Reduction is carried out after additional heating (or heating) of pipes to 850-1100 ° C by rolling them on multi-stand continuous mills (with up to 24 stands) without using an internal tool (mandrel). Depending on the adopted system of work, this process can proceed with an increase in the wall thickness or with a decrease in it. In the first case, rolling is carried out without tension (or with very slight tension); and in the second - with a high tension. The second case, as a more progressive one, has become widespread in the last decade, since it allows a much greater reduction, and a decrease in the wall thickness at the same time expands the range of rolled pipes with more economical thin-walled pipes.
The possibility of wall thinning during reduction makes it possible to produce pipes with a slightly larger wall thickness (sometimes by 20-30%) on the main pipe-rolling unit. This significantly increases the productivity of the unit.
At the same time, in many cases, the older principle of operation - free reduction without tension - retained its significance. Basically, this refers to the cases of reduction of relatively thick-walled pipes, when even at high tensions it becomes difficult to significantly reduce the wall thickness. It should be noted that reduction mills are installed in many pipe rolling shops, which are designed for free rolling. These mills will be in operation for a long time and, therefore, tension-free reduction will be widely used.
Let us consider how the pipe wall thickness changes during free reduction, when there are no axial tension or back-up forces, and the stress state diagram is characterized by compressive stresses. B. JI. Kolmogorov and A. 3. Gleiberg, proceeding from the fact that the actual change in the wall corresponds to the minimum work of deformation, and using the principle of possible displacements, gave a theoretical definition of the change in wall thickness during reduction. In this case, the assumption was made that the nonuniformity * of deformation does not significantly affect the change in the wall thickness, and the forces of external friction were not taken into account, since they are much less than the internal resistances. Figure 89 shows the curves of the change in wall thickness from the initial SQ to the given S for low-strength steels depending on the degree of reduction from the initial diameter DT0 to the final DT (ratio DT / DTO) and the geometric factor - pipe fineness (ratio S0 / DT0).
At low degrees of reduction, the resistance to longitudinal outflow turns out to be greater than the resistance to inward outflow, which causes wall thickening. With an increase in the value of deformation, the intensity of wall thickening increases. However, at the same time, the resistance to the outflow inside the pipe also increases. At a certain amount of reduction, the wall thickening reaches its maximum and a subsequent increase in the degree of reduction leads to a more intensive increase in the resistance to outflow inward and, as a result, the thickening begins to decrease.
Meanwhile, only the wall thickness of the finished reduced pipe is usually known, and when using these curves it is necessary to set the desired value, that is, to use the method of successive approximation.
The nature of the change in wall thickness changes dramatically if the process is carried out with tension. As already mentioned, the presence and magnitude of axial stresses are characterized by the rate conditions of deformation on a continuous mill, the indicator of which is the coefficient of kinematic tension.
When reducing with tension, the deformation conditions of the pipe ends differ from the deformation conditions of the middle of the pipe, when the rolling process has already stabilized. In the process of filling the mill or when the pipe leaves the mill, the ends of the pipe perceive only part of the tension, and rolling, for example in the first stand until the pipe enters the second stand, proceeds without tension at all. As a result, the pipe ends always thicken, which is a disadvantage of the tension reduction process.
The amount of trim may be slightly less than the length of the thickened end due to the plus tolerance for wall thickness. The presence of thickened ends significantly affects the economy of the reduction process, since these ends must be cut off and are a sunk production cost. In this regard, the process of rolling with tension is used only in the case of obtaining after reduction of pipes with a length of more than 40-50 m, when the relative losses in cuttings are reduced to a level characteristic of any other rolling method.
The above methods for calculating the change in the thickness of the stays allow ultimately to determine the stretch ratio both for the case of free reduction and for the case of rolling with tension.
With a reduction of 8-10% and a plastic tension coefficient of 0.7-0.75, the slip is characterized by a coefficient of ix = 0.83-0.88.
From consideration of formulas (166 and 167), it is easy to see how exactly the speed parameters in each stand must be observed in order for rolling to proceed according to the design mode.
The group drive of the rolls in the reduction mills of the old design has a constant ratio of the number of revolutions of the rolls in all stands, which only in a particular case for pipes of the same size can correspond to the free rolling mode. Reduction of pipes of all other sizes will occur with other hoods, therefore, free rolling will not be maintained. In practice, in such mills, the process always proceeds with a slight tension. The individual drive of the rolls of each stand with fine adjustment of their speed allows creating different tension modes, including the free rolling mode.
