A design method for the spigot and socket thickness of a spigot-and-socket pipe

Abstract

The present invention discloses a design method for the spigot and the thickness of the socket of a spigot-and-socket type pipe. The design method for the spigot thickness is as follows: a1: obtaining the differential equation of radial deformation of the ring and the general solution of the differential equation according to the deflection curve differential equation and the moment balance equation of the ring; a2: calculating the calculation formula for the maximum radial deformation of the ring; a3: finding the minimum spigot thickness of the base pipe that meets the deformation requirements; the design method for the spigot thickness includes the following: b1: selecting multiple locations on the inner wall of the socket where stress is easily concentrated, and the selection principle is: if the wall thickness of these locations meets the stress strength requirements, then the wall thickness of each location of the socket meets the strength requirements; b2: determining the minimum wall thickness of each selected location. The present invention can obtain the minimum or near minimum spigot thickness of the spigot that meets the deformation requirements and the minimum or near minimum thickness of the socket that meets the strength requirements of spigot-and-socket type pipes of different pipe diameters through theoretical analysis and calculation, which can reduce the production, manufacturing and transportation costs of the pipes.

Description

Technical Field

[0001] The invention belongs to the technical field of pipe design, and in particular relates to a design method for a spigot and socket thickness of a spigot-and-socket type pipe. Background Art

[0002] Most of the water pipes in the water supply and drainage systems for life and production are socket-and-spigot pipes, with a socket at one end and a spigot at the other. During installation, the spigot of one pipe is inserted into the socket of another pipe and sealed with a seal, thus achieving the connection of each pipe in the pipe network. Figure 5 and 6 In the figure, M is the spigot and F is the socket. For water supply pipes in normal use, they will be subjected to a large internal water supply pressure, which is a positive pressure, so the pipes must meet the specified strength requirements. Some existing standards (group standards and national standards) specify the nominal wall thickness under different pressure levels and different nominal diameters. Pipes that meet the standards can meet the strength requirements within the corresponding pressure level range. Therefore, the pipes produced by existing pipe manufacturers generally meet the corresponding standard requirements.

[0003] However, when a pipe network fails, for example, a pipe bursts in the pipe network, water in the pipe network will spray out from the burst, and the pressure in the pipe network will drop rapidly, even forming negative pressure. In addition, the pipe will also be subject to some external pressure, for example, the pipe buried in the soil will be subject to the gravity of the soil above it. Under the above external pressure and internal negative pressure, the pipe will deform radially. If the deformation of the socket is too large, the socket will separate from the socket connected to it, causing leakage at the connection between the socket and the socket, causing the inside of the water pipe to be contaminated. Therefore, it is necessary to ensure that the deformation of the socket of the pipe does not exceed a certain range under the above circumstances. To this end, for the socket, the minimum socket thickness that meets the deformation requirements must be obtained. If the socket thickness of the selected pipe is less than the minimum socket thickness that meets the deformation requirements, measures need to be taken to make it meet the deformation requirements. For example, during the secondary processing or installation of the pipe, an annular reinforcement ring is sleeved on the socket to enhance the ability to resist deformation. As for the socket F, the existing standards do not give its wall thickness requirements, but generally it is necessary to ensure that its thickness is sufficient to meet the strength requirements. It is best to make the thickness of the socket F at various locations the minimum or close to the minimum while meeting the use strength. Summary of the invention

[0004] In view of the above-mentioned problems existing in the prior art, the purpose of the present invention is to provide a design method for the thickness of the spigot and the socket of a socket-and-spigot pipe. The minimum or near-minimum thickness of the spigot that meets the deformation requirements and the minimum or near-minimum thickness of the socket that meets the strength requirements of the socket-and-spigot pipes with different pipe diameters can be obtained through theoretical analysis and calculation, thereby saving materials and reducing the production, manufacturing and transportation costs of the pipes. The method for designing the minimum wall thickness is theoretical calculation, which has low cost and high efficiency, provides strong support for experiments and pipe design, and provides a reference for secondary processing and installation. If the thickness of the spigot or the socket of the pipe is less than the calculated minimum thickness, the spigot or the socket thickness can be increased by installing a reinforcement ring on the spigot or the socket so that the spigot meets the deformation requirements and the socket meets the strength requirements. The pipes and pipe network systems installed in this way are more reliable to use, greatly reducing the leakage and water supply pollution caused by the deformation and separation of the spigots and the sockets of adjacent pipes when the pipe bursts, as well as the cracking of the socket.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for designing the spigot and the thickness of the spigot of a spigot-and-socket type pipe, the method for designing the spigot thickness comprising the following steps:

[0007] Step a1: Obtain the differential equation of radial deformation of the ring and the general solution of the differential equation according to the differential equation of the deflection curve of the ring and the moment balance equation;

[0008] Step a2: Calculate and obtain a calculation formula for the maximum radial deformation of the ring according to the general solution of the differential equation obtained in step a1;

[0009] Step a3: Calculating the minimum thickness of the socket of the base pipe that meets the deformation requirements according to the calculation formula of the maximum radial deformation obtained in step a2;

[0010] The design method of the socket thickness includes the following steps:

[0011] Step b1: Select multiple locations on the inner wall of the socket where stress is likely to concentrate. The selection principle is: if the wall thickness of these locations meets the stress strength requirements, then the wall thickness of each location of the socket designed according to the outer wall design requirements will meet the strength requirements;

[0012] Step b2: Determine the minimum wall thickness of each selected location in step b1, and obtain the outer wall of each selected location. The determination principle is: when the material of the socket and the material of the pipe body are the same, the stress at each selected location is not greater than the stress of the inner wall of the pipe body; when the material of the socket and the material of the pipe body are different, the ratio of the stress at each selected location to the yield strength of the socket material is not greater than the ratio of the stress of the inner wall of the pipe body to the yield strength of the pipe body material.

