A detection method for the assembly of a three-layer extrusion cylinder

By measuring and calculating the interference amount and inner diameter changes of each layer of cylinder, combined with the theoretical stress equation, we can determine whether the assembly of the three-layer extrusion cylinder is qualified, which solves the problem of insufficient prestress after assembly of a large extruder, and achieves comprehensive inspection and quality control of the extrusion cylinder.

CN115628891BActive Publication Date: 2025-08-01CHINA NAT HEAVY MACHINERY RES INSTCO
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Patent Information

Application Number
CN202211152957.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-09-21
Publication Date
2025-08-01
Estimated Expiration
2042-09-21

AI Technical Summary

Technical Problem

The existing three-layer extrusion cylinder assembly detection method cannot effectively ensure that the three-layer extrusion cylinders of large and heavy-duty extruders meet the design requirements after prestressing assembly. There is a problem of insufficient prestress after assembly, which affects the stiffness and service life of the extrusion cylinder.

Method used

By measuring the interference amount of each layer of cylinder and the inner diameter change of the inner cylinder before and after assembly, combining theoretical calculations and stress equations, the inner surface shrinkage of the inner cylinder after assembly is determined, the difference in the inner diameter change before and after assembly is compared, and whether the assembly is qualified, ensuring that the prestressed state and deformation amount meet the design requirements.

Benefits of technology

The comprehensive inspection of the assembly of the three-layer extrusion cylinder is achieved, which can not only detect geometric defects but also discover physical defects, ensure that the prestressed state and deformation of the assembly meet the design requirements, and improve the stiffness and service life of the extrusion cylinder.

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Abstract

The present invention provides a method for detecting the assembly of a three-layer extrusion cylinder; Step 1: Determine the interference amount between the cylinders of each layer; Step 2: Carry out the assembly process: obtain that the inner surface of the inner cylinder (1) is u0; Step 3: Measure the inner diameter of the inner cylinder (1) before assembly and record it as r o0 ; Step 4: Measure the inner diameter of the inner cylinder (1) after assembly and record it as r p0 ; Step 5: Calculate the inner surface compression amount u of the inner cylinder (1) after assembly p0 = r p0 - r o0 ; Step 6: Compare the u0 of the inner surface of the inner cylinder (1) calculated with the actually measured inner surface compression amount u of the inner cylinder (1) p0 . If the difference between the two is ≤ 3%, it is qualified; otherwise, it is unqualified. The method involved in the present invention can not only perform the geometric detection function of the traditional detection method, but also detect the physical defects of the assembled parts, ensuring that the prestress state and deformation amount of the three-layer extrusion cylinder meet the design requirements.
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Description

Technical Field

[0001] The present invention belongs to the field of metallurgical equipment; in particular, it relates to a detection method for the assembly of a three-layer extrusion cylinder. Background Art

[0002] The extrusion cylinder is a core component of the extrusion equipment and is the most expensive among all extrusion tools. When the extrusion cylinder is working, it needs to withstand the effects of high temperature, high pressure, alternating loads, and high friction, and the working conditions are very harsh. Therefore, the extrusion cylinder generally adopts a prestressed cylinder structure composed of three layers of cylinders through interference fitting. These three layers of cylinders are respectively called the inner cylinder, the middle cylinder, and the outer cylinder from the inside to the outside. The advantages of this structure are: (1) improving its bearing capacity and at the same time making the stress distribution in the cylinder wall uniform, that is, reducing the stress peak value on the inner wall of the cylinder; (2) only the inner sleeve needs to be replaced after the cylinder is worn, and there is no need to replace the entire extrusion cylinder, which can save materials.

[0003] The existing detection methods for the assembly of a three-layer extrusion cylinder: generally, the external geometric dimensions of the inner cylinder, the middle cylinder, and the outer cylinder are respectively detected to ensure that the interference amount of the assembly of each layer of the cylinder reaches the requirements of the drawing design. Then, according to the requirements of the assembly drawing, the assembly is carried out according to the process regulations of the interference fitting of the three-layer cylinder. After completion, it is regarded as qualified. The deficiencies of this method are as follows: it is only applicable to small three-layer extrusion cylinders. Because the external geometric dimensions of the inner cylinder, the middle cylinder, and the outer cylinder of the extrusion cylinder of a small extrusion press are relatively small, there is no problem of insufficient forging penetration, and each layer of the cylinder is relatively uniform along the diameter direction.