Since the front and rear tensions create moments directed in different directions, the total moment of rotation of the rolls in each stand can increase or decrease depending on the ratio of the forces of the front and rear tension.
In this respect, the conditions in which the initial and last 2-3 stands are located are not the same. If the rolling moment in the first stands as the pipe passes in the subsequent stands decreases due to tension, then the rolling moment in the last stands, on the contrary, should be higher, since these stands are mainly experiencing back tension. And only in the middle stands, due to the close values of the front and rear tension, the rolling moment at steady state differs little from the calculated one. When calculating the strength of the drive units of a rolling mill operating with tension, it should be borne in mind that the rolling moment increases for a short time, but very sharply during the period when the pipe is captured by the rolls, which is explained by the large difference in the speeds of the pipe and rolls. The resulting peak load, which sometimes exceeds the steady-state one by several times (especially when reducing with a high tension), can cause breakdowns of the drive mechanism. Therefore, in the calculations, this peak load is taken into account by introducing an appropriate coefficient, taken equal to 2-3.
480 RUB | UAH 150 | $ 7.5 ", MOUSEOFF, FGCOLOR," #FFFFCC ", BGCOLOR," # 393939 ");" onMouseOut = "return nd ();"> Dissertation - 480 rubles, delivery 10 minutes, around the clock, seven days a week
Kholkin Evgeny Gennadievich. Study local sustainability thin-walled trapezoidal profiles at longitudinal and transverse bending: dissertation ... Candidate of Technical Sciences: 01.02.06 / Kholkin Evgeniy Gennadevich; [Place of protection: Ohm. state tech. un-t] .- Omsk, 2010.- 118 p .: ill. RSL OD, 61 10-5 / 3206
Introduction
1. Review of stability studies of compressed plate structural elements 11
1.1. Basic definitions and methods for studying the stability of mechanical systems 12
1.1.1, Algorithm for studying the stability of mechanical systems by a static method 16
1.1.2. Static approach. Methods: Euler, Imperfect, Energetic 17
1.2. Mathematical model and main results of analytical studies of Euler stability. Stability factor 20
1.3. Methods for studying the stability of plate elements and structures of them 27
1.4. Engineering methods for calculating plates and composite plate elements. The concept of the reduction method 31
1.5. Numerical studies of Euler stability by the finite element method: possibilities, advantages and disadvantages 37
1.6. Review of experimental studies of the stability of plates and composite plate elements 40
1.7. Conclusions and objectives of theoretical studies of the stability of thin-walled trapezoidal profiles 44
2. Development of mathematical models and algorithms for calculating the stability of thin-walled plate elements of trapezoidal profiles: 47
2.1. Longitudinal-transverse bending of thin-walled plate elements of trapezoidal profiles 47
2.1.1. Problem statement, basic assumptions 48
2.1.2. Mathematical model in ordinary differential equations. Boundary conditions, imperfection method 50
2.1.3. Algorithm for numerical integration, determining the critical
tension and its implementation in MS Excel 52
2.1.4. Calculation results and their comparison with known solutions 57
2.2. Calculation of critical stresses for a single plate element
as part of a profile ^ .. 59
2.2.1. A model that takes into account the elastic conjugation of the profile plate elements. Basic assumptions and problems of numerical research 61
2.2.2. Numerical Study of Mate Rigidity and Approximation of Results 63
2.2.3. Numerical investigation of the buckling half-wave length at the first critical load and approximation of the results 64
2.2.4. Calculation of the coefficient k (/ 3x, / 32). Approximation of calculation results (A, /? 2) 66
2.3. Evaluation of the adequacy of calculations by comparison with numerical solutions by the finite element method and known analytical solutions 70
2.4. Conclusions and objectives of the experimental study 80
3. Experimental studies on the local stability of thin-walled trapezoidal profiles 82
3.1. Description of prototypes and experimental setup 82
3.2. Testing of samples 85
3.2.1. Test procedure and content G. 85
3.2.2. Compression test results 92
3.3. Conclusions 96
4. Taking into account local sustainability in calculations load-bearing structures from thin-walled trapezoidal profiles with flat longitudinal - transverse bending 97
4.1. Calculation of critical stresses of local buckling of plate elements and the limiting thickness of a thin-walled trapezoidal profile 98
4.2. The area of permissible loads without taking into account the local loss of stability 99
4.3. Reduction factor 101
4.4. Taking into account local buckling and reduction 101
Conclusions 105
Bibliographic list
Introduction to work
The relevance of the work.