[0013] As a further improvement of the above technical solution:

[0014] Step a2 includes the following steps:

[0015] Step a21: Assuming that the annular ring is subjected to at least two radial concentrated forces that are symmetrical relative to the center of the circle, based on the assumption, calculating the constant term in the general solution of the differential equation to obtain the first form of the differential equation;

[0016] Step a22: Based on the first form of the differential equation obtained in step a21, assuming that the annulus is subjected to only two radial concentrated forces that are symmetrical relative to the center of the circle, the first form of the differential equation is transformed into a second form of the differential equation;

[0017] Step a23: introducing the internal negative pressure of the ring into the second form of the differential equation by introducing a coefficient, so as to obtain the third form of the differential equation;

[0018] Step a24: Obtain a calculation formula for the maximum change in the diameter of the circular ring with coefficients according to the third form of the differential equation obtained in step a23.

[0019] Step a3 includes the following steps:

[0020] Step a31: Calculate the parameters of a reference pipe according to an existing shear load formula, wherein the material and outer diameter of the reference pipe are respectively the same as the material and outer diameter of the base pipe;

[0021] Step a32: obtaining the maximum deformation of the reference pipe socket through simulation according to the parameters calculated in step a31;

[0022] Step a33: Substitute the maximum deformation of the socket obtained in step a32 into the calculation formula of step a2 to obtain the coefficient value in the calculation formula, thereby obtaining a calculation formula for the maximum radial deformation of the ring with a known coefficient;

[0023] Step a34: Calculate the minimum thickness of the base pipe socket that meets the deformation requirements based on the allowable deformation regulations and the formula obtained in step a33.

[0024] In step a1, the radial deformation obtained is u The differential equation is:

[0025] ;

[0026] The general solution is: ;

[0027] in, R is the average value of the outer circle radius and the inner circle radius of the ring; E is the elastic modulus of the pipe, Pa; I is the moment of inertia of the circular pipe section, m 4 ; Mis the bending moment borne by a certain section of the ring in the local area, in units of N*m; establish a two-dimensional coordinate system, The deformation is u The angle between the line connecting the point at and the origin of the coordinate system and the positive direction of the x-axis in the two-dimensional coordinate system, ; A1, A2, A3, B2, B3 are constants.

[0028] In step a2, it is assumed that the ring is subjected to at least two radial concentrated forces P symmetrically relative to the center of the circle, and the angle between two adjacent radial concentrated forces P is , the ring satisfies the following three boundary conditions:

[0029] (1) Because of symmetry, The rotation angle of the section at is 0, which satisfies the following formula: ;

[0030] (2) Due to symmetry, the total tangential displacement of the arc in each equally divided segment is 0; that is, ;

[0031] (3) Cutting near point A, removing point A and the acting force P, it can be seen from the symmetry and equilibrium conditions that the shear force on the cross section of the circular cut is , that is: ;

[0032] Combining the above three formulas with the general solution of the differential equation, we get the first form of the differential equation:

[0033] ;

[0034] Assuming that the annulus is subjected to only two radial concentrated forces P which are symmetrical relative to the center of the circle, then: , we get the second form of the differential equation:

[0035] ;

[0036] Introducing the coefficient m, we get the third form of the differential equation:

[0037] ;

[0038] Point of application of force P The point is the point of maximum deformation, and the change in the diameter of the ring is:

[0039] , where I = S 3 / 12, S is the thickness of the tube.

[0040] The shear load formula used in step a31 is:

[0041] ,

[0042] in: W is the shear load, in Newton (N); F n is the shear force acting on the interface, in Newton (N); M P is the weight of the test assembly pipe and the weight of the object in the pipe, in kilograms (kg); a The distance between the shear load application point and the end face of the socket inserted into the socket, in millimeters (mm); b The distance between the center of gravity of the spigot end pipe and the end face of the spigot inserted into the socket, in millimeters (mm); c It is the distance between the support point of the pad and the end face of the socket that has been inserted into the socket, in millimeters (mm).

[0043] For the same base pipe, along the direction from the socket to the spigot, the inner wall of the socket includes the first step, the second step, the third step, the fourth step, and the fifth step arranged in sequence, and one end of the inner wall of the pipe body is the sixth step, and the corresponding inner diameters are: D2, D1, (D3-2F0), D3, D4, (D0-2S), and (D0-2S) < D2 < D4 < (D3-2F0) < D3 < D1, the first step, the second step, the third step, the fourth step The lengths of the fifth step are: T3, T4, T5, (T2-T4-T5), (T1-T2-T3), the chamfer at the connection of the fourth step and the fifth step is the first chamfer, the chamfer at the connection of the fifth step and the sixth step is the second chamfer, the chamfer at the connection of the second step and the third step is the third chamfer, the chamfer at the connection of the first step and the second step is the fourth chamfer, and the chamfer at the connection of the third step and the fourth step is the fifth chamfer, and D0 is the outer diameter of the base pipe.

[0044] In step b1, the selected locations on the inner wall of the socket where stress is likely to be concentrated are the first chamfer, the second chamfer and the third chamfer.

[0045] In step b2, the minimum wall thickness of each selected point in step b1 is calculated by the stress calculation formula, and the socket is regarded as a pressure vessel including at least two coaxially connected pressure vessels with conical inner walls and at least one annular reinforcement ring installed on the inner wall of the pressure vessel. , ,in, is the hoop stress of the pipe body, is the hoop stress at the selected location, D0 is the outer diameter of the base pipe, D is the diameter of the selected location, p is the pressure of the fluid in the base pipe, S is the thickness of the base pipe, S0 is the wall thickness at the selected location, and α is the semi-cone angle of the cone at the selected location.

[0046] When the material of the socket is the same as that of the pipe body, the stress calculation formula is: .

[0047] When the material of the socket is different from that of the pipe body, the stress calculation formula is: , where Q0 is the yield strength of the pipe body material and Q1 is the yield strength of the socket material.