[0004] With the continuous emergence of large and heavy extrusion presses, the size of the extrusion cylinder is getting larger and larger, and the thickness of each layer of the cylinder is also getting thicker. According to the traditional detection method, even if the external geometric dimensions of the inner cylinder, the middle cylinder, and the outer cylinder are detected to be qualified, it is difficult to ensure that the finally assembled three-layer extrusion cylinder is qualified. Because the individual components of the inner cylinder, the middle cylinder, and the outer cylinder of the extrusion cylinder of a large press are relatively large and the thickness is relatively thick, there may be subtle forging defects such as non-uniform material quality and insufficient forging penetration during the forging process. Although these defects will not affect the mechanical properties of the material sampling test, after the prestressed assembly, it will cause the problem of insufficient prestress after assembly, thereby affecting the stiffness and service life of the extrusion cylinder. [[ID=I6]]Summary of the Invention

[0005] The purpose of the present invention is to provide a detection method for the assembly of a three-layer extrusion cylinder.

[0006] The present invention is realized through the following technical solutions:

[0007] The present invention relates to a detection method for the assembly of a three-layer extrusion cylinder, including the following steps:

[0008] Step 1: Determine the interference amount between each layer of cylinders: The interference amount between the inner cylinder 1 and the middle cylinder 2 is δ1, and the interference amount between the middle cylinder 2 and the outer cylinder 3 is δ2; before assembly, δ1 can be obtained by measuring the outer diameter of the inner cylinder 1 of the extrusion cylinder and the inner diameter of the middle cylinder 2 of the extrusion cylinder and subtracting the two. δ2 can be obtained by measuring the outer diameter of the middle cylinder 2 of the extrusion cylinder and the inner diameter of the outer cylinder 3 of the extrusion cylinder and subtracting the two;

[0009] Step 2: Carry out the assembly process: Calculate the assembly stress and the shrinkage amount of the inner surface of the inner cylinder 1 after assembly, and obtain that the inner surface of the inner cylinder 1 is u0;

[0010] Step 3: Measure the inner diameter of the inner cylinder 1 before assembly and record it as r o0 ;

[0011] Step 4: Measure the inner diameter of the inner cylinder 1 after assembly and record it as r p0 ;

[0012] Step 5: Calculate the compression amount u of the inner surface of the inner cylinder 1 after assembly p0 = r p0 - r o0 ;

[0013] Step 6: Compare the calculated u0 of the inner surface of the inner cylinder 1 with the actually measured compression amount u of the inner surface of the inner cylinder 1 p0 . If the difference between the two is ≤ 3%, it is qualified; otherwise, it is unqualified. If u0 and u p0 are equal or approximately equal (the result difference does not exceed 3%), it is determined that the assembly is qualified. If the two are not equal, it is determined that the assembly is unqualified, and it is necessary to detect whether there are geometric defects or physical defects in the inner cylinder, middle cylinder, and outer cylinder of the extrusion cylinder.

[0014] Preferably, the mechanical equilibrium equations of the inner cylinder 1 and the middle cylinder 2, and the middle cylinder 2 and the outer cylinder 3 in the assembly process are shown in formulas (1) and (2):

[0015] p 12 = p 21 = p s1 (1)

[0016] p 23 = p s2 = p s2 (2)

[0017] Among them, the pressure on the outer surface of the inner cylinder 1 by the middle cylinder 2 is recorded as p 21 ; the radial pressure on the inner surface of the middle cylinder 2 by the inner cylinder 1 is recorded as p 12 , and the radial pressure on the outer surface of the middle cylinder 2 by the outer cylinder 3 is recorded as p s2 ; the radial pressure on the inner surface of the outer cylinder 3 by the middle cylinder 2 is p 23 ; p s1Denoted as the compressive stress between the inner cylinder 1 and the middle cylinder 2, p s2 Denoted as the compressive stress between the middle cylinder 2 and the outer cylinder 3.

[0018] Preferably, the geometric equations of the inner cylinder 1 and the middle cylinder 2, and the middle cylinder 2 and the outer cylinder 3 in the assembly process are shown in formulas (3) and (4):

[0019] Δr gr11 -Δr gr12 =δ1 (3)

[0020] Δr gr22 -Δr gr23 =δ2 (4)

[0021] Wherein, Δr gr11 is the radial deformation of the outer diameter of the inner cylinder 1; Δr gr12 is the radial deformation of the inner diameter of the middle cylinder 2; Δr gr22 is the radial deformation of the outer diameter of the middle cylinder 2; Δr gr23 is the radial deformation of the inner diameter of the outer cylinder 3.