The creation of lightweight, strong and reliable structures is an urgent task. One of the main requirements in mechanical engineering and construction is a reduction in metal consumption. This leads to the fact that structural elements must be calculated according to more precise constitutive relations, taking into account the danger of both general and local buckling.
One of the ways to solve the problem of minimizing weight is the use of high-tech thin-walled trapezoidal rolled profiles (TTP). Profiles are made by rolling thin sheet steel with a thickness of 0.4 ... 1.5 mm in stationary conditions or directly at the assembly site as flat or arched elements. Structures using load-bearing arched coverings from a thin-walled trapezoidal profile are distinguished by their lightness, aesthetic appearance, ease of installation and a number of other advantages over traditional types of coverings.
The main type of profile loading is longitudinal-transverse bending. Tone-
jfflF dMF " lamellar elements
profile experiencing
median compression
bones can lose places
new stability. Local
loss of stability
Rice. 1. An example of local buckling
Yam,
^ J
Rice. 2. Scheme reduced section profile
(MPA) is observed in limited areas along the length of the profile (Fig. 1) at significantly lower loads than the total buckling and stresses comparable to the permissible ones. With MPU, a separate compressed plate element of the profile completely or partially ceases to perceive the load, which is redistributed between the rest of the plate elements of the profile section. Moreover, in the section where the MPA occurred, the stresses do not necessarily exceed the permissible ones. This phenomenon is called reduction. Reduction
is to reduce, in comparison with the real, area cross section profile when reduced to an idealized design scheme (Fig. 2). In this regard, the development and implementation of engineering methods for accounting for local buckling of plate elements of a thin-walled trapezoidal profile is an urgent task.
Prominent scientists were engaged in the issues of plate stability: B.M. Bro-ude, F. Bleich, J. Brudka, I.G. Bubnov, V.Z. Vlasov, A.S. Volmir, A.A. Ilyushin, Miles, Melan, Ya.G. Panovko, SP. Timoshenko, Southwell, E. Stowell, Winderberg, Khvalla and others. Engineering approaches to the analysis of critical stresses with local buckling were developed in the works of E.L. Ayrumyan, Burggraf, A.L. Vasil'eva, B. Ya. Volodarsky, M.K. Glouman, Caldwell, V.I. Klimanova, V.G. Krokhaleva, D.V. Martsinkevich, E.A. Pav-linova, A.K. Pertseva, F.F. Tamplona, S.A. Timashev.
In these engineering calculation methods for profiles with a complex cross-section, the danger of an MPU is practically not taken into account. At the stage of sketch design of structures from thin-walled profiles it is important to have a simple apparatus for assessing the bearing capacity of a particular standard size. In this regard, there is a need for the development of engineering calculation methods that allow in the process of designing structures from thin-walled profiles to quickly assess their bearing capacity. A verification calculation of the bearing capacity of a structure made of a thin-walled profile can be performed using refined methods using existing software products and adjusted if necessary. Such a two-stage system for calculating the bearing capacity of structures made of thin-walled profiles is the most rational. Therefore, the development and implementation of engineering methods for calculating the bearing capacity of structures made of thin-walled profiles, taking into account the local buckling of plate elements, is an urgent task.
The purpose of the dissertation work: study of local buckling in plate elements of thin-walled trapezoidal profiles during their longitudinal-transverse bending and development of an engineering method for calculating the bearing capacity taking into account local stability.
To achieve the goal, the following are set research objectives.
Extension of analytical solutions for the stability of compressed rectangular plates to a system of conjugated plates in the profile.
Numerical study of the mathematical model of the local stability of the profile and obtaining adequate analytical expressions for the minimum critical stress of the MPU of a plate element.
Experimental evaluation of the degree of reduction in the section of a thin-walled profile with local loss of stability.
Development of an engineering methodology for verification and design calculation of a thin-walled profile, taking into account local buckling.