[0048] The beneficial effects of the present invention are as follows: the minimum or near minimum thickness of the spigot that meets the deformation requirements and the minimum or near minimum thickness of the socket that meets the strength requirements of the spigot-type pipes with different pipe diameters can be obtained through theoretical analysis and calculation, thereby saving materials and reducing the production, manufacturing and transportation costs of the pipes. The method for designing the minimum wall thickness is theoretical calculation, which has low cost and high efficiency, provides strong support for experiments and pipe design, and provides a reference for secondary processing and installation. If the thickness of the spigot or the socket of the pipe is less than the minimum thickness obtained by calculation, the spigot or the socket can be increased by installing a reinforcement ring on the spigot or the socket to make the spigot meet the deformation requirements and the socket meet the strength requirements. The pipes and pipe network systems installed in this way are more reliable to use, greatly reducing the leakage and water supply pollution caused by the separation of the spigot and the socket of the adjacent pipe due to excessive deformation of the spigot when the pipe bursts, as well as the cracking of the socket. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Schematic diagram of the cross-section deformation before and after the socket is subjected to a pair of radially symmetrical concentrated forces.

[0050] Figure 2 for Figure 1 Schematic diagram of local analysis.

[0051] Figure 3 Schematic diagram of a circular ring subjected to multiple uniformly arranged radial concentrated forces.

[0052] Figure 4 This is the stress analysis diagram of socket-type pipe.

[0053] Figure 5 Schematic diagram of the socket and the spigot connection of the present invention Figure 1 .

[0054] Figure 6 Schematic diagram of the socket and the spigot connection of the present invention Figure 2 . DETAILED DESCRIPTION

[0055] The specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation described here is only used to illustrate and explain the present invention, and is not used to limit the present invention.

[0056] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used here to describe the spatial positional relationship between a device or feature and other devices or features as shown in the figure. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figure. For example, if the device in the accompanying drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below other devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0057] A method for designing the socket and the thickness of the socket of a spigot-and-socket pipe is provided, assuming that the pipe in factory setting is a base pipe, that is, the base pipe is not installed with a reinforcement ring, and is not subjected to secondary processing such as a composite process. The base pipe comprises a socket F, a pipe body and a socket M connected in sequence, such as Figure 5 and 6 As shown. The pipe body can be divided into two parts, namely the main body and the transition part. The transition part is used for the transition connection between the main body and the socket F, that is, the socket F, the transition part, the main body and the socket M are connected in sequence. The inner wall surface of the pipe body is a cylindrical surface, that is, the inner diameter of the transition part is equal to the inner diameter of the main body. The main body is cylindrical, and the outer wall surface of the transition part is a conical surface. In other words, the thickness of the main body is uniform or basically uniform everywhere, and the thickness of the transition part gradually decreases along the direction from the socket F to the socket M. The outer diameter of the pipe body refers to the outer diameter of the main body, the outer diameter of the base pipe is the outer diameter of the pipe body, and the thickness of the pipe body refers to the thickness of the main body. Figure 5 and 6 In the figure, X is the length of the chamfer at the end of the socket M along the axial direction, Y is the height of the chamfer at the end of the socket M (i.e. the radial dimension), DE is the outer diameter of the socket M, and T6 is the length of the socket M.

[0058] The thickness of the socket M and the thickness of the socket F are calculated respectively. The design method of the thickness of the socket M includes the following steps:

[0059] Step a1: Obtain the radial deformation of the ring based on the differential equation of the deflection curve and the moment equilibrium equation of the ring The differential equation and the general solution of the differential equation; Because the cross-section of the pipe body and the socket M is a circular ring, the deformation of the socket is analyzed by analyzing the radial deformation of the circular ring. In addition, the cylinder of unit length can be regarded as a circular ring.

[0060] Step a2: Calculate and obtain a calculation formula for the maximum radial deformation of the ring based on the general solution of the differential equation obtained in step a1.

[0061] Step a3: The minimum thickness of the socket of the base pipe that meets the deformation requirements is obtained according to the calculation formula of the maximum radial deformation obtained in step a2.

[0062] The following is a detailed introduction to each step.

[0063] In step a1, the radial deformation obtained The differential equation is:

[0064] (1)

[0065] in ，R is half of the sum of the outer radius and the inner radius of the ring. In other words, R One quarter of the sum of the outer and inner diameters of the ring 。E is the elastic modulus of the pipe, Pa. I is the moment of inertia of the tube cross section, m 4 . M It is the bending moment borne by a certain section of the ring in the local area, in N*m. Establish a two-dimensional coordinate system, The deformation is u The angle between the line connecting the point at and the origin of the coordinate system and the positive direction of the x-axis in the two-dimensional coordinate system, In this embodiment, establish xy Coordinate system, point O is the coordinate origin and the center of the ring, such as Figure 1 Point m 1 The radial deformation at u， but om 1 and x The angle between the positive directions of the axes is 。

[0066] The above differential equation (1) is obtained as follows:

[0067] like Figure 1 and 2 As shown in the figure, the dotted line is the ring that has not been deformed by external force, and the solid line is the shape of the ring after being deformed by two symmetrical radial external forces P. The center point of the ring before and after deformation is O The position remains unchanged. Figure 1 midpoint O Too xy Vertex of the coordinate system ， point m and n are two points on the ring before deformation; m 1 and n1 are two points on the deformed shape of the ring, and the points m 1 and n 1 Located on the line segment om and on superior, The deformation is u The line connecting the point at and point O is x The angle between the positive directions of the axes, om and on The angle between ， set up u Centripetal movement is positive. Figure 2 Middle, straight line m 1 t Passing point m 1 and perpendicular to the line segment om ,straight line m 1 t 1 For passing point m 1 A tangent line to n 1 t’ Passing point n 1 and perpendicular to on ,straight line n 1 t 1 ’ For passing point n 1 tangent.

[0068] Arc before deformation mn The arc length is ds , whose curvature is k 1 , arc after deformation m 1 n 1 The curvature is k 2 , du Yes m and Point n The difference in radial deformation is The arc before deformation mn exist m Tangent line of point and n The angle between the tangent lines of a point, The deformation amount is u The radius corresponding to the point at after deformation is, Is an arc mn Deform to Arc m 1 n 1 back ds The increment of The arc after deformation m 1 n 1 exist m 1 Tangent line of point and n 1 The angle between the tangent lines of the point is m 1 t 1 and The angle between , then:

[0069] (2)

[0070] (3)

[0071] (4)

[0072] (5)

[0073] m 1 t 1 and m 1 t The angle between , n 1 t 1 ’ and n 1 t’ The angle between .

