.
3. With the help of a mathematical model, the quantitative influence of physical, technological and structural factors on the power parameters of the process of profiling of multifaceted pipes with displeasure drawing is established.
4. Developed methods for estimating the fillerness of corners of the corners of wolves and tias of the faces in case of irrelevant drawing of multifaceted pipes.
5. A method is developed for calculating the strength of the shaped wolves, taking into account normal loads in the channel, based on the function of ery stresses, the method of conformal mappings and the third strength theory.
6. A three-factor mathematical model of profiling of square pipes was experimentally constructed, which allows you to select technological parameters that ensure the accuracy of the geometry of the obtained pipes.
7. Developed and brought to the engineering level, the method of calculating technological parameters with simultaneous profiling and twisting multifaceted pipes by irrelevant drawing.
8. Experimental studies of the process of profiling of multi-faceted pipes by irrelevant drawing showed satisfactory convergence of results theoretical Analysis with experimental data.
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