Scientific novelty work is to develop an adequate mathematical model of local buckling for a separate plate
element in the profile and obtaining analytical dependencies for calculating critical stresses.
Reasonableness and reliability The obtained results are provided by basing on fundamental analytical solutions of the problem of stability of rectangular plates, correct application of the mathematical apparatus, sufficient for practical calculations coincidence with the results of calculations of the FEM and experimental studies.
Practical significance consists in the development of an engineering methodology for calculating the bearing capacity of profiles, taking into account local buckling. The results of the work are implemented in Montazhproekt LLC in the form of a system of tables and graphical representations of the areas of permissible loads for the entire assortment of produced profiles, taking into account local buckling, and are used for preliminary selection of the type and thickness of the profile material for specific design solutions and types of loading.
The main provisions for the defense.
A mathematical model of plane bending and compression of a thin-walled profile as a system of conjugated plate elements and a method for determining the critical stresses of the MPA in the sense of Euler on its basis.
Analytical dependences for calculating the critical stresses of local buckling for each plate element of the profile at plane longitudinal-transverse bending.
Engineering method for verification and design calculation of a thin-walled trapezoidal profile, taking into account local buckling. Approbation of work and publication.
The main provisions of the dissertation were reported and discussed at scientific and technical conferences of various levels: International Congress "Machines, technologies and processes in construction" dedicated to the 45th anniversary of the faculty "Transport and technological machines" (Omsk, SibADI, December 6-7, 2007); All-Russian scientific and technical conference, "YOUNG RUSSIA: advanced technologies into industry" (Omsk, Om-GTU, November 12-13, 2008).
Structure and scope of work. The thesis is presented on 118 pages of text, consists of an introduction, 4 chapters and one annex, contains 48 figures, 5 tables. The list of references includes 124 titles.
Any engineering project relies on the solution of differential equations of a mathematical model of motion and equilibrium of a mechanical system. Drafting a design of a structure, mechanism, machine is accompanied by some manufacturing tolerances, and later on - imperfections. Imperfections can also occur during operation in the form of dents, gaps due to wear and other factors. It is impossible to foresee all the variants of external influences. The design is forced to work under the influence of random disturbing forces that are not taken into account in the differential equations.
Factors not taken into account in the mathematical model - imperfections, random forces or perturbations - can make serious adjustments to the results obtained.
The unperturbed state of the system is distinguished - the calculated state at zero perturbations, and the perturbed state, which is formed as a result of perturbations.
In one case, due to the perturbation, there is no significant change in the equilibrium position of the structure, or its movement differs little from the calculated one. This state of the mechanical system is called stable. In other cases, the equilibrium position or the nature of the movement differs significantly from the calculated one, such a state is called unstable.
The theory of stability of motion and equilibrium of mechanical systems deals with the establishment of signs that allow one to judge whether the considered motion or equilibrium will be stable or unstable.
A typical sign of the transition of a system from a stable state to an unstable one is the achievement of a value called critical by some parameter - critical force, critical speed, etc.
The appearance of imperfections or the impact of unaccounted forces inevitably leads to the movement of the system. Therefore, in the general case, it is necessary to investigate the stability of the motion of a mechanical system under perturbations. This approach to the study of stability is called dynamic, and the corresponding research methods are called dynamic.
In practice, it is often sufficient to restrict ourselves to a static approach, i.e. static methods of stability research. In this case, the final result of the perturbation is investigated - a new steady-state equilibrium position of the mechanical system and the degree of its deviation from the calculated, unperturbed equilibrium position.
The static formulation of the problem presupposes not to consider the forces of inertia and the time parameter. This formulation of the problem often makes it possible to translate the model from equations of mathematical physics into ordinary differential equations. This greatly simplifies the mathematical model and facilitates the analytical study of stability.
A positive result of the analysis of the stability of the equilibrium by the static method does not always guarantee dynamic stability. However, for conservative systems, the static approach in determining critical loads and new equilibrium states leads to exactly the same results as the dynamic one.
In a conservative system, the work of the internal and external forces of the system, performed during the transition from one state to another, is determined only by these states and does not depend on the trajectory of motion.
The concept of "system" combines a deformable structure and loads, the behavior of which must be specified. Hence, two necessary and sufficient conditions for the conservatism of the system follow: 1) the elasticity of the deformable structure, i.e. reversibility of deformations; 2) conservatism of the load, i.e. the independence of the work performed by her from the trajectory. In some cases, the static method also gives satisfactory results for non-conservative systems.