[0074] m 1 section to n 1 The variable of the cross-section rotation is :

[0075] (6)

[0076] in, m The cross section is through om and perpendicular to the cross section of the ring, in other words, m The cross section is through the center axis and point of the corresponding pipe of the ring m The cross section of n The cross section is through on and perpendicular to the cross section of the ring, in other words, nThe cross section is through the center axis and point of the corresponding pipe of the ring n cross section. m 1 t 1 and m 1 t The angle between m 1 The cross-sectional angle, n 1 t 1 ’ and n 1 t’ The angle between n 1 The corner of the cross section.

[0077] Substituting formula (5) and (6) into formula (4) yields:

[0078] (7)

[0079] By series expansion we have:

[0080] Ignoring the higher-order terms, substituting the series expansion into (7) yields: (8)

[0081] Substituting (2) into (8), we obtain: (9)

[0082] Omitting the higher-order terms, we get: (10)

[0083] For a thin ring (i.e. a ring with a small difference between the outer diameter and the inner diameter relative to the diameter), we have: , by definition: ,therefore, , substituting into (10) we get, , combining formula (2) to obtain radial deformation The differential equation formula (1).

[0084] The general solution of the above differential equation (1) is:

[0085] (11)

[0086] Among them, A1, A2, A3, B2, and B3 are constants. If the external force is symmetrical, the odd function terms in the solution can be deleted, and the deflection curve equation is obtained as follows:

[0087] (12)

[0088] Step a2: Calculating and obtaining a calculation formula for the maximum radial deformation of the ring according to the general solution of the differential equation obtained in step a1, comprising the following steps:

[0089] Step a21: Assume that the circular ring is subjected to at least two radial concentrated forces P that are symmetrical relative to the center of the circle. Based on this assumption, calculate the constant term in the general solution of the differential equation to obtain the first form of the differential equation.

[0090] Step a22: Based on the first form of the differential equation obtained in step a21, assuming that the annulus is subjected to only two radial concentrated forces P that are symmetrical relative to the center of the circle, the first form of the differential equation is transformed into the second form of the differential equation.

[0091] Step a23: Introduce the internal negative pressure on the annulus into the second form of the differential equation by introducing coefficients to obtain the third form of the differential equation.

[0092] Step a24: Obtain a calculation formula for the maximum change in the diameter of the circular ring with coefficients according to the third form of the differential equation obtained in step a23.

[0093] In step a21, it is assumed that the ring is subjected to at least two radial concentrated forces P symmetrically relative to the center of the circle. The radial concentrated force P means that the direction of the force P is radial to the ring and points to the center of the circle, and the angle between two adjacent radial concentrated forces P is, such as Figure 3 shown. Figure 1 The circular ring shown in FIG. 1 is subjected to two radial concentrated forces P which are symmetrical relative to the center of the circle, and the two radial concentrated forces P are located on the y-axis.

[0094] The ring satisfies the following three boundary conditions:

[0095] (1) Due to symmetry, the rotation angle of the section at this location is 0, which satisfies the following formula:

[0096] (13)

[0097] (2) Due to symmetry, the total tangential displacement of the arc in each equally divided segment is 0; that is,

[0098] (14)

[0099] (3) Cutting near point A, removing point A and the acting force P, it can be seen from the symmetry and equilibrium conditions that the shear force on the cross section of the circular cut is , that is:

[0100] (15)

[0101] in, dMrepresents the differential with respect to M. It should be noted that point (3) is not a real cut of the ring, but an assumption.

[0102] By combining formulas (13), (14) and (15), we get:

[0103] (16)

[0104] (17)

[0105] (18)

[0106] Substituting formulas (16), (17), and (18) into formula (12), we obtain:

[0107] (19)

[0108] Formula (19) is the first form of the differential equation obtained in step a21. is the radial deformation of the ring.

[0109] In step a22, if only one pair of radial forces P is applied to the ring, then , the deflection curve equation (19) becomes:

[0110] (20)

[0111] Formula (20) is the second form of the differential equation obtained in step a22.

[0112] In step a23, considering that the pipe generally needs to withstand an internal negative pressure of 0.1 MPa during testing, a coefficient m is introduced, that is,

[0113] (twenty one)

[0114] For water supply pipes, if a fault occurs during actual use, such as a burst pipe, a certain negative pressure will be formed inside the pipe. Therefore, when testing the pipe, a negative pressure will be created inside the pipe to ensure that the pipe performance meets the standards.

[0115] Formula (21) is the third form of the differential equation obtained in step a23.

[0116] In step a24, the maximum deformation is At the point where the force P acts, the change in the diameter of the ring is the maximum change in the diameter of the ring. u max :

[0117] (twenty two)

[0118] Formula (22) is the third form of the differential equation obtained in step a24.

[0119] Step a3: Calculate the minimum thickness of the base pipe that meets the deformation requirements based on the calculation formula of the maximum radial deformation obtained in step a2. It includes the following steps:

[0120] Step a31: Calculate the parameters of a reference pipe according to the existing shear load formula. The material and outer diameter of the reference pipe are respectively the same as the material and outer diameter of the base pipe.

[0121] Step a32: Obtain the maximum deformation of the reference pipe socket through simulation based on the parameters calculated in step a31.

[0122] Step a33: Substitute the maximum deformation of the socket obtained in step a32 into the calculation formula of step a2 to obtain the coefficient value in the calculation formula, thereby obtaining the calculation formula for the maximum radial deformation of the ring with a known coefficient.

[0123] Step a34: Calculate the minimum thickness of the base pipe socket that meets the deformation requirements based on the national standard allowable deformation regulations and the formula obtained in step a33.