[0022] Preferably, the physical equations of the inner cylinder 1 and the middle cylinder 2, and the middle cylinder 2 and the outer cylinder 3 in the assembly process are shown in formulas (5)-(8):

[0023]

[0024]

[0025]

[0026]

[0027] Wherein, the inner diameter of the inner cylinder 1 is r0, the outer diameter is r1; the inner diameter of the middle cylinder 2 is r1, the outer diameter is r2; the inner diameter of the outer cylinder 3 is r2, the outer diameter is r3, and μ is the Poisson's ratio.

[0028] Preferably, the assembly stresses of the inner cylinder 1 and the middle cylinder 2, and the middle cylinder 2 and the outer cylinder 3 in the assembly process are shown in formulas (9) and (10):

[0029]

[0030]

[0031] Wherein, ε1 and ε2 are the fitting coefficients between the inner lining and the middle lining, and between the middle lining and the outer casing, respectively.

[0032] Preferably, the surface stress equations of each layer of cylinder are as follows:

[0033] The stress equations of the inner surface of the outer cylinder 3 are shown in formulas (11) and (12):

[0034]

[0035]

[0036] The stress equations of the inner surface of the middle tube 2 are shown in formulas (13) and (14):

[0037]

[0038]

[0039] The inner surface stress equations of the inner cylinder 1 are shown in formulas (15) and (16):

[0040]

[0041]

[0042] Preferably, the radial compression amount of the inner surface of the inner cylinder (1) is calculated as follows:

[0043]

[0044] ε r is the tangential strain, E is the elastic modulus, and μ is the Poisson's ratio.

[0045] u0 in formula (17) is calculated based on the values of r0, r1, r2, r3, δ1 and δ1, which can be obtained by measuring the external dimensions of each layer of the cylinder; u0 is the theoretical shrinkage of the inner diameter of the inner cylinder of the extrusion cylinder after assembly; the inner diameter of the inner cylinder (1) is measured before assembly and recorded as r o0 , after assembly is completed, measure the inner diameter of the inner cylinder again and record it as r p0 ,u p0 =r p0 -r o0 Finally, u0 and u p0 If the two are equal, it means that the assembly of the three-layer extrusion cylinder is qualified. If the two are not equal, then there must be defects in the parts in terms of external dimensions, forgeability or material uniformity, and the assembly parts have not reached the designed prestressed state and deformation, then the assembly parts are unqualified.

[0046] The present invention has the following advantages:

[0047] The method involved in the present invention first determines the interference amount of the three-layer extrusion barrel of the extruder, then uses the method of theoretical calculation to obtain the shrinkage amount u0 of the inner surface of the inner barrel after assembly, and then measures the inner diameters of the inner barrel before and after assembly respectively to obtain the shrinkage amount u of the inner surface of the inner barrel after assembly p0 , and then compare u0 and u p0 . If the two are equal or approximately equal, it is determined that the assembly is qualified; if the two are not equal, it is determined that the assembly is unqualified, and it is necessary to check whether there are defects in the parts; this detection method can not only perform the function of geometric detection of the traditional detection method, but also detect the physical defects of the assembled parts to ensure that the prestress state and deformation amount of the three-layer extrusion barrel meet the design requirements Description of the Drawings

[0048] Figure 1 is the process flow chart of the method of the present invention

[0049] Figure 2 is the schematic diagram of the structural calculation process of the present invention

[0050] Figure 3 is the effect diagram of the present invention implemented on the extrusion barrel of a 125MN extruder

[0051] In the drawings, the reference numerals are: 1 is the inner barrel, 2 is the middle barrel, and 3 is the outer barrel Detailed Description of the Invention

[0052] The present invention will be described in detail below with reference to specific embodiments. It should be noted that the following embodiments are only further descriptions of the present invention, but the protection scope of the present invention is not limited to the following embodiments

[0053] Embodiment

[0054] This embodiment relates to a method for detecting the assembly of a three-layer extrusion barrel, as shown in Figure 1 - Figure 2 , and at least includes: the inner barrel 1, the middle barrel 2, and the outer barrel 3 of the extrusion barrel