For clarity of the above, we will consider several examples from theoretical mechanics and strength of materials.
1. A ball of weight Q is located in a depression of the bearing surface (Fig. 1.3). Under the action of the disturbing force 5Р Q sina, the equilibrium position of the ball does not change, i.e. it is stable.
With a short-term action of the force 5Р Q sina, without considering rolling friction, a transition to a new equilibrium position or oscillations around the initial equilibrium position is possible. When friction is taken into account, the oscillatory motion will be damped, that is, stable. The static approach allows you to determine only the critical value of the disturbing force, which is equal to: Ркр = Q sina. The nature of the movement when the critical value of the disturbing action is exceeded and the critical duration of the action can be analyzed only by dynamic methods.
2. Rod length / compressed by force P (Fig. 1.4). It is known from the resistance of materials based on the static method that a critical value of the compressive force exists during loading within the elastic range.
The solution of the same problem with a tracking force, the direction of which coincides with the direction of the tangent at the point of application, by the static method leads to the conclusion about the absolute stability of the rectilinear form of equilibrium.
Engineering analysis falls into two categories: classical and numerical methods. Using classical methods, they try to solve the problems of stress and strain fields distribution directly, forming systems of differential equations based on fundamental principles. The exact solution, if it is possible to obtain equations in a closed form, is possible only for the simplest cases of geometry, loads, and boundary conditions. A fairly wide range of classical problems can be solved using approximate solutions of systems of differential equations. These solutions are in the form of series in which the lowest terms are discarded after convergence analysis. Like exact solutions, approximate ones require a regular geometric shape, simple boundary conditions, and a convenient application of loads. Accordingly, these solutions cannot be applied to most practical problems. The fundamental advantage of classical methods is that they provide a deep understanding of the problem under study. A wider range of problems can be investigated using numerical methods. Numerical methods include: 1) energy method; 2) the method of boundary elements; 3) the method of finite differences; 4) finite element method.
Energy methods allow one to find a minimum expression for the total potential energy of a structure over the entire given area. This approach only works well for certain tasks.
The boundary element method approximates functions that satisfy the system of differential equations to be solved, but not the boundary conditions. The dimension of the problem is reduced because the elements represent only the boundaries of the modeled area. However, the application of this method requires knowledge of the fundamental solution of the system of equations, which can be difficult to obtain.
The finite difference method transforms the system of differential equations and boundary conditions into the corresponding system of algebraic -equations. This method allows solving problems of analysis of structures with complex geometry, boundary conditions and combined loads. However, the finite difference method is often too slow due to the fact that the requirement of a regular grid over the entire study area leads to systems of equations of very high orders.
The finite element method can be extended to an almost unlimited class of problems due to the fact that it allows the use of elements of simple and various shapes to obtain partitions. The sizes of finite elements, which can be combined to obtain an approximation to any irregular boundaries, sometimes differ in the partition by tens of times. It is allowed to apply an arbitrary type of load to the elements of the model, as well as to impose any type of fastening on them. The main problem is the increase in costs to obtain a result. For the generality of the solution, one has to pay with the loss of intuition, since a finite element solution is, in fact, a set of numbers that are applicable only to a specific problem posed using a finite element model. Changing any significant aspect in the model usually requires a complete re-solution of the problem. However, this is an insignificant cost, since the finite element method is often the only one. possible way her decisions. The method is applicable to all classes of field distribution problems, which include structural analysis, heat transfer, fluid flow, and electromagnetism. The disadvantages of numerical methods include: 1) high cost of finite element analysis programs; 2) long training to work with the program and the possibility of full-fledged work only for highly qualified personnel; 3) quite often it is impossible to verify by a physical experiment the correctness of the result of the solution obtained by the finite element method, including in nonlinear problems. m Review of experimental studies of the stability of plates and composite plate elements
Currently used for building structures profiles are made from metal sheets with a thickness of 0.5 to 5 mm and are therefore considered thin-walled. Their faces can be both flat and curved.
The main feature of the operation of thin-walled profiles is that faces with a high value of the width-to-thickness ratio undergo large buckling deformations under loading. A particularly intense growth of deflections is observed when the magnitude of the stresses acting in the face approaches the critical value. There is a loss of local stability, deflections become comparable to the thickness of the edge. As a result, the cross-section of the profile is greatly distorted.