[0124] In step a31, the shear load formula used is derived from the group standard "Corrosion-resistant steel pipe with socket-type flexible joint for water supply and drainage" (T / CISA 108-2021), which is:

[0125] (twenty three)

[0126] like Figure 4 As shown, W is the shear load, in Newton (N); F n is the shear force acting on the interface, in Newton (N); M P is the weight of the test assembly steel tube and the weight of the object in the steel tube, in kilograms (kg); a The distance between the shear load application point and the end face of the socket inserted into the socket, in millimeters (mm); b The distance between the center of gravity of the steel pipe at the spigot end and the end face of the spigot inserted into the socket, in millimeters (mm); c It is the distance between the support point of the pad and the end face of the socket that has been inserted into the socket, in millimeters (mm).

[0127] In this embodiment, the nominal diameter of the base pipe is DN=600mm, and the material is Q235 steel. The nominal diameter of the reference pipe is DN=600mm, and the material is Q235. Its wall thickness is selected according to the provisions of the group standard, and the wall thickness when the nominal pressure is 3.0MPa, that is, the nominal wall thickness S=7mm. At this time, the outer diameter of the base pipe D0=630mm, R =312mm. In addition, the shear force F n It should be no less than 30 times of the nominal diameter DN. In this embodiment, 30 times is taken, that is, F n =DN×30=600×30=18000N. Take the pipe length as 1m, c=800mm.

[0128] In this embodiment, the parameters in formula (23) are M P and W The calculation process is as follows:

[0129]

[0130]

[0131] in, is the density of water, is the density of steel. M P The diameter used in the calculation is the outer diameter D0 of the base pipe, and the calculation error is within the allowable range. In addition, in this embodiment, the material of the pipe socket is Q235 steel, the elastic modulus of the steel pipe material is E=200GPa, I=S 3 / 12. It should be noted that the calculation formula for the moment of inertia I of the circular tube section also needs to be multiplied by the length, but this solution considers a cylinder of unit length (i.e., the circular ring), so the length is 1.

[0132] Step a31 is thus completed.

[0133] In step a32, based on the parameters obtained by the above calculation, simulation software is used. In this embodiment, the maximum deformation of the socket of the reference pipe is simulated by finite element simulation. u max =12.19 mm. During simulation, the material parameter Poisson's ratio = 0.3. The simulation method is well known to those skilled in the art and will not be described in detail here.

[0134] In step a33, u max =12.19 Substituting into formula (22) we get m=1.18 (Note: When calculating, the length units are meters, and the unit of elastic modulus E is Pa), thus:

[0135] (twenty four)

[0136] From formula (24), we can see that u max The value is related to the pipe diameter and pipe thickness.

[0137] In this embodiment, in step a34, for a pipe with DN=600mm, the national standard stipulates that the allowable deformation must not be greater than 3.6% of the outer diameter of the socket DE=635mm, that is, u max =22.86 mm, and substituting it into formula (24), we can calculate that for a pipe with DN=600 mm, the minimum wall thickness of the socket is S=5.7 mm.

[0138] Table 1 Nominal wall thickness and absolute deformation of DN=600mm pipes at various nominal pressures

[0139]

[0140] In Table 1, each wall thickness is the nominal wall thickness under the corresponding nominal pressure specified in the industry standard, and the absolute deformation is calculated according to formula (24).

[0141] It can be seen from Table 1 that if the base tube purchased by the secondary processing enterprise or user is processed in accordance with the provisions of the industry standard, the base tubes with serial numbers 1, 2, and 3 in Table 1 have a socket thickness greater than 5.7 mm and an absolute deformation less than 22.86 mm, which meet the deformation requirements, while the base tubes with serial numbers 4, 5, and 6 have a socket thickness less than 5.7 mm and an absolute deformation greater than 22.86 mm, which do not meet the deformation requirements.

[0142] If the use requirement of the pipe in a certain occasion is to meet the nominal pressure within 2MPa, the general user will choose the pipe with serial number 4, and will not choose the pipe with serial number 1, 2 or 3 to meet the deformation requirement, because if one of these three is selected, although it will meet both the strength requirement and the deformation requirement, their thickness is larger and the cost will be much greater than the pipe with serial number 4. If the pipe with serial number 4 is selected, its strength meets the use requirement. For the deformation requirement, some measures can be taken, such as sleeve-fitting an annular reinforcement ring in the socket to increase the thickness of the socket and improve its ability to resist deformation, and this measure is low in cost.

[0143] Based on the above, the design calculation of the minimum thickness of the socket is completed.

[0144] The design method of the thickness of the socket F is as follows:

[0145] The inner wall shape of the pipe socket F is in accordance with the inner wall shape specified in the group standard "Corrosion-resistant steel pipe with socket and spigot flexible joint for water supply and drainage" (T / CISA 108-2021) and GB / T 13295-2008, such as Figure 5 As shown. The inner wall of the socket F is stepped. For the same base pipe, along the direction from the socket F to the spigot M, the inner wall of the socket F includes the first step 1, the second step 2, the third step 3, the fourth step 4, and the fifth step 5 arranged in sequence. One end of the inner wall of the pipe body is the sixth step 6, and the corresponding inner diameters are: D2, D1, (D3-2F0), D3, D4, (D0-2S), among which the inner diameters of the sixth step 6, the first step 1, the fifth step 5, the third step 3, the fourth step 4, and the second step 2 increase in sequence, that is: (D0-2S) < D2 < D4 < (D3-2F0) < D3 < D1. The lengths of the first step 1, the second step 2, the third step 3, the fourth step 4, and the fifth step 5 are respectively: T3, T4, T5, (T2-T4-T5), (T1-T2-T3), that is, T1 is the sum of the lengths of the first step 1, the second step 2, the third step 3, the fourth step 4, and the fifth step 5, and T2 is the sum of the lengths of the second step 2, the third step 3, and the fourth step 4. The lengths refer to the dimensions of the corresponding parts in the axial direction of the base pipe. S is the wall thickness of the pipe body, and F0 is the height of the third step 3 protruding from the fourth step 4, and F0 ≥ 0. The connection of each step is processed with chamfers, wherein the chamfer at the connection of the fourth step 4 and the fifth step 5 is the first chamfer R1, the chamfer at the connection of the fifth step 5 and the sixth step 6 is the second chamfer R2, the chamfer at the connection of the second step 2 and the third step 3 is the third chamfer R3, the chamfer at the connection of the first step 1 and the second step 2 is the fourth chamfer R4, and the chamfer at the connection of the third step 3 and the fourth step 4 is the fifth chamfer R5. Wherein, D0 is the base pipe outer diameter of the pipe.