[0055] Taking the assembly detection of the three-layer extrusion barrel of a 125MN extruder as an example, the method of the present invention will be further described

[0056] As shown in Figure 1 , the process flow of the method of the present invention is: first determine the interference amount of the three-layer extrusion barrel of a 125MN extruder, then use the method of theoretical calculation to obtain the shrinkage amount u0 of the inner surface of the inner barrel after assembly, and then measure the inner diameters of the inner barrel before and after assembly respectively to obtain the shrinkage amount u of the inner surface of the inner barrel after assembly p0 , and then compare u0 and u p0Compare them. If they are equal or approximately equal, it is determined that the assembly is qualified; if they are not equal, it is determined to be unqualified, and it is necessary to check whether there are defects in the components.

[0057] The specific implementation process is as follows:

[0058] As Figure 2 shown, the inner diameter of the inner cylinder 1 is denoted as r0, and the outer diameter is denoted as r1; the inner diameter of the middle cylinder 2 is denoted as r1, and the outer diameter is denoted as r2; the inner diameter of the outer cylinder 3 is denoted as r2, and the outer diameter is denoted as r3; the interference between the outer diameter of the inner cylinder 1 and the inner diameter of the middle cylinder 2 is denoted as δ1; the interference between the outer diameter of the middle cylinder 2 and the inner diameter of the outer cylinder 3 is denoted as δ2.

[0059] The pressure exerted on the outer surface of the inner cylinder 1 by the middle cylinder 2 is denoted as p 21 ; the radial pressure exerted on the inner surface of the middle cylinder 2 by the inner cylinder 2 is denoted as p 12 , and the radial pressure exerted on the outer surface of the middle cylinder 2 by the outer cylinder 3 is denoted as p s2 ; the radial pressure p exerted on the inner surface of the outer cylinder 3 by the middle cylinder 2 23 .

[0060] Taking the three-layer extrusion cylinder of a 125MN extrusion press as an example, the inner diameter of its extrusion cylinder is with a length of 2200mm. The dimensions of the three-layer cylinder are: inner layer: middle layer: outer layer: Among them, the interference between the inner layer and the middle layer is 1.368mm; the interference between the middle layer and the outer layer is 1.944mm. That is, r0 = 600mm, r1 = 760mm, r2 = 1080mm, r3 = 1940mm, δ1 = 1.368mm, δ2 = 1.944mm.

[0061] In the symbols of the following companies, the subscript g represents the pre-tightening state, the subscript p represents the working state, r represents the radial direction, t represents the tangential direction, and the subscript r x represents at the radius r x . For example: Δr pr22 is the radial displacement of the outer surface of the middle cylinder 2 in the working state, and σ gtr11 represents the tangential stress at the outer surface of the inner cylinder 2 in the pre-tightening state.

[0062] From the force balance equations, see Formulas (1) and (2):

[0063] p 12 = p 21 = p s1 (1)

[0064] p 23 = p s2 = p s2(2)

[0065] Where: p s1 is denoted as the compressive stress between the inner cylinder 1 and the middle cylinder 2, p s2 is denoted as the compressive stress between the middle cylinder 2 and the outer cylinder 3.

[0066] It is obtained from the geometric deformation coordination as shown in formulas (3) and (4):

[0067] Δr gr11 -Δr gr12 = δ1 (3)

[0068] Δr gr22 -Δr gr23 = δ2 (4)

[0069] Where: Δr gr11 is the radial deformation of the outer diameter of the inner cylinder 1; Δr gr12 is the radial deformation of the inner diameter of the middle cylinder 2; Δr gr22 is the radial deformation of the outer diameter of the middle cylinder 2; Δr gr23 is the radial deformation of the inner diameter of the outer cylinder 3.

[0070] The physical equations are shown in formulas (5)-(8):

[0071]

[0072]

[0073]

[0074]

[0075] By jointly solving the above equations (1)-(8), the assembly stresses of the three-layer combined cylinder are shown in formulas (9) and (10):

[0076]

[0077]

[0078] Among them, ε1 and ε2 are the fitting coefficients between the inner lining and the middle lining, and between the middle lining and the outer sleeve respectively. The calculation formulas are shown in (I) and formula (II). K1, K2, and K3 are the ratios of the outer diameter to the inner diameter of the inner cylinder, middle cylinder, and outer cylinder of the extrusion cylinder, respectively, that is

[0079]