In the literature on the stability of plates, a special place is occupied by the work of the Russian scientist SP. Tymoshenko. He is credited with developing an energy method for solving elastic stability problems. Using this method, SP. Timoshenko gave a theoretical solution to the problems of stability of plates loaded in the median plane under different boundary conditions. The theoretical solutions were tested by a series of tests on freely supported plates under uniform compression. Tests confirmed the theory.
To check the reliability of the results obtained, numerical studies were carried out using the finite element method (FEM). Recently, numerical studies of FEM have found more and more widespread use due to objective reasons, such as the absence of test problems, the impossibility of meeting all conditions when testing samples. Numerical methods make it possible to carry out research under "ideal" conditions, have a minimum error, which is practically impossible to implement in real tests. Numerical studies were carried out using the ANSYS program.
Numerical studies were carried out with samples: rectangular plate; U-shaped and trapezoidal profile element with a longitudinal ridge and without ridge; profile sheet (Figure 2.11). Samples with a thickness of 0.7; 0.8; 0.9 and 1mm.
A uniform compressive load sgw was applied to the samples (Fig. 2.11) at the ends, followed by an increase in the Det step by step. The load corresponding to the local loss of stability of the flat shape corresponded to the value of the critical compressive stress σcr. Then, using the formula (2.24), the stability coefficient & (/? I, /? G) was calculated and compared with the value from Table 2.
Consider a rectangular plate with a length of a = 100 mm and a width of 6 = 50 mm, compressed at the ends by a uniform compressive load. In the first case, the plate has a hinge fixation along the contour, in the second - a rigid fixation along the side edges and a hinge fixation at the ends (Figure 2.12).
In the ANSYS program, a uniform compressive load was applied to the end faces, the critical load, stress, and stability coefficient & (/?], /? 2) of the plate were determined. When hinged along the contour, the plate lost its stability in the second shape (two bulges were observed) (Fig. 2.13). Then the coefficients of resistance to, / 32) of the plate, found numerically and analytically, were compared. The calculation results are presented in Table 3.
Table 3 shows that the difference between the results of the analytical and numerical solution was less than 1%. Hence, it was concluded that the proposed algorithm for the study of stability can be applied in the calculation of critical loads for more complex structures.
To extend the proposed method for calculating the local stability of thin-walled profiles to the general loading case, numerical studies were carried out in the ANSYS program to find out how the nature of the compressive load affects the coefficient k (y). The research results are presented in a graph (Fig. 2.14).
The next step in checking the proposed calculation methodology was the study of a separate element of the profile (Figure 2.11, b, c). It is hinged along the contour and compressed at the ends by a uniform compressive load of the USL (Fig. 2.15). The sample was examined for stability in the ANSYS program and according to the proposed method. After that, the results obtained were compared.
When creating a model in the ANSYS program, to uniformly distribute the compressive load along the end, a thin-walled profile was placed between two thick plates and a compressive load was applied to them.
The result of the study in the ANSYS program of the element of the U-shaped profile is shown in Figure 2.16, which shows that, first of all, the loss of local stability occurs at the widest plate.
For supporting structures made of high-tech thin-walled trapezoidal profiles, the calculation is carried out according to the methods of permissible stresses. An engineering method is proposed for taking into account local buckling when calculating the bearing capacity of structures made of a thin-walled trapezoidal profile. The technique is implemented in MS Excel, is available for widespread use and can serve as a basis for appropriate additions to regulations in terms of calculating thin-walled profiles. It is built on the basis of research and obtained analytical dependences for calculating the critical stresses of local buckling of plate elements of a thin-walled trapezoidal profile. The task is divided into three components: 1) determination of the minimum profile thickness (limiting t \ at which there is no need to take into account local buckling in this type of calculation; 2) determination of the area of permissible loads of a thin-walled trapezoidal profile, within which the bearing capacity is ensured without local loss of stability; 3) determination of the range of permissible values of NuM, within which the bearing capacity is ensured with local loss of stability of one or more plate elements of a thin-walled trapezoidal profile (taking into account the reduction of the profile section).