[0146] Since the dimensions of the inner wall of the socket F are fully given by the relevant standards, it is necessary to design some key dimensions of the outer wall on this basis, aiming to save material costs and meet strength requirements. In other words, the thickness of the socket F is designed to be the minimum or close to the minimum while meeting the use strength, so as to reduce the production, manufacturing and transportation costs of the pipe.

[0147] The design method of the socket F includes the following steps:

[0148] Step b1: Select multiple locations on the inner wall of the socket F where stress is likely to concentrate. The selection principle is: if the wall thickness of these locations meets the stress strength requirements, then the wall thickness of each location of the socket F meets the strength requirements.

[0149] Step b2: Determine the minimum wall thickness of each selected location in step b1, and obtain the outer wall of each selected location. The determination principle is: when the material of the socket F is the same as the material of the pipe body, the stress at each selected location is not greater than the stress of the inner wall of the pipe body; when the material of the socket F is different from the material of the pipe body, the ratio of the stress at each selected location to the yield strength of the socket F material is not greater than the ratio of the stress of the inner wall of the pipe body to the yield strength of the pipe body material.

[0150] Step b3: Connect the outer walls of the selected locations in sequence to obtain the outer wall shape and thickness of the socket F at various locations.

[0151] In step b1, based on material mechanics knowledge and experience, several locations on the inner wall of the socket F where stress is most likely to be concentrated are selected as the first chamfer R1, the second chamfer R2, and the third chamfer R3. The analysis is as follows:

[0152] For the inner wall of the stepped socket F, according to mechanical knowledge, the stress concentration point is located at the connection between adjacent steps, that is, at each chamfer. Since the socket F is a trumpet-like shape, the outer diameter of the socket F tends to decrease from the socket F to the spigot M of the same base pipe.

[0153] Based on the above premise, since the inner diameter at the fourth chamfer R4 is equal to the inner diameter at the third chamfer R3, both are equal to D1, the wall thickness at the fourth chamfer R4 must be greater than the wall thickness at the third chamfer R3 to meet the requirement that the socket F is shaped like a trumpet. Therefore, it is equivalent to the wall thickness at the fourth chamfer R4 being greater than the third chamfer R3. At this time, as long as the wall thickness at the third chamfer R3 meets the stress strength requirement, the wall thickness at the fourth chamfer R4 must meet the strength requirement. Similarly, the inner diameter at the fifth chamfer R5 is equal to the inner diameter at the first chamfer R1, both are D3, so the wall thickness at the fifth chamfer R5 must be greater than the wall thickness at the first chamfer R1 to meet the requirement that the socket F is shaped like a trumpet. Therefore, as long as the wall thickness at the first chamfer R1 meets the stress strength requirement, the wall thickness at the fifth chamfer R5 must meet the strength requirement. Therefore, the stress concentration points finally selected are the first chamfer R1, the second chamfer R2, and the third chamfer R3. In other words, the analysis area of ​​the socket F is the area between the third chamfer R3 and the second chamfer R2.

[0154] In step b2, the minimum wall thickness of each location selected in step b1 is calculated by the stress calculation formula. The specific method is as follows: the analysis area of ​​the socket F is regarded as consisting of at least two coaxial pressure vessels with conical inner walls connected end to end and several internal reinforcement rings, and the reinforcement rings are connected to the inner wall of the pressure vessel. In other words, the analysis area of ​​the socket F is regarded as consisting of at least two conical pressure vessels and several internal reinforcement rings. At this time, as long as the corresponding conical pressure vessel meets the strength requirements, the socket F will definitely meet the strength requirements, such as Figure 5 and 6shown.

[0155] For a thin-walled cylindrical pressure vessel, its wall thickness is S, its diameter is D0, and its internal pressure is p. From material mechanics, we can get the axial stress σ of the pressure vessel wall: 轴 and hoop stress σ 环 They are as follows:

[0156] (25)

[0157] (26)

[0158] The hoop stress σ 环 That is, the circumferential stress, wherein the diameter D0 is half of the sum of the outer diameter and the inner diameter of the cylinder, or the inner diameter of the cylinder, or the outer diameter of the cylinder.

[0159] Similarly, for a thin-walled conical pressure vessel, when the wall thickness is S and the internal pressure is p, the stress σ in the axial direction of the vessel wall at the diameter D is 轴 and hoop stress σ 环 They are:

[0160] (27)

[0161] (28)

[0162] in α It is the semi-cone angle of the conical pressure vessel, that is, half of the opening angle. In other words, in the section passing through the central axis of the cone, the angle between the cone wall and the central axis is the semi-cone angle. Wherein, the diameter D is half of the sum of the outer diameter and the inner diameter of the corresponding part of the cone, or the inner diameter of the corresponding part, or the outer diameter of the corresponding part.

[0163] From the above, in this embodiment, the analysis area of ​​the socket F includes two coaxially connected conical pressure vessels plus several internal reinforcement rings. The two coaxially connected conical pressure vessels are respectively a first cone and a second cone, which share the same central axis with the socket F, wherein the first chamfer R1 and the second chamfer R2 are located on the inner wall of the first cone, as shown in FIG. Figure 5 The dotted line between the first chamfer R1 and the second chamfer R2 is the inner wall section of the first cone. The first chamfer R1 and the third chamfer R3 are located on the inner wall of the second cone. Figure 5The dotted line between the first chamfer R1 and the third chamfer R3 is the inner wall section of the second cone. For the area between the first chamfer R1 and the second chamfer R2, the portion between the inner wall of the first cone and the outer wall of the socket F is the entire side wall of the first cone, and the portion between the inner wall of the first cone and the inner wall of the socket F is an annular reinforcement ring j. Similarly, for the area between the first chamfer R1 and the third chamfer R3, the portion between the inner wall of the second cone and the outer wall of the socket F is the entire side wall of the second cone, and the portion between the inner wall of the second cone and the inner wall of the socket F is another annular reinforcement ring.