[0080] Substituting the above parameters, we get P 12 = 119.18 MPa, P 23= 124.4 MPa

[0081] By jointly solving the geometric equations, equilibrium equations and the above equation, the stresses of each cylinder are as follows:

[0082] The calculation of the inner surface of the outer cylinder 3 can be seen in formulas (11) and (12):

[0083]

[0084]

[0085] Substituting the above parameters, we get

[0086] The calculation of the inner surface of the middle cylinder 2 can be seen in formulas (13) and (14):

[0087]

[0088]

[0089] Substituting the above parameters, we get

[0090] The calculation of the inner surface of the inner cylinder 1 can be seen in formulas (15) and (16):

[0091]

[0092]

[0093] Substituting the above parameters, we get

[0094] From the generalized Hooke's law, the radial compression of the inner surface can be calculated as seen in formula (17):

[0095]

[0096] Substituting the above parameters, we get u o0 = -0.912 mm

[0097] As Figure 3 shown, measure the change value of the inner diameter of the inner cylinder 1 before and after the assembly of the three-layer extrusion cylinder of the 125 MN extrusion press, that is, the compression amount u of the inner diameter of the inner cylinder 1 p0 , if the measured result is equal to or approximately equal to u o0 (the error does not exceed 1%), it is determined that the assembly is qualified. If the measured result is not equal to u o0 , it is determined that the assembly is unqualified, and it is necessary to detect whether there are geometric defects or physical defects in the inner cylinder, middle cylinder and outer cylinder of the extrusion cylinder.

[0098] For the method involved in the present invention, first determine the interference amount of the three-layer extrusion barrel of the extruder, then obtain the shrinkage amount u0 of the inner surface of the inner barrel after assembly by means of theoretical calculation, and then measure the inner diameter of the inner barrel before and after assembly respectively to obtain the shrinkage amount u of the inner surface of the inner barrel after assembly. p0 , and then compare u0 and u p0 . If the two are equal or approximately equal, it is determined that the assembly is qualified; if the two are not equal, it is determined that the assembly is unqualified, and it is necessary to check whether there are defects in the components. This detection method can not only perform the function of geometric detection of the traditional detection method, but also detect the physical defects of the assembled parts to ensure that the prestress state and deformation amount of the three-layer extrusion barrel meet the design requirements.

[0099] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various deformations or modifications within the scope of the claims, which does not affect the essence of the present invention.

Claims

1. A three-layer extrusion cylinder assembly detection method, characterized in that, It includes the following steps: Step 1: Determine the interference amounts between the cylinders: the interference amount between the inner cylinder (1) and the middle cylinder (2) is δ1, and the interference amount between the middle cylinder (2) and the outer cylinder (3) is δ2; Step 2: Conduct the assembly process: calculate the assembly stress and the shrinkage amount of the inner surface of the inner cylinder (1) after assembly, and obtain u0 on the inner surface of the inner cylinder (1); Step 3: Measure the inner diameter of the inner cylinder (1) before assembly, denoted as r o0 ; Step 4: After the assembly is completed, measure the inner diameter of the inner cylinder (1) and record it as r p0 ; Step Five: Calculate the internal surface compression amount u of the inner cylinder (1) after assembly p0 = r p0 - r o0 ; Step 6: Compare u0 of the inner surface of the inner cylinder (1) calculated with the compression amount u of the inner surface of the actually measured inner cylinder (1). If the difference between the two is ≤ 3%, it is qualified; otherwise, it is unqualified. p0 Compare them. If the difference between the two is ≤ 3%, it is qualified; otherwise, it is unqualified. The calculation of the radial compression amount of the inner surface of the inner cylinder (1) is shown in formula (17): Among them, ε in formula (17) t is the tangential strain, E represents the elastic modulus, μ is the Poisson's ratio, and σ gz is the stress generated in the Z direction under the prestress state. The stress in the Z direction is 0, that is, σ gz is 0; Among them, r represents any radius in the inner cylinder (1) of the extrusion cylinder; σ is the stress, g is the prestressed state, t represents the tangential stress, r represents the radial stress, so σ gr(r) represents the radial stress generated at the radius r of the inner cylinder (1) under the prestressed state, σ gt(r) represents the tangential stress generated at the radius r of the inner cylinder (1) under the prestressed state; p 12 is the pressure exerted by the middle cylinder (2) on the outer surface of the inner cylinder (1); r0 is the inner diameter of the inner cylinder (1), and r1 is the outer diameter of the inner cylinder (1).