In this case, it is believed that the dependence of the bending moment on the longitudinal force M = f (N) for the calculated structure was obtained by the methods of resistance of materials or structural mechanics (Figure 2.1). The permissible stresses [t] and the yield point of the material sgt are known, as well as the residual stresses sgstі in the plate elements. In the calculations after local buckling, the "reduction" method was applied. In case of loss of stability, 96% of the width of the corresponding plate element is excluded.
Calculation of the critical stresses of local buckling of plate elements and the limiting thickness of a thin-walled trapezoidal profile The thin-walled trapezoidal profile is divided into a set of plate elements as shown in Figure 4.1. At the same time, the angle of mutual arrangement of neighboring elements does not affect the value of the critical stress of the local
Profile H60-845 CURVED buckling. Replacement of curved corrugations with straight-line elements is allowed. Critical compressive stresses of local buckling in the sense of Euler for an individual i-th plate element of a thin-walled trapezoidal profile with width bt at thickness t, elastic modulus of material E, and Poisson's ratio ju in the elastic stage of loading are determined by the formula
The coefficients k (px, P2) and k (v) take into account, respectively, the effect of the stiffness of the adjacent plate elements and the nature of the distribution of compressive stresses over the width of the plate element. The value of the coefficients: k (px, P2) is determined according to table 2, or calculated by the formula
Normal stresses in a plate element are determined in the central axes by the well-known formula for the resistance of materials. The area of permissible loads without taking into account local buckling (Fig.4.2) is determined by the expression and is a quadrangle, where J is the moment of inertia of the section of the profile period during bending, F is the sectional area of the profile period, ymax and Utin are the coordinates of the extreme points of the profile section (Fig. 4.1).
Here, the sectional area of the profile F and the moment of inertia of the section J are calculated for a periodic element of length L, and the longitudinal force iV and the bending moment Mb of the profile refer to L.
The bearing capacity is provided when the actual load curve M = f (N) falls into the range of permissible loads minus the area of local buckling (Figure 4.3). Fig 4.2. The area of permissible loads without taking into account local buckling
The loss of local stability of one of the shelves leads to its partial exclusion from the perception of workloads - reduction. The degree of reduction is taken into account by the reduction factor
The bearing capacity is ensured when the actual load curve falls within the range of permissible loads minus the range of local buckling loads. At smaller thicknesses, the line of local buckling decreases the area of permissible loads. Local buckling is not possible if the actual load curve is located in a reduced area. When the curve of actual loads goes beyond the line minimum value critical stress of local buckling, it is necessary to rebuild the area of permissible loads, taking into account the reduction of the profile, which is determined by the expression
3.2 Calculation of the rolling table
The basic principle of constructing a technological process in modern installations is to obtain pipes of the same constant diameter on a continuous mill, which makes it possible to use a workpiece and a sleeve of a constant diameter as well. Obtaining pipes of the required diameter is ensured by reduction. Such a system of work greatly facilitates and simplifies the setup of the mills, reduces the tool park and, most importantly, allows you to maintain high productivity of the entire unit even when rolling pipes of the minimum (after reduction) diameter.
We calculate the rolling table against the rolling course according to the method described in Art. The outer diameter of the pipe after reduction is determined by the dimensions of the last pair of rolls.
D p 3 = (1.010..1.015) * D o = 1.01 * 33.7 = 34 mm
where D p is the diameter of the finished pipe after the reduction mill.
Since a pipe of the same diameter comes out after a continuous mill, we take D n = 94 mm. In continuous mills, the calibration of the rolls ensures that in the last pairs of rolls the inner diameter of the pipe is 1-2 mm larger than the diameter of the mandrel, so that the diameter of the mandrel will be equal to:
H = d n - (1..2) = D n -2S n -2 = 94-2 * 3.2-2 = 85.6 mm.
We accept the diameter of the mandrels equal to 85 mm.
The inner diameter of the sleeve should provide free insertion of the mandrel and is taken 5-10 mm larger than the diameter of the mandrel
d g = n + (5..10) = 85 + 10 = 95 mm.
We accept the liner wall:
S g = S n + (11..14) = 3.2 + 11.8 = 15 mm.
The outer diameter of the sleeves is determined based on the size of the inner diameter and wall thickness:
D g = d g + 2S g = 95 + 2 * 15 = 125 mm.
The diameter of the workpiece used D z = 120 mm.