[0164] exist Figure 5 In the cross section shown, the angle between the straight line passing through the first chamfer R1 and the second chamfer R2 and the axis of the tube is the semi-cone angle of the first cone, set as α1. The angle between the straight line passing through the first chamfer R1 and the third chamfer R3 and the axis of the tube is the semi-cone angle of the second cone, set as α2.

[0165] but:

[0166] (29)

[0167] (30)

[0168] When the pipe body meets the strength requirements and the socket material is consistent with the pipe body material, in order to make the socket meet the strength requirements, the hoop stress at the first chamfer R1 is Not greater than the hoop stress of the pipe body , hoop stress at the second chamfer R2 Not greater than the hoop stress of the pipe body , Hoop stress at the third chamfer R3 Not greater than the hoop stress of the pipe body , that is:

[0169] (31)

[0170] (32)

[0171] (33)

[0172] Then we have:

[0173] (34)

[0174] (35)

[0175] (36)

[0176] Among them, S1, S2, S 3The wall thicknesses at the first chamfer R1, the second chamfer R2, and the third chamfer R3 are obtained:

[0177] (37)

[0178] (38)

[0179] (39)

[0180] Since there is a sealing ring z at the third chamfer R3, in order to achieve sealing, the pressure of the sealing ring z on the socket F must be greater than the pressure p of the fluid in the pipe. According to existing research, the average pressure of the sealing ring z on the inner wall of the socket F is generally 1.4 times the fluid pressure. It can be obtained from formulas (27) and (28) that the stress is proportional to the pressure and inversely proportional to the wall thickness. When the pressure increases to 1.4 times, in order to keep the stress unchanged, the wall thickness should be increased to 1.4 times at the same time. Then formula (39) is corrected to:

[0181] (40)

[0182] So we have:

[0183] (41)

[0184] (42)

[0185] (43)

[0186] Among them, S 1m , S 2m , S 3m They are the minimum wall thickness at the first chamfer R1, the second chamfer R2, and the third chamfer R3 respectively.

[0187] From above, Figure 6 As shown, the minimum outer diameter at the second chamfer R2 d 1. Minimum outer diameter at the first chamfer R1 d 2 , the minimum outer diameter at the third chamfer R3 d 3 are as follows:

[0188] (44)

[0189] (45)

[0190] (46)

[0191] The following example is used to calculate the wall thickness parameters of the socket F.

[0192] In this embodiment, the material of the pipe body and the socket F is Q235.

[0193] Table 2 is the socket size parameter table for the nominal pipe diameters of 600mm and 1200mm at a pressure of 3MPa as specified in the relevant standards:

[0194] Table 2 Dimensional parameters of sockets with nominal pipe diameters of 600 mm and 1200 mm as specified in relevant standards

[0195]

[0196] Based on this scheme, the wall thickness dimensions of the two sockets F in Table 2 are calculated and shown in Table 3.

[0197] Table 3 Wall thickness, outer diameter and semi-cone angle of two sockets

[0198]

[0199] In step b3, the outer diameter of the end face of the socket F only needs to be larger than the outer diameter at the third chamfer R3, and the specific value can be flexibly selected.

[0200] When the pipe body meets the strength requirements and the socket material is inconsistent with the pipe body material, in order to make the socket F meet the strength requirements, the stress at the first chamfer R1, the second chamfer R2, and the third chamfer R3 and the stress on the inner wall of the pipe body should meet the following conditions:

[0201] (47)

[0202] (48)

[0203] (49)

[0204] Among them, Q0 is the yield strength of the pipe body material, and Q1 is the yield strength of the material used for the socket F.

[0205] Then we have:

[0206] (50)

[0207] (51)

[0208] (52)

[0209] Similarly, considering the influence of the sealing ring at the third chamfer R3, the wall thickness of each chamfer is:

[0210] (53)

[0211] (54)

[0212] (55)

[0213] Therefore, the minimum wall thickness at the first chamfer R1, the second chamfer R2, and the third chamfer R3 are as follows:

[0214] (56)

[0215] (57)

[0216] (58)

[0217] Minimum diameter at the second chamfer R2 d 1. Minimum diameter at the first chamfer R1 d 2 , the minimum diameter at the third chamfer R3 d 3 are as follows:

[0218] (59)

[0219] (60)

[0220] (61)

[0221] Based on the above, the design calculation of the minimum thickness of the socket F is completed.

[0222] Finally, it is necessary to explain here that the above embodiments are only used to further illustrate the technical solution of the present invention in detail and cannot be understood as limiting the scope of protection of the present invention. Some non-essential improvements and adjustments made by technicians in this field based on the above content of the present invention all fall within the scope of protection of the present invention.

Claims

1. A method for designing the spigot and socket thickness of a spigot-and-socket pipe, characterized in that: The design method of the socket thickness includes the following steps: Step a1: Obtain the differential equation of radial deformation of the ring and the general solution of the differential equation according to the differential equation of the deflection curve of the ring and the moment balance equation; Step a2: Calculate and obtain a calculation formula for the maximum radial deformation of the ring according to the general solution of the differential equation obtained in step a1; Step a3: Calculating the minimum thickness of the socket of the base pipe that meets the deformation requirements according to the calculation formula of the maximum radial deformation obtained in step a2; The design method of the socket thickness includes the following steps: Step b1: Select multiple locations on the inner wall of the socket where stress is likely to be concentrated. The selection principle is: if the wall thickness of these locations meets the stress strength requirements, then the wall thickness of each location of the socket meets the strength requirements; Step b2: Determine the minimum wall thickness of each selected location in step b1, and obtain the outer wall of each selected location. The determination principle is: when the material of the socket and the material of the pipe body are the same, the stress at each selected location is not greater than the stress of the inner wall of the pipe body; when the material of the socket and the material of the pipe body are different, the ratio of the stress at each selected location to the yield strength of the socket material is not greater than the ratio of the stress of the inner wall of the pipe body to the yield strength of the pipe body material.