2. The three-layer extrusion cylinder assembly detection method according to claim 1, wherein The mechanical equilibrium equations of the inner cylinder (1) and the middle cylinder (2), and the middle cylinder (2) and the outer cylinder (3) during the assembly process are shown in formula (1) and formula (2): p 12 = p 21 = p s1 (1) p 23 = p 32 = p s2 (2) Among them, the pressure exerted on the outer surface of the inner cylinder (1) by the middle cylinder (2) is denoted as p 21 ; the radial pressure exerted on the inner surface of the middle cylinder (2) by the inner cylinder (1) is denoted as p 12 , and the radial pressure exerted on the outer surface of the middle cylinder (2) by the outer cylinder (3) is denoted as p 32 ; the radial pressure exerted on the inner surface of the outer cylinder (3) by the middle cylinder (2) is p 23 ; p s1 is denoted as the compressive stress between the inner cylinder (1) and the middle cylinder (2), and p s2 is denoted as the compressive stress between the middle cylinder (2) and the outer cylinder (3).

3. The three-layer extrusion cylinder assembly detection method according to claim 2, characterized in that The geometric equations of the inner cylinder (1) and the middle cylinder (2), and the middle cylinder (2) and the outer cylinder (3) during the assembly process are shown in formula (3) and formula (4): Δr gr11 -Δr gr12 = δ1 (3) Δr gr22 -Δr gr23 = δ2 (4) Among them, Δr gr11 is the radial deformation of the outer diameter of the inner cylinder (1); Δr gr12 is the radial deformation of the inner diameter of the middle cylinder (2); Δr gr22 is the radial deformation of the outer diameter of the middle cylinder (2); Δr gr23 is the radial deformation of the inner diameter of the outer cylinder (3).

4. The three-layer extrusion cylinder assembly detection method according to claim 3, wherein, The physical equations of the inner cylinder (1) and the middle cylinder (2), and the middle cylinder (2) and the outer cylinder (3) during the assembly process are shown in formula (5)-(8): Among them, the inner diameter of the inner cylinder (1) is r0, and the outer diameter is r1; the inner diameter of the middle cylinder (2) is r1, and the outer diameter is r2; the inner diameter of the outer cylinder (3) is r2, and the outer diameter is r3, and μ is the Poisson's ratio; Δr gr11 is the radial deformation of the outer diameter of the inner cylinder (1); Δr gr12 is the radial deformation of the inner diameter of the middle cylinder (2); Δr gr22 is the radial deformation of the outer diameter of the middle cylinder (2); Δr gr23 is the radial deformation of the inner diameter of the outer cylinder (3).

5. The three-layer extrusion cylinder assembly detection method according to claim 4, characterized in that, The assembly stresses of the inner cylinder (1) and the middle cylinder (2), and the middle cylinder (2) and the outer cylinder (3) during the assembly process are shown in formula (9) and formula (10): Among them, ε1 and ε2 are the fitting coefficients between the inner cylinder and the middle cylinder, and the middle cylinder and the outer cylinder respectively; K1, K2, and K3 are the ratios of the outer diameter to the inner diameter of the inner cylinder (1), the middle cylinder (2), and the outer cylinder (3) respectively.

6. The three-layer extrusion cylinder assembly detection method according to claim 5, characterized in that, The surface stress equations of the outer cylinder and the middle cylinder are as follows: The relevant equations of the inner surface stress of the outer cylinder (3) are shown in formula (11) and formula (12): Among them, r represents any radius of the outer cylinder (3) of the extrusion cylinder; σ is the stress, g is the prestressed state, t represents the tangential stress, r represents the radial stress, thus, σ gr(r) represents the radial stress generated at the radius r of the outer cylinder (3) under the prestressed state; σ gt(r) represents the tangential stress generated at the radius r of the outer cylinder (3) under the prestressed state; The relevant equations of the inner surface stress of the middle cylinder (2) are shown in formula (13) and formula (14): Among them, r represents any radius of the inner cylinder (2) in the extrusion cylinder; σ is the stress, g is the prestressed state, t represents the tangential stress, and r represents the radial stress. Therefore, σ gr(r) represents the radial stress generated at the radius r of the inner cylinder (2) under the prestressed state; σ gt(r) represents the tangential stress generated at the radius r of the inner cylinder (2) under the prestressed state.

Citation Information

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