The diameter of the mandrel of the piercing mill is selected taking into account the amount of rolling, i.e. rise of the inner diameter of the sleeve, constituting from 3% to 7% of the inner diameter:
P = (0.92 ... 0.97) d g = 0.93 * 95 = 88 mm.
Elongation coefficients for piercing, continuous and reduction mills are determined by the formulas:
,
The overall stretch ratio is:
The rolling table for pipes with dimensions 48.3 × 4.0 mm and 60.3 × 5.0 mm is calculated in a similar way.
The rolling table is presented in table. 3.1.
|
Finished pipes size, mm |
Workpiece diameter, mm |
Piercing mill |
Continuous mill |
Reduction mill |
Overall stretch ratio |
||||||||||
|
Outside diameter |
Wall thickness |
Sleeve size, mm |
Mandrel diameter, mm |
Draw ratio |
Pipe dimensions, mm |
Mandrel diameter, mm |
Draw ratio |
Pipe size, mm |
Number of stands |
Draw ratio |
|||||
|
Wall thickness |
Wall thickness |
Wall thickness |
|||||||||||||
3.3 Calculation of the calibration of the rolls of the reduction mill
Roll calibration is important part of calculation of the mill operating mode. It largely determines the quality of pipes, tool life, distribution of loads in the working stands and the drive.
Calculation of roll sizing includes:
distribution of partial deformations in mill stands and calculation of average diameters of calibers;
determination of the sizes of roll grooves.
3.3.1 Distribution of partial deformations
By the nature of the change in the partial deformations, the stands of the reduction mill can be divided into three groups: the head one at the beginning of the mill, in which the reductions intensively increase in the course of rolling; sizing (at the end of the mill), in which the deformations are reduced to a minimum value, and a group of stands between them (middle), in which the partial deformations are maximum or close to them.
When rolling pipes with tension, the values of partial deformations are taken based on the condition of the stability of the pipe profile at the value of plastic tension that ensures the production of a pipe of a given size.
The coefficient of total plastic tension can be determined by the formula:
,
where 
- axial and tangential deformations taken in logarithmic form; T is the value determined in the case of a three-roll caliber according to the formula
where (S / D) cp is the average ratio of wall thickness to diameter over the period of pipe deformation in the mill; k-factor 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 along the diameter.
.
The value of the critical partial reduction with such a coefficient of plastic tension, according to, can reach 6% in the second stand, 7.5% in the third stand and 10% in the fourth stand. In the first stand, it is recommended to take in the range of 2.5–3%. However, to ensure stable grip, the amount of reduction is usually reduced.
In the pre-finishing and finishing stands of the mill, the reduction is also reduced, but to reduce the loads on the rolls and increase the accuracy of the finished pipes. In the last stand of the calibrating group, the reduction is taken equal to zero, in the penultimate stand, up to 0.2 of the reduction in the last stand of the middle group.
V middle group of stands practice uniform and uneven distribution of partial deformations. With a uniform distribution of reduction in all stands of this group, they are assumed to be constant. The uneven distribution of partial deformations can have several variants and can be characterized by the following regularities:
the reduction in the middle group is proportionally reduced from the first stands to the last - falling mode;
in the first few stands of the middle group, partial deformations are reduced, and the rest are left constant;
the compression in the middle group is first increased and then decreased;
in the first few stands of the middle group, the partial deformations are left constant, and in the rest they are reduced.
With falling deformation modes in the middle group of stands, the differences in the value of rolling power and the load on the drive, caused by an increase in the resistance to deformation of the metal during rolling, due to a decrease in its temperature and an increase in the deformation rate, decrease. It is believed that a decrease in reductions towards the end of the mill also improves the quality of the outer surface of the pipes and reduces the transverse wall thickness.
When calculating the calibration of the rolls, we take a uniform distribution of reductions.
The values of partial deformations along the mill stands are shown in Fig. 3.1.
Compression distribution
Based on the accepted values of partial deformations, the average diameters of the calibers can be calculated using the production formula pipes, and, directly, ... failures) during production foam concrete. At production foam concrete are used by various ... workers directly related to production foam concrete, special clothing, ...
Rental Production pipes by the method of centrifugal rolling. Reinforced concrete pipes made ... by centrifugal method production pipes... Loading of concrete centrifuges ... allows for demoulding of forms. Production pipes by radial pressing. This...