2. The design method according to claim 1, characterized in that: Step a2 includes the following steps: Step a21: Assuming that the annular ring is subjected to at least two radial concentrated forces that are symmetrical relative to the center of the circle, based on the assumption, calculating the constant term in the general solution of the differential equation to obtain the first form of the differential equation; Step a22: Based on the first form of the differential equation obtained in step a21, assuming that the annulus is subjected to only two radial concentrated forces that are symmetrical relative to the center of the circle, the first form of the differential equation is transformed into a second form of the differential equation; Step a23: introducing the internal negative pressure of the ring into the second form of the differential equation by introducing a coefficient, so as to obtain the third form of the differential equation; Step a24: Obtain a calculation formula for the maximum change in the diameter of the circular ring with coefficients according to the third form of the differential equation obtained in step a23.

3. The design method according to claim 1, characterized in that: Step a3 includes the following steps: Step a31: Calculate the parameters of a reference pipe according to an existing shear load formula, wherein the material and outer diameter of the reference pipe are respectively the same as the material and outer diameter of the base pipe; Step a32: obtaining the maximum deformation of the reference pipe socket through simulation according to the parameters calculated in step a31; Step a33: Substitute the maximum deformation of the socket obtained in step a32 into the calculation formula of step a2 to obtain the coefficient value in the calculation formula, thereby obtaining a calculation formula for the maximum radial deformation of the ring with a known coefficient; Step a34: Calculate the minimum thickness of the base pipe socket that meets the deformation requirements based on the allowable deformation regulations and the formula obtained in step a33.

4. The design method according to any one of claims 1 to 3, characterized in that: In step a1, the radial deformation obtained is u The differential equation is: ； The general solution is: ； in, R is the average value of the outer circle radius and the inner circle radius of the ring; E is the elastic modulus of the pipe, Pa; I is the moment of inertia of the circular pipe section, m 4 ; M is the bending moment borne by a certain section of the ring in the local area, in units of N*m; establish a two-dimensional coordinate system, The deformation is u The angle between the line connecting the point at and the origin of the coordinate system and the positive direction of the x-axis in the two-dimensional coordinate system, ; A1, A2, A3, B2, B3 are constants.

5. The design method according to claim 4, characterized in that: In step a2, it is assumed that the ring is subjected to at least two radial concentrated forces P symmetrically relative to the center of the circle, and the angle between two adjacent radial concentrated forces P is , the ring satisfies the following three boundary conditions: First, in Because of symmetry, The rotation angle of the section at is 0, which satisfies the following formula: ； Second, due to symmetry, the total tangential displacement of the arc in each equally divided segment is 0; That is: ； Third, cut near point A, remove point A and the force P, and from the symmetry and equilibrium conditions, we know that the shear force on the section at the circular cut is , that is: ; Combining the above three formulas with the general solution of the differential equation, we get the first form of the differential equation: ； Assuming that the annulus is subjected to only two radial concentrated forces P which are symmetrical relative to the center of the circle, then: , we get the second form of the differential equation: ； Introducing the coefficient m, we get the third form of the differential equation: ； Point of application of force P The point is the point of maximum deformation, and the change in the diameter of the ring is: , where I = S 3 / 12, S is the wall thickness of the tube.

6. The design method according to claim 3, characterized in that: The shear load formula used in step a31 is: ， in: W is the shear load, in N; F n is the shear force acting on the interface, in N; M P The weight of the test assembly pipe and the weight of the object in the pipe, in kg; a The distance between the shear load application point and the end face of the socket that has been inserted into the socket, in mm; b It is the distance between the center of gravity of the spigot end pipe and the spigot end face inserted into the socket, in mm; c It is the distance between the support point of the pad and the end face of the socket that has been inserted into the socket, in mm.

7. The design method according to claim 1, characterized in that: For the same base pipe, along the direction from the socket to the spigot, the inner wall of the socket includes a first step (1), a second step (2), a third step (3), a fourth step (4), and a fifth step (5) arranged in sequence, and one end of the inner wall of the pipe body is a sixth step (6), and the corresponding inner diameters are: D2, D1, (D3-2F0), D3, D4, (D0-2S), respectively, and the chamfer at the connection between the fourth step (4) and the fifth step (5) is the first chamfer (R1), and the fifth step (5 ) and the sixth step (6) is the second chamfer (R2), the second step (2) and the third step (3) is the third chamfer (R3), the first step (1) and the second step (2) are connected to the fourth chamfer (R4), the third step (3) and the fourth step (4) are connected to the fifth chamfer (R5), D0 is the outer diameter of the base pipe, S is the wall thickness of the pipe body, F0 is the height of the third step (3) protruding from the fourth step (4), and F0 ≥ 0.

8. The design method according to claim 7, characterized in that: In step b2, the minimum wall thickness of each selected point in step b1 is calculated by the stress calculation formula, and the socket is regarded as a pressure vessel including at least two coaxially connected pressure vessels with conical inner walls and at least one annular reinforcement ring installed on the inner wall of the pressure vessel. , ,in, is the hoop stress of the pipe body, is the hoop stress at the selected location, D0 is the outer diameter of the base pipe, D is the diameter of the selected location, p is the pressure of the fluid in the base pipe, S is the thickness of the base pipe, S0 is the wall thickness of the selected location, and α is the semi-cone angle of the cone at the selected location.

9. The design method according to claim 8, characterized in that: When the material of the socket is the same as that of the pipe body, the stress calculation formula is: .

10. The design method according to claim 8, characterized in that: When the material of the socket is different from that of the pipe body, the stress calculation formula is: , where Q0 is the yield strength of the pipe body material and Q1 is the yield strength of the socket material.

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